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Research Article Calculating Heat of Formation Values of Energetic Compounds: A Comparative Study Michael S. Elioff, 1 Jordan Hoy, 2 and John A. Bumpus 2 1 Department of Chemistry, Millersville University of Pennsylvania, Millersville, PA 17551, USA 2 Department of Chemistry and Biochemistry, University of Northern Iowa, Cedar Falls, IA 50614, USA Correspondence should be addressed to John A. Bumpus; [email protected] Received 9 October 2015; Revised 26 December 2015; Accepted 27 December 2015 Academic Editor: Dennis Salahub Copyright © 2016 Michael S. Elioff et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Heat of formation is one of several important parameters used to assess the performance of energetic compounds. We evaluated the ability of six different methods to accurately calculate gas-phase heat of formation (Δ 298,g ) values for a test set of 45 nitrogen- containing energetic compounds. Density functional theory coupled with the use of isodesmic or other balanced equations yielded calculated results in which 82% (37 of 45) of the Δ 298,g values were within ±2.0 kcal/mol of the most recently recommended experimental/reference values available. is was compared to a procedure using density functional theory (DFT) coupled with an atom and group contribution method in which 51% (23 of 45) of the Δ 298,g values were within ±2.0 kcal/mol of these values. e T1 procedure and Benson’s group additivity method yielded results in which 51% (23 of 45) and 64% (23 of 36) of the Δ 298,g values, respectively, were within ±2.0 kcal/mol of these values. We also compared two relatively new semiempirical approaches (PM7 and RM1) with regard to their ability to accurately calculate Δ 298,g . Although semiempirical methods continue to improve, they were found to be less accurate than the other approaches for the test set used in this investigation. 1. Introduction ere is substantial interest in the discovery and development of new energetic compounds which include high explosives and propellants and there is special interest in the discovery and development of high energy density materials (HEDMs). Collectively, compounds that have densities greater than or equal to 1.9 g/cm 3 , detonation velocities greater than or equal to 9.0 km/s, and detonation pressures greater than or equal to 40.0 GPa are known as HEDMs [1]. e usefulness of HEDMs in a variety of processes has been understood for at least a century [2]. Two important considerations with regard to HEDMs are that they can be dangerous and costly to synthesize. Moreover, increasing environmental concerns call for more effective ways of predicting performance of HEDMs [3]. Manufacturers must be able to determine the amount of energy that can be stored in a molecule while maintaining an acceptable level of stability [4]. e condensed-phase heat of formation (Δ 298,s or Δ 298,l ) is one of several important parameters used to assess the performance of energetic materials [5]. In prac- tice, most theoretical approaches calculate gas-phase heat of formation (Δ 298,g ) values. Solid- or liquid-phase val- ues are then calculated by subtracting heat of sublimation (Δ 298,sub ) or heat of vaporization (Δ 298,vap ) values, respectively, from the gas-phase value. Our interest concerns the use of relatively rapid methods for the calculation/prediction of accurate gas-phase heat of formation values. During the past several years two relatively rapid computational procedures have been described for use in determining Δ 298,g values [6–8]. One procedure, devel- oped by Byrd and Rice [6, 7], uses density functional theory (DFT) coupled with an atom and group contribution method to determine Δ 298,g for energetic compounds. Another procedure, developed by Ohlinger et al. [8], was designed to be applicable to a broader range of compounds. e latter relies on a novel multilevel computational approach known as T1 that approaches the accuracy of the G3MP2 method [9] while simultaneously reducing the computation time by 2-3 orders of magnitude [8]. In the investigations reported here, Hindawi Publishing Corporation Advances in Physical Chemistry Volume 2016, Article ID 5082084, 11 pages http://dx.doi.org/10.1155/2016/5082084

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Research ArticleCalculating Heat of Formation Values of EnergeticCompounds A Comparative Study

Michael S Elioff1 Jordan Hoy2 and John A Bumpus2

1Department of Chemistry Millersville University of Pennsylvania Millersville PA 17551 USA2Department of Chemistry and Biochemistry University of Northern Iowa Cedar Falls IA 50614 USA

Correspondence should be addressed to John A Bumpus johnbumpusuniedu

Received 9 October 2015 Revised 26 December 2015 Accepted 27 December 2015

Academic Editor Dennis Salahub

Copyright copy 2016 Michael S Elioff et alThis is an open access article distributed under theCreativeCommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Heat of formation is one of several important parameters used to assess the performance of energetic compounds We evaluatedthe ability of six different methods to accurately calculate gas-phase heat of formation (Δ119891119867

119900298g) values for a test set of 45 nitrogen-

containing energetic compounds Density functional theory coupled with the use of isodesmic or other balanced equations yieldedcalculated results in which 82 (37 of 45) of the Δ119891119867

119900298g values were within plusmn20 kcalmol of the most recently recommended

experimentalreference values available This was compared to a procedure using density functional theory (DFT) coupled with anatom and group contribution method in which 51 (23 of 45) of the Δ119891119867

119900298g values were within plusmn20 kcalmol of these valuesThe

T1 procedure andBensonrsquos group additivitymethod yielded results inwhich 51 (23 of 45) and 64 (23 of 36) of theΔ119891119867119900298g values

respectively were within plusmn20 kcalmol of these values We also compared two relatively new semiempirical approaches (PM7 andRM1) with regard to their ability to accurately calculate Δ119891119867

119900298g Although semiempirical methods continue to improve they were

found to be less accurate than the other approaches for the test set used in this investigation

1 Introduction

There is substantial interest in the discovery and developmentof new energetic compounds which include high explosivesand propellants and there is special interest in the discoveryand development of high energy density materials (HEDMs)Collectively compounds that have densities greater than orequal to 19 gcm3 detonation velocities greater than or equalto 90 kms and detonation pressures greater than or equalto 400GPa are known as HEDMs [1] The usefulness ofHEDMs in a variety of processes has been understood forat least a century [2] Two important considerations withregard toHEDMs are that they can be dangerous and costly tosynthesizeMoreover increasing environmental concerns callfor more effective ways of predicting performance of HEDMs[3] Manufacturers must be able to determine the amount ofenergy that can be stored in a molecule while maintaining anacceptable level of stability [4]

The condensed-phase heat of formation (Δ119891119867119900298s or

Δ119891119867119900298l) is one of several important parameters used to

assess the performance of energetic materials [5] In prac-tice most theoretical approaches calculate gas-phase heatof formation (Δ119891119867

119900298g) values Solid- or liquid-phase val-

ues are then calculated by subtracting heat of sublimation(Δ119891119867

119900298sub) or heat of vaporization (Δ119891119867

119900298vap) values

respectively from the gas-phase valueOur interest concerns the use of relatively rapid methods

for the calculationprediction of accurate gas-phase heat offormation values During the past several years two relativelyrapid computational procedures have been described for usein determining Δ119891119867

119900298g values [6ndash8] One procedure devel-

oped by Byrd and Rice [6 7] uses density functional theory(DFT) coupled with an atom and group contributionmethodto determine Δ119891119867

119900298g for energetic compounds Another

procedure developed by Ohlinger et al [8] was designed tobe applicable to a broader range of compounds The latterrelies on a novel multilevel computational approach knownas T1 that approaches the accuracy of the G3MP2method [9]while simultaneously reducing the computation time by 2-3orders of magnitude [8] In the investigations reported here

Hindawi Publishing CorporationAdvances in Physical ChemistryVolume 2016 Article ID 5082084 11 pageshttpdxdoiorg10115520165082084

2 Advances in Physical Chemistry

we have compared the effectiveness of these two procedureswith regard to their ability to accurately calculate Δ119891119867

119900298g

values of nitrogen-containing energetic compounds Oper-ating under the assumption that newer procedures are notnecessarily more reliable than more established methods wealso assessed and compared the ability of two other well-established procedures used to calculate Δ119891119867

119900298g Specif-

ically we assessed and compared results using the groupadditivity method developed by Benson and his colleagues[10 11] as well as density functional theory coupled with theuse of isodesmic isogyric or other balanced equations [12]We also used and compared two relatively new semiempiricalmodels (PM7 and RM1) [13 14] to calculate Δ119891119867

119900298g

2 Methods

The test set used in this investigation consisted of the gas-phase heat of formation (Δ119891119867

119900298g) values for forty-five

nitrogen-containing energetic compounds studied by Byrdand Rice [6 7] Δ119891119867

119900298g values were calculated using the

T1 procedure which is based on the G3MP2 [9] multilevelab initio model chemistry as implemented in the Spartanrsquo10and 14 suite of programs Semiempirical theory using theRM1 and PM7 model chemistries [13 14] were used to cal-culate Δ119891119867

119900298g as implemented in Spartan 14 (Wavefunction

Inc Irvine CA) and MOPAC2012 (httpopenmopacnet)respectively

Gas-phase heat of formation values were also calculatedusing density functional theory as implemented in Spartan 10and 14 coupled with the use of isodesmic isogyric and otherbalanced equations An informative account of the detailsconcerning the calculation of Δ119891119867

119900298g using this approach

has been presented by Cramer [12] Most of the equationsused were isodesmic equations For the studies reportedherein total electronic energies (119864Tot) zero point energies(ZPE) and thermal correction (119867119879) values for compoundsin all of the equations were calculated using the M06 2Xfunctional [15 16] and the 6-31Glowast basis set The 6-31Glowast basisset is a medium size basis set It was selected for use so thatexcessive computation time could be avoided In Spartanit is necessary that the ldquocompute IRrdquo box be selected inorder to make these calculations When this is done thecalculated119867119900298 value required for use in isodesmic isogyricor other balanced equations is computed and appears inthe Thermodynamics Window This window is accessed bythe following path Display gt Properties gtThermodynamicsExperimental values for Δ119891119867

119900298g required for compounds

used in these studies were acquired from the NISTWebBook[17] Pedleyrsquos Thermochemical Data of Organic Compounds2nd ed [18] Cox and Pilcherrsquos Thermochemistry of Organicand Organometallic Compounds [19] and publications byDorofeeva and her colleagues [20ndash24]

Gas-phase heat of formation values were calculated fortwenty-five compounds using the Group Additivity approachas implemented in the NIST WebBook (httpwebbooknistgovchemistry) applet [17] This applet uses Benson GroupAdditivity values [10 11] Eight compounds in our testset contained an azido group Unfortunately the azido

group value is not among those included in the databasefor the NIST WebBook applet To address this problemwe first calculated an enthalpy group value for an azidogroup attached to a carbon atom The Δ119891119867

119900298g of methyl

azide has been determined experimentally and by highlevel computation We used the value of 712 kcalmol(plusmn10 kcalmol) recommended by Dorofeeva et al [21]Subtracting the methyl group value (minus102 kcalmol) fromthe heat of formation of methyl azide gives a value of814 kcalmol for the azido group The group additivityapproach was then used to calculate Δ119891119867

119900298g values of

azido-containing compounds as follows First the NISTapplet was used to calculate the Δ119891119867

119900298g value for the amino

analog of the azido compound Then the azido group valueof 814 kcalmol was used in the calculation instead of theamino group value Using this simple modification of thegroup additivity approach Δ119891119867

119900298g values were calculated

for six of the eight compounds in our test set that containedan azido group Calculation of Δ119891119867

119900298g for the remaining

compounds that contained an azido group is described belowTheASTMCHETAH 80 software program [25] was used

to calculateΔ119891119867119900298g values for a few other compounds in our

test set whose Δ119891119867119900298g values could not be calculated using

the NIST appletThe group additivity difference method as described by

Cohen and Benson [26] was used to calculate the Δ119891119867119900298g

value for nitromethane For nitromethane it should be men-tioned that experimental values of minus178 and minus193 kcalmolhave been reported and used extensively Interestingly thereis considerable theoretical as well as experimental support forboth values [20 22ndash24 27ndash29] In the present investigationthe group additivity value for nitromethane (minus180 kcalmol)was calculated by subtracting the group value (minus66 kcalmol)for a methylene (ndashCH2ndash) group bound to a nitrogen atomfrom the calculated Δ119891119867

119900298g value of minus246 kcalmol for

nitroethane We note that this value is 15 kcalmol greaterthan that previously reported by Bumpus and Willoughby[27] It should also be noted that recent experimentalresults [24] support a slightly greater Δ119891119867

119900298g value of

minus1709 kcalmol for nitromethane and it is this value that wasultimately included in the alternative experimental referenceset

The calculation of Δ119891119867119900298g for 1-azido-11-dinitroethane

was accomplished using the group values for the methylgroup and azido group coupled with the group value for acarbon attached to an azido group and two nitro groupsThislater value was assumed to be equivalent to the group value(minus99 kcalmol) for a carbon attached to a hydrogen and twonitro groups

For azidotrinitromethane the group value for the trini-tromethyl group (minus145 kcalmol) listed in CHETAH 80 wasadded to the azido group value of 814 kcalmol giving acalculated Δ119891119867

119900298g value of 7995 kcalmol (= 800 kcalmol)

for azidotrinitromethaneAll calculated Δ119891119867

119900298g values were compared with

experimental values and with values published by Byrd andRice [6 7] who calculated Δ119891119867

119900298g values using density

Advances in Physical Chemistry 3

functional theory coupledwith an atom and group equivalentmethod Calculated Δ119891119867

119900298g values were also compared to

an alternative experimental reference set in which eighteenpresumably more accurate Δ119891119867

119900298g values recommended

by Dorofeeva and colleagues [20ndash24] were substituted forcorresponding values in the original set of experimentalvalues Also substituted in this alternative experimentalreference set was the Δ119891119867

119900298g value for 246-trinitrotoluene

listed in Cox and Pilcherrsquos ldquoThermochemistry of Organic andOrganometallic Compoundsrdquo [19] Finally it should be notedthat during the course of this investigation it appeared thatthe experimental Δ119891119867

119900298g value for dinitromethylbenzene

might be several kcalmol too low To address this possibilitywe used an approach similar to that used successfully byDorofeeva et al [21ndash23] to deal with such issues Specificallywe used density functional theory (EDF2 [30] functional andthe 6-311++G (2df2p) basis set) coupled with the use of tenisodesmic equations to calculate a Δ119891119867

119900298g reference value

of 142 plusmn 03 for dinitromethylbenzene This value was alsoincluded in the alternative reference set

It should be mentioned that many of the computedRM1 and PM7 Δ119891119867

119900298g values for compounds appearing

in Table 1 have been previously reported [13 14] Similarlymost of the T1 Δ119891119867

119900298g values appear in the Spartan Spectra

and Properties Database (SSPD) data base that accompaniesSpartan 14 In general our results are quite consistent withthese previously reported values In some instances howeverslightly lower Δ119891119867

119900298g values were calculated indicating the

existence of lower-energy equilibrium geometries than thoseused in previous investigations

3 Results and Discussion

The ultimate goal of any computational strategy designedto estimate values for Δ119891119867

119900298g is to reduce uncertainties

to within plusmn10 or 20 kcalmol (1 kcalmol = 4184 kJmol)which is taken to be experimental error One reason for thisgoal is that small errors in Δ119891119867

119900298g become magnified when

propagated to obtain other values which depend onΔ119891119867119900298g

The standard Gibbs energy change of a reaction for exampleis a function of the reaction enthalpy change as follows

Δ rxn119866∘= Δ rxn119867

∘minus 119879Δ rxn119878

∘ (1)

Reaction enthalpies can be calculated in accord with Hessrsquoslaw by taking the difference of the standard heat of formationvalues of the products and reactants of the reaction Theequilibrium constant (119870eq) of a reaction and Δ rxn119866

∘ arerelated by the expression

119870eq = 119890minusΔ rxn119866

∘119877119879 (2)

Since the equilibrium constant depends exponentially uponΔ rxn119866

∘ a small error in Δ rxn119867119900 can result in dramatically

different values for 119870eq when it is the calculated parameterof interest

For energetic compounds calculation of equilibriumconstants using heat of formation values is typically not

a concern sincemost reactions of interest are highly exergonicwith equilibrium constants that indicate product formationis highly favored It must be noted however that severalparameters (eg heat of detonation heat of explosion powerindex explosive velocity and explosive pressure) used tocharacterize high explosives require the condensed-phaseheat of formation value This is somewhat problematic fortheoretical compounds since calculations are performedon single molecules which are by definition gas-phasemolecules To calculate solid-phase heat of formation valuesheat of sublimation (or vaporization) values are calculatedby one of several computational methods available and thesevalues are then subtracted from the gas-phase values tocalculate the condensed-phase values This represents stillanother source of uncertainty in subsequent calculations It istherefore important to be able to identify and use proceduresthat provide the most accurate heat of formation valuespossible

Our initial objective was to compare the abilities of theT1 multilevel ab initio approach developed by Ohlinger etal [8] with the atom and group equivalent DFT approachdescribed by Byrd and Rice [6 7] To make this comparisonwe selected the forty-five nitrogen-containing compoundsstudied by Byrd and Rice [6 7] which we designated as ourtest set and acquiredT1Δ119891119867

119900298g values for these compounds

These results and the results of all comparisons made in thisinvestigation are presented inTables 1 2 and 3 and in Figure 1

When making comparisons such as those under con-sideration here it is necessary to use the most accurateexperimental Δ119891119867

119900298g reference values available This is

problematic for no fewer than twenty of the experimentalΔ119891119867119900298g values used in this investigation and it is of sub-

stantial concern for the eight organic azide compounds in thetest set Indeed Dorofeeva et al [21] note that ldquoenthalpiesof formation of organic azides are scanty and not alwaysreliablerdquo To address this problem Dorofeeva et al [21] useda combination of multilevel ab initio model chemistries anddensity functional theory coupled with the use of isodesmicisogyric and other balanced equations to calculate andrecommend Δ119891119867

119900298g values for twenty-nine organic azides

including the eight organic azide compounds in our test setThe implication of their work is that their calculated valuesmay be more accurate than the experimental values thatwere originally available to Byrd and Rice [6 7] This samegroup [20 22ndash24] conducted similar studies of the Δ119891119867

119900298g

values for fifty-seven other energetic nitrogen-containingcompounds and recommended the use of several Δ119891119867

119900298g

values that are slightly different than those that were availableto Byrd and Rice [6 7]

In light of these findings we compared computed datawith the original experimental data set used by Byrd and Rice[6 7] and with a newer alternative experimental referenceset (also referred to elsewhere herein as the most recentlyrecommended experimentalreference values available) inwhich a total of eighteen Δ119891119867

119900298g reference values recom-

mended by Dorofeeva et al [18 20 21] were substituted forthe original corresponding experimental values in the test set[6 7] We also note that at least three experimental values

4 Advances in Physical ChemistryTa

ble1Com

paris

onof

experim

entalgas-phase

heatof

form

ationvalues

with

values

calculated

usingseveraltheoreticalapproaches

Com

poun

dname

Experim

entallowast

Δ119891119867119900 298g

(kcalm

ol)

T1Δ119891119867119900 298g

(kcalm

ol)

DFT

Atom

icandGroup

contrib

ution

Δ119891119867119900 298g

(kcalm

ol)lowast

DFT

Isod

esmiclowastlowast

Δ119891119867119900 298g

(kcalm

ol)

Group

Additiv

ityΔ119891119867119900 298g

(kcalm

ol)

PM7

Δ119891119867119900 298g

(kcalm

ol)

RM1

Δ119891119867119900 298g

(kcalm

ol)

Nitro

methane

minus193(minus1709)

minus158

minus186

minus168

minus180

minus172

minus124

Tetra

nitro

methane

197(2110)

234

206

223

mdash284

181

Azidotrin

itrom

ethane

842(8532)

884

856

840

816

952

792

DMNO(N

-methyl-N

-nitrom

ethanamine)

minus12

05

minus10

minus11

minus16

minus58

minus35

1-Azido-11-d

initroethane

604(6286)

616

604

597

613

682

576

Hexanitroethane

428(291

8)293

337

289

mdash473

302

Nitro

glycerin

minus6671

minus658

minus667

minus698

minus815

minus826

minus720

TTT

943

984

941

938

mdash404

354

RDX(cyclotrimethylen

e-trinitra

mine)

458(4579)

490

440

468

mdash218

457

14-D

initrosopiperazine

464

527

467

466

368lowastlowastlowast

172

127

14-D

initropiperazine

139(1546

)177

126

149

112

20

167

N-N

itro-bis-2

22-tr

initroethylam

ine

2142

212

231

191

mdash346

334

Nitro

benzene

1638(1568)

152

141

148

161

182

182

2-Nitro

phenol

minus3162

minus296

minus311

minus314

minus260

minus310

minus289

3-Nitro

phenol

minus2612

minus260

minus260

minus270

minus260

minus258

minus268

4-Nitro

phenol

minus2741

minus260

minus280

minus282

minus260

minus281

minus285

m-N

itroanilin

e149

169

153

161

171

166

114

p-Nitro

aniline

132

165

128

141

171

129

83

Azidobenzene

930(9919)

948

998

968

974

990

945

1-Azido-4-nitrobenzene

931(9417)

928

918

931

937

947

903

N-N

itrobis-22-dinitro

propylam

ine(DNPN

)minus317

minus287

minus256

minus338

mdashminus150

minus91

PNT(1-

methyl-4

-nitrobenzene)

738

72

63

73

81

75

84

24-DNT(1-

methyl-2

4-dinitrobenzene)

793

86

44

85

44

70

85

Azidom

ethylbenzene

995(9680)

924

991

962

968

947

914

3-Az

ido-3-ethylpentane

406(315

5)281

414

315

329

367

338

TNT(tr

initrotoluene)

575

(123)

136

71

115

08

108

126

22-Dinitroadamantane

minus3688(minus4278)

minus394

minus347

minus413

minus354lowastlowastlowast

minus286

minus439

1-Azidoadam

antane

516(4374)

400

496

446

480

470

289

2-Az

ido-2-phenylp

ropane

874(795

9)750

819

803

798

842

776

HNS

5698

639

595

608

358

582

616

Methylnitrite

minus1564

minus133

minus146

minus139

minus161

minus192

minus219

Methylnitrate

minus292

minus270

minus272

minus273

minus296

minus314

minus284

Dinitrom

ethane

minus141(minus92

0)minus76

minus132

minus78

mdashminus82

minus45

Ethylnitrite

minus259

minus219

minus224

minus249

minus242

minus326

minus323

Ethylnitrate

minus370

minus351

minus349

minus361

minus377

minus395

minus356

Propylnitrite

minus284

minus270

minus273

minus292

minus291

minus377

minus372

2-Methyl-2

-nitropropane

minus4232

(minus4190)

minus402

minus383

minus426

minus423

minus357

minus364

n-Bu

tylnitrite

minus348

minus320

minus320

minus355

minus340

minus426

minus422

t-Butylnitrite

minus410

minus387

minus354

minus408

minus425

minus482

minus486

34-Fu

razand

imethanoldinitrate

26

98

91

minus04

mdashminus40

194

1-Nitropiperidine

minus106(minus887)

minus74

minus99

minus89

minus81

minus155

minus92

Advances in Physical Chemistry 5

Table1Con

tinued

Com

poun

dname

Experim

entallowast

Δ119891119867119900 298g

(kcalm

ol)

T1Δ119891119867119900 298g

(kcalm

ol)

DFT

Atom

icandGroup

contrib

ution

Δ119891119867119900 298g

(kcalm

ol)lowast

DFT

Isod

esmiclowastlowast

Δ119891119867119900 298g

(kcalm

ol)

Group

Additiv

ityΔ119891119867119900 298g

(kcalm

ol)

PM7

Δ119891119867119900 298g

(kcalm

ol)

RM1

Δ119891119867119900 298g

(kcalm

ol)

Nitro

sobenzene

481

471

488

455

mdash412

331

Nitro

methylbenzene

734

87

94

90

76113

130

Dinitrom

ethylbenzene

83(14

2)

139

136

145

121

196

184

13-D

imethyl-2

-nitrobenzene

21

14

43

32

02

minus02

14

HNS=111015840 -(12-ethenediyl)b

is[246-trinitrob

enzene]TT

T=hexahydro-13

5-tr

initroso-13

5-tr

iazine

lowastVa

luesfro

mBy

rdandRice

[67]Va

luesin

parenthesesa

rethosethath

aveb

eensubstituted

forcorrespon

ding

valuesin

theo

riginalreferences

etandareu

sedin

thea

lternativee

xperim

entalreference

setSeetext

ford

etailsandexplanation

lowastlowastMosto

fvaluesintheD

FTiso

desm

iccolumnwerec

alculated

usingiso

desm

icreactio

nsH

owever

somev

aluesw

erec

alculated

usingiso

gyric

orotherb

alancedequatio

ns

lowastlowastlowastVa

lues

calculated

usingCH

ETAH80

6 Advances in Physical Chemistry

Table 2 Statistical comparison of experimental gas-phase heat of formation valueswith values calculated using several theoretical approaches

T1Δ119891119867298g(kcalmol)

DFT Atomicand GroupcontributionΔ119891119867298g

(kcalmol)lowast

DFTisodesmicΔ119891119867298g(kcalmol)

Group AddΔ119891119867298g(kcalmol)

PM7Δ119891119867298g(kcalmol)

RM1Δ119891119867298g(kcalmol)

rms deviation 50 30 37 54 (34)lowast 118 (60) 129 (59)MAE 37 21 25 33 (25)lowast 75 (49) 79 (48)Max Dev (kcalmol) 135 91 139 212 (96)lowast 539 (132) 589 (126)Number of values plusmn20 kcalmol 17 28 27 19 10 12Number of values plusmn30 kcalmol 25 35 33 24 14 17Number of values plusmn40 kcalmol 32 37 37 28 18 18

1198772 098728 09958 099277 09863

(099435)092817(098063)

091605(098141)

lowastValues in parentheses represent data in which values for compounds having deviations from experiment greater than 140 kcalmol were omitted See text forexplanation

Table 3 Statistical comparison of alternative experimental gas-phase heat of formation values with values calculated using several theoreticalapproaches

T1Δ119891119867298g(kcalmol)

DFT Atomicand GroupcontributionΔ119891119867298g(kcalmol)lowast

DFTisodesmicΔ119891119867298g(kcalmol)

Group AddΔ119891119867298g(kcalmol)

PM7lowastΔ119891119867298g(kcalmol)

RM1lowastΔ119891119867298g(kcalmol)

rms deviation 29 33 15 55 (35)lowast 120 (54) 122 (45)MAE 23 24 11 31 (23)lowast 73 (42) 68 (36)Max Dev (kcalmol) 69 99 38 212 (115)lowast 539 (132) 589 (120)Number of values plusmn20 kcalmol 23 23 37 23 13 14Number of values plusmn30 kcalmol 31 33 42 25 18 19Number of values plusmn40 kcalmol 38 37 45 28 21 21

1198772 099648 099477 099884 098549

(099353)092435(098574)

092367(09889)

lowastValues in parentheses represent data in which values for compounds having deviations from experiment greater than 140 kcalmol were omitted See text forexplanation

have been reported for 246-trinitrotoluene Thus in placeof the Δ119891119867

119900298g value of 575 kcalmol used by Byrd and Rice

[6 7] we have substituted the value of 123 kcalmol (reportedin ldquoThermochemistry of Organic and Organometallic Com-poundsrdquo by Cox and Pilcher [19]) in the new alternativeexperimental reference data set During the course of thisinvestigation it also appeared that the experimental value fordinitromethylbenzene may be several kcalmol too lowThuswe used procedures similar to those described by Dorofeevaet al [21ndash23] to calculate a Δ119891119867

119900298g reference value of 142 plusmn

03 kcalmol for this compoundThis value was also includedin the alternative reference set These results are found inSupplemental Tables 1S and 2S (see Supplementary Materialavailable online at httpdxdoiorg10115520165082084)

A comparison of Tables 2 and 3 supports the conclusionthat the alternative recommended values as a group areindeed more accurate than the original experimental valuesthat were available to and used by Byrd and Rice [6 7] intheir investigations Except for the DFTAtomic and Groupcontribution approach the mean absolute error (MAE) was

greater for the original experimental reference set than forthe new alternative experimental reference set The fact thatthe opposite was found for the DFTAtomic and Groupcontribution approach is not surprising as many of the com-pounds in the original experimental reference set were usedto parameterize and develop this computational approachNevertheless this approach still performed quite well whencompared to the alternative experimental reference set Ourresults also suggest that the accuracy of the DFTAtomic andGroup contribution approach might benefit from reparame-terization using the alternative experimental reference set

Because the alternative experimental reference setappeared to be more accurate than the original reference setit was used for the comparisons described below

The atom and group equivalent DFT approach describedby Byrd and Rice [6 7] and the T1 procedure both yieldedcalculated results in which 51 (2345) of the predictedΔ119891119867119900298g values were within plusmn20 kcalmol of values in the

reference set The rms deviation from experiment for thepredicted T1 gas-phase heat of formation values was found

Advances in Physical Chemistry 7

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

0minus50 50 100minus100

Experimental values (kcalmol)

(a) T1

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(b) DFTAtomic and Group contribution

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(c) DFTisodesmic

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(d) Group Add

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus100 0 50 100minus50

Experimental values (kcalmol)

(e) PM7

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(f) RM1

Figure 1 Calculated gas-phase heat of formation values versus experimental values Gas-phase heat of formation values were calculated using(1) the multilevel ab initio approach (T1) described by Ohlinger et al [8] as implemented in the Spartanrsquo10 and 14 suite of programs (a) (2) theDFTAtomic and Group contribution approach developed and described by Byrd and Rice [6 7] (b)The experimental values and calculatedvalues used to construct (b) are those published by Byrd and Rice [6 7] (b) is identical to Figure 1a in their manuscript except for the fact thatthe alternative set of experimental Δ119891119867

119900298g reference values are also included (3) Density functional theory using isodesmic isogyric and

other balanced equations as described herein (c) (4)The Benson Group Additivity approach as implemented in the and NIST and CHETAH80 software programs (d) (5) semiempirical theory (PM7 andRM1) as implemented inMOPAC2012 and the Spartan 14 suite of programs ((e)and (f) resp) Open squares represent calculatedΔ119891119867

119900298g values versus the experimentalΔ119891119867

119900298g values Closed circles represent calculated

Δ119891119867119900298g values versus the alternative experimental Δ119891119867

119900298g reference values as described in the text Least square regression analysis and

calculation of 1198772 values were accomplished using KaleidaGraph graphing software (Synergy Software Reading PA) 1198772 values are presentedin Tables 2 and 3

8 Advances in Physical Chemistry

Table 4 Balanced equations used to calculate heat of formation values of compounds in the test set

Isodesmic isogyric or other balanced equations1 Dinitromethane + methanerarr2 nitromethane2 2 dinitromethanerarrmethane + tetranitromethane3 Methyl azide + trinitromethanerarrmethane + azidotrinitromethane4 N-Ethyl-N-nitroethanamine + dimethylaminerarr N-ethyl-N-ethanamine + N-methyl-N-nitromethanamine (DMNO)5 11-Dinitropropane + methyl aziderarr ethane + 1-azido-11-dinitroethane6 2 111-Trinitropropanerarr butane + hexanitroethane7 3 propylnitraterarr2 propane + nitroglycerin8 RDX + 3 nitrosyl hydriderarr3 HNO2 + TTT (hexahydro-135-trinitroso-135-triazine)9 3 1-nitropiperidinerarr2 cyclohexane + RDX10 1-Nitrosopiperidine + TTTrarr2 14-dinitrosopiperazine11 Piperazine + 2 dimethylnitraminerarr 2 dimethylamine + 14-dinitropiperazine12 Bis-222-trinitroethylamine + HNO2 rarr H2 + N-nitro-bis-222-trinitroethylamine13 Benzene + 4-nitroanilinerarr aniline + nitrobenzene14 Phenol + nitrobenzenerarr benzene + 2-nitrophenol15 Phenol + nitrobenzenerarr benzene + 3-nitrophenol16 Phenol + nitrobenzenerarr benzene + 4-nitrophenol17 Aniline + nitrobenzenerarr benzene + m-nitroaniline18 Aniline + nitrobenzenerarr benzene + p-nitroaniline19 Methyl azide + benzenerarrmethane + azidobenzene20 Methyl azide + nitrobenzenerarrmethane + 1-azido-4-nitrobenzene

21 N-Propylpropanamine + 4 1-nitropropane + dimethylnitraminerarr dimethylamine + N-nitro-bis-22-dinitropropylamine (DNPN)+ 4 propane

22 Toluene + nitrobenzenerarr benzene + PNT (1-methyl-4-nitrobenzene)23 Toluene + 2 nitrobenzenerarr2 benzene + 24-DNT (1-methyl-24-dinitrobenzene)24 Methyl azide + toluenerarrmethane + azidomethylbenzene25 Methyl azide + 3-ethylpentanerarrmethane + 3-azido-3-ethylpentane26 Toluene + 135-trinitrobenzenerarr benzene + TNT (246-trinitrotoluene)27 2 2-nitropropane + adamantanerarr2 propane + 22-dinitroadamantane28 Methyl azide + adamantanerarrmethane + 1-azidoadamantane29 Methyl azide + 2-phenylpropanerarrmethane + 2-azido-2-phenylpropane30 trans-Stilbene + 2 135-trinitrobenzenerarr2 benzene + HNS (111015840-(12-ethenediyl)bis[246- trinitrobenzene])31 Isopropyl nitrite + methanerarr propane + methyl nitrite32 Propyl nitrate + methanerarr propane + methyl nitrate33 2 1-Nitropropane + methanerarr2 propane + dinitromethane34 Propyl nitrite + ethanerarr propane + ethyl nitrite35 Propyl nitrate + ethanerarr propane + ethyl nitrate36 Isopropyl nitriterarr propyl nitrite37 2-Nitropropane + 2-methylpropanerarr 2-methyl-2-nitropropane + propane38 Isopropyl nitrite + butanerarr n-butyl nitrite + propane39 Isopropyl nitrite + isobutanerarr t-butyl nitrite + propane40 2 1-pyrroline + tetrahydrofuran + 2methyl nitraterarr H2 + 34-furazandimethanol dinitrate + 2 cyclopentane41 Piperidine + dimethylnitraminerarr 1-nitropiperidine + dimethylamine42 Phenyl radical + nitric oxiderarr nitrosobenzene43 Toluene + 1-nitropropanerarr propane + nitromethylbenzene44 Toluene + 11-dinitropropanerarr propane + dinitromethylbenzene45 2 Toluene + nitrobenzenerarr2 benzene + 13-dimethyl-2-nitrobenzene

Advances in Physical Chemistry 9

to be 29 kcalmol with a mean absolute error (MAE) of23 kcalmol and a maximum deviation of 69 kcalmol Thiscompares with an rms deviation of 33 kcalmol a MAE of24 kcalmol and a maximum deviation of 99 kcalmol usingdata calculated by Byrd andRice [6 7] It should be noted thatthe T1 procedure has been previously shown to reproduceexperimental heat of formation values of a large (1805) set oforganicmolecules with an rms deviation of 275 kcalmol anda MAE of 203 kcalmol [8] Clearly the rms andMAE valuesfor the T1 approach reported here agree well with those valuesreported for the larger data set

These results led us to compare older approaches usedto predictcalculate Δ119891119867

119900298g values Specifically we used

Bensonrsquos group additivity (or group contribution) approach[10 11] We also used density functional theory coupled withthe use of selected isodesmic isogyric and other balancedequations One disadvantage of Bensonrsquos group additivityapproach is that group values for some of the substructuresof several compounds in the test set are not availableWe were partially able to overcome this problem by usingexisting data which allowed us to calculate some of thesegroup values In total we were able to use Bensonrsquos groupadditivity approach to calculate Δ119891119867

119900298g values for 36 of 45

compounds in the test set This approach yielded calculatedresults in which 64 (2336) of the calculated Δ119891119867

119900298g

values were within plusmn20 kcalmol of experimental valuesThe rms deviation from experiment for the predicted groupadditivity gas-phase heat of formation valueswas 55 kcalmolwith an MAE of 31 kcalmol with a maximum deviationof 212 kcalmol for HNS A relatively large deviation fromexperiment of 148 kcalmol was also found for nitroglycerinA significant drawback to the use of group additivity theoryis that calculated Δ119891119867

119900298g values are sometimes affected

by structural features that are not adequately addressed bytheory Although Δ119891119867

119900298g values for some strained com-

pounds can be accurately predicted by adding correctionfactors for structural characteristics such as ring strain thepresence of gauche carbons and C1ndashC5 repulsions contri-bution of certain other structural features do not appear tobe adequately addressed by group additivity theory HNSand nitroglycerin seem to fall into this category Whenthese compounds were eliminated from the test set the rmsdeviation from experiment for the predicted group additivityΔ119891119867119900298g values was found to be 35 kcalmol with an MAE

of 22 kcalmol and a maximum deviation of 115 kcalmol forthe remaining 34 compoundsThe relevant point is that groupadditivity theory is often quite accurate however onemust becareful regarding its application

Density functional theory coupledwith the use of selectedbalanced reactions was also used to calculate Δ119891119867

119900298g values

for comparison to the test setThe reactions used in this inves-tigation are presented in Table 4 We determined that therms deviation from experiment for the calculated Δ119891119867

119900298g

values was 15 kcalmol with an MAE of 11 kcalmol and amaximum deviation of 38 kcalmol This approach yieldedcalculated results in which 82 (3745) of theΔ119891119867

119900298g values

werewithinplusmn20 kcalmol of experimental values Despite thefact that for time considerations we selected a medium size

basis set density functional theory coupled with the use ofisodesmic and other balanced equations was still the mostaccurate approach of the sixmethodswe compared Althoughaccurate it is necessary to mention some problems with thisapproach First of all different balanced equations can leadto different Δ119891119867

119900298g values Often such differences are small

But sometimes such differences can be substantial Cramer[12] has noted that ldquothe construction of an isodesmic equationis something of an art depending on chemical intuition andavailable experimental datardquo

It should also be mentioned that when computationtime is not a consideration the use of larger basis setsmight be expected to result in even greater accuracy IndeedDorofeeva and colleagues [21ndash23] have have shown thatthe use of high level computational theory coupled withmultiple isodesmic isogyric and other balanced equationscan result in calculation of Δ119891119867

119900298g values that are suffi-

ciently accurate that they feel confident in recommendingconsensus values in many cases where there is discrep-ancy between experimental values andor between computedvalues

Finally two semiempirical models (RM1 and PM7) wereused to calculate Δ119891119867

119900298g Semiempirical models are attrac-

tive because they are very rapid and their accuracy continuesto improve [13 14] However RM1 and PM7 were found tobe less accurate than the other approaches used to calculateΔ119891119867119900298g values for compounds in the test set used for this

investigation Even when Δ119891119867119900298g values having very large

(greater than 14 kcalmol) deviations from reference valueswere omitted rms and MAE values for calculated RM1 andPM7 data sets were substantially greater than those of thefour other computational approaches investigated (Tables 2and 3)

4 Conclusion

Because substantial interest exists in developing relativelyrapid and accurate procedures for predicting gas-phase heatof formation values for energetic compounds our overall goalwas to determine which of several computational approachesis most suitable for this endeavor None of the computationalapproaches were uniformly accurate within plusmn20 kcalmolof experimental values (ie the presumably more accuratealternative experimental values)

However four of the computational approaches investi-gated were able tomeet this level of accuracy greater than 51of the time Moreover these four computational approacheswere accurate to within plusmn40 kcal greater than 77 of thetime For relatively simple compounds in which correctionfactors can be used to account for ring strain and so forthand other factors do not make substantial contribution toΔ119891119867119900298g we conclude that the group additivity approach is

about as accurate as those approaches based on higher levelsof theory For compounds that are structurallymore complexthe approach using DFT coupled with the use of isodesmicisogyric and other balanced equations is more accurate butmore time consuming than the DFTAtomic and Groupcontribution method described by Byrd and Rice [6 7] and

10 Advances in Physical Chemistry

the T1 method [8] for this set of compounds However sincecalculated values are often similar and mutually supportiveit seems that a reasonable approach would be to use any (orall) of these four procedures when this level of accuracy isacceptable and the goal is to compare predicted properties ofnew or theoretical compounds with those of structurally sim-ilar compounds whose experimental values andor computedvalues are well established

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] H M Xiao X J Xu and L Qiu Theoretical Design of HighEnergy Density Materials Science Press Beijing China 2008

[2] R E Kirk and D F Othmer Encyclopedia of Chemical Technol-ogy vol 5 Wiley New York NY USA 2004

[3] J Giles ldquoGreen explosives collateral damagerdquo Nature vol 427no 6975 pp 580ndash581 2004

[4] J P Agrawal and J E Field ldquoRecent trends in high-energymaterialsrdquo Progress in Energy and Combustion Science vol 24no 1 pp 1ndash30 1998

[5] J Akhavan The Chemistry of Explosives Royal Society ofChemistry Cambridge UK 2004

[6] E F C Byrd and B M Rice ldquoImproved prediction of heatsof formation of energetic materials using quantum mechanicalcalculationsrdquo Journal of Physical Chemistry A vol 110 no 3 pp1005ndash1013 2006

[7] E F C Byrd and B M Rice ldquoCorrection improved predictionof heats of formation of energetic materials using quantummechanical calculationsrdquo The Journal of Physical Chemistry Avol 113 no 9 p 5813 2009

[8] W S Ohlinger P E Klunzinger B J Deppmeier and W JHehre ldquoEfficient calculation of heats of formationrdquo Journal ofPhysical Chemistry A vol 113 no 10 pp 2165ndash2175 2009

[9] L A Curtiss P C Redfern K Raghavachari V Rassolov andJ A Pople ldquoGaussian-3 theory using reduced Moslashller-PlessetorderrdquoThe Journal of Chemical Physics vol 110 no 10 pp 4703ndash4709 1999

[10] S W Benson and J H Buss ldquoAdditivity rules for the estima-tion of molecular properties Thermodynamic propertiesrdquo TheJournal of Chemical Physics vol 29 no 3 pp 546ndash572 1958

[11] SW Benson F R Cruickshank DM Golden et al ldquoAdditivityrules for the estimation of thermochemical propertiesrdquo Chemi-cal Reviews vol 69 no 3 pp 279ndash324 1969

[12] C J Cramer Essentials of Computational Chemistry Theoriesand Models John Wiley amp Sons New York NY USA 2ndedition 2004

[13] G B Rocha R O Freire A M Simas and J J P Stewart ldquoRM1a reparameterization of AM1 for H C N O P S F Cl Br and IrdquoJournal of Computational Chemistry vol 27 no 10 pp 1101ndash11112006

[14] J J P Stewart ldquoOptimization of parameters for semiempiricalmethods VI more modifications to the NDDO approximationsand re-optimization of parametersrdquo Journal of Molecular Mod-eling vol 19 no 1 pp 1ndash32 2013

[15] Y Zhao andDG Truhlar ldquoTheM06 suite of density functionalsfor main group thermochemistry thermochemical kineticsnoncovalent interactions excited states and transition ele-ments two new functionals and systematic testing of fourM06-class functionals and 12 other functionalsrdquo TheoreticalChemistry Accounts vol 120 no 1ndash3 pp 215ndash241 2008

[16] Y Zhao and D G Truhlar ldquoDensity functionals with broadapplicability in chemistryrdquo Accounts of Chemical Research vol41 no 2 pp 157ndash167 2008

[17] H Y Afeefy J F Liebman and S E Stein ldquoNeutral thermo-chemical datardquo in NIST Chemistry WebBook P J Linstrom andW G Mallard Eds NIST Standard Reference Database no 69National Institute of Standards and Technology GaithersburgMd USA 2005

[18] J B Pedley R D Naylor and S P KirbyThermochemical Dataof Organic Compounds Chapman amp Hall New York NY USA1986

[19] J O Cox and G Pilcher Thermochemistry of Organic andOrganometallic Compounds Academic Press New York NYUSA 1970

[20] OVDorofeeva andMA Suntsova ldquoEnthalpies of formation ofnitromethane and nitrobenzene theory vs experimentrdquo Journalof Chemical Thermodynamics vol 58 pp 221ndash225 2013

[21] O V Dorofeeva O N Ryzhova and M A Suntsova ldquoAccurateprediction of enthalpies of formation of organic azides bycombining G4 theory calculations with an isodesmic reactionschemerdquo Journal of Physical Chemistry A vol 117 no 31 pp6835ndash6845 2013

[22] M A Suntsova and O V Dorofeeva ldquoUse of G4 theoryfor the assessment of inaccuracies in experimental enthalpiesof formation of aliphatic nitro compounds and nitraminesrdquoJournal of Chemical amp Engineering Data vol 59 no 9 pp 2813ndash2826 2014

[23] M A Suntsova and O V Dorofeeva ldquoComment on lsquouse ofG4 theory for the assessment of inaccuracies in experimentalenthalpies of formation of aliphatic nitro compounds andnitraminesrsquordquo Journal of Chemical amp Engineering Data vol 60no 5 pp 1532ndash1533 2015

[24] S P Verevkin V N EmelrsquoYanenko V Diky and O V Doro-feeva ldquoEnthalpies of formation of nitromethane and nitroben-zene new experiments vs quantum chemical calculationsrdquoTheJournal of ChemicalThermodynamics vol 73 pp 163ndash170 2014

[25] CHETAHTheComputer Program for ChemicalThermodynam-ics and Energy Release Evaluation University of SouthAlabamaMobile Ala USA ASTM International West ConshohockenPa USA 2009

[26] NCohen and SWBenson ldquoEstimation of heats of formation oforganic compounds by additivity methodsrdquo Chemical Reviewsvol 93 no 7 pp 2419ndash2438 1993

[27] J A Bumpus and P H Willoughby ldquoOn the heat of formationof nitromethanerdquo Journal of Physical Organic Chemistry vol 21no 9 pp 747ndash757 2008

[28] Y K Knobelrsquo E A Miroshnichenko and Y A LebedevldquoHeats of combustion of nitromethane and dinitromethaneenthalpies of formation of nitromethyl radicals and energies ofdissociation of bonds in nitro derivatives of methanerdquo Bulletinof the Academy of Sciences of the USSR Division of ChemicalScience vol 20 no 3 pp 425ndash428 1971

[29] E A Miroshnichenko T S Konrsquokova Y O Inozemtsev VP VorobrsquoEva Y N Matymhin and S A Shevelev ldquoBondenergies and formation enthalpies of mono- and polyradicals in

Advances in Physical Chemistry 11

nitroalkanes 1 Nitromethanesrdquo Russian Chemical Bulletin vol58 no 4 pp 772ndash776 2009

[30] C Y Lin M W George and P M W Gill ldquoEDF2 a densityfunctional for predicting molecular vibrational frequenciesrdquoAustralian Journal of Chemistry vol 57 no 4 pp 365ndash370 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Page 2: Research Article Calculating Heat of Formation Values of Energetic Compounds…downloads.hindawi.com/journals/apc/2016/5082084.pdf ·  · 2016-03-14Research Article Calculating Heat

2 Advances in Physical Chemistry

we have compared the effectiveness of these two procedureswith regard to their ability to accurately calculate Δ119891119867

119900298g

values of nitrogen-containing energetic compounds Oper-ating under the assumption that newer procedures are notnecessarily more reliable than more established methods wealso assessed and compared the ability of two other well-established procedures used to calculate Δ119891119867

119900298g Specif-

ically we assessed and compared results using the groupadditivity method developed by Benson and his colleagues[10 11] as well as density functional theory coupled with theuse of isodesmic isogyric or other balanced equations [12]We also used and compared two relatively new semiempiricalmodels (PM7 and RM1) [13 14] to calculate Δ119891119867

119900298g

2 Methods

The test set used in this investigation consisted of the gas-phase heat of formation (Δ119891119867

119900298g) values for forty-five

nitrogen-containing energetic compounds studied by Byrdand Rice [6 7] Δ119891119867

119900298g values were calculated using the

T1 procedure which is based on the G3MP2 [9] multilevelab initio model chemistry as implemented in the Spartanrsquo10and 14 suite of programs Semiempirical theory using theRM1 and PM7 model chemistries [13 14] were used to cal-culate Δ119891119867

119900298g as implemented in Spartan 14 (Wavefunction

Inc Irvine CA) and MOPAC2012 (httpopenmopacnet)respectively

Gas-phase heat of formation values were also calculatedusing density functional theory as implemented in Spartan 10and 14 coupled with the use of isodesmic isogyric and otherbalanced equations An informative account of the detailsconcerning the calculation of Δ119891119867

119900298g using this approach

has been presented by Cramer [12] Most of the equationsused were isodesmic equations For the studies reportedherein total electronic energies (119864Tot) zero point energies(ZPE) and thermal correction (119867119879) values for compoundsin all of the equations were calculated using the M06 2Xfunctional [15 16] and the 6-31Glowast basis set The 6-31Glowast basisset is a medium size basis set It was selected for use so thatexcessive computation time could be avoided In Spartanit is necessary that the ldquocompute IRrdquo box be selected inorder to make these calculations When this is done thecalculated119867119900298 value required for use in isodesmic isogyricor other balanced equations is computed and appears inthe Thermodynamics Window This window is accessed bythe following path Display gt Properties gtThermodynamicsExperimental values for Δ119891119867

119900298g required for compounds

used in these studies were acquired from the NISTWebBook[17] Pedleyrsquos Thermochemical Data of Organic Compounds2nd ed [18] Cox and Pilcherrsquos Thermochemistry of Organicand Organometallic Compounds [19] and publications byDorofeeva and her colleagues [20ndash24]

Gas-phase heat of formation values were calculated fortwenty-five compounds using the Group Additivity approachas implemented in the NIST WebBook (httpwebbooknistgovchemistry) applet [17] This applet uses Benson GroupAdditivity values [10 11] Eight compounds in our testset contained an azido group Unfortunately the azido

group value is not among those included in the databasefor the NIST WebBook applet To address this problemwe first calculated an enthalpy group value for an azidogroup attached to a carbon atom The Δ119891119867

119900298g of methyl

azide has been determined experimentally and by highlevel computation We used the value of 712 kcalmol(plusmn10 kcalmol) recommended by Dorofeeva et al [21]Subtracting the methyl group value (minus102 kcalmol) fromthe heat of formation of methyl azide gives a value of814 kcalmol for the azido group The group additivityapproach was then used to calculate Δ119891119867

119900298g values of

azido-containing compounds as follows First the NISTapplet was used to calculate the Δ119891119867

119900298g value for the amino

analog of the azido compound Then the azido group valueof 814 kcalmol was used in the calculation instead of theamino group value Using this simple modification of thegroup additivity approach Δ119891119867

119900298g values were calculated

for six of the eight compounds in our test set that containedan azido group Calculation of Δ119891119867

119900298g for the remaining

compounds that contained an azido group is described belowTheASTMCHETAH 80 software program [25] was used

to calculateΔ119891119867119900298g values for a few other compounds in our

test set whose Δ119891119867119900298g values could not be calculated using

the NIST appletThe group additivity difference method as described by

Cohen and Benson [26] was used to calculate the Δ119891119867119900298g

value for nitromethane For nitromethane it should be men-tioned that experimental values of minus178 and minus193 kcalmolhave been reported and used extensively Interestingly thereis considerable theoretical as well as experimental support forboth values [20 22ndash24 27ndash29] In the present investigationthe group additivity value for nitromethane (minus180 kcalmol)was calculated by subtracting the group value (minus66 kcalmol)for a methylene (ndashCH2ndash) group bound to a nitrogen atomfrom the calculated Δ119891119867

119900298g value of minus246 kcalmol for

nitroethane We note that this value is 15 kcalmol greaterthan that previously reported by Bumpus and Willoughby[27] It should also be noted that recent experimentalresults [24] support a slightly greater Δ119891119867

119900298g value of

minus1709 kcalmol for nitromethane and it is this value that wasultimately included in the alternative experimental referenceset

The calculation of Δ119891119867119900298g for 1-azido-11-dinitroethane

was accomplished using the group values for the methylgroup and azido group coupled with the group value for acarbon attached to an azido group and two nitro groupsThislater value was assumed to be equivalent to the group value(minus99 kcalmol) for a carbon attached to a hydrogen and twonitro groups

For azidotrinitromethane the group value for the trini-tromethyl group (minus145 kcalmol) listed in CHETAH 80 wasadded to the azido group value of 814 kcalmol giving acalculated Δ119891119867

119900298g value of 7995 kcalmol (= 800 kcalmol)

for azidotrinitromethaneAll calculated Δ119891119867

119900298g values were compared with

experimental values and with values published by Byrd andRice [6 7] who calculated Δ119891119867

119900298g values using density

Advances in Physical Chemistry 3

functional theory coupledwith an atom and group equivalentmethod Calculated Δ119891119867

119900298g values were also compared to

an alternative experimental reference set in which eighteenpresumably more accurate Δ119891119867

119900298g values recommended

by Dorofeeva and colleagues [20ndash24] were substituted forcorresponding values in the original set of experimentalvalues Also substituted in this alternative experimentalreference set was the Δ119891119867

119900298g value for 246-trinitrotoluene

listed in Cox and Pilcherrsquos ldquoThermochemistry of Organic andOrganometallic Compoundsrdquo [19] Finally it should be notedthat during the course of this investigation it appeared thatthe experimental Δ119891119867

119900298g value for dinitromethylbenzene

might be several kcalmol too low To address this possibilitywe used an approach similar to that used successfully byDorofeeva et al [21ndash23] to deal with such issues Specificallywe used density functional theory (EDF2 [30] functional andthe 6-311++G (2df2p) basis set) coupled with the use of tenisodesmic equations to calculate a Δ119891119867

119900298g reference value

of 142 plusmn 03 for dinitromethylbenzene This value was alsoincluded in the alternative reference set

It should be mentioned that many of the computedRM1 and PM7 Δ119891119867

119900298g values for compounds appearing

in Table 1 have been previously reported [13 14] Similarlymost of the T1 Δ119891119867

119900298g values appear in the Spartan Spectra

and Properties Database (SSPD) data base that accompaniesSpartan 14 In general our results are quite consistent withthese previously reported values In some instances howeverslightly lower Δ119891119867

119900298g values were calculated indicating the

existence of lower-energy equilibrium geometries than thoseused in previous investigations

3 Results and Discussion

The ultimate goal of any computational strategy designedto estimate values for Δ119891119867

119900298g is to reduce uncertainties

to within plusmn10 or 20 kcalmol (1 kcalmol = 4184 kJmol)which is taken to be experimental error One reason for thisgoal is that small errors in Δ119891119867

119900298g become magnified when

propagated to obtain other values which depend onΔ119891119867119900298g

The standard Gibbs energy change of a reaction for exampleis a function of the reaction enthalpy change as follows

Δ rxn119866∘= Δ rxn119867

∘minus 119879Δ rxn119878

∘ (1)

Reaction enthalpies can be calculated in accord with Hessrsquoslaw by taking the difference of the standard heat of formationvalues of the products and reactants of the reaction Theequilibrium constant (119870eq) of a reaction and Δ rxn119866

∘ arerelated by the expression

119870eq = 119890minusΔ rxn119866

∘119877119879 (2)

Since the equilibrium constant depends exponentially uponΔ rxn119866

∘ a small error in Δ rxn119867119900 can result in dramatically

different values for 119870eq when it is the calculated parameterof interest

For energetic compounds calculation of equilibriumconstants using heat of formation values is typically not

a concern sincemost reactions of interest are highly exergonicwith equilibrium constants that indicate product formationis highly favored It must be noted however that severalparameters (eg heat of detonation heat of explosion powerindex explosive velocity and explosive pressure) used tocharacterize high explosives require the condensed-phaseheat of formation value This is somewhat problematic fortheoretical compounds since calculations are performedon single molecules which are by definition gas-phasemolecules To calculate solid-phase heat of formation valuesheat of sublimation (or vaporization) values are calculatedby one of several computational methods available and thesevalues are then subtracted from the gas-phase values tocalculate the condensed-phase values This represents stillanother source of uncertainty in subsequent calculations It istherefore important to be able to identify and use proceduresthat provide the most accurate heat of formation valuespossible

Our initial objective was to compare the abilities of theT1 multilevel ab initio approach developed by Ohlinger etal [8] with the atom and group equivalent DFT approachdescribed by Byrd and Rice [6 7] To make this comparisonwe selected the forty-five nitrogen-containing compoundsstudied by Byrd and Rice [6 7] which we designated as ourtest set and acquiredT1Δ119891119867

119900298g values for these compounds

These results and the results of all comparisons made in thisinvestigation are presented inTables 1 2 and 3 and in Figure 1

When making comparisons such as those under con-sideration here it is necessary to use the most accurateexperimental Δ119891119867

119900298g reference values available This is

problematic for no fewer than twenty of the experimentalΔ119891119867119900298g values used in this investigation and it is of sub-

stantial concern for the eight organic azide compounds in thetest set Indeed Dorofeeva et al [21] note that ldquoenthalpiesof formation of organic azides are scanty and not alwaysreliablerdquo To address this problem Dorofeeva et al [21] useda combination of multilevel ab initio model chemistries anddensity functional theory coupled with the use of isodesmicisogyric and other balanced equations to calculate andrecommend Δ119891119867

119900298g values for twenty-nine organic azides

including the eight organic azide compounds in our test setThe implication of their work is that their calculated valuesmay be more accurate than the experimental values thatwere originally available to Byrd and Rice [6 7] This samegroup [20 22ndash24] conducted similar studies of the Δ119891119867

119900298g

values for fifty-seven other energetic nitrogen-containingcompounds and recommended the use of several Δ119891119867

119900298g

values that are slightly different than those that were availableto Byrd and Rice [6 7]

In light of these findings we compared computed datawith the original experimental data set used by Byrd and Rice[6 7] and with a newer alternative experimental referenceset (also referred to elsewhere herein as the most recentlyrecommended experimentalreference values available) inwhich a total of eighteen Δ119891119867

119900298g reference values recom-

mended by Dorofeeva et al [18 20 21] were substituted forthe original corresponding experimental values in the test set[6 7] We also note that at least three experimental values

4 Advances in Physical ChemistryTa

ble1Com

paris

onof

experim

entalgas-phase

heatof

form

ationvalues

with

values

calculated

usingseveraltheoreticalapproaches

Com

poun

dname

Experim

entallowast

Δ119891119867119900 298g

(kcalm

ol)

T1Δ119891119867119900 298g

(kcalm

ol)

DFT

Atom

icandGroup

contrib

ution

Δ119891119867119900 298g

(kcalm

ol)lowast

DFT

Isod

esmiclowastlowast

Δ119891119867119900 298g

(kcalm

ol)

Group

Additiv

ityΔ119891119867119900 298g

(kcalm

ol)

PM7

Δ119891119867119900 298g

(kcalm

ol)

RM1

Δ119891119867119900 298g

(kcalm

ol)

Nitro

methane

minus193(minus1709)

minus158

minus186

minus168

minus180

minus172

minus124

Tetra

nitro

methane

197(2110)

234

206

223

mdash284

181

Azidotrin

itrom

ethane

842(8532)

884

856

840

816

952

792

DMNO(N

-methyl-N

-nitrom

ethanamine)

minus12

05

minus10

minus11

minus16

minus58

minus35

1-Azido-11-d

initroethane

604(6286)

616

604

597

613

682

576

Hexanitroethane

428(291

8)293

337

289

mdash473

302

Nitro

glycerin

minus6671

minus658

minus667

minus698

minus815

minus826

minus720

TTT

943

984

941

938

mdash404

354

RDX(cyclotrimethylen

e-trinitra

mine)

458(4579)

490

440

468

mdash218

457

14-D

initrosopiperazine

464

527

467

466

368lowastlowastlowast

172

127

14-D

initropiperazine

139(1546

)177

126

149

112

20

167

N-N

itro-bis-2

22-tr

initroethylam

ine

2142

212

231

191

mdash346

334

Nitro

benzene

1638(1568)

152

141

148

161

182

182

2-Nitro

phenol

minus3162

minus296

minus311

minus314

minus260

minus310

minus289

3-Nitro

phenol

minus2612

minus260

minus260

minus270

minus260

minus258

minus268

4-Nitro

phenol

minus2741

minus260

minus280

minus282

minus260

minus281

minus285

m-N

itroanilin

e149

169

153

161

171

166

114

p-Nitro

aniline

132

165

128

141

171

129

83

Azidobenzene

930(9919)

948

998

968

974

990

945

1-Azido-4-nitrobenzene

931(9417)

928

918

931

937

947

903

N-N

itrobis-22-dinitro

propylam

ine(DNPN

)minus317

minus287

minus256

minus338

mdashminus150

minus91

PNT(1-

methyl-4

-nitrobenzene)

738

72

63

73

81

75

84

24-DNT(1-

methyl-2

4-dinitrobenzene)

793

86

44

85

44

70

85

Azidom

ethylbenzene

995(9680)

924

991

962

968

947

914

3-Az

ido-3-ethylpentane

406(315

5)281

414

315

329

367

338

TNT(tr

initrotoluene)

575

(123)

136

71

115

08

108

126

22-Dinitroadamantane

minus3688(minus4278)

minus394

minus347

minus413

minus354lowastlowastlowast

minus286

minus439

1-Azidoadam

antane

516(4374)

400

496

446

480

470

289

2-Az

ido-2-phenylp

ropane

874(795

9)750

819

803

798

842

776

HNS

5698

639

595

608

358

582

616

Methylnitrite

minus1564

minus133

minus146

minus139

minus161

minus192

minus219

Methylnitrate

minus292

minus270

minus272

minus273

minus296

minus314

minus284

Dinitrom

ethane

minus141(minus92

0)minus76

minus132

minus78

mdashminus82

minus45

Ethylnitrite

minus259

minus219

minus224

minus249

minus242

minus326

minus323

Ethylnitrate

minus370

minus351

minus349

minus361

minus377

minus395

minus356

Propylnitrite

minus284

minus270

minus273

minus292

minus291

minus377

minus372

2-Methyl-2

-nitropropane

minus4232

(minus4190)

minus402

minus383

minus426

minus423

minus357

minus364

n-Bu

tylnitrite

minus348

minus320

minus320

minus355

minus340

minus426

minus422

t-Butylnitrite

minus410

minus387

minus354

minus408

minus425

minus482

minus486

34-Fu

razand

imethanoldinitrate

26

98

91

minus04

mdashminus40

194

1-Nitropiperidine

minus106(minus887)

minus74

minus99

minus89

minus81

minus155

minus92

Advances in Physical Chemistry 5

Table1Con

tinued

Com

poun

dname

Experim

entallowast

Δ119891119867119900 298g

(kcalm

ol)

T1Δ119891119867119900 298g

(kcalm

ol)

DFT

Atom

icandGroup

contrib

ution

Δ119891119867119900 298g

(kcalm

ol)lowast

DFT

Isod

esmiclowastlowast

Δ119891119867119900 298g

(kcalm

ol)

Group

Additiv

ityΔ119891119867119900 298g

(kcalm

ol)

PM7

Δ119891119867119900 298g

(kcalm

ol)

RM1

Δ119891119867119900 298g

(kcalm

ol)

Nitro

sobenzene

481

471

488

455

mdash412

331

Nitro

methylbenzene

734

87

94

90

76113

130

Dinitrom

ethylbenzene

83(14

2)

139

136

145

121

196

184

13-D

imethyl-2

-nitrobenzene

21

14

43

32

02

minus02

14

HNS=111015840 -(12-ethenediyl)b

is[246-trinitrob

enzene]TT

T=hexahydro-13

5-tr

initroso-13

5-tr

iazine

lowastVa

luesfro

mBy

rdandRice

[67]Va

luesin

parenthesesa

rethosethath

aveb

eensubstituted

forcorrespon

ding

valuesin

theo

riginalreferences

etandareu

sedin

thea

lternativee

xperim

entalreference

setSeetext

ford

etailsandexplanation

lowastlowastMosto

fvaluesintheD

FTiso

desm

iccolumnwerec

alculated

usingiso

desm

icreactio

nsH

owever

somev

aluesw

erec

alculated

usingiso

gyric

orotherb

alancedequatio

ns

lowastlowastlowastVa

lues

calculated

usingCH

ETAH80

6 Advances in Physical Chemistry

Table 2 Statistical comparison of experimental gas-phase heat of formation valueswith values calculated using several theoretical approaches

T1Δ119891119867298g(kcalmol)

DFT Atomicand GroupcontributionΔ119891119867298g

(kcalmol)lowast

DFTisodesmicΔ119891119867298g(kcalmol)

Group AddΔ119891119867298g(kcalmol)

PM7Δ119891119867298g(kcalmol)

RM1Δ119891119867298g(kcalmol)

rms deviation 50 30 37 54 (34)lowast 118 (60) 129 (59)MAE 37 21 25 33 (25)lowast 75 (49) 79 (48)Max Dev (kcalmol) 135 91 139 212 (96)lowast 539 (132) 589 (126)Number of values plusmn20 kcalmol 17 28 27 19 10 12Number of values plusmn30 kcalmol 25 35 33 24 14 17Number of values plusmn40 kcalmol 32 37 37 28 18 18

1198772 098728 09958 099277 09863

(099435)092817(098063)

091605(098141)

lowastValues in parentheses represent data in which values for compounds having deviations from experiment greater than 140 kcalmol were omitted See text forexplanation

Table 3 Statistical comparison of alternative experimental gas-phase heat of formation values with values calculated using several theoreticalapproaches

T1Δ119891119867298g(kcalmol)

DFT Atomicand GroupcontributionΔ119891119867298g(kcalmol)lowast

DFTisodesmicΔ119891119867298g(kcalmol)

Group AddΔ119891119867298g(kcalmol)

PM7lowastΔ119891119867298g(kcalmol)

RM1lowastΔ119891119867298g(kcalmol)

rms deviation 29 33 15 55 (35)lowast 120 (54) 122 (45)MAE 23 24 11 31 (23)lowast 73 (42) 68 (36)Max Dev (kcalmol) 69 99 38 212 (115)lowast 539 (132) 589 (120)Number of values plusmn20 kcalmol 23 23 37 23 13 14Number of values plusmn30 kcalmol 31 33 42 25 18 19Number of values plusmn40 kcalmol 38 37 45 28 21 21

1198772 099648 099477 099884 098549

(099353)092435(098574)

092367(09889)

lowastValues in parentheses represent data in which values for compounds having deviations from experiment greater than 140 kcalmol were omitted See text forexplanation

have been reported for 246-trinitrotoluene Thus in placeof the Δ119891119867

119900298g value of 575 kcalmol used by Byrd and Rice

[6 7] we have substituted the value of 123 kcalmol (reportedin ldquoThermochemistry of Organic and Organometallic Com-poundsrdquo by Cox and Pilcher [19]) in the new alternativeexperimental reference data set During the course of thisinvestigation it also appeared that the experimental value fordinitromethylbenzene may be several kcalmol too lowThuswe used procedures similar to those described by Dorofeevaet al [21ndash23] to calculate a Δ119891119867

119900298g reference value of 142 plusmn

03 kcalmol for this compoundThis value was also includedin the alternative reference set These results are found inSupplemental Tables 1S and 2S (see Supplementary Materialavailable online at httpdxdoiorg10115520165082084)

A comparison of Tables 2 and 3 supports the conclusionthat the alternative recommended values as a group areindeed more accurate than the original experimental valuesthat were available to and used by Byrd and Rice [6 7] intheir investigations Except for the DFTAtomic and Groupcontribution approach the mean absolute error (MAE) was

greater for the original experimental reference set than forthe new alternative experimental reference set The fact thatthe opposite was found for the DFTAtomic and Groupcontribution approach is not surprising as many of the com-pounds in the original experimental reference set were usedto parameterize and develop this computational approachNevertheless this approach still performed quite well whencompared to the alternative experimental reference set Ourresults also suggest that the accuracy of the DFTAtomic andGroup contribution approach might benefit from reparame-terization using the alternative experimental reference set

Because the alternative experimental reference setappeared to be more accurate than the original reference setit was used for the comparisons described below

The atom and group equivalent DFT approach describedby Byrd and Rice [6 7] and the T1 procedure both yieldedcalculated results in which 51 (2345) of the predictedΔ119891119867119900298g values were within plusmn20 kcalmol of values in the

reference set The rms deviation from experiment for thepredicted T1 gas-phase heat of formation values was found

Advances in Physical Chemistry 7

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

0minus50 50 100minus100

Experimental values (kcalmol)

(a) T1

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(b) DFTAtomic and Group contribution

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(c) DFTisodesmic

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(d) Group Add

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus100 0 50 100minus50

Experimental values (kcalmol)

(e) PM7

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(f) RM1

Figure 1 Calculated gas-phase heat of formation values versus experimental values Gas-phase heat of formation values were calculated using(1) the multilevel ab initio approach (T1) described by Ohlinger et al [8] as implemented in the Spartanrsquo10 and 14 suite of programs (a) (2) theDFTAtomic and Group contribution approach developed and described by Byrd and Rice [6 7] (b)The experimental values and calculatedvalues used to construct (b) are those published by Byrd and Rice [6 7] (b) is identical to Figure 1a in their manuscript except for the fact thatthe alternative set of experimental Δ119891119867

119900298g reference values are also included (3) Density functional theory using isodesmic isogyric and

other balanced equations as described herein (c) (4)The Benson Group Additivity approach as implemented in the and NIST and CHETAH80 software programs (d) (5) semiempirical theory (PM7 andRM1) as implemented inMOPAC2012 and the Spartan 14 suite of programs ((e)and (f) resp) Open squares represent calculatedΔ119891119867

119900298g values versus the experimentalΔ119891119867

119900298g values Closed circles represent calculated

Δ119891119867119900298g values versus the alternative experimental Δ119891119867

119900298g reference values as described in the text Least square regression analysis and

calculation of 1198772 values were accomplished using KaleidaGraph graphing software (Synergy Software Reading PA) 1198772 values are presentedin Tables 2 and 3

8 Advances in Physical Chemistry

Table 4 Balanced equations used to calculate heat of formation values of compounds in the test set

Isodesmic isogyric or other balanced equations1 Dinitromethane + methanerarr2 nitromethane2 2 dinitromethanerarrmethane + tetranitromethane3 Methyl azide + trinitromethanerarrmethane + azidotrinitromethane4 N-Ethyl-N-nitroethanamine + dimethylaminerarr N-ethyl-N-ethanamine + N-methyl-N-nitromethanamine (DMNO)5 11-Dinitropropane + methyl aziderarr ethane + 1-azido-11-dinitroethane6 2 111-Trinitropropanerarr butane + hexanitroethane7 3 propylnitraterarr2 propane + nitroglycerin8 RDX + 3 nitrosyl hydriderarr3 HNO2 + TTT (hexahydro-135-trinitroso-135-triazine)9 3 1-nitropiperidinerarr2 cyclohexane + RDX10 1-Nitrosopiperidine + TTTrarr2 14-dinitrosopiperazine11 Piperazine + 2 dimethylnitraminerarr 2 dimethylamine + 14-dinitropiperazine12 Bis-222-trinitroethylamine + HNO2 rarr H2 + N-nitro-bis-222-trinitroethylamine13 Benzene + 4-nitroanilinerarr aniline + nitrobenzene14 Phenol + nitrobenzenerarr benzene + 2-nitrophenol15 Phenol + nitrobenzenerarr benzene + 3-nitrophenol16 Phenol + nitrobenzenerarr benzene + 4-nitrophenol17 Aniline + nitrobenzenerarr benzene + m-nitroaniline18 Aniline + nitrobenzenerarr benzene + p-nitroaniline19 Methyl azide + benzenerarrmethane + azidobenzene20 Methyl azide + nitrobenzenerarrmethane + 1-azido-4-nitrobenzene

21 N-Propylpropanamine + 4 1-nitropropane + dimethylnitraminerarr dimethylamine + N-nitro-bis-22-dinitropropylamine (DNPN)+ 4 propane

22 Toluene + nitrobenzenerarr benzene + PNT (1-methyl-4-nitrobenzene)23 Toluene + 2 nitrobenzenerarr2 benzene + 24-DNT (1-methyl-24-dinitrobenzene)24 Methyl azide + toluenerarrmethane + azidomethylbenzene25 Methyl azide + 3-ethylpentanerarrmethane + 3-azido-3-ethylpentane26 Toluene + 135-trinitrobenzenerarr benzene + TNT (246-trinitrotoluene)27 2 2-nitropropane + adamantanerarr2 propane + 22-dinitroadamantane28 Methyl azide + adamantanerarrmethane + 1-azidoadamantane29 Methyl azide + 2-phenylpropanerarrmethane + 2-azido-2-phenylpropane30 trans-Stilbene + 2 135-trinitrobenzenerarr2 benzene + HNS (111015840-(12-ethenediyl)bis[246- trinitrobenzene])31 Isopropyl nitrite + methanerarr propane + methyl nitrite32 Propyl nitrate + methanerarr propane + methyl nitrate33 2 1-Nitropropane + methanerarr2 propane + dinitromethane34 Propyl nitrite + ethanerarr propane + ethyl nitrite35 Propyl nitrate + ethanerarr propane + ethyl nitrate36 Isopropyl nitriterarr propyl nitrite37 2-Nitropropane + 2-methylpropanerarr 2-methyl-2-nitropropane + propane38 Isopropyl nitrite + butanerarr n-butyl nitrite + propane39 Isopropyl nitrite + isobutanerarr t-butyl nitrite + propane40 2 1-pyrroline + tetrahydrofuran + 2methyl nitraterarr H2 + 34-furazandimethanol dinitrate + 2 cyclopentane41 Piperidine + dimethylnitraminerarr 1-nitropiperidine + dimethylamine42 Phenyl radical + nitric oxiderarr nitrosobenzene43 Toluene + 1-nitropropanerarr propane + nitromethylbenzene44 Toluene + 11-dinitropropanerarr propane + dinitromethylbenzene45 2 Toluene + nitrobenzenerarr2 benzene + 13-dimethyl-2-nitrobenzene

Advances in Physical Chemistry 9

to be 29 kcalmol with a mean absolute error (MAE) of23 kcalmol and a maximum deviation of 69 kcalmol Thiscompares with an rms deviation of 33 kcalmol a MAE of24 kcalmol and a maximum deviation of 99 kcalmol usingdata calculated by Byrd andRice [6 7] It should be noted thatthe T1 procedure has been previously shown to reproduceexperimental heat of formation values of a large (1805) set oforganicmolecules with an rms deviation of 275 kcalmol anda MAE of 203 kcalmol [8] Clearly the rms andMAE valuesfor the T1 approach reported here agree well with those valuesreported for the larger data set

These results led us to compare older approaches usedto predictcalculate Δ119891119867

119900298g values Specifically we used

Bensonrsquos group additivity (or group contribution) approach[10 11] We also used density functional theory coupled withthe use of selected isodesmic isogyric and other balancedequations One disadvantage of Bensonrsquos group additivityapproach is that group values for some of the substructuresof several compounds in the test set are not availableWe were partially able to overcome this problem by usingexisting data which allowed us to calculate some of thesegroup values In total we were able to use Bensonrsquos groupadditivity approach to calculate Δ119891119867

119900298g values for 36 of 45

compounds in the test set This approach yielded calculatedresults in which 64 (2336) of the calculated Δ119891119867

119900298g

values were within plusmn20 kcalmol of experimental valuesThe rms deviation from experiment for the predicted groupadditivity gas-phase heat of formation valueswas 55 kcalmolwith an MAE of 31 kcalmol with a maximum deviationof 212 kcalmol for HNS A relatively large deviation fromexperiment of 148 kcalmol was also found for nitroglycerinA significant drawback to the use of group additivity theoryis that calculated Δ119891119867

119900298g values are sometimes affected

by structural features that are not adequately addressed bytheory Although Δ119891119867

119900298g values for some strained com-

pounds can be accurately predicted by adding correctionfactors for structural characteristics such as ring strain thepresence of gauche carbons and C1ndashC5 repulsions contri-bution of certain other structural features do not appear tobe adequately addressed by group additivity theory HNSand nitroglycerin seem to fall into this category Whenthese compounds were eliminated from the test set the rmsdeviation from experiment for the predicted group additivityΔ119891119867119900298g values was found to be 35 kcalmol with an MAE

of 22 kcalmol and a maximum deviation of 115 kcalmol forthe remaining 34 compoundsThe relevant point is that groupadditivity theory is often quite accurate however onemust becareful regarding its application

Density functional theory coupledwith the use of selectedbalanced reactions was also used to calculate Δ119891119867

119900298g values

for comparison to the test setThe reactions used in this inves-tigation are presented in Table 4 We determined that therms deviation from experiment for the calculated Δ119891119867

119900298g

values was 15 kcalmol with an MAE of 11 kcalmol and amaximum deviation of 38 kcalmol This approach yieldedcalculated results in which 82 (3745) of theΔ119891119867

119900298g values

werewithinplusmn20 kcalmol of experimental values Despite thefact that for time considerations we selected a medium size

basis set density functional theory coupled with the use ofisodesmic and other balanced equations was still the mostaccurate approach of the sixmethodswe compared Althoughaccurate it is necessary to mention some problems with thisapproach First of all different balanced equations can leadto different Δ119891119867

119900298g values Often such differences are small

But sometimes such differences can be substantial Cramer[12] has noted that ldquothe construction of an isodesmic equationis something of an art depending on chemical intuition andavailable experimental datardquo

It should also be mentioned that when computationtime is not a consideration the use of larger basis setsmight be expected to result in even greater accuracy IndeedDorofeeva and colleagues [21ndash23] have have shown thatthe use of high level computational theory coupled withmultiple isodesmic isogyric and other balanced equationscan result in calculation of Δ119891119867

119900298g values that are suffi-

ciently accurate that they feel confident in recommendingconsensus values in many cases where there is discrep-ancy between experimental values andor between computedvalues

Finally two semiempirical models (RM1 and PM7) wereused to calculate Δ119891119867

119900298g Semiempirical models are attrac-

tive because they are very rapid and their accuracy continuesto improve [13 14] However RM1 and PM7 were found tobe less accurate than the other approaches used to calculateΔ119891119867119900298g values for compounds in the test set used for this

investigation Even when Δ119891119867119900298g values having very large

(greater than 14 kcalmol) deviations from reference valueswere omitted rms and MAE values for calculated RM1 andPM7 data sets were substantially greater than those of thefour other computational approaches investigated (Tables 2and 3)

4 Conclusion

Because substantial interest exists in developing relativelyrapid and accurate procedures for predicting gas-phase heatof formation values for energetic compounds our overall goalwas to determine which of several computational approachesis most suitable for this endeavor None of the computationalapproaches were uniformly accurate within plusmn20 kcalmolof experimental values (ie the presumably more accuratealternative experimental values)

However four of the computational approaches investi-gated were able tomeet this level of accuracy greater than 51of the time Moreover these four computational approacheswere accurate to within plusmn40 kcal greater than 77 of thetime For relatively simple compounds in which correctionfactors can be used to account for ring strain and so forthand other factors do not make substantial contribution toΔ119891119867119900298g we conclude that the group additivity approach is

about as accurate as those approaches based on higher levelsof theory For compounds that are structurallymore complexthe approach using DFT coupled with the use of isodesmicisogyric and other balanced equations is more accurate butmore time consuming than the DFTAtomic and Groupcontribution method described by Byrd and Rice [6 7] and

10 Advances in Physical Chemistry

the T1 method [8] for this set of compounds However sincecalculated values are often similar and mutually supportiveit seems that a reasonable approach would be to use any (orall) of these four procedures when this level of accuracy isacceptable and the goal is to compare predicted properties ofnew or theoretical compounds with those of structurally sim-ilar compounds whose experimental values andor computedvalues are well established

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] H M Xiao X J Xu and L Qiu Theoretical Design of HighEnergy Density Materials Science Press Beijing China 2008

[2] R E Kirk and D F Othmer Encyclopedia of Chemical Technol-ogy vol 5 Wiley New York NY USA 2004

[3] J Giles ldquoGreen explosives collateral damagerdquo Nature vol 427no 6975 pp 580ndash581 2004

[4] J P Agrawal and J E Field ldquoRecent trends in high-energymaterialsrdquo Progress in Energy and Combustion Science vol 24no 1 pp 1ndash30 1998

[5] J Akhavan The Chemistry of Explosives Royal Society ofChemistry Cambridge UK 2004

[6] E F C Byrd and B M Rice ldquoImproved prediction of heatsof formation of energetic materials using quantum mechanicalcalculationsrdquo Journal of Physical Chemistry A vol 110 no 3 pp1005ndash1013 2006

[7] E F C Byrd and B M Rice ldquoCorrection improved predictionof heats of formation of energetic materials using quantummechanical calculationsrdquo The Journal of Physical Chemistry Avol 113 no 9 p 5813 2009

[8] W S Ohlinger P E Klunzinger B J Deppmeier and W JHehre ldquoEfficient calculation of heats of formationrdquo Journal ofPhysical Chemistry A vol 113 no 10 pp 2165ndash2175 2009

[9] L A Curtiss P C Redfern K Raghavachari V Rassolov andJ A Pople ldquoGaussian-3 theory using reduced Moslashller-PlessetorderrdquoThe Journal of Chemical Physics vol 110 no 10 pp 4703ndash4709 1999

[10] S W Benson and J H Buss ldquoAdditivity rules for the estima-tion of molecular properties Thermodynamic propertiesrdquo TheJournal of Chemical Physics vol 29 no 3 pp 546ndash572 1958

[11] SW Benson F R Cruickshank DM Golden et al ldquoAdditivityrules for the estimation of thermochemical propertiesrdquo Chemi-cal Reviews vol 69 no 3 pp 279ndash324 1969

[12] C J Cramer Essentials of Computational Chemistry Theoriesand Models John Wiley amp Sons New York NY USA 2ndedition 2004

[13] G B Rocha R O Freire A M Simas and J J P Stewart ldquoRM1a reparameterization of AM1 for H C N O P S F Cl Br and IrdquoJournal of Computational Chemistry vol 27 no 10 pp 1101ndash11112006

[14] J J P Stewart ldquoOptimization of parameters for semiempiricalmethods VI more modifications to the NDDO approximationsand re-optimization of parametersrdquo Journal of Molecular Mod-eling vol 19 no 1 pp 1ndash32 2013

[15] Y Zhao andDG Truhlar ldquoTheM06 suite of density functionalsfor main group thermochemistry thermochemical kineticsnoncovalent interactions excited states and transition ele-ments two new functionals and systematic testing of fourM06-class functionals and 12 other functionalsrdquo TheoreticalChemistry Accounts vol 120 no 1ndash3 pp 215ndash241 2008

[16] Y Zhao and D G Truhlar ldquoDensity functionals with broadapplicability in chemistryrdquo Accounts of Chemical Research vol41 no 2 pp 157ndash167 2008

[17] H Y Afeefy J F Liebman and S E Stein ldquoNeutral thermo-chemical datardquo in NIST Chemistry WebBook P J Linstrom andW G Mallard Eds NIST Standard Reference Database no 69National Institute of Standards and Technology GaithersburgMd USA 2005

[18] J B Pedley R D Naylor and S P KirbyThermochemical Dataof Organic Compounds Chapman amp Hall New York NY USA1986

[19] J O Cox and G Pilcher Thermochemistry of Organic andOrganometallic Compounds Academic Press New York NYUSA 1970

[20] OVDorofeeva andMA Suntsova ldquoEnthalpies of formation ofnitromethane and nitrobenzene theory vs experimentrdquo Journalof Chemical Thermodynamics vol 58 pp 221ndash225 2013

[21] O V Dorofeeva O N Ryzhova and M A Suntsova ldquoAccurateprediction of enthalpies of formation of organic azides bycombining G4 theory calculations with an isodesmic reactionschemerdquo Journal of Physical Chemistry A vol 117 no 31 pp6835ndash6845 2013

[22] M A Suntsova and O V Dorofeeva ldquoUse of G4 theoryfor the assessment of inaccuracies in experimental enthalpiesof formation of aliphatic nitro compounds and nitraminesrdquoJournal of Chemical amp Engineering Data vol 59 no 9 pp 2813ndash2826 2014

[23] M A Suntsova and O V Dorofeeva ldquoComment on lsquouse ofG4 theory for the assessment of inaccuracies in experimentalenthalpies of formation of aliphatic nitro compounds andnitraminesrsquordquo Journal of Chemical amp Engineering Data vol 60no 5 pp 1532ndash1533 2015

[24] S P Verevkin V N EmelrsquoYanenko V Diky and O V Doro-feeva ldquoEnthalpies of formation of nitromethane and nitroben-zene new experiments vs quantum chemical calculationsrdquoTheJournal of ChemicalThermodynamics vol 73 pp 163ndash170 2014

[25] CHETAHTheComputer Program for ChemicalThermodynam-ics and Energy Release Evaluation University of SouthAlabamaMobile Ala USA ASTM International West ConshohockenPa USA 2009

[26] NCohen and SWBenson ldquoEstimation of heats of formation oforganic compounds by additivity methodsrdquo Chemical Reviewsvol 93 no 7 pp 2419ndash2438 1993

[27] J A Bumpus and P H Willoughby ldquoOn the heat of formationof nitromethanerdquo Journal of Physical Organic Chemistry vol 21no 9 pp 747ndash757 2008

[28] Y K Knobelrsquo E A Miroshnichenko and Y A LebedevldquoHeats of combustion of nitromethane and dinitromethaneenthalpies of formation of nitromethyl radicals and energies ofdissociation of bonds in nitro derivatives of methanerdquo Bulletinof the Academy of Sciences of the USSR Division of ChemicalScience vol 20 no 3 pp 425ndash428 1971

[29] E A Miroshnichenko T S Konrsquokova Y O Inozemtsev VP VorobrsquoEva Y N Matymhin and S A Shevelev ldquoBondenergies and formation enthalpies of mono- and polyradicals in

Advances in Physical Chemistry 11

nitroalkanes 1 Nitromethanesrdquo Russian Chemical Bulletin vol58 no 4 pp 772ndash776 2009

[30] C Y Lin M W George and P M W Gill ldquoEDF2 a densityfunctional for predicting molecular vibrational frequenciesrdquoAustralian Journal of Chemistry vol 57 no 4 pp 365ndash370 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Page 3: Research Article Calculating Heat of Formation Values of Energetic Compounds…downloads.hindawi.com/journals/apc/2016/5082084.pdf ·  · 2016-03-14Research Article Calculating Heat

Advances in Physical Chemistry 3

functional theory coupledwith an atom and group equivalentmethod Calculated Δ119891119867

119900298g values were also compared to

an alternative experimental reference set in which eighteenpresumably more accurate Δ119891119867

119900298g values recommended

by Dorofeeva and colleagues [20ndash24] were substituted forcorresponding values in the original set of experimentalvalues Also substituted in this alternative experimentalreference set was the Δ119891119867

119900298g value for 246-trinitrotoluene

listed in Cox and Pilcherrsquos ldquoThermochemistry of Organic andOrganometallic Compoundsrdquo [19] Finally it should be notedthat during the course of this investigation it appeared thatthe experimental Δ119891119867

119900298g value for dinitromethylbenzene

might be several kcalmol too low To address this possibilitywe used an approach similar to that used successfully byDorofeeva et al [21ndash23] to deal with such issues Specificallywe used density functional theory (EDF2 [30] functional andthe 6-311++G (2df2p) basis set) coupled with the use of tenisodesmic equations to calculate a Δ119891119867

119900298g reference value

of 142 plusmn 03 for dinitromethylbenzene This value was alsoincluded in the alternative reference set

It should be mentioned that many of the computedRM1 and PM7 Δ119891119867

119900298g values for compounds appearing

in Table 1 have been previously reported [13 14] Similarlymost of the T1 Δ119891119867

119900298g values appear in the Spartan Spectra

and Properties Database (SSPD) data base that accompaniesSpartan 14 In general our results are quite consistent withthese previously reported values In some instances howeverslightly lower Δ119891119867

119900298g values were calculated indicating the

existence of lower-energy equilibrium geometries than thoseused in previous investigations

3 Results and Discussion

The ultimate goal of any computational strategy designedto estimate values for Δ119891119867

119900298g is to reduce uncertainties

to within plusmn10 or 20 kcalmol (1 kcalmol = 4184 kJmol)which is taken to be experimental error One reason for thisgoal is that small errors in Δ119891119867

119900298g become magnified when

propagated to obtain other values which depend onΔ119891119867119900298g

The standard Gibbs energy change of a reaction for exampleis a function of the reaction enthalpy change as follows

Δ rxn119866∘= Δ rxn119867

∘minus 119879Δ rxn119878

∘ (1)

Reaction enthalpies can be calculated in accord with Hessrsquoslaw by taking the difference of the standard heat of formationvalues of the products and reactants of the reaction Theequilibrium constant (119870eq) of a reaction and Δ rxn119866

∘ arerelated by the expression

119870eq = 119890minusΔ rxn119866

∘119877119879 (2)

Since the equilibrium constant depends exponentially uponΔ rxn119866

∘ a small error in Δ rxn119867119900 can result in dramatically

different values for 119870eq when it is the calculated parameterof interest

For energetic compounds calculation of equilibriumconstants using heat of formation values is typically not

a concern sincemost reactions of interest are highly exergonicwith equilibrium constants that indicate product formationis highly favored It must be noted however that severalparameters (eg heat of detonation heat of explosion powerindex explosive velocity and explosive pressure) used tocharacterize high explosives require the condensed-phaseheat of formation value This is somewhat problematic fortheoretical compounds since calculations are performedon single molecules which are by definition gas-phasemolecules To calculate solid-phase heat of formation valuesheat of sublimation (or vaporization) values are calculatedby one of several computational methods available and thesevalues are then subtracted from the gas-phase values tocalculate the condensed-phase values This represents stillanother source of uncertainty in subsequent calculations It istherefore important to be able to identify and use proceduresthat provide the most accurate heat of formation valuespossible

Our initial objective was to compare the abilities of theT1 multilevel ab initio approach developed by Ohlinger etal [8] with the atom and group equivalent DFT approachdescribed by Byrd and Rice [6 7] To make this comparisonwe selected the forty-five nitrogen-containing compoundsstudied by Byrd and Rice [6 7] which we designated as ourtest set and acquiredT1Δ119891119867

119900298g values for these compounds

These results and the results of all comparisons made in thisinvestigation are presented inTables 1 2 and 3 and in Figure 1

When making comparisons such as those under con-sideration here it is necessary to use the most accurateexperimental Δ119891119867

119900298g reference values available This is

problematic for no fewer than twenty of the experimentalΔ119891119867119900298g values used in this investigation and it is of sub-

stantial concern for the eight organic azide compounds in thetest set Indeed Dorofeeva et al [21] note that ldquoenthalpiesof formation of organic azides are scanty and not alwaysreliablerdquo To address this problem Dorofeeva et al [21] useda combination of multilevel ab initio model chemistries anddensity functional theory coupled with the use of isodesmicisogyric and other balanced equations to calculate andrecommend Δ119891119867

119900298g values for twenty-nine organic azides

including the eight organic azide compounds in our test setThe implication of their work is that their calculated valuesmay be more accurate than the experimental values thatwere originally available to Byrd and Rice [6 7] This samegroup [20 22ndash24] conducted similar studies of the Δ119891119867

119900298g

values for fifty-seven other energetic nitrogen-containingcompounds and recommended the use of several Δ119891119867

119900298g

values that are slightly different than those that were availableto Byrd and Rice [6 7]

In light of these findings we compared computed datawith the original experimental data set used by Byrd and Rice[6 7] and with a newer alternative experimental referenceset (also referred to elsewhere herein as the most recentlyrecommended experimentalreference values available) inwhich a total of eighteen Δ119891119867

119900298g reference values recom-

mended by Dorofeeva et al [18 20 21] were substituted forthe original corresponding experimental values in the test set[6 7] We also note that at least three experimental values

4 Advances in Physical ChemistryTa

ble1Com

paris

onof

experim

entalgas-phase

heatof

form

ationvalues

with

values

calculated

usingseveraltheoreticalapproaches

Com

poun

dname

Experim

entallowast

Δ119891119867119900 298g

(kcalm

ol)

T1Δ119891119867119900 298g

(kcalm

ol)

DFT

Atom

icandGroup

contrib

ution

Δ119891119867119900 298g

(kcalm

ol)lowast

DFT

Isod

esmiclowastlowast

Δ119891119867119900 298g

(kcalm

ol)

Group

Additiv

ityΔ119891119867119900 298g

(kcalm

ol)

PM7

Δ119891119867119900 298g

(kcalm

ol)

RM1

Δ119891119867119900 298g

(kcalm

ol)

Nitro

methane

minus193(minus1709)

minus158

minus186

minus168

minus180

minus172

minus124

Tetra

nitro

methane

197(2110)

234

206

223

mdash284

181

Azidotrin

itrom

ethane

842(8532)

884

856

840

816

952

792

DMNO(N

-methyl-N

-nitrom

ethanamine)

minus12

05

minus10

minus11

minus16

minus58

minus35

1-Azido-11-d

initroethane

604(6286)

616

604

597

613

682

576

Hexanitroethane

428(291

8)293

337

289

mdash473

302

Nitro

glycerin

minus6671

minus658

minus667

minus698

minus815

minus826

minus720

TTT

943

984

941

938

mdash404

354

RDX(cyclotrimethylen

e-trinitra

mine)

458(4579)

490

440

468

mdash218

457

14-D

initrosopiperazine

464

527

467

466

368lowastlowastlowast

172

127

14-D

initropiperazine

139(1546

)177

126

149

112

20

167

N-N

itro-bis-2

22-tr

initroethylam

ine

2142

212

231

191

mdash346

334

Nitro

benzene

1638(1568)

152

141

148

161

182

182

2-Nitro

phenol

minus3162

minus296

minus311

minus314

minus260

minus310

minus289

3-Nitro

phenol

minus2612

minus260

minus260

minus270

minus260

minus258

minus268

4-Nitro

phenol

minus2741

minus260

minus280

minus282

minus260

minus281

minus285

m-N

itroanilin

e149

169

153

161

171

166

114

p-Nitro

aniline

132

165

128

141

171

129

83

Azidobenzene

930(9919)

948

998

968

974

990

945

1-Azido-4-nitrobenzene

931(9417)

928

918

931

937

947

903

N-N

itrobis-22-dinitro

propylam

ine(DNPN

)minus317

minus287

minus256

minus338

mdashminus150

minus91

PNT(1-

methyl-4

-nitrobenzene)

738

72

63

73

81

75

84

24-DNT(1-

methyl-2

4-dinitrobenzene)

793

86

44

85

44

70

85

Azidom

ethylbenzene

995(9680)

924

991

962

968

947

914

3-Az

ido-3-ethylpentane

406(315

5)281

414

315

329

367

338

TNT(tr

initrotoluene)

575

(123)

136

71

115

08

108

126

22-Dinitroadamantane

minus3688(minus4278)

minus394

minus347

minus413

minus354lowastlowastlowast

minus286

minus439

1-Azidoadam

antane

516(4374)

400

496

446

480

470

289

2-Az

ido-2-phenylp

ropane

874(795

9)750

819

803

798

842

776

HNS

5698

639

595

608

358

582

616

Methylnitrite

minus1564

minus133

minus146

minus139

minus161

minus192

minus219

Methylnitrate

minus292

minus270

minus272

minus273

minus296

minus314

minus284

Dinitrom

ethane

minus141(minus92

0)minus76

minus132

minus78

mdashminus82

minus45

Ethylnitrite

minus259

minus219

minus224

minus249

minus242

minus326

minus323

Ethylnitrate

minus370

minus351

minus349

minus361

minus377

minus395

minus356

Propylnitrite

minus284

minus270

minus273

minus292

minus291

minus377

minus372

2-Methyl-2

-nitropropane

minus4232

(minus4190)

minus402

minus383

minus426

minus423

minus357

minus364

n-Bu

tylnitrite

minus348

minus320

minus320

minus355

minus340

minus426

minus422

t-Butylnitrite

minus410

minus387

minus354

minus408

minus425

minus482

minus486

34-Fu

razand

imethanoldinitrate

26

98

91

minus04

mdashminus40

194

1-Nitropiperidine

minus106(minus887)

minus74

minus99

minus89

minus81

minus155

minus92

Advances in Physical Chemistry 5

Table1Con

tinued

Com

poun

dname

Experim

entallowast

Δ119891119867119900 298g

(kcalm

ol)

T1Δ119891119867119900 298g

(kcalm

ol)

DFT

Atom

icandGroup

contrib

ution

Δ119891119867119900 298g

(kcalm

ol)lowast

DFT

Isod

esmiclowastlowast

Δ119891119867119900 298g

(kcalm

ol)

Group

Additiv

ityΔ119891119867119900 298g

(kcalm

ol)

PM7

Δ119891119867119900 298g

(kcalm

ol)

RM1

Δ119891119867119900 298g

(kcalm

ol)

Nitro

sobenzene

481

471

488

455

mdash412

331

Nitro

methylbenzene

734

87

94

90

76113

130

Dinitrom

ethylbenzene

83(14

2)

139

136

145

121

196

184

13-D

imethyl-2

-nitrobenzene

21

14

43

32

02

minus02

14

HNS=111015840 -(12-ethenediyl)b

is[246-trinitrob

enzene]TT

T=hexahydro-13

5-tr

initroso-13

5-tr

iazine

lowastVa

luesfro

mBy

rdandRice

[67]Va

luesin

parenthesesa

rethosethath

aveb

eensubstituted

forcorrespon

ding

valuesin

theo

riginalreferences

etandareu

sedin

thea

lternativee

xperim

entalreference

setSeetext

ford

etailsandexplanation

lowastlowastMosto

fvaluesintheD

FTiso

desm

iccolumnwerec

alculated

usingiso

desm

icreactio

nsH

owever

somev

aluesw

erec

alculated

usingiso

gyric

orotherb

alancedequatio

ns

lowastlowastlowastVa

lues

calculated

usingCH

ETAH80

6 Advances in Physical Chemistry

Table 2 Statistical comparison of experimental gas-phase heat of formation valueswith values calculated using several theoretical approaches

T1Δ119891119867298g(kcalmol)

DFT Atomicand GroupcontributionΔ119891119867298g

(kcalmol)lowast

DFTisodesmicΔ119891119867298g(kcalmol)

Group AddΔ119891119867298g(kcalmol)

PM7Δ119891119867298g(kcalmol)

RM1Δ119891119867298g(kcalmol)

rms deviation 50 30 37 54 (34)lowast 118 (60) 129 (59)MAE 37 21 25 33 (25)lowast 75 (49) 79 (48)Max Dev (kcalmol) 135 91 139 212 (96)lowast 539 (132) 589 (126)Number of values plusmn20 kcalmol 17 28 27 19 10 12Number of values plusmn30 kcalmol 25 35 33 24 14 17Number of values plusmn40 kcalmol 32 37 37 28 18 18

1198772 098728 09958 099277 09863

(099435)092817(098063)

091605(098141)

lowastValues in parentheses represent data in which values for compounds having deviations from experiment greater than 140 kcalmol were omitted See text forexplanation

Table 3 Statistical comparison of alternative experimental gas-phase heat of formation values with values calculated using several theoreticalapproaches

T1Δ119891119867298g(kcalmol)

DFT Atomicand GroupcontributionΔ119891119867298g(kcalmol)lowast

DFTisodesmicΔ119891119867298g(kcalmol)

Group AddΔ119891119867298g(kcalmol)

PM7lowastΔ119891119867298g(kcalmol)

RM1lowastΔ119891119867298g(kcalmol)

rms deviation 29 33 15 55 (35)lowast 120 (54) 122 (45)MAE 23 24 11 31 (23)lowast 73 (42) 68 (36)Max Dev (kcalmol) 69 99 38 212 (115)lowast 539 (132) 589 (120)Number of values plusmn20 kcalmol 23 23 37 23 13 14Number of values plusmn30 kcalmol 31 33 42 25 18 19Number of values plusmn40 kcalmol 38 37 45 28 21 21

1198772 099648 099477 099884 098549

(099353)092435(098574)

092367(09889)

lowastValues in parentheses represent data in which values for compounds having deviations from experiment greater than 140 kcalmol were omitted See text forexplanation

have been reported for 246-trinitrotoluene Thus in placeof the Δ119891119867

119900298g value of 575 kcalmol used by Byrd and Rice

[6 7] we have substituted the value of 123 kcalmol (reportedin ldquoThermochemistry of Organic and Organometallic Com-poundsrdquo by Cox and Pilcher [19]) in the new alternativeexperimental reference data set During the course of thisinvestigation it also appeared that the experimental value fordinitromethylbenzene may be several kcalmol too lowThuswe used procedures similar to those described by Dorofeevaet al [21ndash23] to calculate a Δ119891119867

119900298g reference value of 142 plusmn

03 kcalmol for this compoundThis value was also includedin the alternative reference set These results are found inSupplemental Tables 1S and 2S (see Supplementary Materialavailable online at httpdxdoiorg10115520165082084)

A comparison of Tables 2 and 3 supports the conclusionthat the alternative recommended values as a group areindeed more accurate than the original experimental valuesthat were available to and used by Byrd and Rice [6 7] intheir investigations Except for the DFTAtomic and Groupcontribution approach the mean absolute error (MAE) was

greater for the original experimental reference set than forthe new alternative experimental reference set The fact thatthe opposite was found for the DFTAtomic and Groupcontribution approach is not surprising as many of the com-pounds in the original experimental reference set were usedto parameterize and develop this computational approachNevertheless this approach still performed quite well whencompared to the alternative experimental reference set Ourresults also suggest that the accuracy of the DFTAtomic andGroup contribution approach might benefit from reparame-terization using the alternative experimental reference set

Because the alternative experimental reference setappeared to be more accurate than the original reference setit was used for the comparisons described below

The atom and group equivalent DFT approach describedby Byrd and Rice [6 7] and the T1 procedure both yieldedcalculated results in which 51 (2345) of the predictedΔ119891119867119900298g values were within plusmn20 kcalmol of values in the

reference set The rms deviation from experiment for thepredicted T1 gas-phase heat of formation values was found

Advances in Physical Chemistry 7

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

0minus50 50 100minus100

Experimental values (kcalmol)

(a) T1

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(b) DFTAtomic and Group contribution

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(c) DFTisodesmic

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(d) Group Add

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus100 0 50 100minus50

Experimental values (kcalmol)

(e) PM7

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(f) RM1

Figure 1 Calculated gas-phase heat of formation values versus experimental values Gas-phase heat of formation values were calculated using(1) the multilevel ab initio approach (T1) described by Ohlinger et al [8] as implemented in the Spartanrsquo10 and 14 suite of programs (a) (2) theDFTAtomic and Group contribution approach developed and described by Byrd and Rice [6 7] (b)The experimental values and calculatedvalues used to construct (b) are those published by Byrd and Rice [6 7] (b) is identical to Figure 1a in their manuscript except for the fact thatthe alternative set of experimental Δ119891119867

119900298g reference values are also included (3) Density functional theory using isodesmic isogyric and

other balanced equations as described herein (c) (4)The Benson Group Additivity approach as implemented in the and NIST and CHETAH80 software programs (d) (5) semiempirical theory (PM7 andRM1) as implemented inMOPAC2012 and the Spartan 14 suite of programs ((e)and (f) resp) Open squares represent calculatedΔ119891119867

119900298g values versus the experimentalΔ119891119867

119900298g values Closed circles represent calculated

Δ119891119867119900298g values versus the alternative experimental Δ119891119867

119900298g reference values as described in the text Least square regression analysis and

calculation of 1198772 values were accomplished using KaleidaGraph graphing software (Synergy Software Reading PA) 1198772 values are presentedin Tables 2 and 3

8 Advances in Physical Chemistry

Table 4 Balanced equations used to calculate heat of formation values of compounds in the test set

Isodesmic isogyric or other balanced equations1 Dinitromethane + methanerarr2 nitromethane2 2 dinitromethanerarrmethane + tetranitromethane3 Methyl azide + trinitromethanerarrmethane + azidotrinitromethane4 N-Ethyl-N-nitroethanamine + dimethylaminerarr N-ethyl-N-ethanamine + N-methyl-N-nitromethanamine (DMNO)5 11-Dinitropropane + methyl aziderarr ethane + 1-azido-11-dinitroethane6 2 111-Trinitropropanerarr butane + hexanitroethane7 3 propylnitraterarr2 propane + nitroglycerin8 RDX + 3 nitrosyl hydriderarr3 HNO2 + TTT (hexahydro-135-trinitroso-135-triazine)9 3 1-nitropiperidinerarr2 cyclohexane + RDX10 1-Nitrosopiperidine + TTTrarr2 14-dinitrosopiperazine11 Piperazine + 2 dimethylnitraminerarr 2 dimethylamine + 14-dinitropiperazine12 Bis-222-trinitroethylamine + HNO2 rarr H2 + N-nitro-bis-222-trinitroethylamine13 Benzene + 4-nitroanilinerarr aniline + nitrobenzene14 Phenol + nitrobenzenerarr benzene + 2-nitrophenol15 Phenol + nitrobenzenerarr benzene + 3-nitrophenol16 Phenol + nitrobenzenerarr benzene + 4-nitrophenol17 Aniline + nitrobenzenerarr benzene + m-nitroaniline18 Aniline + nitrobenzenerarr benzene + p-nitroaniline19 Methyl azide + benzenerarrmethane + azidobenzene20 Methyl azide + nitrobenzenerarrmethane + 1-azido-4-nitrobenzene

21 N-Propylpropanamine + 4 1-nitropropane + dimethylnitraminerarr dimethylamine + N-nitro-bis-22-dinitropropylamine (DNPN)+ 4 propane

22 Toluene + nitrobenzenerarr benzene + PNT (1-methyl-4-nitrobenzene)23 Toluene + 2 nitrobenzenerarr2 benzene + 24-DNT (1-methyl-24-dinitrobenzene)24 Methyl azide + toluenerarrmethane + azidomethylbenzene25 Methyl azide + 3-ethylpentanerarrmethane + 3-azido-3-ethylpentane26 Toluene + 135-trinitrobenzenerarr benzene + TNT (246-trinitrotoluene)27 2 2-nitropropane + adamantanerarr2 propane + 22-dinitroadamantane28 Methyl azide + adamantanerarrmethane + 1-azidoadamantane29 Methyl azide + 2-phenylpropanerarrmethane + 2-azido-2-phenylpropane30 trans-Stilbene + 2 135-trinitrobenzenerarr2 benzene + HNS (111015840-(12-ethenediyl)bis[246- trinitrobenzene])31 Isopropyl nitrite + methanerarr propane + methyl nitrite32 Propyl nitrate + methanerarr propane + methyl nitrate33 2 1-Nitropropane + methanerarr2 propane + dinitromethane34 Propyl nitrite + ethanerarr propane + ethyl nitrite35 Propyl nitrate + ethanerarr propane + ethyl nitrate36 Isopropyl nitriterarr propyl nitrite37 2-Nitropropane + 2-methylpropanerarr 2-methyl-2-nitropropane + propane38 Isopropyl nitrite + butanerarr n-butyl nitrite + propane39 Isopropyl nitrite + isobutanerarr t-butyl nitrite + propane40 2 1-pyrroline + tetrahydrofuran + 2methyl nitraterarr H2 + 34-furazandimethanol dinitrate + 2 cyclopentane41 Piperidine + dimethylnitraminerarr 1-nitropiperidine + dimethylamine42 Phenyl radical + nitric oxiderarr nitrosobenzene43 Toluene + 1-nitropropanerarr propane + nitromethylbenzene44 Toluene + 11-dinitropropanerarr propane + dinitromethylbenzene45 2 Toluene + nitrobenzenerarr2 benzene + 13-dimethyl-2-nitrobenzene

Advances in Physical Chemistry 9

to be 29 kcalmol with a mean absolute error (MAE) of23 kcalmol and a maximum deviation of 69 kcalmol Thiscompares with an rms deviation of 33 kcalmol a MAE of24 kcalmol and a maximum deviation of 99 kcalmol usingdata calculated by Byrd andRice [6 7] It should be noted thatthe T1 procedure has been previously shown to reproduceexperimental heat of formation values of a large (1805) set oforganicmolecules with an rms deviation of 275 kcalmol anda MAE of 203 kcalmol [8] Clearly the rms andMAE valuesfor the T1 approach reported here agree well with those valuesreported for the larger data set

These results led us to compare older approaches usedto predictcalculate Δ119891119867

119900298g values Specifically we used

Bensonrsquos group additivity (or group contribution) approach[10 11] We also used density functional theory coupled withthe use of selected isodesmic isogyric and other balancedequations One disadvantage of Bensonrsquos group additivityapproach is that group values for some of the substructuresof several compounds in the test set are not availableWe were partially able to overcome this problem by usingexisting data which allowed us to calculate some of thesegroup values In total we were able to use Bensonrsquos groupadditivity approach to calculate Δ119891119867

119900298g values for 36 of 45

compounds in the test set This approach yielded calculatedresults in which 64 (2336) of the calculated Δ119891119867

119900298g

values were within plusmn20 kcalmol of experimental valuesThe rms deviation from experiment for the predicted groupadditivity gas-phase heat of formation valueswas 55 kcalmolwith an MAE of 31 kcalmol with a maximum deviationof 212 kcalmol for HNS A relatively large deviation fromexperiment of 148 kcalmol was also found for nitroglycerinA significant drawback to the use of group additivity theoryis that calculated Δ119891119867

119900298g values are sometimes affected

by structural features that are not adequately addressed bytheory Although Δ119891119867

119900298g values for some strained com-

pounds can be accurately predicted by adding correctionfactors for structural characteristics such as ring strain thepresence of gauche carbons and C1ndashC5 repulsions contri-bution of certain other structural features do not appear tobe adequately addressed by group additivity theory HNSand nitroglycerin seem to fall into this category Whenthese compounds were eliminated from the test set the rmsdeviation from experiment for the predicted group additivityΔ119891119867119900298g values was found to be 35 kcalmol with an MAE

of 22 kcalmol and a maximum deviation of 115 kcalmol forthe remaining 34 compoundsThe relevant point is that groupadditivity theory is often quite accurate however onemust becareful regarding its application

Density functional theory coupledwith the use of selectedbalanced reactions was also used to calculate Δ119891119867

119900298g values

for comparison to the test setThe reactions used in this inves-tigation are presented in Table 4 We determined that therms deviation from experiment for the calculated Δ119891119867

119900298g

values was 15 kcalmol with an MAE of 11 kcalmol and amaximum deviation of 38 kcalmol This approach yieldedcalculated results in which 82 (3745) of theΔ119891119867

119900298g values

werewithinplusmn20 kcalmol of experimental values Despite thefact that for time considerations we selected a medium size

basis set density functional theory coupled with the use ofisodesmic and other balanced equations was still the mostaccurate approach of the sixmethodswe compared Althoughaccurate it is necessary to mention some problems with thisapproach First of all different balanced equations can leadto different Δ119891119867

119900298g values Often such differences are small

But sometimes such differences can be substantial Cramer[12] has noted that ldquothe construction of an isodesmic equationis something of an art depending on chemical intuition andavailable experimental datardquo

It should also be mentioned that when computationtime is not a consideration the use of larger basis setsmight be expected to result in even greater accuracy IndeedDorofeeva and colleagues [21ndash23] have have shown thatthe use of high level computational theory coupled withmultiple isodesmic isogyric and other balanced equationscan result in calculation of Δ119891119867

119900298g values that are suffi-

ciently accurate that they feel confident in recommendingconsensus values in many cases where there is discrep-ancy between experimental values andor between computedvalues

Finally two semiempirical models (RM1 and PM7) wereused to calculate Δ119891119867

119900298g Semiempirical models are attrac-

tive because they are very rapid and their accuracy continuesto improve [13 14] However RM1 and PM7 were found tobe less accurate than the other approaches used to calculateΔ119891119867119900298g values for compounds in the test set used for this

investigation Even when Δ119891119867119900298g values having very large

(greater than 14 kcalmol) deviations from reference valueswere omitted rms and MAE values for calculated RM1 andPM7 data sets were substantially greater than those of thefour other computational approaches investigated (Tables 2and 3)

4 Conclusion

Because substantial interest exists in developing relativelyrapid and accurate procedures for predicting gas-phase heatof formation values for energetic compounds our overall goalwas to determine which of several computational approachesis most suitable for this endeavor None of the computationalapproaches were uniformly accurate within plusmn20 kcalmolof experimental values (ie the presumably more accuratealternative experimental values)

However four of the computational approaches investi-gated were able tomeet this level of accuracy greater than 51of the time Moreover these four computational approacheswere accurate to within plusmn40 kcal greater than 77 of thetime For relatively simple compounds in which correctionfactors can be used to account for ring strain and so forthand other factors do not make substantial contribution toΔ119891119867119900298g we conclude that the group additivity approach is

about as accurate as those approaches based on higher levelsof theory For compounds that are structurallymore complexthe approach using DFT coupled with the use of isodesmicisogyric and other balanced equations is more accurate butmore time consuming than the DFTAtomic and Groupcontribution method described by Byrd and Rice [6 7] and

10 Advances in Physical Chemistry

the T1 method [8] for this set of compounds However sincecalculated values are often similar and mutually supportiveit seems that a reasonable approach would be to use any (orall) of these four procedures when this level of accuracy isacceptable and the goal is to compare predicted properties ofnew or theoretical compounds with those of structurally sim-ilar compounds whose experimental values andor computedvalues are well established

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] H M Xiao X J Xu and L Qiu Theoretical Design of HighEnergy Density Materials Science Press Beijing China 2008

[2] R E Kirk and D F Othmer Encyclopedia of Chemical Technol-ogy vol 5 Wiley New York NY USA 2004

[3] J Giles ldquoGreen explosives collateral damagerdquo Nature vol 427no 6975 pp 580ndash581 2004

[4] J P Agrawal and J E Field ldquoRecent trends in high-energymaterialsrdquo Progress in Energy and Combustion Science vol 24no 1 pp 1ndash30 1998

[5] J Akhavan The Chemistry of Explosives Royal Society ofChemistry Cambridge UK 2004

[6] E F C Byrd and B M Rice ldquoImproved prediction of heatsof formation of energetic materials using quantum mechanicalcalculationsrdquo Journal of Physical Chemistry A vol 110 no 3 pp1005ndash1013 2006

[7] E F C Byrd and B M Rice ldquoCorrection improved predictionof heats of formation of energetic materials using quantummechanical calculationsrdquo The Journal of Physical Chemistry Avol 113 no 9 p 5813 2009

[8] W S Ohlinger P E Klunzinger B J Deppmeier and W JHehre ldquoEfficient calculation of heats of formationrdquo Journal ofPhysical Chemistry A vol 113 no 10 pp 2165ndash2175 2009

[9] L A Curtiss P C Redfern K Raghavachari V Rassolov andJ A Pople ldquoGaussian-3 theory using reduced Moslashller-PlessetorderrdquoThe Journal of Chemical Physics vol 110 no 10 pp 4703ndash4709 1999

[10] S W Benson and J H Buss ldquoAdditivity rules for the estima-tion of molecular properties Thermodynamic propertiesrdquo TheJournal of Chemical Physics vol 29 no 3 pp 546ndash572 1958

[11] SW Benson F R Cruickshank DM Golden et al ldquoAdditivityrules for the estimation of thermochemical propertiesrdquo Chemi-cal Reviews vol 69 no 3 pp 279ndash324 1969

[12] C J Cramer Essentials of Computational Chemistry Theoriesand Models John Wiley amp Sons New York NY USA 2ndedition 2004

[13] G B Rocha R O Freire A M Simas and J J P Stewart ldquoRM1a reparameterization of AM1 for H C N O P S F Cl Br and IrdquoJournal of Computational Chemistry vol 27 no 10 pp 1101ndash11112006

[14] J J P Stewart ldquoOptimization of parameters for semiempiricalmethods VI more modifications to the NDDO approximationsand re-optimization of parametersrdquo Journal of Molecular Mod-eling vol 19 no 1 pp 1ndash32 2013

[15] Y Zhao andDG Truhlar ldquoTheM06 suite of density functionalsfor main group thermochemistry thermochemical kineticsnoncovalent interactions excited states and transition ele-ments two new functionals and systematic testing of fourM06-class functionals and 12 other functionalsrdquo TheoreticalChemistry Accounts vol 120 no 1ndash3 pp 215ndash241 2008

[16] Y Zhao and D G Truhlar ldquoDensity functionals with broadapplicability in chemistryrdquo Accounts of Chemical Research vol41 no 2 pp 157ndash167 2008

[17] H Y Afeefy J F Liebman and S E Stein ldquoNeutral thermo-chemical datardquo in NIST Chemistry WebBook P J Linstrom andW G Mallard Eds NIST Standard Reference Database no 69National Institute of Standards and Technology GaithersburgMd USA 2005

[18] J B Pedley R D Naylor and S P KirbyThermochemical Dataof Organic Compounds Chapman amp Hall New York NY USA1986

[19] J O Cox and G Pilcher Thermochemistry of Organic andOrganometallic Compounds Academic Press New York NYUSA 1970

[20] OVDorofeeva andMA Suntsova ldquoEnthalpies of formation ofnitromethane and nitrobenzene theory vs experimentrdquo Journalof Chemical Thermodynamics vol 58 pp 221ndash225 2013

[21] O V Dorofeeva O N Ryzhova and M A Suntsova ldquoAccurateprediction of enthalpies of formation of organic azides bycombining G4 theory calculations with an isodesmic reactionschemerdquo Journal of Physical Chemistry A vol 117 no 31 pp6835ndash6845 2013

[22] M A Suntsova and O V Dorofeeva ldquoUse of G4 theoryfor the assessment of inaccuracies in experimental enthalpiesof formation of aliphatic nitro compounds and nitraminesrdquoJournal of Chemical amp Engineering Data vol 59 no 9 pp 2813ndash2826 2014

[23] M A Suntsova and O V Dorofeeva ldquoComment on lsquouse ofG4 theory for the assessment of inaccuracies in experimentalenthalpies of formation of aliphatic nitro compounds andnitraminesrsquordquo Journal of Chemical amp Engineering Data vol 60no 5 pp 1532ndash1533 2015

[24] S P Verevkin V N EmelrsquoYanenko V Diky and O V Doro-feeva ldquoEnthalpies of formation of nitromethane and nitroben-zene new experiments vs quantum chemical calculationsrdquoTheJournal of ChemicalThermodynamics vol 73 pp 163ndash170 2014

[25] CHETAHTheComputer Program for ChemicalThermodynam-ics and Energy Release Evaluation University of SouthAlabamaMobile Ala USA ASTM International West ConshohockenPa USA 2009

[26] NCohen and SWBenson ldquoEstimation of heats of formation oforganic compounds by additivity methodsrdquo Chemical Reviewsvol 93 no 7 pp 2419ndash2438 1993

[27] J A Bumpus and P H Willoughby ldquoOn the heat of formationof nitromethanerdquo Journal of Physical Organic Chemistry vol 21no 9 pp 747ndash757 2008

[28] Y K Knobelrsquo E A Miroshnichenko and Y A LebedevldquoHeats of combustion of nitromethane and dinitromethaneenthalpies of formation of nitromethyl radicals and energies ofdissociation of bonds in nitro derivatives of methanerdquo Bulletinof the Academy of Sciences of the USSR Division of ChemicalScience vol 20 no 3 pp 425ndash428 1971

[29] E A Miroshnichenko T S Konrsquokova Y O Inozemtsev VP VorobrsquoEva Y N Matymhin and S A Shevelev ldquoBondenergies and formation enthalpies of mono- and polyradicals in

Advances in Physical Chemistry 11

nitroalkanes 1 Nitromethanesrdquo Russian Chemical Bulletin vol58 no 4 pp 772ndash776 2009

[30] C Y Lin M W George and P M W Gill ldquoEDF2 a densityfunctional for predicting molecular vibrational frequenciesrdquoAustralian Journal of Chemistry vol 57 no 4 pp 365ndash370 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Page 4: Research Article Calculating Heat of Formation Values of Energetic Compounds…downloads.hindawi.com/journals/apc/2016/5082084.pdf ·  · 2016-03-14Research Article Calculating Heat

4 Advances in Physical ChemistryTa

ble1Com

paris

onof

experim

entalgas-phase

heatof

form

ationvalues

with

values

calculated

usingseveraltheoreticalapproaches

Com

poun

dname

Experim

entallowast

Δ119891119867119900 298g

(kcalm

ol)

T1Δ119891119867119900 298g

(kcalm

ol)

DFT

Atom

icandGroup

contrib

ution

Δ119891119867119900 298g

(kcalm

ol)lowast

DFT

Isod

esmiclowastlowast

Δ119891119867119900 298g

(kcalm

ol)

Group

Additiv

ityΔ119891119867119900 298g

(kcalm

ol)

PM7

Δ119891119867119900 298g

(kcalm

ol)

RM1

Δ119891119867119900 298g

(kcalm

ol)

Nitro

methane

minus193(minus1709)

minus158

minus186

minus168

minus180

minus172

minus124

Tetra

nitro

methane

197(2110)

234

206

223

mdash284

181

Azidotrin

itrom

ethane

842(8532)

884

856

840

816

952

792

DMNO(N

-methyl-N

-nitrom

ethanamine)

minus12

05

minus10

minus11

minus16

minus58

minus35

1-Azido-11-d

initroethane

604(6286)

616

604

597

613

682

576

Hexanitroethane

428(291

8)293

337

289

mdash473

302

Nitro

glycerin

minus6671

minus658

minus667

minus698

minus815

minus826

minus720

TTT

943

984

941

938

mdash404

354

RDX(cyclotrimethylen

e-trinitra

mine)

458(4579)

490

440

468

mdash218

457

14-D

initrosopiperazine

464

527

467

466

368lowastlowastlowast

172

127

14-D

initropiperazine

139(1546

)177

126

149

112

20

167

N-N

itro-bis-2

22-tr

initroethylam

ine

2142

212

231

191

mdash346

334

Nitro

benzene

1638(1568)

152

141

148

161

182

182

2-Nitro

phenol

minus3162

minus296

minus311

minus314

minus260

minus310

minus289

3-Nitro

phenol

minus2612

minus260

minus260

minus270

minus260

minus258

minus268

4-Nitro

phenol

minus2741

minus260

minus280

minus282

minus260

minus281

minus285

m-N

itroanilin

e149

169

153

161

171

166

114

p-Nitro

aniline

132

165

128

141

171

129

83

Azidobenzene

930(9919)

948

998

968

974

990

945

1-Azido-4-nitrobenzene

931(9417)

928

918

931

937

947

903

N-N

itrobis-22-dinitro

propylam

ine(DNPN

)minus317

minus287

minus256

minus338

mdashminus150

minus91

PNT(1-

methyl-4

-nitrobenzene)

738

72

63

73

81

75

84

24-DNT(1-

methyl-2

4-dinitrobenzene)

793

86

44

85

44

70

85

Azidom

ethylbenzene

995(9680)

924

991

962

968

947

914

3-Az

ido-3-ethylpentane

406(315

5)281

414

315

329

367

338

TNT(tr

initrotoluene)

575

(123)

136

71

115

08

108

126

22-Dinitroadamantane

minus3688(minus4278)

minus394

minus347

minus413

minus354lowastlowastlowast

minus286

minus439

1-Azidoadam

antane

516(4374)

400

496

446

480

470

289

2-Az

ido-2-phenylp

ropane

874(795

9)750

819

803

798

842

776

HNS

5698

639

595

608

358

582

616

Methylnitrite

minus1564

minus133

minus146

minus139

minus161

minus192

minus219

Methylnitrate

minus292

minus270

minus272

minus273

minus296

minus314

minus284

Dinitrom

ethane

minus141(minus92

0)minus76

minus132

minus78

mdashminus82

minus45

Ethylnitrite

minus259

minus219

minus224

minus249

minus242

minus326

minus323

Ethylnitrate

minus370

minus351

minus349

minus361

minus377

minus395

minus356

Propylnitrite

minus284

minus270

minus273

minus292

minus291

minus377

minus372

2-Methyl-2

-nitropropane

minus4232

(minus4190)

minus402

minus383

minus426

minus423

minus357

minus364

n-Bu

tylnitrite

minus348

minus320

minus320

minus355

minus340

minus426

minus422

t-Butylnitrite

minus410

minus387

minus354

minus408

minus425

minus482

minus486

34-Fu

razand

imethanoldinitrate

26

98

91

minus04

mdashminus40

194

1-Nitropiperidine

minus106(minus887)

minus74

minus99

minus89

minus81

minus155

minus92

Advances in Physical Chemistry 5

Table1Con

tinued

Com

poun

dname

Experim

entallowast

Δ119891119867119900 298g

(kcalm

ol)

T1Δ119891119867119900 298g

(kcalm

ol)

DFT

Atom

icandGroup

contrib

ution

Δ119891119867119900 298g

(kcalm

ol)lowast

DFT

Isod

esmiclowastlowast

Δ119891119867119900 298g

(kcalm

ol)

Group

Additiv

ityΔ119891119867119900 298g

(kcalm

ol)

PM7

Δ119891119867119900 298g

(kcalm

ol)

RM1

Δ119891119867119900 298g

(kcalm

ol)

Nitro

sobenzene

481

471

488

455

mdash412

331

Nitro

methylbenzene

734

87

94

90

76113

130

Dinitrom

ethylbenzene

83(14

2)

139

136

145

121

196

184

13-D

imethyl-2

-nitrobenzene

21

14

43

32

02

minus02

14

HNS=111015840 -(12-ethenediyl)b

is[246-trinitrob

enzene]TT

T=hexahydro-13

5-tr

initroso-13

5-tr

iazine

lowastVa

luesfro

mBy

rdandRice

[67]Va

luesin

parenthesesa

rethosethath

aveb

eensubstituted

forcorrespon

ding

valuesin

theo

riginalreferences

etandareu

sedin

thea

lternativee

xperim

entalreference

setSeetext

ford

etailsandexplanation

lowastlowastMosto

fvaluesintheD

FTiso

desm

iccolumnwerec

alculated

usingiso

desm

icreactio

nsH

owever

somev

aluesw

erec

alculated

usingiso

gyric

orotherb

alancedequatio

ns

lowastlowastlowastVa

lues

calculated

usingCH

ETAH80

6 Advances in Physical Chemistry

Table 2 Statistical comparison of experimental gas-phase heat of formation valueswith values calculated using several theoretical approaches

T1Δ119891119867298g(kcalmol)

DFT Atomicand GroupcontributionΔ119891119867298g

(kcalmol)lowast

DFTisodesmicΔ119891119867298g(kcalmol)

Group AddΔ119891119867298g(kcalmol)

PM7Δ119891119867298g(kcalmol)

RM1Δ119891119867298g(kcalmol)

rms deviation 50 30 37 54 (34)lowast 118 (60) 129 (59)MAE 37 21 25 33 (25)lowast 75 (49) 79 (48)Max Dev (kcalmol) 135 91 139 212 (96)lowast 539 (132) 589 (126)Number of values plusmn20 kcalmol 17 28 27 19 10 12Number of values plusmn30 kcalmol 25 35 33 24 14 17Number of values plusmn40 kcalmol 32 37 37 28 18 18

1198772 098728 09958 099277 09863

(099435)092817(098063)

091605(098141)

lowastValues in parentheses represent data in which values for compounds having deviations from experiment greater than 140 kcalmol were omitted See text forexplanation

Table 3 Statistical comparison of alternative experimental gas-phase heat of formation values with values calculated using several theoreticalapproaches

T1Δ119891119867298g(kcalmol)

DFT Atomicand GroupcontributionΔ119891119867298g(kcalmol)lowast

DFTisodesmicΔ119891119867298g(kcalmol)

Group AddΔ119891119867298g(kcalmol)

PM7lowastΔ119891119867298g(kcalmol)

RM1lowastΔ119891119867298g(kcalmol)

rms deviation 29 33 15 55 (35)lowast 120 (54) 122 (45)MAE 23 24 11 31 (23)lowast 73 (42) 68 (36)Max Dev (kcalmol) 69 99 38 212 (115)lowast 539 (132) 589 (120)Number of values plusmn20 kcalmol 23 23 37 23 13 14Number of values plusmn30 kcalmol 31 33 42 25 18 19Number of values plusmn40 kcalmol 38 37 45 28 21 21

1198772 099648 099477 099884 098549

(099353)092435(098574)

092367(09889)

lowastValues in parentheses represent data in which values for compounds having deviations from experiment greater than 140 kcalmol were omitted See text forexplanation

have been reported for 246-trinitrotoluene Thus in placeof the Δ119891119867

119900298g value of 575 kcalmol used by Byrd and Rice

[6 7] we have substituted the value of 123 kcalmol (reportedin ldquoThermochemistry of Organic and Organometallic Com-poundsrdquo by Cox and Pilcher [19]) in the new alternativeexperimental reference data set During the course of thisinvestigation it also appeared that the experimental value fordinitromethylbenzene may be several kcalmol too lowThuswe used procedures similar to those described by Dorofeevaet al [21ndash23] to calculate a Δ119891119867

119900298g reference value of 142 plusmn

03 kcalmol for this compoundThis value was also includedin the alternative reference set These results are found inSupplemental Tables 1S and 2S (see Supplementary Materialavailable online at httpdxdoiorg10115520165082084)

A comparison of Tables 2 and 3 supports the conclusionthat the alternative recommended values as a group areindeed more accurate than the original experimental valuesthat were available to and used by Byrd and Rice [6 7] intheir investigations Except for the DFTAtomic and Groupcontribution approach the mean absolute error (MAE) was

greater for the original experimental reference set than forthe new alternative experimental reference set The fact thatthe opposite was found for the DFTAtomic and Groupcontribution approach is not surprising as many of the com-pounds in the original experimental reference set were usedto parameterize and develop this computational approachNevertheless this approach still performed quite well whencompared to the alternative experimental reference set Ourresults also suggest that the accuracy of the DFTAtomic andGroup contribution approach might benefit from reparame-terization using the alternative experimental reference set

Because the alternative experimental reference setappeared to be more accurate than the original reference setit was used for the comparisons described below

The atom and group equivalent DFT approach describedby Byrd and Rice [6 7] and the T1 procedure both yieldedcalculated results in which 51 (2345) of the predictedΔ119891119867119900298g values were within plusmn20 kcalmol of values in the

reference set The rms deviation from experiment for thepredicted T1 gas-phase heat of formation values was found

Advances in Physical Chemistry 7

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

0minus50 50 100minus100

Experimental values (kcalmol)

(a) T1

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(b) DFTAtomic and Group contribution

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(c) DFTisodesmic

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(d) Group Add

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus100 0 50 100minus50

Experimental values (kcalmol)

(e) PM7

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(f) RM1

Figure 1 Calculated gas-phase heat of formation values versus experimental values Gas-phase heat of formation values were calculated using(1) the multilevel ab initio approach (T1) described by Ohlinger et al [8] as implemented in the Spartanrsquo10 and 14 suite of programs (a) (2) theDFTAtomic and Group contribution approach developed and described by Byrd and Rice [6 7] (b)The experimental values and calculatedvalues used to construct (b) are those published by Byrd and Rice [6 7] (b) is identical to Figure 1a in their manuscript except for the fact thatthe alternative set of experimental Δ119891119867

119900298g reference values are also included (3) Density functional theory using isodesmic isogyric and

other balanced equations as described herein (c) (4)The Benson Group Additivity approach as implemented in the and NIST and CHETAH80 software programs (d) (5) semiempirical theory (PM7 andRM1) as implemented inMOPAC2012 and the Spartan 14 suite of programs ((e)and (f) resp) Open squares represent calculatedΔ119891119867

119900298g values versus the experimentalΔ119891119867

119900298g values Closed circles represent calculated

Δ119891119867119900298g values versus the alternative experimental Δ119891119867

119900298g reference values as described in the text Least square regression analysis and

calculation of 1198772 values were accomplished using KaleidaGraph graphing software (Synergy Software Reading PA) 1198772 values are presentedin Tables 2 and 3

8 Advances in Physical Chemistry

Table 4 Balanced equations used to calculate heat of formation values of compounds in the test set

Isodesmic isogyric or other balanced equations1 Dinitromethane + methanerarr2 nitromethane2 2 dinitromethanerarrmethane + tetranitromethane3 Methyl azide + trinitromethanerarrmethane + azidotrinitromethane4 N-Ethyl-N-nitroethanamine + dimethylaminerarr N-ethyl-N-ethanamine + N-methyl-N-nitromethanamine (DMNO)5 11-Dinitropropane + methyl aziderarr ethane + 1-azido-11-dinitroethane6 2 111-Trinitropropanerarr butane + hexanitroethane7 3 propylnitraterarr2 propane + nitroglycerin8 RDX + 3 nitrosyl hydriderarr3 HNO2 + TTT (hexahydro-135-trinitroso-135-triazine)9 3 1-nitropiperidinerarr2 cyclohexane + RDX10 1-Nitrosopiperidine + TTTrarr2 14-dinitrosopiperazine11 Piperazine + 2 dimethylnitraminerarr 2 dimethylamine + 14-dinitropiperazine12 Bis-222-trinitroethylamine + HNO2 rarr H2 + N-nitro-bis-222-trinitroethylamine13 Benzene + 4-nitroanilinerarr aniline + nitrobenzene14 Phenol + nitrobenzenerarr benzene + 2-nitrophenol15 Phenol + nitrobenzenerarr benzene + 3-nitrophenol16 Phenol + nitrobenzenerarr benzene + 4-nitrophenol17 Aniline + nitrobenzenerarr benzene + m-nitroaniline18 Aniline + nitrobenzenerarr benzene + p-nitroaniline19 Methyl azide + benzenerarrmethane + azidobenzene20 Methyl azide + nitrobenzenerarrmethane + 1-azido-4-nitrobenzene

21 N-Propylpropanamine + 4 1-nitropropane + dimethylnitraminerarr dimethylamine + N-nitro-bis-22-dinitropropylamine (DNPN)+ 4 propane

22 Toluene + nitrobenzenerarr benzene + PNT (1-methyl-4-nitrobenzene)23 Toluene + 2 nitrobenzenerarr2 benzene + 24-DNT (1-methyl-24-dinitrobenzene)24 Methyl azide + toluenerarrmethane + azidomethylbenzene25 Methyl azide + 3-ethylpentanerarrmethane + 3-azido-3-ethylpentane26 Toluene + 135-trinitrobenzenerarr benzene + TNT (246-trinitrotoluene)27 2 2-nitropropane + adamantanerarr2 propane + 22-dinitroadamantane28 Methyl azide + adamantanerarrmethane + 1-azidoadamantane29 Methyl azide + 2-phenylpropanerarrmethane + 2-azido-2-phenylpropane30 trans-Stilbene + 2 135-trinitrobenzenerarr2 benzene + HNS (111015840-(12-ethenediyl)bis[246- trinitrobenzene])31 Isopropyl nitrite + methanerarr propane + methyl nitrite32 Propyl nitrate + methanerarr propane + methyl nitrate33 2 1-Nitropropane + methanerarr2 propane + dinitromethane34 Propyl nitrite + ethanerarr propane + ethyl nitrite35 Propyl nitrate + ethanerarr propane + ethyl nitrate36 Isopropyl nitriterarr propyl nitrite37 2-Nitropropane + 2-methylpropanerarr 2-methyl-2-nitropropane + propane38 Isopropyl nitrite + butanerarr n-butyl nitrite + propane39 Isopropyl nitrite + isobutanerarr t-butyl nitrite + propane40 2 1-pyrroline + tetrahydrofuran + 2methyl nitraterarr H2 + 34-furazandimethanol dinitrate + 2 cyclopentane41 Piperidine + dimethylnitraminerarr 1-nitropiperidine + dimethylamine42 Phenyl radical + nitric oxiderarr nitrosobenzene43 Toluene + 1-nitropropanerarr propane + nitromethylbenzene44 Toluene + 11-dinitropropanerarr propane + dinitromethylbenzene45 2 Toluene + nitrobenzenerarr2 benzene + 13-dimethyl-2-nitrobenzene

Advances in Physical Chemistry 9

to be 29 kcalmol with a mean absolute error (MAE) of23 kcalmol and a maximum deviation of 69 kcalmol Thiscompares with an rms deviation of 33 kcalmol a MAE of24 kcalmol and a maximum deviation of 99 kcalmol usingdata calculated by Byrd andRice [6 7] It should be noted thatthe T1 procedure has been previously shown to reproduceexperimental heat of formation values of a large (1805) set oforganicmolecules with an rms deviation of 275 kcalmol anda MAE of 203 kcalmol [8] Clearly the rms andMAE valuesfor the T1 approach reported here agree well with those valuesreported for the larger data set

These results led us to compare older approaches usedto predictcalculate Δ119891119867

119900298g values Specifically we used

Bensonrsquos group additivity (or group contribution) approach[10 11] We also used density functional theory coupled withthe use of selected isodesmic isogyric and other balancedequations One disadvantage of Bensonrsquos group additivityapproach is that group values for some of the substructuresof several compounds in the test set are not availableWe were partially able to overcome this problem by usingexisting data which allowed us to calculate some of thesegroup values In total we were able to use Bensonrsquos groupadditivity approach to calculate Δ119891119867

119900298g values for 36 of 45

compounds in the test set This approach yielded calculatedresults in which 64 (2336) of the calculated Δ119891119867

119900298g

values were within plusmn20 kcalmol of experimental valuesThe rms deviation from experiment for the predicted groupadditivity gas-phase heat of formation valueswas 55 kcalmolwith an MAE of 31 kcalmol with a maximum deviationof 212 kcalmol for HNS A relatively large deviation fromexperiment of 148 kcalmol was also found for nitroglycerinA significant drawback to the use of group additivity theoryis that calculated Δ119891119867

119900298g values are sometimes affected

by structural features that are not adequately addressed bytheory Although Δ119891119867

119900298g values for some strained com-

pounds can be accurately predicted by adding correctionfactors for structural characteristics such as ring strain thepresence of gauche carbons and C1ndashC5 repulsions contri-bution of certain other structural features do not appear tobe adequately addressed by group additivity theory HNSand nitroglycerin seem to fall into this category Whenthese compounds were eliminated from the test set the rmsdeviation from experiment for the predicted group additivityΔ119891119867119900298g values was found to be 35 kcalmol with an MAE

of 22 kcalmol and a maximum deviation of 115 kcalmol forthe remaining 34 compoundsThe relevant point is that groupadditivity theory is often quite accurate however onemust becareful regarding its application

Density functional theory coupledwith the use of selectedbalanced reactions was also used to calculate Δ119891119867

119900298g values

for comparison to the test setThe reactions used in this inves-tigation are presented in Table 4 We determined that therms deviation from experiment for the calculated Δ119891119867

119900298g

values was 15 kcalmol with an MAE of 11 kcalmol and amaximum deviation of 38 kcalmol This approach yieldedcalculated results in which 82 (3745) of theΔ119891119867

119900298g values

werewithinplusmn20 kcalmol of experimental values Despite thefact that for time considerations we selected a medium size

basis set density functional theory coupled with the use ofisodesmic and other balanced equations was still the mostaccurate approach of the sixmethodswe compared Althoughaccurate it is necessary to mention some problems with thisapproach First of all different balanced equations can leadto different Δ119891119867

119900298g values Often such differences are small

But sometimes such differences can be substantial Cramer[12] has noted that ldquothe construction of an isodesmic equationis something of an art depending on chemical intuition andavailable experimental datardquo

It should also be mentioned that when computationtime is not a consideration the use of larger basis setsmight be expected to result in even greater accuracy IndeedDorofeeva and colleagues [21ndash23] have have shown thatthe use of high level computational theory coupled withmultiple isodesmic isogyric and other balanced equationscan result in calculation of Δ119891119867

119900298g values that are suffi-

ciently accurate that they feel confident in recommendingconsensus values in many cases where there is discrep-ancy between experimental values andor between computedvalues

Finally two semiempirical models (RM1 and PM7) wereused to calculate Δ119891119867

119900298g Semiempirical models are attrac-

tive because they are very rapid and their accuracy continuesto improve [13 14] However RM1 and PM7 were found tobe less accurate than the other approaches used to calculateΔ119891119867119900298g values for compounds in the test set used for this

investigation Even when Δ119891119867119900298g values having very large

(greater than 14 kcalmol) deviations from reference valueswere omitted rms and MAE values for calculated RM1 andPM7 data sets were substantially greater than those of thefour other computational approaches investigated (Tables 2and 3)

4 Conclusion

Because substantial interest exists in developing relativelyrapid and accurate procedures for predicting gas-phase heatof formation values for energetic compounds our overall goalwas to determine which of several computational approachesis most suitable for this endeavor None of the computationalapproaches were uniformly accurate within plusmn20 kcalmolof experimental values (ie the presumably more accuratealternative experimental values)

However four of the computational approaches investi-gated were able tomeet this level of accuracy greater than 51of the time Moreover these four computational approacheswere accurate to within plusmn40 kcal greater than 77 of thetime For relatively simple compounds in which correctionfactors can be used to account for ring strain and so forthand other factors do not make substantial contribution toΔ119891119867119900298g we conclude that the group additivity approach is

about as accurate as those approaches based on higher levelsof theory For compounds that are structurallymore complexthe approach using DFT coupled with the use of isodesmicisogyric and other balanced equations is more accurate butmore time consuming than the DFTAtomic and Groupcontribution method described by Byrd and Rice [6 7] and

10 Advances in Physical Chemistry

the T1 method [8] for this set of compounds However sincecalculated values are often similar and mutually supportiveit seems that a reasonable approach would be to use any (orall) of these four procedures when this level of accuracy isacceptable and the goal is to compare predicted properties ofnew or theoretical compounds with those of structurally sim-ilar compounds whose experimental values andor computedvalues are well established

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] H M Xiao X J Xu and L Qiu Theoretical Design of HighEnergy Density Materials Science Press Beijing China 2008

[2] R E Kirk and D F Othmer Encyclopedia of Chemical Technol-ogy vol 5 Wiley New York NY USA 2004

[3] J Giles ldquoGreen explosives collateral damagerdquo Nature vol 427no 6975 pp 580ndash581 2004

[4] J P Agrawal and J E Field ldquoRecent trends in high-energymaterialsrdquo Progress in Energy and Combustion Science vol 24no 1 pp 1ndash30 1998

[5] J Akhavan The Chemistry of Explosives Royal Society ofChemistry Cambridge UK 2004

[6] E F C Byrd and B M Rice ldquoImproved prediction of heatsof formation of energetic materials using quantum mechanicalcalculationsrdquo Journal of Physical Chemistry A vol 110 no 3 pp1005ndash1013 2006

[7] E F C Byrd and B M Rice ldquoCorrection improved predictionof heats of formation of energetic materials using quantummechanical calculationsrdquo The Journal of Physical Chemistry Avol 113 no 9 p 5813 2009

[8] W S Ohlinger P E Klunzinger B J Deppmeier and W JHehre ldquoEfficient calculation of heats of formationrdquo Journal ofPhysical Chemistry A vol 113 no 10 pp 2165ndash2175 2009

[9] L A Curtiss P C Redfern K Raghavachari V Rassolov andJ A Pople ldquoGaussian-3 theory using reduced Moslashller-PlessetorderrdquoThe Journal of Chemical Physics vol 110 no 10 pp 4703ndash4709 1999

[10] S W Benson and J H Buss ldquoAdditivity rules for the estima-tion of molecular properties Thermodynamic propertiesrdquo TheJournal of Chemical Physics vol 29 no 3 pp 546ndash572 1958

[11] SW Benson F R Cruickshank DM Golden et al ldquoAdditivityrules for the estimation of thermochemical propertiesrdquo Chemi-cal Reviews vol 69 no 3 pp 279ndash324 1969

[12] C J Cramer Essentials of Computational Chemistry Theoriesand Models John Wiley amp Sons New York NY USA 2ndedition 2004

[13] G B Rocha R O Freire A M Simas and J J P Stewart ldquoRM1a reparameterization of AM1 for H C N O P S F Cl Br and IrdquoJournal of Computational Chemistry vol 27 no 10 pp 1101ndash11112006

[14] J J P Stewart ldquoOptimization of parameters for semiempiricalmethods VI more modifications to the NDDO approximationsand re-optimization of parametersrdquo Journal of Molecular Mod-eling vol 19 no 1 pp 1ndash32 2013

[15] Y Zhao andDG Truhlar ldquoTheM06 suite of density functionalsfor main group thermochemistry thermochemical kineticsnoncovalent interactions excited states and transition ele-ments two new functionals and systematic testing of fourM06-class functionals and 12 other functionalsrdquo TheoreticalChemistry Accounts vol 120 no 1ndash3 pp 215ndash241 2008

[16] Y Zhao and D G Truhlar ldquoDensity functionals with broadapplicability in chemistryrdquo Accounts of Chemical Research vol41 no 2 pp 157ndash167 2008

[17] H Y Afeefy J F Liebman and S E Stein ldquoNeutral thermo-chemical datardquo in NIST Chemistry WebBook P J Linstrom andW G Mallard Eds NIST Standard Reference Database no 69National Institute of Standards and Technology GaithersburgMd USA 2005

[18] J B Pedley R D Naylor and S P KirbyThermochemical Dataof Organic Compounds Chapman amp Hall New York NY USA1986

[19] J O Cox and G Pilcher Thermochemistry of Organic andOrganometallic Compounds Academic Press New York NYUSA 1970

[20] OVDorofeeva andMA Suntsova ldquoEnthalpies of formation ofnitromethane and nitrobenzene theory vs experimentrdquo Journalof Chemical Thermodynamics vol 58 pp 221ndash225 2013

[21] O V Dorofeeva O N Ryzhova and M A Suntsova ldquoAccurateprediction of enthalpies of formation of organic azides bycombining G4 theory calculations with an isodesmic reactionschemerdquo Journal of Physical Chemistry A vol 117 no 31 pp6835ndash6845 2013

[22] M A Suntsova and O V Dorofeeva ldquoUse of G4 theoryfor the assessment of inaccuracies in experimental enthalpiesof formation of aliphatic nitro compounds and nitraminesrdquoJournal of Chemical amp Engineering Data vol 59 no 9 pp 2813ndash2826 2014

[23] M A Suntsova and O V Dorofeeva ldquoComment on lsquouse ofG4 theory for the assessment of inaccuracies in experimentalenthalpies of formation of aliphatic nitro compounds andnitraminesrsquordquo Journal of Chemical amp Engineering Data vol 60no 5 pp 1532ndash1533 2015

[24] S P Verevkin V N EmelrsquoYanenko V Diky and O V Doro-feeva ldquoEnthalpies of formation of nitromethane and nitroben-zene new experiments vs quantum chemical calculationsrdquoTheJournal of ChemicalThermodynamics vol 73 pp 163ndash170 2014

[25] CHETAHTheComputer Program for ChemicalThermodynam-ics and Energy Release Evaluation University of SouthAlabamaMobile Ala USA ASTM International West ConshohockenPa USA 2009

[26] NCohen and SWBenson ldquoEstimation of heats of formation oforganic compounds by additivity methodsrdquo Chemical Reviewsvol 93 no 7 pp 2419ndash2438 1993

[27] J A Bumpus and P H Willoughby ldquoOn the heat of formationof nitromethanerdquo Journal of Physical Organic Chemistry vol 21no 9 pp 747ndash757 2008

[28] Y K Knobelrsquo E A Miroshnichenko and Y A LebedevldquoHeats of combustion of nitromethane and dinitromethaneenthalpies of formation of nitromethyl radicals and energies ofdissociation of bonds in nitro derivatives of methanerdquo Bulletinof the Academy of Sciences of the USSR Division of ChemicalScience vol 20 no 3 pp 425ndash428 1971

[29] E A Miroshnichenko T S Konrsquokova Y O Inozemtsev VP VorobrsquoEva Y N Matymhin and S A Shevelev ldquoBondenergies and formation enthalpies of mono- and polyradicals in

Advances in Physical Chemistry 11

nitroalkanes 1 Nitromethanesrdquo Russian Chemical Bulletin vol58 no 4 pp 772ndash776 2009

[30] C Y Lin M W George and P M W Gill ldquoEDF2 a densityfunctional for predicting molecular vibrational frequenciesrdquoAustralian Journal of Chemistry vol 57 no 4 pp 365ndash370 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Page 5: Research Article Calculating Heat of Formation Values of Energetic Compounds…downloads.hindawi.com/journals/apc/2016/5082084.pdf ·  · 2016-03-14Research Article Calculating Heat

Advances in Physical Chemistry 5

Table1Con

tinued

Com

poun

dname

Experim

entallowast

Δ119891119867119900 298g

(kcalm

ol)

T1Δ119891119867119900 298g

(kcalm

ol)

DFT

Atom

icandGroup

contrib

ution

Δ119891119867119900 298g

(kcalm

ol)lowast

DFT

Isod

esmiclowastlowast

Δ119891119867119900 298g

(kcalm

ol)

Group

Additiv

ityΔ119891119867119900 298g

(kcalm

ol)

PM7

Δ119891119867119900 298g

(kcalm

ol)

RM1

Δ119891119867119900 298g

(kcalm

ol)

Nitro

sobenzene

481

471

488

455

mdash412

331

Nitro

methylbenzene

734

87

94

90

76113

130

Dinitrom

ethylbenzene

83(14

2)

139

136

145

121

196

184

13-D

imethyl-2

-nitrobenzene

21

14

43

32

02

minus02

14

HNS=111015840 -(12-ethenediyl)b

is[246-trinitrob

enzene]TT

T=hexahydro-13

5-tr

initroso-13

5-tr

iazine

lowastVa

luesfro

mBy

rdandRice

[67]Va

luesin

parenthesesa

rethosethath

aveb

eensubstituted

forcorrespon

ding

valuesin

theo

riginalreferences

etandareu

sedin

thea

lternativee

xperim

entalreference

setSeetext

ford

etailsandexplanation

lowastlowastMosto

fvaluesintheD

FTiso

desm

iccolumnwerec

alculated

usingiso

desm

icreactio

nsH

owever

somev

aluesw

erec

alculated

usingiso

gyric

orotherb

alancedequatio

ns

lowastlowastlowastVa

lues

calculated

usingCH

ETAH80

6 Advances in Physical Chemistry

Table 2 Statistical comparison of experimental gas-phase heat of formation valueswith values calculated using several theoretical approaches

T1Δ119891119867298g(kcalmol)

DFT Atomicand GroupcontributionΔ119891119867298g

(kcalmol)lowast

DFTisodesmicΔ119891119867298g(kcalmol)

Group AddΔ119891119867298g(kcalmol)

PM7Δ119891119867298g(kcalmol)

RM1Δ119891119867298g(kcalmol)

rms deviation 50 30 37 54 (34)lowast 118 (60) 129 (59)MAE 37 21 25 33 (25)lowast 75 (49) 79 (48)Max Dev (kcalmol) 135 91 139 212 (96)lowast 539 (132) 589 (126)Number of values plusmn20 kcalmol 17 28 27 19 10 12Number of values plusmn30 kcalmol 25 35 33 24 14 17Number of values plusmn40 kcalmol 32 37 37 28 18 18

1198772 098728 09958 099277 09863

(099435)092817(098063)

091605(098141)

lowastValues in parentheses represent data in which values for compounds having deviations from experiment greater than 140 kcalmol were omitted See text forexplanation

Table 3 Statistical comparison of alternative experimental gas-phase heat of formation values with values calculated using several theoreticalapproaches

T1Δ119891119867298g(kcalmol)

DFT Atomicand GroupcontributionΔ119891119867298g(kcalmol)lowast

DFTisodesmicΔ119891119867298g(kcalmol)

Group AddΔ119891119867298g(kcalmol)

PM7lowastΔ119891119867298g(kcalmol)

RM1lowastΔ119891119867298g(kcalmol)

rms deviation 29 33 15 55 (35)lowast 120 (54) 122 (45)MAE 23 24 11 31 (23)lowast 73 (42) 68 (36)Max Dev (kcalmol) 69 99 38 212 (115)lowast 539 (132) 589 (120)Number of values plusmn20 kcalmol 23 23 37 23 13 14Number of values plusmn30 kcalmol 31 33 42 25 18 19Number of values plusmn40 kcalmol 38 37 45 28 21 21

1198772 099648 099477 099884 098549

(099353)092435(098574)

092367(09889)

lowastValues in parentheses represent data in which values for compounds having deviations from experiment greater than 140 kcalmol were omitted See text forexplanation

have been reported for 246-trinitrotoluene Thus in placeof the Δ119891119867

119900298g value of 575 kcalmol used by Byrd and Rice

[6 7] we have substituted the value of 123 kcalmol (reportedin ldquoThermochemistry of Organic and Organometallic Com-poundsrdquo by Cox and Pilcher [19]) in the new alternativeexperimental reference data set During the course of thisinvestigation it also appeared that the experimental value fordinitromethylbenzene may be several kcalmol too lowThuswe used procedures similar to those described by Dorofeevaet al [21ndash23] to calculate a Δ119891119867

119900298g reference value of 142 plusmn

03 kcalmol for this compoundThis value was also includedin the alternative reference set These results are found inSupplemental Tables 1S and 2S (see Supplementary Materialavailable online at httpdxdoiorg10115520165082084)

A comparison of Tables 2 and 3 supports the conclusionthat the alternative recommended values as a group areindeed more accurate than the original experimental valuesthat were available to and used by Byrd and Rice [6 7] intheir investigations Except for the DFTAtomic and Groupcontribution approach the mean absolute error (MAE) was

greater for the original experimental reference set than forthe new alternative experimental reference set The fact thatthe opposite was found for the DFTAtomic and Groupcontribution approach is not surprising as many of the com-pounds in the original experimental reference set were usedto parameterize and develop this computational approachNevertheless this approach still performed quite well whencompared to the alternative experimental reference set Ourresults also suggest that the accuracy of the DFTAtomic andGroup contribution approach might benefit from reparame-terization using the alternative experimental reference set

Because the alternative experimental reference setappeared to be more accurate than the original reference setit was used for the comparisons described below

The atom and group equivalent DFT approach describedby Byrd and Rice [6 7] and the T1 procedure both yieldedcalculated results in which 51 (2345) of the predictedΔ119891119867119900298g values were within plusmn20 kcalmol of values in the

reference set The rms deviation from experiment for thepredicted T1 gas-phase heat of formation values was found

Advances in Physical Chemistry 7

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

0minus50 50 100minus100

Experimental values (kcalmol)

(a) T1

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(b) DFTAtomic and Group contribution

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(c) DFTisodesmic

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(d) Group Add

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus100 0 50 100minus50

Experimental values (kcalmol)

(e) PM7

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(f) RM1

Figure 1 Calculated gas-phase heat of formation values versus experimental values Gas-phase heat of formation values were calculated using(1) the multilevel ab initio approach (T1) described by Ohlinger et al [8] as implemented in the Spartanrsquo10 and 14 suite of programs (a) (2) theDFTAtomic and Group contribution approach developed and described by Byrd and Rice [6 7] (b)The experimental values and calculatedvalues used to construct (b) are those published by Byrd and Rice [6 7] (b) is identical to Figure 1a in their manuscript except for the fact thatthe alternative set of experimental Δ119891119867

119900298g reference values are also included (3) Density functional theory using isodesmic isogyric and

other balanced equations as described herein (c) (4)The Benson Group Additivity approach as implemented in the and NIST and CHETAH80 software programs (d) (5) semiempirical theory (PM7 andRM1) as implemented inMOPAC2012 and the Spartan 14 suite of programs ((e)and (f) resp) Open squares represent calculatedΔ119891119867

119900298g values versus the experimentalΔ119891119867

119900298g values Closed circles represent calculated

Δ119891119867119900298g values versus the alternative experimental Δ119891119867

119900298g reference values as described in the text Least square regression analysis and

calculation of 1198772 values were accomplished using KaleidaGraph graphing software (Synergy Software Reading PA) 1198772 values are presentedin Tables 2 and 3

8 Advances in Physical Chemistry

Table 4 Balanced equations used to calculate heat of formation values of compounds in the test set

Isodesmic isogyric or other balanced equations1 Dinitromethane + methanerarr2 nitromethane2 2 dinitromethanerarrmethane + tetranitromethane3 Methyl azide + trinitromethanerarrmethane + azidotrinitromethane4 N-Ethyl-N-nitroethanamine + dimethylaminerarr N-ethyl-N-ethanamine + N-methyl-N-nitromethanamine (DMNO)5 11-Dinitropropane + methyl aziderarr ethane + 1-azido-11-dinitroethane6 2 111-Trinitropropanerarr butane + hexanitroethane7 3 propylnitraterarr2 propane + nitroglycerin8 RDX + 3 nitrosyl hydriderarr3 HNO2 + TTT (hexahydro-135-trinitroso-135-triazine)9 3 1-nitropiperidinerarr2 cyclohexane + RDX10 1-Nitrosopiperidine + TTTrarr2 14-dinitrosopiperazine11 Piperazine + 2 dimethylnitraminerarr 2 dimethylamine + 14-dinitropiperazine12 Bis-222-trinitroethylamine + HNO2 rarr H2 + N-nitro-bis-222-trinitroethylamine13 Benzene + 4-nitroanilinerarr aniline + nitrobenzene14 Phenol + nitrobenzenerarr benzene + 2-nitrophenol15 Phenol + nitrobenzenerarr benzene + 3-nitrophenol16 Phenol + nitrobenzenerarr benzene + 4-nitrophenol17 Aniline + nitrobenzenerarr benzene + m-nitroaniline18 Aniline + nitrobenzenerarr benzene + p-nitroaniline19 Methyl azide + benzenerarrmethane + azidobenzene20 Methyl azide + nitrobenzenerarrmethane + 1-azido-4-nitrobenzene

21 N-Propylpropanamine + 4 1-nitropropane + dimethylnitraminerarr dimethylamine + N-nitro-bis-22-dinitropropylamine (DNPN)+ 4 propane

22 Toluene + nitrobenzenerarr benzene + PNT (1-methyl-4-nitrobenzene)23 Toluene + 2 nitrobenzenerarr2 benzene + 24-DNT (1-methyl-24-dinitrobenzene)24 Methyl azide + toluenerarrmethane + azidomethylbenzene25 Methyl azide + 3-ethylpentanerarrmethane + 3-azido-3-ethylpentane26 Toluene + 135-trinitrobenzenerarr benzene + TNT (246-trinitrotoluene)27 2 2-nitropropane + adamantanerarr2 propane + 22-dinitroadamantane28 Methyl azide + adamantanerarrmethane + 1-azidoadamantane29 Methyl azide + 2-phenylpropanerarrmethane + 2-azido-2-phenylpropane30 trans-Stilbene + 2 135-trinitrobenzenerarr2 benzene + HNS (111015840-(12-ethenediyl)bis[246- trinitrobenzene])31 Isopropyl nitrite + methanerarr propane + methyl nitrite32 Propyl nitrate + methanerarr propane + methyl nitrate33 2 1-Nitropropane + methanerarr2 propane + dinitromethane34 Propyl nitrite + ethanerarr propane + ethyl nitrite35 Propyl nitrate + ethanerarr propane + ethyl nitrate36 Isopropyl nitriterarr propyl nitrite37 2-Nitropropane + 2-methylpropanerarr 2-methyl-2-nitropropane + propane38 Isopropyl nitrite + butanerarr n-butyl nitrite + propane39 Isopropyl nitrite + isobutanerarr t-butyl nitrite + propane40 2 1-pyrroline + tetrahydrofuran + 2methyl nitraterarr H2 + 34-furazandimethanol dinitrate + 2 cyclopentane41 Piperidine + dimethylnitraminerarr 1-nitropiperidine + dimethylamine42 Phenyl radical + nitric oxiderarr nitrosobenzene43 Toluene + 1-nitropropanerarr propane + nitromethylbenzene44 Toluene + 11-dinitropropanerarr propane + dinitromethylbenzene45 2 Toluene + nitrobenzenerarr2 benzene + 13-dimethyl-2-nitrobenzene

Advances in Physical Chemistry 9

to be 29 kcalmol with a mean absolute error (MAE) of23 kcalmol and a maximum deviation of 69 kcalmol Thiscompares with an rms deviation of 33 kcalmol a MAE of24 kcalmol and a maximum deviation of 99 kcalmol usingdata calculated by Byrd andRice [6 7] It should be noted thatthe T1 procedure has been previously shown to reproduceexperimental heat of formation values of a large (1805) set oforganicmolecules with an rms deviation of 275 kcalmol anda MAE of 203 kcalmol [8] Clearly the rms andMAE valuesfor the T1 approach reported here agree well with those valuesreported for the larger data set

These results led us to compare older approaches usedto predictcalculate Δ119891119867

119900298g values Specifically we used

Bensonrsquos group additivity (or group contribution) approach[10 11] We also used density functional theory coupled withthe use of selected isodesmic isogyric and other balancedequations One disadvantage of Bensonrsquos group additivityapproach is that group values for some of the substructuresof several compounds in the test set are not availableWe were partially able to overcome this problem by usingexisting data which allowed us to calculate some of thesegroup values In total we were able to use Bensonrsquos groupadditivity approach to calculate Δ119891119867

119900298g values for 36 of 45

compounds in the test set This approach yielded calculatedresults in which 64 (2336) of the calculated Δ119891119867

119900298g

values were within plusmn20 kcalmol of experimental valuesThe rms deviation from experiment for the predicted groupadditivity gas-phase heat of formation valueswas 55 kcalmolwith an MAE of 31 kcalmol with a maximum deviationof 212 kcalmol for HNS A relatively large deviation fromexperiment of 148 kcalmol was also found for nitroglycerinA significant drawback to the use of group additivity theoryis that calculated Δ119891119867

119900298g values are sometimes affected

by structural features that are not adequately addressed bytheory Although Δ119891119867

119900298g values for some strained com-

pounds can be accurately predicted by adding correctionfactors for structural characteristics such as ring strain thepresence of gauche carbons and C1ndashC5 repulsions contri-bution of certain other structural features do not appear tobe adequately addressed by group additivity theory HNSand nitroglycerin seem to fall into this category Whenthese compounds were eliminated from the test set the rmsdeviation from experiment for the predicted group additivityΔ119891119867119900298g values was found to be 35 kcalmol with an MAE

of 22 kcalmol and a maximum deviation of 115 kcalmol forthe remaining 34 compoundsThe relevant point is that groupadditivity theory is often quite accurate however onemust becareful regarding its application

Density functional theory coupledwith the use of selectedbalanced reactions was also used to calculate Δ119891119867

119900298g values

for comparison to the test setThe reactions used in this inves-tigation are presented in Table 4 We determined that therms deviation from experiment for the calculated Δ119891119867

119900298g

values was 15 kcalmol with an MAE of 11 kcalmol and amaximum deviation of 38 kcalmol This approach yieldedcalculated results in which 82 (3745) of theΔ119891119867

119900298g values

werewithinplusmn20 kcalmol of experimental values Despite thefact that for time considerations we selected a medium size

basis set density functional theory coupled with the use ofisodesmic and other balanced equations was still the mostaccurate approach of the sixmethodswe compared Althoughaccurate it is necessary to mention some problems with thisapproach First of all different balanced equations can leadto different Δ119891119867

119900298g values Often such differences are small

But sometimes such differences can be substantial Cramer[12] has noted that ldquothe construction of an isodesmic equationis something of an art depending on chemical intuition andavailable experimental datardquo

It should also be mentioned that when computationtime is not a consideration the use of larger basis setsmight be expected to result in even greater accuracy IndeedDorofeeva and colleagues [21ndash23] have have shown thatthe use of high level computational theory coupled withmultiple isodesmic isogyric and other balanced equationscan result in calculation of Δ119891119867

119900298g values that are suffi-

ciently accurate that they feel confident in recommendingconsensus values in many cases where there is discrep-ancy between experimental values andor between computedvalues

Finally two semiempirical models (RM1 and PM7) wereused to calculate Δ119891119867

119900298g Semiempirical models are attrac-

tive because they are very rapid and their accuracy continuesto improve [13 14] However RM1 and PM7 were found tobe less accurate than the other approaches used to calculateΔ119891119867119900298g values for compounds in the test set used for this

investigation Even when Δ119891119867119900298g values having very large

(greater than 14 kcalmol) deviations from reference valueswere omitted rms and MAE values for calculated RM1 andPM7 data sets were substantially greater than those of thefour other computational approaches investigated (Tables 2and 3)

4 Conclusion

Because substantial interest exists in developing relativelyrapid and accurate procedures for predicting gas-phase heatof formation values for energetic compounds our overall goalwas to determine which of several computational approachesis most suitable for this endeavor None of the computationalapproaches were uniformly accurate within plusmn20 kcalmolof experimental values (ie the presumably more accuratealternative experimental values)

However four of the computational approaches investi-gated were able tomeet this level of accuracy greater than 51of the time Moreover these four computational approacheswere accurate to within plusmn40 kcal greater than 77 of thetime For relatively simple compounds in which correctionfactors can be used to account for ring strain and so forthand other factors do not make substantial contribution toΔ119891119867119900298g we conclude that the group additivity approach is

about as accurate as those approaches based on higher levelsof theory For compounds that are structurallymore complexthe approach using DFT coupled with the use of isodesmicisogyric and other balanced equations is more accurate butmore time consuming than the DFTAtomic and Groupcontribution method described by Byrd and Rice [6 7] and

10 Advances in Physical Chemistry

the T1 method [8] for this set of compounds However sincecalculated values are often similar and mutually supportiveit seems that a reasonable approach would be to use any (orall) of these four procedures when this level of accuracy isacceptable and the goal is to compare predicted properties ofnew or theoretical compounds with those of structurally sim-ilar compounds whose experimental values andor computedvalues are well established

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] H M Xiao X J Xu and L Qiu Theoretical Design of HighEnergy Density Materials Science Press Beijing China 2008

[2] R E Kirk and D F Othmer Encyclopedia of Chemical Technol-ogy vol 5 Wiley New York NY USA 2004

[3] J Giles ldquoGreen explosives collateral damagerdquo Nature vol 427no 6975 pp 580ndash581 2004

[4] J P Agrawal and J E Field ldquoRecent trends in high-energymaterialsrdquo Progress in Energy and Combustion Science vol 24no 1 pp 1ndash30 1998

[5] J Akhavan The Chemistry of Explosives Royal Society ofChemistry Cambridge UK 2004

[6] E F C Byrd and B M Rice ldquoImproved prediction of heatsof formation of energetic materials using quantum mechanicalcalculationsrdquo Journal of Physical Chemistry A vol 110 no 3 pp1005ndash1013 2006

[7] E F C Byrd and B M Rice ldquoCorrection improved predictionof heats of formation of energetic materials using quantummechanical calculationsrdquo The Journal of Physical Chemistry Avol 113 no 9 p 5813 2009

[8] W S Ohlinger P E Klunzinger B J Deppmeier and W JHehre ldquoEfficient calculation of heats of formationrdquo Journal ofPhysical Chemistry A vol 113 no 10 pp 2165ndash2175 2009

[9] L A Curtiss P C Redfern K Raghavachari V Rassolov andJ A Pople ldquoGaussian-3 theory using reduced Moslashller-PlessetorderrdquoThe Journal of Chemical Physics vol 110 no 10 pp 4703ndash4709 1999

[10] S W Benson and J H Buss ldquoAdditivity rules for the estima-tion of molecular properties Thermodynamic propertiesrdquo TheJournal of Chemical Physics vol 29 no 3 pp 546ndash572 1958

[11] SW Benson F R Cruickshank DM Golden et al ldquoAdditivityrules for the estimation of thermochemical propertiesrdquo Chemi-cal Reviews vol 69 no 3 pp 279ndash324 1969

[12] C J Cramer Essentials of Computational Chemistry Theoriesand Models John Wiley amp Sons New York NY USA 2ndedition 2004

[13] G B Rocha R O Freire A M Simas and J J P Stewart ldquoRM1a reparameterization of AM1 for H C N O P S F Cl Br and IrdquoJournal of Computational Chemistry vol 27 no 10 pp 1101ndash11112006

[14] J J P Stewart ldquoOptimization of parameters for semiempiricalmethods VI more modifications to the NDDO approximationsand re-optimization of parametersrdquo Journal of Molecular Mod-eling vol 19 no 1 pp 1ndash32 2013

[15] Y Zhao andDG Truhlar ldquoTheM06 suite of density functionalsfor main group thermochemistry thermochemical kineticsnoncovalent interactions excited states and transition ele-ments two new functionals and systematic testing of fourM06-class functionals and 12 other functionalsrdquo TheoreticalChemistry Accounts vol 120 no 1ndash3 pp 215ndash241 2008

[16] Y Zhao and D G Truhlar ldquoDensity functionals with broadapplicability in chemistryrdquo Accounts of Chemical Research vol41 no 2 pp 157ndash167 2008

[17] H Y Afeefy J F Liebman and S E Stein ldquoNeutral thermo-chemical datardquo in NIST Chemistry WebBook P J Linstrom andW G Mallard Eds NIST Standard Reference Database no 69National Institute of Standards and Technology GaithersburgMd USA 2005

[18] J B Pedley R D Naylor and S P KirbyThermochemical Dataof Organic Compounds Chapman amp Hall New York NY USA1986

[19] J O Cox and G Pilcher Thermochemistry of Organic andOrganometallic Compounds Academic Press New York NYUSA 1970

[20] OVDorofeeva andMA Suntsova ldquoEnthalpies of formation ofnitromethane and nitrobenzene theory vs experimentrdquo Journalof Chemical Thermodynamics vol 58 pp 221ndash225 2013

[21] O V Dorofeeva O N Ryzhova and M A Suntsova ldquoAccurateprediction of enthalpies of formation of organic azides bycombining G4 theory calculations with an isodesmic reactionschemerdquo Journal of Physical Chemistry A vol 117 no 31 pp6835ndash6845 2013

[22] M A Suntsova and O V Dorofeeva ldquoUse of G4 theoryfor the assessment of inaccuracies in experimental enthalpiesof formation of aliphatic nitro compounds and nitraminesrdquoJournal of Chemical amp Engineering Data vol 59 no 9 pp 2813ndash2826 2014

[23] M A Suntsova and O V Dorofeeva ldquoComment on lsquouse ofG4 theory for the assessment of inaccuracies in experimentalenthalpies of formation of aliphatic nitro compounds andnitraminesrsquordquo Journal of Chemical amp Engineering Data vol 60no 5 pp 1532ndash1533 2015

[24] S P Verevkin V N EmelrsquoYanenko V Diky and O V Doro-feeva ldquoEnthalpies of formation of nitromethane and nitroben-zene new experiments vs quantum chemical calculationsrdquoTheJournal of ChemicalThermodynamics vol 73 pp 163ndash170 2014

[25] CHETAHTheComputer Program for ChemicalThermodynam-ics and Energy Release Evaluation University of SouthAlabamaMobile Ala USA ASTM International West ConshohockenPa USA 2009

[26] NCohen and SWBenson ldquoEstimation of heats of formation oforganic compounds by additivity methodsrdquo Chemical Reviewsvol 93 no 7 pp 2419ndash2438 1993

[27] J A Bumpus and P H Willoughby ldquoOn the heat of formationof nitromethanerdquo Journal of Physical Organic Chemistry vol 21no 9 pp 747ndash757 2008

[28] Y K Knobelrsquo E A Miroshnichenko and Y A LebedevldquoHeats of combustion of nitromethane and dinitromethaneenthalpies of formation of nitromethyl radicals and energies ofdissociation of bonds in nitro derivatives of methanerdquo Bulletinof the Academy of Sciences of the USSR Division of ChemicalScience vol 20 no 3 pp 425ndash428 1971

[29] E A Miroshnichenko T S Konrsquokova Y O Inozemtsev VP VorobrsquoEva Y N Matymhin and S A Shevelev ldquoBondenergies and formation enthalpies of mono- and polyradicals in

Advances in Physical Chemistry 11

nitroalkanes 1 Nitromethanesrdquo Russian Chemical Bulletin vol58 no 4 pp 772ndash776 2009

[30] C Y Lin M W George and P M W Gill ldquoEDF2 a densityfunctional for predicting molecular vibrational frequenciesrdquoAustralian Journal of Chemistry vol 57 no 4 pp 365ndash370 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Page 6: Research Article Calculating Heat of Formation Values of Energetic Compounds…downloads.hindawi.com/journals/apc/2016/5082084.pdf ·  · 2016-03-14Research Article Calculating Heat

6 Advances in Physical Chemistry

Table 2 Statistical comparison of experimental gas-phase heat of formation valueswith values calculated using several theoretical approaches

T1Δ119891119867298g(kcalmol)

DFT Atomicand GroupcontributionΔ119891119867298g

(kcalmol)lowast

DFTisodesmicΔ119891119867298g(kcalmol)

Group AddΔ119891119867298g(kcalmol)

PM7Δ119891119867298g(kcalmol)

RM1Δ119891119867298g(kcalmol)

rms deviation 50 30 37 54 (34)lowast 118 (60) 129 (59)MAE 37 21 25 33 (25)lowast 75 (49) 79 (48)Max Dev (kcalmol) 135 91 139 212 (96)lowast 539 (132) 589 (126)Number of values plusmn20 kcalmol 17 28 27 19 10 12Number of values plusmn30 kcalmol 25 35 33 24 14 17Number of values plusmn40 kcalmol 32 37 37 28 18 18

1198772 098728 09958 099277 09863

(099435)092817(098063)

091605(098141)

lowastValues in parentheses represent data in which values for compounds having deviations from experiment greater than 140 kcalmol were omitted See text forexplanation

Table 3 Statistical comparison of alternative experimental gas-phase heat of formation values with values calculated using several theoreticalapproaches

T1Δ119891119867298g(kcalmol)

DFT Atomicand GroupcontributionΔ119891119867298g(kcalmol)lowast

DFTisodesmicΔ119891119867298g(kcalmol)

Group AddΔ119891119867298g(kcalmol)

PM7lowastΔ119891119867298g(kcalmol)

RM1lowastΔ119891119867298g(kcalmol)

rms deviation 29 33 15 55 (35)lowast 120 (54) 122 (45)MAE 23 24 11 31 (23)lowast 73 (42) 68 (36)Max Dev (kcalmol) 69 99 38 212 (115)lowast 539 (132) 589 (120)Number of values plusmn20 kcalmol 23 23 37 23 13 14Number of values plusmn30 kcalmol 31 33 42 25 18 19Number of values plusmn40 kcalmol 38 37 45 28 21 21

1198772 099648 099477 099884 098549

(099353)092435(098574)

092367(09889)

lowastValues in parentheses represent data in which values for compounds having deviations from experiment greater than 140 kcalmol were omitted See text forexplanation

have been reported for 246-trinitrotoluene Thus in placeof the Δ119891119867

119900298g value of 575 kcalmol used by Byrd and Rice

[6 7] we have substituted the value of 123 kcalmol (reportedin ldquoThermochemistry of Organic and Organometallic Com-poundsrdquo by Cox and Pilcher [19]) in the new alternativeexperimental reference data set During the course of thisinvestigation it also appeared that the experimental value fordinitromethylbenzene may be several kcalmol too lowThuswe used procedures similar to those described by Dorofeevaet al [21ndash23] to calculate a Δ119891119867

119900298g reference value of 142 plusmn

03 kcalmol for this compoundThis value was also includedin the alternative reference set These results are found inSupplemental Tables 1S and 2S (see Supplementary Materialavailable online at httpdxdoiorg10115520165082084)

A comparison of Tables 2 and 3 supports the conclusionthat the alternative recommended values as a group areindeed more accurate than the original experimental valuesthat were available to and used by Byrd and Rice [6 7] intheir investigations Except for the DFTAtomic and Groupcontribution approach the mean absolute error (MAE) was

greater for the original experimental reference set than forthe new alternative experimental reference set The fact thatthe opposite was found for the DFTAtomic and Groupcontribution approach is not surprising as many of the com-pounds in the original experimental reference set were usedto parameterize and develop this computational approachNevertheless this approach still performed quite well whencompared to the alternative experimental reference set Ourresults also suggest that the accuracy of the DFTAtomic andGroup contribution approach might benefit from reparame-terization using the alternative experimental reference set

Because the alternative experimental reference setappeared to be more accurate than the original reference setit was used for the comparisons described below

The atom and group equivalent DFT approach describedby Byrd and Rice [6 7] and the T1 procedure both yieldedcalculated results in which 51 (2345) of the predictedΔ119891119867119900298g values were within plusmn20 kcalmol of values in the

reference set The rms deviation from experiment for thepredicted T1 gas-phase heat of formation values was found

Advances in Physical Chemistry 7

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

0minus50 50 100minus100

Experimental values (kcalmol)

(a) T1

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(b) DFTAtomic and Group contribution

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(c) DFTisodesmic

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(d) Group Add

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus100 0 50 100minus50

Experimental values (kcalmol)

(e) PM7

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(f) RM1

Figure 1 Calculated gas-phase heat of formation values versus experimental values Gas-phase heat of formation values were calculated using(1) the multilevel ab initio approach (T1) described by Ohlinger et al [8] as implemented in the Spartanrsquo10 and 14 suite of programs (a) (2) theDFTAtomic and Group contribution approach developed and described by Byrd and Rice [6 7] (b)The experimental values and calculatedvalues used to construct (b) are those published by Byrd and Rice [6 7] (b) is identical to Figure 1a in their manuscript except for the fact thatthe alternative set of experimental Δ119891119867

119900298g reference values are also included (3) Density functional theory using isodesmic isogyric and

other balanced equations as described herein (c) (4)The Benson Group Additivity approach as implemented in the and NIST and CHETAH80 software programs (d) (5) semiempirical theory (PM7 andRM1) as implemented inMOPAC2012 and the Spartan 14 suite of programs ((e)and (f) resp) Open squares represent calculatedΔ119891119867

119900298g values versus the experimentalΔ119891119867

119900298g values Closed circles represent calculated

Δ119891119867119900298g values versus the alternative experimental Δ119891119867

119900298g reference values as described in the text Least square regression analysis and

calculation of 1198772 values were accomplished using KaleidaGraph graphing software (Synergy Software Reading PA) 1198772 values are presentedin Tables 2 and 3

8 Advances in Physical Chemistry

Table 4 Balanced equations used to calculate heat of formation values of compounds in the test set

Isodesmic isogyric or other balanced equations1 Dinitromethane + methanerarr2 nitromethane2 2 dinitromethanerarrmethane + tetranitromethane3 Methyl azide + trinitromethanerarrmethane + azidotrinitromethane4 N-Ethyl-N-nitroethanamine + dimethylaminerarr N-ethyl-N-ethanamine + N-methyl-N-nitromethanamine (DMNO)5 11-Dinitropropane + methyl aziderarr ethane + 1-azido-11-dinitroethane6 2 111-Trinitropropanerarr butane + hexanitroethane7 3 propylnitraterarr2 propane + nitroglycerin8 RDX + 3 nitrosyl hydriderarr3 HNO2 + TTT (hexahydro-135-trinitroso-135-triazine)9 3 1-nitropiperidinerarr2 cyclohexane + RDX10 1-Nitrosopiperidine + TTTrarr2 14-dinitrosopiperazine11 Piperazine + 2 dimethylnitraminerarr 2 dimethylamine + 14-dinitropiperazine12 Bis-222-trinitroethylamine + HNO2 rarr H2 + N-nitro-bis-222-trinitroethylamine13 Benzene + 4-nitroanilinerarr aniline + nitrobenzene14 Phenol + nitrobenzenerarr benzene + 2-nitrophenol15 Phenol + nitrobenzenerarr benzene + 3-nitrophenol16 Phenol + nitrobenzenerarr benzene + 4-nitrophenol17 Aniline + nitrobenzenerarr benzene + m-nitroaniline18 Aniline + nitrobenzenerarr benzene + p-nitroaniline19 Methyl azide + benzenerarrmethane + azidobenzene20 Methyl azide + nitrobenzenerarrmethane + 1-azido-4-nitrobenzene

21 N-Propylpropanamine + 4 1-nitropropane + dimethylnitraminerarr dimethylamine + N-nitro-bis-22-dinitropropylamine (DNPN)+ 4 propane

22 Toluene + nitrobenzenerarr benzene + PNT (1-methyl-4-nitrobenzene)23 Toluene + 2 nitrobenzenerarr2 benzene + 24-DNT (1-methyl-24-dinitrobenzene)24 Methyl azide + toluenerarrmethane + azidomethylbenzene25 Methyl azide + 3-ethylpentanerarrmethane + 3-azido-3-ethylpentane26 Toluene + 135-trinitrobenzenerarr benzene + TNT (246-trinitrotoluene)27 2 2-nitropropane + adamantanerarr2 propane + 22-dinitroadamantane28 Methyl azide + adamantanerarrmethane + 1-azidoadamantane29 Methyl azide + 2-phenylpropanerarrmethane + 2-azido-2-phenylpropane30 trans-Stilbene + 2 135-trinitrobenzenerarr2 benzene + HNS (111015840-(12-ethenediyl)bis[246- trinitrobenzene])31 Isopropyl nitrite + methanerarr propane + methyl nitrite32 Propyl nitrate + methanerarr propane + methyl nitrate33 2 1-Nitropropane + methanerarr2 propane + dinitromethane34 Propyl nitrite + ethanerarr propane + ethyl nitrite35 Propyl nitrate + ethanerarr propane + ethyl nitrate36 Isopropyl nitriterarr propyl nitrite37 2-Nitropropane + 2-methylpropanerarr 2-methyl-2-nitropropane + propane38 Isopropyl nitrite + butanerarr n-butyl nitrite + propane39 Isopropyl nitrite + isobutanerarr t-butyl nitrite + propane40 2 1-pyrroline + tetrahydrofuran + 2methyl nitraterarr H2 + 34-furazandimethanol dinitrate + 2 cyclopentane41 Piperidine + dimethylnitraminerarr 1-nitropiperidine + dimethylamine42 Phenyl radical + nitric oxiderarr nitrosobenzene43 Toluene + 1-nitropropanerarr propane + nitromethylbenzene44 Toluene + 11-dinitropropanerarr propane + dinitromethylbenzene45 2 Toluene + nitrobenzenerarr2 benzene + 13-dimethyl-2-nitrobenzene

Advances in Physical Chemistry 9

to be 29 kcalmol with a mean absolute error (MAE) of23 kcalmol and a maximum deviation of 69 kcalmol Thiscompares with an rms deviation of 33 kcalmol a MAE of24 kcalmol and a maximum deviation of 99 kcalmol usingdata calculated by Byrd andRice [6 7] It should be noted thatthe T1 procedure has been previously shown to reproduceexperimental heat of formation values of a large (1805) set oforganicmolecules with an rms deviation of 275 kcalmol anda MAE of 203 kcalmol [8] Clearly the rms andMAE valuesfor the T1 approach reported here agree well with those valuesreported for the larger data set

These results led us to compare older approaches usedto predictcalculate Δ119891119867

119900298g values Specifically we used

Bensonrsquos group additivity (or group contribution) approach[10 11] We also used density functional theory coupled withthe use of selected isodesmic isogyric and other balancedequations One disadvantage of Bensonrsquos group additivityapproach is that group values for some of the substructuresof several compounds in the test set are not availableWe were partially able to overcome this problem by usingexisting data which allowed us to calculate some of thesegroup values In total we were able to use Bensonrsquos groupadditivity approach to calculate Δ119891119867

119900298g values for 36 of 45

compounds in the test set This approach yielded calculatedresults in which 64 (2336) of the calculated Δ119891119867

119900298g

values were within plusmn20 kcalmol of experimental valuesThe rms deviation from experiment for the predicted groupadditivity gas-phase heat of formation valueswas 55 kcalmolwith an MAE of 31 kcalmol with a maximum deviationof 212 kcalmol for HNS A relatively large deviation fromexperiment of 148 kcalmol was also found for nitroglycerinA significant drawback to the use of group additivity theoryis that calculated Δ119891119867

119900298g values are sometimes affected

by structural features that are not adequately addressed bytheory Although Δ119891119867

119900298g values for some strained com-

pounds can be accurately predicted by adding correctionfactors for structural characteristics such as ring strain thepresence of gauche carbons and C1ndashC5 repulsions contri-bution of certain other structural features do not appear tobe adequately addressed by group additivity theory HNSand nitroglycerin seem to fall into this category Whenthese compounds were eliminated from the test set the rmsdeviation from experiment for the predicted group additivityΔ119891119867119900298g values was found to be 35 kcalmol with an MAE

of 22 kcalmol and a maximum deviation of 115 kcalmol forthe remaining 34 compoundsThe relevant point is that groupadditivity theory is often quite accurate however onemust becareful regarding its application

Density functional theory coupledwith the use of selectedbalanced reactions was also used to calculate Δ119891119867

119900298g values

for comparison to the test setThe reactions used in this inves-tigation are presented in Table 4 We determined that therms deviation from experiment for the calculated Δ119891119867

119900298g

values was 15 kcalmol with an MAE of 11 kcalmol and amaximum deviation of 38 kcalmol This approach yieldedcalculated results in which 82 (3745) of theΔ119891119867

119900298g values

werewithinplusmn20 kcalmol of experimental values Despite thefact that for time considerations we selected a medium size

basis set density functional theory coupled with the use ofisodesmic and other balanced equations was still the mostaccurate approach of the sixmethodswe compared Althoughaccurate it is necessary to mention some problems with thisapproach First of all different balanced equations can leadto different Δ119891119867

119900298g values Often such differences are small

But sometimes such differences can be substantial Cramer[12] has noted that ldquothe construction of an isodesmic equationis something of an art depending on chemical intuition andavailable experimental datardquo

It should also be mentioned that when computationtime is not a consideration the use of larger basis setsmight be expected to result in even greater accuracy IndeedDorofeeva and colleagues [21ndash23] have have shown thatthe use of high level computational theory coupled withmultiple isodesmic isogyric and other balanced equationscan result in calculation of Δ119891119867

119900298g values that are suffi-

ciently accurate that they feel confident in recommendingconsensus values in many cases where there is discrep-ancy between experimental values andor between computedvalues

Finally two semiempirical models (RM1 and PM7) wereused to calculate Δ119891119867

119900298g Semiempirical models are attrac-

tive because they are very rapid and their accuracy continuesto improve [13 14] However RM1 and PM7 were found tobe less accurate than the other approaches used to calculateΔ119891119867119900298g values for compounds in the test set used for this

investigation Even when Δ119891119867119900298g values having very large

(greater than 14 kcalmol) deviations from reference valueswere omitted rms and MAE values for calculated RM1 andPM7 data sets were substantially greater than those of thefour other computational approaches investigated (Tables 2and 3)

4 Conclusion

Because substantial interest exists in developing relativelyrapid and accurate procedures for predicting gas-phase heatof formation values for energetic compounds our overall goalwas to determine which of several computational approachesis most suitable for this endeavor None of the computationalapproaches were uniformly accurate within plusmn20 kcalmolof experimental values (ie the presumably more accuratealternative experimental values)

However four of the computational approaches investi-gated were able tomeet this level of accuracy greater than 51of the time Moreover these four computational approacheswere accurate to within plusmn40 kcal greater than 77 of thetime For relatively simple compounds in which correctionfactors can be used to account for ring strain and so forthand other factors do not make substantial contribution toΔ119891119867119900298g we conclude that the group additivity approach is

about as accurate as those approaches based on higher levelsof theory For compounds that are structurallymore complexthe approach using DFT coupled with the use of isodesmicisogyric and other balanced equations is more accurate butmore time consuming than the DFTAtomic and Groupcontribution method described by Byrd and Rice [6 7] and

10 Advances in Physical Chemistry

the T1 method [8] for this set of compounds However sincecalculated values are often similar and mutually supportiveit seems that a reasonable approach would be to use any (orall) of these four procedures when this level of accuracy isacceptable and the goal is to compare predicted properties ofnew or theoretical compounds with those of structurally sim-ilar compounds whose experimental values andor computedvalues are well established

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] H M Xiao X J Xu and L Qiu Theoretical Design of HighEnergy Density Materials Science Press Beijing China 2008

[2] R E Kirk and D F Othmer Encyclopedia of Chemical Technol-ogy vol 5 Wiley New York NY USA 2004

[3] J Giles ldquoGreen explosives collateral damagerdquo Nature vol 427no 6975 pp 580ndash581 2004

[4] J P Agrawal and J E Field ldquoRecent trends in high-energymaterialsrdquo Progress in Energy and Combustion Science vol 24no 1 pp 1ndash30 1998

[5] J Akhavan The Chemistry of Explosives Royal Society ofChemistry Cambridge UK 2004

[6] E F C Byrd and B M Rice ldquoImproved prediction of heatsof formation of energetic materials using quantum mechanicalcalculationsrdquo Journal of Physical Chemistry A vol 110 no 3 pp1005ndash1013 2006

[7] E F C Byrd and B M Rice ldquoCorrection improved predictionof heats of formation of energetic materials using quantummechanical calculationsrdquo The Journal of Physical Chemistry Avol 113 no 9 p 5813 2009

[8] W S Ohlinger P E Klunzinger B J Deppmeier and W JHehre ldquoEfficient calculation of heats of formationrdquo Journal ofPhysical Chemistry A vol 113 no 10 pp 2165ndash2175 2009

[9] L A Curtiss P C Redfern K Raghavachari V Rassolov andJ A Pople ldquoGaussian-3 theory using reduced Moslashller-PlessetorderrdquoThe Journal of Chemical Physics vol 110 no 10 pp 4703ndash4709 1999

[10] S W Benson and J H Buss ldquoAdditivity rules for the estima-tion of molecular properties Thermodynamic propertiesrdquo TheJournal of Chemical Physics vol 29 no 3 pp 546ndash572 1958

[11] SW Benson F R Cruickshank DM Golden et al ldquoAdditivityrules for the estimation of thermochemical propertiesrdquo Chemi-cal Reviews vol 69 no 3 pp 279ndash324 1969

[12] C J Cramer Essentials of Computational Chemistry Theoriesand Models John Wiley amp Sons New York NY USA 2ndedition 2004

[13] G B Rocha R O Freire A M Simas and J J P Stewart ldquoRM1a reparameterization of AM1 for H C N O P S F Cl Br and IrdquoJournal of Computational Chemistry vol 27 no 10 pp 1101ndash11112006

[14] J J P Stewart ldquoOptimization of parameters for semiempiricalmethods VI more modifications to the NDDO approximationsand re-optimization of parametersrdquo Journal of Molecular Mod-eling vol 19 no 1 pp 1ndash32 2013

[15] Y Zhao andDG Truhlar ldquoTheM06 suite of density functionalsfor main group thermochemistry thermochemical kineticsnoncovalent interactions excited states and transition ele-ments two new functionals and systematic testing of fourM06-class functionals and 12 other functionalsrdquo TheoreticalChemistry Accounts vol 120 no 1ndash3 pp 215ndash241 2008

[16] Y Zhao and D G Truhlar ldquoDensity functionals with broadapplicability in chemistryrdquo Accounts of Chemical Research vol41 no 2 pp 157ndash167 2008

[17] H Y Afeefy J F Liebman and S E Stein ldquoNeutral thermo-chemical datardquo in NIST Chemistry WebBook P J Linstrom andW G Mallard Eds NIST Standard Reference Database no 69National Institute of Standards and Technology GaithersburgMd USA 2005

[18] J B Pedley R D Naylor and S P KirbyThermochemical Dataof Organic Compounds Chapman amp Hall New York NY USA1986

[19] J O Cox and G Pilcher Thermochemistry of Organic andOrganometallic Compounds Academic Press New York NYUSA 1970

[20] OVDorofeeva andMA Suntsova ldquoEnthalpies of formation ofnitromethane and nitrobenzene theory vs experimentrdquo Journalof Chemical Thermodynamics vol 58 pp 221ndash225 2013

[21] O V Dorofeeva O N Ryzhova and M A Suntsova ldquoAccurateprediction of enthalpies of formation of organic azides bycombining G4 theory calculations with an isodesmic reactionschemerdquo Journal of Physical Chemistry A vol 117 no 31 pp6835ndash6845 2013

[22] M A Suntsova and O V Dorofeeva ldquoUse of G4 theoryfor the assessment of inaccuracies in experimental enthalpiesof formation of aliphatic nitro compounds and nitraminesrdquoJournal of Chemical amp Engineering Data vol 59 no 9 pp 2813ndash2826 2014

[23] M A Suntsova and O V Dorofeeva ldquoComment on lsquouse ofG4 theory for the assessment of inaccuracies in experimentalenthalpies of formation of aliphatic nitro compounds andnitraminesrsquordquo Journal of Chemical amp Engineering Data vol 60no 5 pp 1532ndash1533 2015

[24] S P Verevkin V N EmelrsquoYanenko V Diky and O V Doro-feeva ldquoEnthalpies of formation of nitromethane and nitroben-zene new experiments vs quantum chemical calculationsrdquoTheJournal of ChemicalThermodynamics vol 73 pp 163ndash170 2014

[25] CHETAHTheComputer Program for ChemicalThermodynam-ics and Energy Release Evaluation University of SouthAlabamaMobile Ala USA ASTM International West ConshohockenPa USA 2009

[26] NCohen and SWBenson ldquoEstimation of heats of formation oforganic compounds by additivity methodsrdquo Chemical Reviewsvol 93 no 7 pp 2419ndash2438 1993

[27] J A Bumpus and P H Willoughby ldquoOn the heat of formationof nitromethanerdquo Journal of Physical Organic Chemistry vol 21no 9 pp 747ndash757 2008

[28] Y K Knobelrsquo E A Miroshnichenko and Y A LebedevldquoHeats of combustion of nitromethane and dinitromethaneenthalpies of formation of nitromethyl radicals and energies ofdissociation of bonds in nitro derivatives of methanerdquo Bulletinof the Academy of Sciences of the USSR Division of ChemicalScience vol 20 no 3 pp 425ndash428 1971

[29] E A Miroshnichenko T S Konrsquokova Y O Inozemtsev VP VorobrsquoEva Y N Matymhin and S A Shevelev ldquoBondenergies and formation enthalpies of mono- and polyradicals in

Advances in Physical Chemistry 11

nitroalkanes 1 Nitromethanesrdquo Russian Chemical Bulletin vol58 no 4 pp 772ndash776 2009

[30] C Y Lin M W George and P M W Gill ldquoEDF2 a densityfunctional for predicting molecular vibrational frequenciesrdquoAustralian Journal of Chemistry vol 57 no 4 pp 365ndash370 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Page 7: Research Article Calculating Heat of Formation Values of Energetic Compounds…downloads.hindawi.com/journals/apc/2016/5082084.pdf ·  · 2016-03-14Research Article Calculating Heat

Advances in Physical Chemistry 7

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

0minus50 50 100minus100

Experimental values (kcalmol)

(a) T1

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(b) DFTAtomic and Group contribution

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(c) DFTisodesmic

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(d) Group Add

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus100 0 50 100minus50

Experimental values (kcalmol)

(e) PM7

minus100

minus50

0

50

100

Calc

ulat

ed v

alue

s (kc

alm

ol)

minus50 0 50 100minus100

Experimental values (kcalmol)

(f) RM1

Figure 1 Calculated gas-phase heat of formation values versus experimental values Gas-phase heat of formation values were calculated using(1) the multilevel ab initio approach (T1) described by Ohlinger et al [8] as implemented in the Spartanrsquo10 and 14 suite of programs (a) (2) theDFTAtomic and Group contribution approach developed and described by Byrd and Rice [6 7] (b)The experimental values and calculatedvalues used to construct (b) are those published by Byrd and Rice [6 7] (b) is identical to Figure 1a in their manuscript except for the fact thatthe alternative set of experimental Δ119891119867

119900298g reference values are also included (3) Density functional theory using isodesmic isogyric and

other balanced equations as described herein (c) (4)The Benson Group Additivity approach as implemented in the and NIST and CHETAH80 software programs (d) (5) semiempirical theory (PM7 andRM1) as implemented inMOPAC2012 and the Spartan 14 suite of programs ((e)and (f) resp) Open squares represent calculatedΔ119891119867

119900298g values versus the experimentalΔ119891119867

119900298g values Closed circles represent calculated

Δ119891119867119900298g values versus the alternative experimental Δ119891119867

119900298g reference values as described in the text Least square regression analysis and

calculation of 1198772 values were accomplished using KaleidaGraph graphing software (Synergy Software Reading PA) 1198772 values are presentedin Tables 2 and 3

8 Advances in Physical Chemistry

Table 4 Balanced equations used to calculate heat of formation values of compounds in the test set

Isodesmic isogyric or other balanced equations1 Dinitromethane + methanerarr2 nitromethane2 2 dinitromethanerarrmethane + tetranitromethane3 Methyl azide + trinitromethanerarrmethane + azidotrinitromethane4 N-Ethyl-N-nitroethanamine + dimethylaminerarr N-ethyl-N-ethanamine + N-methyl-N-nitromethanamine (DMNO)5 11-Dinitropropane + methyl aziderarr ethane + 1-azido-11-dinitroethane6 2 111-Trinitropropanerarr butane + hexanitroethane7 3 propylnitraterarr2 propane + nitroglycerin8 RDX + 3 nitrosyl hydriderarr3 HNO2 + TTT (hexahydro-135-trinitroso-135-triazine)9 3 1-nitropiperidinerarr2 cyclohexane + RDX10 1-Nitrosopiperidine + TTTrarr2 14-dinitrosopiperazine11 Piperazine + 2 dimethylnitraminerarr 2 dimethylamine + 14-dinitropiperazine12 Bis-222-trinitroethylamine + HNO2 rarr H2 + N-nitro-bis-222-trinitroethylamine13 Benzene + 4-nitroanilinerarr aniline + nitrobenzene14 Phenol + nitrobenzenerarr benzene + 2-nitrophenol15 Phenol + nitrobenzenerarr benzene + 3-nitrophenol16 Phenol + nitrobenzenerarr benzene + 4-nitrophenol17 Aniline + nitrobenzenerarr benzene + m-nitroaniline18 Aniline + nitrobenzenerarr benzene + p-nitroaniline19 Methyl azide + benzenerarrmethane + azidobenzene20 Methyl azide + nitrobenzenerarrmethane + 1-azido-4-nitrobenzene

21 N-Propylpropanamine + 4 1-nitropropane + dimethylnitraminerarr dimethylamine + N-nitro-bis-22-dinitropropylamine (DNPN)+ 4 propane

22 Toluene + nitrobenzenerarr benzene + PNT (1-methyl-4-nitrobenzene)23 Toluene + 2 nitrobenzenerarr2 benzene + 24-DNT (1-methyl-24-dinitrobenzene)24 Methyl azide + toluenerarrmethane + azidomethylbenzene25 Methyl azide + 3-ethylpentanerarrmethane + 3-azido-3-ethylpentane26 Toluene + 135-trinitrobenzenerarr benzene + TNT (246-trinitrotoluene)27 2 2-nitropropane + adamantanerarr2 propane + 22-dinitroadamantane28 Methyl azide + adamantanerarrmethane + 1-azidoadamantane29 Methyl azide + 2-phenylpropanerarrmethane + 2-azido-2-phenylpropane30 trans-Stilbene + 2 135-trinitrobenzenerarr2 benzene + HNS (111015840-(12-ethenediyl)bis[246- trinitrobenzene])31 Isopropyl nitrite + methanerarr propane + methyl nitrite32 Propyl nitrate + methanerarr propane + methyl nitrate33 2 1-Nitropropane + methanerarr2 propane + dinitromethane34 Propyl nitrite + ethanerarr propane + ethyl nitrite35 Propyl nitrate + ethanerarr propane + ethyl nitrate36 Isopropyl nitriterarr propyl nitrite37 2-Nitropropane + 2-methylpropanerarr 2-methyl-2-nitropropane + propane38 Isopropyl nitrite + butanerarr n-butyl nitrite + propane39 Isopropyl nitrite + isobutanerarr t-butyl nitrite + propane40 2 1-pyrroline + tetrahydrofuran + 2methyl nitraterarr H2 + 34-furazandimethanol dinitrate + 2 cyclopentane41 Piperidine + dimethylnitraminerarr 1-nitropiperidine + dimethylamine42 Phenyl radical + nitric oxiderarr nitrosobenzene43 Toluene + 1-nitropropanerarr propane + nitromethylbenzene44 Toluene + 11-dinitropropanerarr propane + dinitromethylbenzene45 2 Toluene + nitrobenzenerarr2 benzene + 13-dimethyl-2-nitrobenzene

Advances in Physical Chemistry 9

to be 29 kcalmol with a mean absolute error (MAE) of23 kcalmol and a maximum deviation of 69 kcalmol Thiscompares with an rms deviation of 33 kcalmol a MAE of24 kcalmol and a maximum deviation of 99 kcalmol usingdata calculated by Byrd andRice [6 7] It should be noted thatthe T1 procedure has been previously shown to reproduceexperimental heat of formation values of a large (1805) set oforganicmolecules with an rms deviation of 275 kcalmol anda MAE of 203 kcalmol [8] Clearly the rms andMAE valuesfor the T1 approach reported here agree well with those valuesreported for the larger data set

These results led us to compare older approaches usedto predictcalculate Δ119891119867

119900298g values Specifically we used

Bensonrsquos group additivity (or group contribution) approach[10 11] We also used density functional theory coupled withthe use of selected isodesmic isogyric and other balancedequations One disadvantage of Bensonrsquos group additivityapproach is that group values for some of the substructuresof several compounds in the test set are not availableWe were partially able to overcome this problem by usingexisting data which allowed us to calculate some of thesegroup values In total we were able to use Bensonrsquos groupadditivity approach to calculate Δ119891119867

119900298g values for 36 of 45

compounds in the test set This approach yielded calculatedresults in which 64 (2336) of the calculated Δ119891119867

119900298g

values were within plusmn20 kcalmol of experimental valuesThe rms deviation from experiment for the predicted groupadditivity gas-phase heat of formation valueswas 55 kcalmolwith an MAE of 31 kcalmol with a maximum deviationof 212 kcalmol for HNS A relatively large deviation fromexperiment of 148 kcalmol was also found for nitroglycerinA significant drawback to the use of group additivity theoryis that calculated Δ119891119867

119900298g values are sometimes affected

by structural features that are not adequately addressed bytheory Although Δ119891119867

119900298g values for some strained com-

pounds can be accurately predicted by adding correctionfactors for structural characteristics such as ring strain thepresence of gauche carbons and C1ndashC5 repulsions contri-bution of certain other structural features do not appear tobe adequately addressed by group additivity theory HNSand nitroglycerin seem to fall into this category Whenthese compounds were eliminated from the test set the rmsdeviation from experiment for the predicted group additivityΔ119891119867119900298g values was found to be 35 kcalmol with an MAE

of 22 kcalmol and a maximum deviation of 115 kcalmol forthe remaining 34 compoundsThe relevant point is that groupadditivity theory is often quite accurate however onemust becareful regarding its application

Density functional theory coupledwith the use of selectedbalanced reactions was also used to calculate Δ119891119867

119900298g values

for comparison to the test setThe reactions used in this inves-tigation are presented in Table 4 We determined that therms deviation from experiment for the calculated Δ119891119867

119900298g

values was 15 kcalmol with an MAE of 11 kcalmol and amaximum deviation of 38 kcalmol This approach yieldedcalculated results in which 82 (3745) of theΔ119891119867

119900298g values

werewithinplusmn20 kcalmol of experimental values Despite thefact that for time considerations we selected a medium size

basis set density functional theory coupled with the use ofisodesmic and other balanced equations was still the mostaccurate approach of the sixmethodswe compared Althoughaccurate it is necessary to mention some problems with thisapproach First of all different balanced equations can leadto different Δ119891119867

119900298g values Often such differences are small

But sometimes such differences can be substantial Cramer[12] has noted that ldquothe construction of an isodesmic equationis something of an art depending on chemical intuition andavailable experimental datardquo

It should also be mentioned that when computationtime is not a consideration the use of larger basis setsmight be expected to result in even greater accuracy IndeedDorofeeva and colleagues [21ndash23] have have shown thatthe use of high level computational theory coupled withmultiple isodesmic isogyric and other balanced equationscan result in calculation of Δ119891119867

119900298g values that are suffi-

ciently accurate that they feel confident in recommendingconsensus values in many cases where there is discrep-ancy between experimental values andor between computedvalues

Finally two semiempirical models (RM1 and PM7) wereused to calculate Δ119891119867

119900298g Semiempirical models are attrac-

tive because they are very rapid and their accuracy continuesto improve [13 14] However RM1 and PM7 were found tobe less accurate than the other approaches used to calculateΔ119891119867119900298g values for compounds in the test set used for this

investigation Even when Δ119891119867119900298g values having very large

(greater than 14 kcalmol) deviations from reference valueswere omitted rms and MAE values for calculated RM1 andPM7 data sets were substantially greater than those of thefour other computational approaches investigated (Tables 2and 3)

4 Conclusion

Because substantial interest exists in developing relativelyrapid and accurate procedures for predicting gas-phase heatof formation values for energetic compounds our overall goalwas to determine which of several computational approachesis most suitable for this endeavor None of the computationalapproaches were uniformly accurate within plusmn20 kcalmolof experimental values (ie the presumably more accuratealternative experimental values)

However four of the computational approaches investi-gated were able tomeet this level of accuracy greater than 51of the time Moreover these four computational approacheswere accurate to within plusmn40 kcal greater than 77 of thetime For relatively simple compounds in which correctionfactors can be used to account for ring strain and so forthand other factors do not make substantial contribution toΔ119891119867119900298g we conclude that the group additivity approach is

about as accurate as those approaches based on higher levelsof theory For compounds that are structurallymore complexthe approach using DFT coupled with the use of isodesmicisogyric and other balanced equations is more accurate butmore time consuming than the DFTAtomic and Groupcontribution method described by Byrd and Rice [6 7] and

10 Advances in Physical Chemistry

the T1 method [8] for this set of compounds However sincecalculated values are often similar and mutually supportiveit seems that a reasonable approach would be to use any (orall) of these four procedures when this level of accuracy isacceptable and the goal is to compare predicted properties ofnew or theoretical compounds with those of structurally sim-ilar compounds whose experimental values andor computedvalues are well established

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] H M Xiao X J Xu and L Qiu Theoretical Design of HighEnergy Density Materials Science Press Beijing China 2008

[2] R E Kirk and D F Othmer Encyclopedia of Chemical Technol-ogy vol 5 Wiley New York NY USA 2004

[3] J Giles ldquoGreen explosives collateral damagerdquo Nature vol 427no 6975 pp 580ndash581 2004

[4] J P Agrawal and J E Field ldquoRecent trends in high-energymaterialsrdquo Progress in Energy and Combustion Science vol 24no 1 pp 1ndash30 1998

[5] J Akhavan The Chemistry of Explosives Royal Society ofChemistry Cambridge UK 2004

[6] E F C Byrd and B M Rice ldquoImproved prediction of heatsof formation of energetic materials using quantum mechanicalcalculationsrdquo Journal of Physical Chemistry A vol 110 no 3 pp1005ndash1013 2006

[7] E F C Byrd and B M Rice ldquoCorrection improved predictionof heats of formation of energetic materials using quantummechanical calculationsrdquo The Journal of Physical Chemistry Avol 113 no 9 p 5813 2009

[8] W S Ohlinger P E Klunzinger B J Deppmeier and W JHehre ldquoEfficient calculation of heats of formationrdquo Journal ofPhysical Chemistry A vol 113 no 10 pp 2165ndash2175 2009

[9] L A Curtiss P C Redfern K Raghavachari V Rassolov andJ A Pople ldquoGaussian-3 theory using reduced Moslashller-PlessetorderrdquoThe Journal of Chemical Physics vol 110 no 10 pp 4703ndash4709 1999

[10] S W Benson and J H Buss ldquoAdditivity rules for the estima-tion of molecular properties Thermodynamic propertiesrdquo TheJournal of Chemical Physics vol 29 no 3 pp 546ndash572 1958

[11] SW Benson F R Cruickshank DM Golden et al ldquoAdditivityrules for the estimation of thermochemical propertiesrdquo Chemi-cal Reviews vol 69 no 3 pp 279ndash324 1969

[12] C J Cramer Essentials of Computational Chemistry Theoriesand Models John Wiley amp Sons New York NY USA 2ndedition 2004

[13] G B Rocha R O Freire A M Simas and J J P Stewart ldquoRM1a reparameterization of AM1 for H C N O P S F Cl Br and IrdquoJournal of Computational Chemistry vol 27 no 10 pp 1101ndash11112006

[14] J J P Stewart ldquoOptimization of parameters for semiempiricalmethods VI more modifications to the NDDO approximationsand re-optimization of parametersrdquo Journal of Molecular Mod-eling vol 19 no 1 pp 1ndash32 2013

[15] Y Zhao andDG Truhlar ldquoTheM06 suite of density functionalsfor main group thermochemistry thermochemical kineticsnoncovalent interactions excited states and transition ele-ments two new functionals and systematic testing of fourM06-class functionals and 12 other functionalsrdquo TheoreticalChemistry Accounts vol 120 no 1ndash3 pp 215ndash241 2008

[16] Y Zhao and D G Truhlar ldquoDensity functionals with broadapplicability in chemistryrdquo Accounts of Chemical Research vol41 no 2 pp 157ndash167 2008

[17] H Y Afeefy J F Liebman and S E Stein ldquoNeutral thermo-chemical datardquo in NIST Chemistry WebBook P J Linstrom andW G Mallard Eds NIST Standard Reference Database no 69National Institute of Standards and Technology GaithersburgMd USA 2005

[18] J B Pedley R D Naylor and S P KirbyThermochemical Dataof Organic Compounds Chapman amp Hall New York NY USA1986

[19] J O Cox and G Pilcher Thermochemistry of Organic andOrganometallic Compounds Academic Press New York NYUSA 1970

[20] OVDorofeeva andMA Suntsova ldquoEnthalpies of formation ofnitromethane and nitrobenzene theory vs experimentrdquo Journalof Chemical Thermodynamics vol 58 pp 221ndash225 2013

[21] O V Dorofeeva O N Ryzhova and M A Suntsova ldquoAccurateprediction of enthalpies of formation of organic azides bycombining G4 theory calculations with an isodesmic reactionschemerdquo Journal of Physical Chemistry A vol 117 no 31 pp6835ndash6845 2013

[22] M A Suntsova and O V Dorofeeva ldquoUse of G4 theoryfor the assessment of inaccuracies in experimental enthalpiesof formation of aliphatic nitro compounds and nitraminesrdquoJournal of Chemical amp Engineering Data vol 59 no 9 pp 2813ndash2826 2014

[23] M A Suntsova and O V Dorofeeva ldquoComment on lsquouse ofG4 theory for the assessment of inaccuracies in experimentalenthalpies of formation of aliphatic nitro compounds andnitraminesrsquordquo Journal of Chemical amp Engineering Data vol 60no 5 pp 1532ndash1533 2015

[24] S P Verevkin V N EmelrsquoYanenko V Diky and O V Doro-feeva ldquoEnthalpies of formation of nitromethane and nitroben-zene new experiments vs quantum chemical calculationsrdquoTheJournal of ChemicalThermodynamics vol 73 pp 163ndash170 2014

[25] CHETAHTheComputer Program for ChemicalThermodynam-ics and Energy Release Evaluation University of SouthAlabamaMobile Ala USA ASTM International West ConshohockenPa USA 2009

[26] NCohen and SWBenson ldquoEstimation of heats of formation oforganic compounds by additivity methodsrdquo Chemical Reviewsvol 93 no 7 pp 2419ndash2438 1993

[27] J A Bumpus and P H Willoughby ldquoOn the heat of formationof nitromethanerdquo Journal of Physical Organic Chemistry vol 21no 9 pp 747ndash757 2008

[28] Y K Knobelrsquo E A Miroshnichenko and Y A LebedevldquoHeats of combustion of nitromethane and dinitromethaneenthalpies of formation of nitromethyl radicals and energies ofdissociation of bonds in nitro derivatives of methanerdquo Bulletinof the Academy of Sciences of the USSR Division of ChemicalScience vol 20 no 3 pp 425ndash428 1971

[29] E A Miroshnichenko T S Konrsquokova Y O Inozemtsev VP VorobrsquoEva Y N Matymhin and S A Shevelev ldquoBondenergies and formation enthalpies of mono- and polyradicals in

Advances in Physical Chemistry 11

nitroalkanes 1 Nitromethanesrdquo Russian Chemical Bulletin vol58 no 4 pp 772ndash776 2009

[30] C Y Lin M W George and P M W Gill ldquoEDF2 a densityfunctional for predicting molecular vibrational frequenciesrdquoAustralian Journal of Chemistry vol 57 no 4 pp 365ndash370 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Page 8: Research Article Calculating Heat of Formation Values of Energetic Compounds…downloads.hindawi.com/journals/apc/2016/5082084.pdf ·  · 2016-03-14Research Article Calculating Heat

8 Advances in Physical Chemistry

Table 4 Balanced equations used to calculate heat of formation values of compounds in the test set

Isodesmic isogyric or other balanced equations1 Dinitromethane + methanerarr2 nitromethane2 2 dinitromethanerarrmethane + tetranitromethane3 Methyl azide + trinitromethanerarrmethane + azidotrinitromethane4 N-Ethyl-N-nitroethanamine + dimethylaminerarr N-ethyl-N-ethanamine + N-methyl-N-nitromethanamine (DMNO)5 11-Dinitropropane + methyl aziderarr ethane + 1-azido-11-dinitroethane6 2 111-Trinitropropanerarr butane + hexanitroethane7 3 propylnitraterarr2 propane + nitroglycerin8 RDX + 3 nitrosyl hydriderarr3 HNO2 + TTT (hexahydro-135-trinitroso-135-triazine)9 3 1-nitropiperidinerarr2 cyclohexane + RDX10 1-Nitrosopiperidine + TTTrarr2 14-dinitrosopiperazine11 Piperazine + 2 dimethylnitraminerarr 2 dimethylamine + 14-dinitropiperazine12 Bis-222-trinitroethylamine + HNO2 rarr H2 + N-nitro-bis-222-trinitroethylamine13 Benzene + 4-nitroanilinerarr aniline + nitrobenzene14 Phenol + nitrobenzenerarr benzene + 2-nitrophenol15 Phenol + nitrobenzenerarr benzene + 3-nitrophenol16 Phenol + nitrobenzenerarr benzene + 4-nitrophenol17 Aniline + nitrobenzenerarr benzene + m-nitroaniline18 Aniline + nitrobenzenerarr benzene + p-nitroaniline19 Methyl azide + benzenerarrmethane + azidobenzene20 Methyl azide + nitrobenzenerarrmethane + 1-azido-4-nitrobenzene

21 N-Propylpropanamine + 4 1-nitropropane + dimethylnitraminerarr dimethylamine + N-nitro-bis-22-dinitropropylamine (DNPN)+ 4 propane

22 Toluene + nitrobenzenerarr benzene + PNT (1-methyl-4-nitrobenzene)23 Toluene + 2 nitrobenzenerarr2 benzene + 24-DNT (1-methyl-24-dinitrobenzene)24 Methyl azide + toluenerarrmethane + azidomethylbenzene25 Methyl azide + 3-ethylpentanerarrmethane + 3-azido-3-ethylpentane26 Toluene + 135-trinitrobenzenerarr benzene + TNT (246-trinitrotoluene)27 2 2-nitropropane + adamantanerarr2 propane + 22-dinitroadamantane28 Methyl azide + adamantanerarrmethane + 1-azidoadamantane29 Methyl azide + 2-phenylpropanerarrmethane + 2-azido-2-phenylpropane30 trans-Stilbene + 2 135-trinitrobenzenerarr2 benzene + HNS (111015840-(12-ethenediyl)bis[246- trinitrobenzene])31 Isopropyl nitrite + methanerarr propane + methyl nitrite32 Propyl nitrate + methanerarr propane + methyl nitrate33 2 1-Nitropropane + methanerarr2 propane + dinitromethane34 Propyl nitrite + ethanerarr propane + ethyl nitrite35 Propyl nitrate + ethanerarr propane + ethyl nitrate36 Isopropyl nitriterarr propyl nitrite37 2-Nitropropane + 2-methylpropanerarr 2-methyl-2-nitropropane + propane38 Isopropyl nitrite + butanerarr n-butyl nitrite + propane39 Isopropyl nitrite + isobutanerarr t-butyl nitrite + propane40 2 1-pyrroline + tetrahydrofuran + 2methyl nitraterarr H2 + 34-furazandimethanol dinitrate + 2 cyclopentane41 Piperidine + dimethylnitraminerarr 1-nitropiperidine + dimethylamine42 Phenyl radical + nitric oxiderarr nitrosobenzene43 Toluene + 1-nitropropanerarr propane + nitromethylbenzene44 Toluene + 11-dinitropropanerarr propane + dinitromethylbenzene45 2 Toluene + nitrobenzenerarr2 benzene + 13-dimethyl-2-nitrobenzene

Advances in Physical Chemistry 9

to be 29 kcalmol with a mean absolute error (MAE) of23 kcalmol and a maximum deviation of 69 kcalmol Thiscompares with an rms deviation of 33 kcalmol a MAE of24 kcalmol and a maximum deviation of 99 kcalmol usingdata calculated by Byrd andRice [6 7] It should be noted thatthe T1 procedure has been previously shown to reproduceexperimental heat of formation values of a large (1805) set oforganicmolecules with an rms deviation of 275 kcalmol anda MAE of 203 kcalmol [8] Clearly the rms andMAE valuesfor the T1 approach reported here agree well with those valuesreported for the larger data set

These results led us to compare older approaches usedto predictcalculate Δ119891119867

119900298g values Specifically we used

Bensonrsquos group additivity (or group contribution) approach[10 11] We also used density functional theory coupled withthe use of selected isodesmic isogyric and other balancedequations One disadvantage of Bensonrsquos group additivityapproach is that group values for some of the substructuresof several compounds in the test set are not availableWe were partially able to overcome this problem by usingexisting data which allowed us to calculate some of thesegroup values In total we were able to use Bensonrsquos groupadditivity approach to calculate Δ119891119867

119900298g values for 36 of 45

compounds in the test set This approach yielded calculatedresults in which 64 (2336) of the calculated Δ119891119867

119900298g

values were within plusmn20 kcalmol of experimental valuesThe rms deviation from experiment for the predicted groupadditivity gas-phase heat of formation valueswas 55 kcalmolwith an MAE of 31 kcalmol with a maximum deviationof 212 kcalmol for HNS A relatively large deviation fromexperiment of 148 kcalmol was also found for nitroglycerinA significant drawback to the use of group additivity theoryis that calculated Δ119891119867

119900298g values are sometimes affected

by structural features that are not adequately addressed bytheory Although Δ119891119867

119900298g values for some strained com-

pounds can be accurately predicted by adding correctionfactors for structural characteristics such as ring strain thepresence of gauche carbons and C1ndashC5 repulsions contri-bution of certain other structural features do not appear tobe adequately addressed by group additivity theory HNSand nitroglycerin seem to fall into this category Whenthese compounds were eliminated from the test set the rmsdeviation from experiment for the predicted group additivityΔ119891119867119900298g values was found to be 35 kcalmol with an MAE

of 22 kcalmol and a maximum deviation of 115 kcalmol forthe remaining 34 compoundsThe relevant point is that groupadditivity theory is often quite accurate however onemust becareful regarding its application

Density functional theory coupledwith the use of selectedbalanced reactions was also used to calculate Δ119891119867

119900298g values

for comparison to the test setThe reactions used in this inves-tigation are presented in Table 4 We determined that therms deviation from experiment for the calculated Δ119891119867

119900298g

values was 15 kcalmol with an MAE of 11 kcalmol and amaximum deviation of 38 kcalmol This approach yieldedcalculated results in which 82 (3745) of theΔ119891119867

119900298g values

werewithinplusmn20 kcalmol of experimental values Despite thefact that for time considerations we selected a medium size

basis set density functional theory coupled with the use ofisodesmic and other balanced equations was still the mostaccurate approach of the sixmethodswe compared Althoughaccurate it is necessary to mention some problems with thisapproach First of all different balanced equations can leadto different Δ119891119867

119900298g values Often such differences are small

But sometimes such differences can be substantial Cramer[12] has noted that ldquothe construction of an isodesmic equationis something of an art depending on chemical intuition andavailable experimental datardquo

It should also be mentioned that when computationtime is not a consideration the use of larger basis setsmight be expected to result in even greater accuracy IndeedDorofeeva and colleagues [21ndash23] have have shown thatthe use of high level computational theory coupled withmultiple isodesmic isogyric and other balanced equationscan result in calculation of Δ119891119867

119900298g values that are suffi-

ciently accurate that they feel confident in recommendingconsensus values in many cases where there is discrep-ancy between experimental values andor between computedvalues

Finally two semiempirical models (RM1 and PM7) wereused to calculate Δ119891119867

119900298g Semiempirical models are attrac-

tive because they are very rapid and their accuracy continuesto improve [13 14] However RM1 and PM7 were found tobe less accurate than the other approaches used to calculateΔ119891119867119900298g values for compounds in the test set used for this

investigation Even when Δ119891119867119900298g values having very large

(greater than 14 kcalmol) deviations from reference valueswere omitted rms and MAE values for calculated RM1 andPM7 data sets were substantially greater than those of thefour other computational approaches investigated (Tables 2and 3)

4 Conclusion

Because substantial interest exists in developing relativelyrapid and accurate procedures for predicting gas-phase heatof formation values for energetic compounds our overall goalwas to determine which of several computational approachesis most suitable for this endeavor None of the computationalapproaches were uniformly accurate within plusmn20 kcalmolof experimental values (ie the presumably more accuratealternative experimental values)

However four of the computational approaches investi-gated were able tomeet this level of accuracy greater than 51of the time Moreover these four computational approacheswere accurate to within plusmn40 kcal greater than 77 of thetime For relatively simple compounds in which correctionfactors can be used to account for ring strain and so forthand other factors do not make substantial contribution toΔ119891119867119900298g we conclude that the group additivity approach is

about as accurate as those approaches based on higher levelsof theory For compounds that are structurallymore complexthe approach using DFT coupled with the use of isodesmicisogyric and other balanced equations is more accurate butmore time consuming than the DFTAtomic and Groupcontribution method described by Byrd and Rice [6 7] and

10 Advances in Physical Chemistry

the T1 method [8] for this set of compounds However sincecalculated values are often similar and mutually supportiveit seems that a reasonable approach would be to use any (orall) of these four procedures when this level of accuracy isacceptable and the goal is to compare predicted properties ofnew or theoretical compounds with those of structurally sim-ilar compounds whose experimental values andor computedvalues are well established

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] H M Xiao X J Xu and L Qiu Theoretical Design of HighEnergy Density Materials Science Press Beijing China 2008

[2] R E Kirk and D F Othmer Encyclopedia of Chemical Technol-ogy vol 5 Wiley New York NY USA 2004

[3] J Giles ldquoGreen explosives collateral damagerdquo Nature vol 427no 6975 pp 580ndash581 2004

[4] J P Agrawal and J E Field ldquoRecent trends in high-energymaterialsrdquo Progress in Energy and Combustion Science vol 24no 1 pp 1ndash30 1998

[5] J Akhavan The Chemistry of Explosives Royal Society ofChemistry Cambridge UK 2004

[6] E F C Byrd and B M Rice ldquoImproved prediction of heatsof formation of energetic materials using quantum mechanicalcalculationsrdquo Journal of Physical Chemistry A vol 110 no 3 pp1005ndash1013 2006

[7] E F C Byrd and B M Rice ldquoCorrection improved predictionof heats of formation of energetic materials using quantummechanical calculationsrdquo The Journal of Physical Chemistry Avol 113 no 9 p 5813 2009

[8] W S Ohlinger P E Klunzinger B J Deppmeier and W JHehre ldquoEfficient calculation of heats of formationrdquo Journal ofPhysical Chemistry A vol 113 no 10 pp 2165ndash2175 2009

[9] L A Curtiss P C Redfern K Raghavachari V Rassolov andJ A Pople ldquoGaussian-3 theory using reduced Moslashller-PlessetorderrdquoThe Journal of Chemical Physics vol 110 no 10 pp 4703ndash4709 1999

[10] S W Benson and J H Buss ldquoAdditivity rules for the estima-tion of molecular properties Thermodynamic propertiesrdquo TheJournal of Chemical Physics vol 29 no 3 pp 546ndash572 1958

[11] SW Benson F R Cruickshank DM Golden et al ldquoAdditivityrules for the estimation of thermochemical propertiesrdquo Chemi-cal Reviews vol 69 no 3 pp 279ndash324 1969

[12] C J Cramer Essentials of Computational Chemistry Theoriesand Models John Wiley amp Sons New York NY USA 2ndedition 2004

[13] G B Rocha R O Freire A M Simas and J J P Stewart ldquoRM1a reparameterization of AM1 for H C N O P S F Cl Br and IrdquoJournal of Computational Chemistry vol 27 no 10 pp 1101ndash11112006

[14] J J P Stewart ldquoOptimization of parameters for semiempiricalmethods VI more modifications to the NDDO approximationsand re-optimization of parametersrdquo Journal of Molecular Mod-eling vol 19 no 1 pp 1ndash32 2013

[15] Y Zhao andDG Truhlar ldquoTheM06 suite of density functionalsfor main group thermochemistry thermochemical kineticsnoncovalent interactions excited states and transition ele-ments two new functionals and systematic testing of fourM06-class functionals and 12 other functionalsrdquo TheoreticalChemistry Accounts vol 120 no 1ndash3 pp 215ndash241 2008

[16] Y Zhao and D G Truhlar ldquoDensity functionals with broadapplicability in chemistryrdquo Accounts of Chemical Research vol41 no 2 pp 157ndash167 2008

[17] H Y Afeefy J F Liebman and S E Stein ldquoNeutral thermo-chemical datardquo in NIST Chemistry WebBook P J Linstrom andW G Mallard Eds NIST Standard Reference Database no 69National Institute of Standards and Technology GaithersburgMd USA 2005

[18] J B Pedley R D Naylor and S P KirbyThermochemical Dataof Organic Compounds Chapman amp Hall New York NY USA1986

[19] J O Cox and G Pilcher Thermochemistry of Organic andOrganometallic Compounds Academic Press New York NYUSA 1970

[20] OVDorofeeva andMA Suntsova ldquoEnthalpies of formation ofnitromethane and nitrobenzene theory vs experimentrdquo Journalof Chemical Thermodynamics vol 58 pp 221ndash225 2013

[21] O V Dorofeeva O N Ryzhova and M A Suntsova ldquoAccurateprediction of enthalpies of formation of organic azides bycombining G4 theory calculations with an isodesmic reactionschemerdquo Journal of Physical Chemistry A vol 117 no 31 pp6835ndash6845 2013

[22] M A Suntsova and O V Dorofeeva ldquoUse of G4 theoryfor the assessment of inaccuracies in experimental enthalpiesof formation of aliphatic nitro compounds and nitraminesrdquoJournal of Chemical amp Engineering Data vol 59 no 9 pp 2813ndash2826 2014

[23] M A Suntsova and O V Dorofeeva ldquoComment on lsquouse ofG4 theory for the assessment of inaccuracies in experimentalenthalpies of formation of aliphatic nitro compounds andnitraminesrsquordquo Journal of Chemical amp Engineering Data vol 60no 5 pp 1532ndash1533 2015

[24] S P Verevkin V N EmelrsquoYanenko V Diky and O V Doro-feeva ldquoEnthalpies of formation of nitromethane and nitroben-zene new experiments vs quantum chemical calculationsrdquoTheJournal of ChemicalThermodynamics vol 73 pp 163ndash170 2014

[25] CHETAHTheComputer Program for ChemicalThermodynam-ics and Energy Release Evaluation University of SouthAlabamaMobile Ala USA ASTM International West ConshohockenPa USA 2009

[26] NCohen and SWBenson ldquoEstimation of heats of formation oforganic compounds by additivity methodsrdquo Chemical Reviewsvol 93 no 7 pp 2419ndash2438 1993

[27] J A Bumpus and P H Willoughby ldquoOn the heat of formationof nitromethanerdquo Journal of Physical Organic Chemistry vol 21no 9 pp 747ndash757 2008

[28] Y K Knobelrsquo E A Miroshnichenko and Y A LebedevldquoHeats of combustion of nitromethane and dinitromethaneenthalpies of formation of nitromethyl radicals and energies ofdissociation of bonds in nitro derivatives of methanerdquo Bulletinof the Academy of Sciences of the USSR Division of ChemicalScience vol 20 no 3 pp 425ndash428 1971

[29] E A Miroshnichenko T S Konrsquokova Y O Inozemtsev VP VorobrsquoEva Y N Matymhin and S A Shevelev ldquoBondenergies and formation enthalpies of mono- and polyradicals in

Advances in Physical Chemistry 11

nitroalkanes 1 Nitromethanesrdquo Russian Chemical Bulletin vol58 no 4 pp 772ndash776 2009

[30] C Y Lin M W George and P M W Gill ldquoEDF2 a densityfunctional for predicting molecular vibrational frequenciesrdquoAustralian Journal of Chemistry vol 57 no 4 pp 365ndash370 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Page 9: Research Article Calculating Heat of Formation Values of Energetic Compounds…downloads.hindawi.com/journals/apc/2016/5082084.pdf ·  · 2016-03-14Research Article Calculating Heat

Advances in Physical Chemistry 9

to be 29 kcalmol with a mean absolute error (MAE) of23 kcalmol and a maximum deviation of 69 kcalmol Thiscompares with an rms deviation of 33 kcalmol a MAE of24 kcalmol and a maximum deviation of 99 kcalmol usingdata calculated by Byrd andRice [6 7] It should be noted thatthe T1 procedure has been previously shown to reproduceexperimental heat of formation values of a large (1805) set oforganicmolecules with an rms deviation of 275 kcalmol anda MAE of 203 kcalmol [8] Clearly the rms andMAE valuesfor the T1 approach reported here agree well with those valuesreported for the larger data set

These results led us to compare older approaches usedto predictcalculate Δ119891119867

119900298g values Specifically we used

Bensonrsquos group additivity (or group contribution) approach[10 11] We also used density functional theory coupled withthe use of selected isodesmic isogyric and other balancedequations One disadvantage of Bensonrsquos group additivityapproach is that group values for some of the substructuresof several compounds in the test set are not availableWe were partially able to overcome this problem by usingexisting data which allowed us to calculate some of thesegroup values In total we were able to use Bensonrsquos groupadditivity approach to calculate Δ119891119867

119900298g values for 36 of 45

compounds in the test set This approach yielded calculatedresults in which 64 (2336) of the calculated Δ119891119867

119900298g

values were within plusmn20 kcalmol of experimental valuesThe rms deviation from experiment for the predicted groupadditivity gas-phase heat of formation valueswas 55 kcalmolwith an MAE of 31 kcalmol with a maximum deviationof 212 kcalmol for HNS A relatively large deviation fromexperiment of 148 kcalmol was also found for nitroglycerinA significant drawback to the use of group additivity theoryis that calculated Δ119891119867

119900298g values are sometimes affected

by structural features that are not adequately addressed bytheory Although Δ119891119867

119900298g values for some strained com-

pounds can be accurately predicted by adding correctionfactors for structural characteristics such as ring strain thepresence of gauche carbons and C1ndashC5 repulsions contri-bution of certain other structural features do not appear tobe adequately addressed by group additivity theory HNSand nitroglycerin seem to fall into this category Whenthese compounds were eliminated from the test set the rmsdeviation from experiment for the predicted group additivityΔ119891119867119900298g values was found to be 35 kcalmol with an MAE

of 22 kcalmol and a maximum deviation of 115 kcalmol forthe remaining 34 compoundsThe relevant point is that groupadditivity theory is often quite accurate however onemust becareful regarding its application

Density functional theory coupledwith the use of selectedbalanced reactions was also used to calculate Δ119891119867

119900298g values

for comparison to the test setThe reactions used in this inves-tigation are presented in Table 4 We determined that therms deviation from experiment for the calculated Δ119891119867

119900298g

values was 15 kcalmol with an MAE of 11 kcalmol and amaximum deviation of 38 kcalmol This approach yieldedcalculated results in which 82 (3745) of theΔ119891119867

119900298g values

werewithinplusmn20 kcalmol of experimental values Despite thefact that for time considerations we selected a medium size

basis set density functional theory coupled with the use ofisodesmic and other balanced equations was still the mostaccurate approach of the sixmethodswe compared Althoughaccurate it is necessary to mention some problems with thisapproach First of all different balanced equations can leadto different Δ119891119867

119900298g values Often such differences are small

But sometimes such differences can be substantial Cramer[12] has noted that ldquothe construction of an isodesmic equationis something of an art depending on chemical intuition andavailable experimental datardquo

It should also be mentioned that when computationtime is not a consideration the use of larger basis setsmight be expected to result in even greater accuracy IndeedDorofeeva and colleagues [21ndash23] have have shown thatthe use of high level computational theory coupled withmultiple isodesmic isogyric and other balanced equationscan result in calculation of Δ119891119867

119900298g values that are suffi-

ciently accurate that they feel confident in recommendingconsensus values in many cases where there is discrep-ancy between experimental values andor between computedvalues

Finally two semiempirical models (RM1 and PM7) wereused to calculate Δ119891119867

119900298g Semiempirical models are attrac-

tive because they are very rapid and their accuracy continuesto improve [13 14] However RM1 and PM7 were found tobe less accurate than the other approaches used to calculateΔ119891119867119900298g values for compounds in the test set used for this

investigation Even when Δ119891119867119900298g values having very large

(greater than 14 kcalmol) deviations from reference valueswere omitted rms and MAE values for calculated RM1 andPM7 data sets were substantially greater than those of thefour other computational approaches investigated (Tables 2and 3)

4 Conclusion

Because substantial interest exists in developing relativelyrapid and accurate procedures for predicting gas-phase heatof formation values for energetic compounds our overall goalwas to determine which of several computational approachesis most suitable for this endeavor None of the computationalapproaches were uniformly accurate within plusmn20 kcalmolof experimental values (ie the presumably more accuratealternative experimental values)

However four of the computational approaches investi-gated were able tomeet this level of accuracy greater than 51of the time Moreover these four computational approacheswere accurate to within plusmn40 kcal greater than 77 of thetime For relatively simple compounds in which correctionfactors can be used to account for ring strain and so forthand other factors do not make substantial contribution toΔ119891119867119900298g we conclude that the group additivity approach is

about as accurate as those approaches based on higher levelsof theory For compounds that are structurallymore complexthe approach using DFT coupled with the use of isodesmicisogyric and other balanced equations is more accurate butmore time consuming than the DFTAtomic and Groupcontribution method described by Byrd and Rice [6 7] and

10 Advances in Physical Chemistry

the T1 method [8] for this set of compounds However sincecalculated values are often similar and mutually supportiveit seems that a reasonable approach would be to use any (orall) of these four procedures when this level of accuracy isacceptable and the goal is to compare predicted properties ofnew or theoretical compounds with those of structurally sim-ilar compounds whose experimental values andor computedvalues are well established

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] H M Xiao X J Xu and L Qiu Theoretical Design of HighEnergy Density Materials Science Press Beijing China 2008

[2] R E Kirk and D F Othmer Encyclopedia of Chemical Technol-ogy vol 5 Wiley New York NY USA 2004

[3] J Giles ldquoGreen explosives collateral damagerdquo Nature vol 427no 6975 pp 580ndash581 2004

[4] J P Agrawal and J E Field ldquoRecent trends in high-energymaterialsrdquo Progress in Energy and Combustion Science vol 24no 1 pp 1ndash30 1998

[5] J Akhavan The Chemistry of Explosives Royal Society ofChemistry Cambridge UK 2004

[6] E F C Byrd and B M Rice ldquoImproved prediction of heatsof formation of energetic materials using quantum mechanicalcalculationsrdquo Journal of Physical Chemistry A vol 110 no 3 pp1005ndash1013 2006

[7] E F C Byrd and B M Rice ldquoCorrection improved predictionof heats of formation of energetic materials using quantummechanical calculationsrdquo The Journal of Physical Chemistry Avol 113 no 9 p 5813 2009

[8] W S Ohlinger P E Klunzinger B J Deppmeier and W JHehre ldquoEfficient calculation of heats of formationrdquo Journal ofPhysical Chemistry A vol 113 no 10 pp 2165ndash2175 2009

[9] L A Curtiss P C Redfern K Raghavachari V Rassolov andJ A Pople ldquoGaussian-3 theory using reduced Moslashller-PlessetorderrdquoThe Journal of Chemical Physics vol 110 no 10 pp 4703ndash4709 1999

[10] S W Benson and J H Buss ldquoAdditivity rules for the estima-tion of molecular properties Thermodynamic propertiesrdquo TheJournal of Chemical Physics vol 29 no 3 pp 546ndash572 1958

[11] SW Benson F R Cruickshank DM Golden et al ldquoAdditivityrules for the estimation of thermochemical propertiesrdquo Chemi-cal Reviews vol 69 no 3 pp 279ndash324 1969

[12] C J Cramer Essentials of Computational Chemistry Theoriesand Models John Wiley amp Sons New York NY USA 2ndedition 2004

[13] G B Rocha R O Freire A M Simas and J J P Stewart ldquoRM1a reparameterization of AM1 for H C N O P S F Cl Br and IrdquoJournal of Computational Chemistry vol 27 no 10 pp 1101ndash11112006

[14] J J P Stewart ldquoOptimization of parameters for semiempiricalmethods VI more modifications to the NDDO approximationsand re-optimization of parametersrdquo Journal of Molecular Mod-eling vol 19 no 1 pp 1ndash32 2013

[15] Y Zhao andDG Truhlar ldquoTheM06 suite of density functionalsfor main group thermochemistry thermochemical kineticsnoncovalent interactions excited states and transition ele-ments two new functionals and systematic testing of fourM06-class functionals and 12 other functionalsrdquo TheoreticalChemistry Accounts vol 120 no 1ndash3 pp 215ndash241 2008

[16] Y Zhao and D G Truhlar ldquoDensity functionals with broadapplicability in chemistryrdquo Accounts of Chemical Research vol41 no 2 pp 157ndash167 2008

[17] H Y Afeefy J F Liebman and S E Stein ldquoNeutral thermo-chemical datardquo in NIST Chemistry WebBook P J Linstrom andW G Mallard Eds NIST Standard Reference Database no 69National Institute of Standards and Technology GaithersburgMd USA 2005

[18] J B Pedley R D Naylor and S P KirbyThermochemical Dataof Organic Compounds Chapman amp Hall New York NY USA1986

[19] J O Cox and G Pilcher Thermochemistry of Organic andOrganometallic Compounds Academic Press New York NYUSA 1970

[20] OVDorofeeva andMA Suntsova ldquoEnthalpies of formation ofnitromethane and nitrobenzene theory vs experimentrdquo Journalof Chemical Thermodynamics vol 58 pp 221ndash225 2013

[21] O V Dorofeeva O N Ryzhova and M A Suntsova ldquoAccurateprediction of enthalpies of formation of organic azides bycombining G4 theory calculations with an isodesmic reactionschemerdquo Journal of Physical Chemistry A vol 117 no 31 pp6835ndash6845 2013

[22] M A Suntsova and O V Dorofeeva ldquoUse of G4 theoryfor the assessment of inaccuracies in experimental enthalpiesof formation of aliphatic nitro compounds and nitraminesrdquoJournal of Chemical amp Engineering Data vol 59 no 9 pp 2813ndash2826 2014

[23] M A Suntsova and O V Dorofeeva ldquoComment on lsquouse ofG4 theory for the assessment of inaccuracies in experimentalenthalpies of formation of aliphatic nitro compounds andnitraminesrsquordquo Journal of Chemical amp Engineering Data vol 60no 5 pp 1532ndash1533 2015

[24] S P Verevkin V N EmelrsquoYanenko V Diky and O V Doro-feeva ldquoEnthalpies of formation of nitromethane and nitroben-zene new experiments vs quantum chemical calculationsrdquoTheJournal of ChemicalThermodynamics vol 73 pp 163ndash170 2014

[25] CHETAHTheComputer Program for ChemicalThermodynam-ics and Energy Release Evaluation University of SouthAlabamaMobile Ala USA ASTM International West ConshohockenPa USA 2009

[26] NCohen and SWBenson ldquoEstimation of heats of formation oforganic compounds by additivity methodsrdquo Chemical Reviewsvol 93 no 7 pp 2419ndash2438 1993

[27] J A Bumpus and P H Willoughby ldquoOn the heat of formationof nitromethanerdquo Journal of Physical Organic Chemistry vol 21no 9 pp 747ndash757 2008

[28] Y K Knobelrsquo E A Miroshnichenko and Y A LebedevldquoHeats of combustion of nitromethane and dinitromethaneenthalpies of formation of nitromethyl radicals and energies ofdissociation of bonds in nitro derivatives of methanerdquo Bulletinof the Academy of Sciences of the USSR Division of ChemicalScience vol 20 no 3 pp 425ndash428 1971

[29] E A Miroshnichenko T S Konrsquokova Y O Inozemtsev VP VorobrsquoEva Y N Matymhin and S A Shevelev ldquoBondenergies and formation enthalpies of mono- and polyradicals in

Advances in Physical Chemistry 11

nitroalkanes 1 Nitromethanesrdquo Russian Chemical Bulletin vol58 no 4 pp 772ndash776 2009

[30] C Y Lin M W George and P M W Gill ldquoEDF2 a densityfunctional for predicting molecular vibrational frequenciesrdquoAustralian Journal of Chemistry vol 57 no 4 pp 365ndash370 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Page 10: Research Article Calculating Heat of Formation Values of Energetic Compounds…downloads.hindawi.com/journals/apc/2016/5082084.pdf ·  · 2016-03-14Research Article Calculating Heat

10 Advances in Physical Chemistry

the T1 method [8] for this set of compounds However sincecalculated values are often similar and mutually supportiveit seems that a reasonable approach would be to use any (orall) of these four procedures when this level of accuracy isacceptable and the goal is to compare predicted properties ofnew or theoretical compounds with those of structurally sim-ilar compounds whose experimental values andor computedvalues are well established

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] H M Xiao X J Xu and L Qiu Theoretical Design of HighEnergy Density Materials Science Press Beijing China 2008

[2] R E Kirk and D F Othmer Encyclopedia of Chemical Technol-ogy vol 5 Wiley New York NY USA 2004

[3] J Giles ldquoGreen explosives collateral damagerdquo Nature vol 427no 6975 pp 580ndash581 2004

[4] J P Agrawal and J E Field ldquoRecent trends in high-energymaterialsrdquo Progress in Energy and Combustion Science vol 24no 1 pp 1ndash30 1998

[5] J Akhavan The Chemistry of Explosives Royal Society ofChemistry Cambridge UK 2004

[6] E F C Byrd and B M Rice ldquoImproved prediction of heatsof formation of energetic materials using quantum mechanicalcalculationsrdquo Journal of Physical Chemistry A vol 110 no 3 pp1005ndash1013 2006

[7] E F C Byrd and B M Rice ldquoCorrection improved predictionof heats of formation of energetic materials using quantummechanical calculationsrdquo The Journal of Physical Chemistry Avol 113 no 9 p 5813 2009

[8] W S Ohlinger P E Klunzinger B J Deppmeier and W JHehre ldquoEfficient calculation of heats of formationrdquo Journal ofPhysical Chemistry A vol 113 no 10 pp 2165ndash2175 2009

[9] L A Curtiss P C Redfern K Raghavachari V Rassolov andJ A Pople ldquoGaussian-3 theory using reduced Moslashller-PlessetorderrdquoThe Journal of Chemical Physics vol 110 no 10 pp 4703ndash4709 1999

[10] S W Benson and J H Buss ldquoAdditivity rules for the estima-tion of molecular properties Thermodynamic propertiesrdquo TheJournal of Chemical Physics vol 29 no 3 pp 546ndash572 1958

[11] SW Benson F R Cruickshank DM Golden et al ldquoAdditivityrules for the estimation of thermochemical propertiesrdquo Chemi-cal Reviews vol 69 no 3 pp 279ndash324 1969

[12] C J Cramer Essentials of Computational Chemistry Theoriesand Models John Wiley amp Sons New York NY USA 2ndedition 2004

[13] G B Rocha R O Freire A M Simas and J J P Stewart ldquoRM1a reparameterization of AM1 for H C N O P S F Cl Br and IrdquoJournal of Computational Chemistry vol 27 no 10 pp 1101ndash11112006

[14] J J P Stewart ldquoOptimization of parameters for semiempiricalmethods VI more modifications to the NDDO approximationsand re-optimization of parametersrdquo Journal of Molecular Mod-eling vol 19 no 1 pp 1ndash32 2013

[15] Y Zhao andDG Truhlar ldquoTheM06 suite of density functionalsfor main group thermochemistry thermochemical kineticsnoncovalent interactions excited states and transition ele-ments two new functionals and systematic testing of fourM06-class functionals and 12 other functionalsrdquo TheoreticalChemistry Accounts vol 120 no 1ndash3 pp 215ndash241 2008

[16] Y Zhao and D G Truhlar ldquoDensity functionals with broadapplicability in chemistryrdquo Accounts of Chemical Research vol41 no 2 pp 157ndash167 2008

[17] H Y Afeefy J F Liebman and S E Stein ldquoNeutral thermo-chemical datardquo in NIST Chemistry WebBook P J Linstrom andW G Mallard Eds NIST Standard Reference Database no 69National Institute of Standards and Technology GaithersburgMd USA 2005

[18] J B Pedley R D Naylor and S P KirbyThermochemical Dataof Organic Compounds Chapman amp Hall New York NY USA1986

[19] J O Cox and G Pilcher Thermochemistry of Organic andOrganometallic Compounds Academic Press New York NYUSA 1970

[20] OVDorofeeva andMA Suntsova ldquoEnthalpies of formation ofnitromethane and nitrobenzene theory vs experimentrdquo Journalof Chemical Thermodynamics vol 58 pp 221ndash225 2013

[21] O V Dorofeeva O N Ryzhova and M A Suntsova ldquoAccurateprediction of enthalpies of formation of organic azides bycombining G4 theory calculations with an isodesmic reactionschemerdquo Journal of Physical Chemistry A vol 117 no 31 pp6835ndash6845 2013

[22] M A Suntsova and O V Dorofeeva ldquoUse of G4 theoryfor the assessment of inaccuracies in experimental enthalpiesof formation of aliphatic nitro compounds and nitraminesrdquoJournal of Chemical amp Engineering Data vol 59 no 9 pp 2813ndash2826 2014

[23] M A Suntsova and O V Dorofeeva ldquoComment on lsquouse ofG4 theory for the assessment of inaccuracies in experimentalenthalpies of formation of aliphatic nitro compounds andnitraminesrsquordquo Journal of Chemical amp Engineering Data vol 60no 5 pp 1532ndash1533 2015

[24] S P Verevkin V N EmelrsquoYanenko V Diky and O V Doro-feeva ldquoEnthalpies of formation of nitromethane and nitroben-zene new experiments vs quantum chemical calculationsrdquoTheJournal of ChemicalThermodynamics vol 73 pp 163ndash170 2014

[25] CHETAHTheComputer Program for ChemicalThermodynam-ics and Energy Release Evaluation University of SouthAlabamaMobile Ala USA ASTM International West ConshohockenPa USA 2009

[26] NCohen and SWBenson ldquoEstimation of heats of formation oforganic compounds by additivity methodsrdquo Chemical Reviewsvol 93 no 7 pp 2419ndash2438 1993

[27] J A Bumpus and P H Willoughby ldquoOn the heat of formationof nitromethanerdquo Journal of Physical Organic Chemistry vol 21no 9 pp 747ndash757 2008

[28] Y K Knobelrsquo E A Miroshnichenko and Y A LebedevldquoHeats of combustion of nitromethane and dinitromethaneenthalpies of formation of nitromethyl radicals and energies ofdissociation of bonds in nitro derivatives of methanerdquo Bulletinof the Academy of Sciences of the USSR Division of ChemicalScience vol 20 no 3 pp 425ndash428 1971

[29] E A Miroshnichenko T S Konrsquokova Y O Inozemtsev VP VorobrsquoEva Y N Matymhin and S A Shevelev ldquoBondenergies and formation enthalpies of mono- and polyradicals in

Advances in Physical Chemistry 11

nitroalkanes 1 Nitromethanesrdquo Russian Chemical Bulletin vol58 no 4 pp 772ndash776 2009

[30] C Y Lin M W George and P M W Gill ldquoEDF2 a densityfunctional for predicting molecular vibrational frequenciesrdquoAustralian Journal of Chemistry vol 57 no 4 pp 365ndash370 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Page 11: Research Article Calculating Heat of Formation Values of Energetic Compounds…downloads.hindawi.com/journals/apc/2016/5082084.pdf ·  · 2016-03-14Research Article Calculating Heat

Advances in Physical Chemistry 11

nitroalkanes 1 Nitromethanesrdquo Russian Chemical Bulletin vol58 no 4 pp 772ndash776 2009

[30] C Y Lin M W George and P M W Gill ldquoEDF2 a densityfunctional for predicting molecular vibrational frequenciesrdquoAustralian Journal of Chemistry vol 57 no 4 pp 365ndash370 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Page 12: Research Article Calculating Heat of Formation Values of Energetic Compounds…downloads.hindawi.com/journals/apc/2016/5082084.pdf ·  · 2016-03-14Research Article Calculating Heat

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of


ASTM D3588: Standard Practice for Calculating Heat Value, … · 2018. 9. 1. · ASTM D3588: Standard Practice for Calculating Heat \rValue, Compressibility Factor, and Relative Density

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Previous Lecture 4 The Relationship of Current, Voltage, and Resistance Calculating Current Calculating Voltage Calculating Resistance

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EXAMPLE EXERCISE CALCULATING HEAT LOSS & HEAT GAIN Several exhibits in the class packet are necessary to understand the entries into the Heat Loss

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seasonal performance factors and calculating methods for ......BSI Standards Publication BS ISO 16358-2:2013 Air-cooled air conditioners and air-to-air heat pumps — Testing and calculating

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Macroeconomic Statistics Definition of Macroeconomics Calculating GDP Statistics & Policy Statistics & Models Business Cycle Calculating Inflation Calculating

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files.transtutors.com€¦  · Web view · 2017-12-14Research Questions6. Literature Review6-8. Methodology9. Management of Data and Ethical ... innumerable individuals tend to

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Calculating the effect of external shading on the solar ... · Calculating the effect of external shading on the solar heat gain coefficient of windows Christian Kohler1, Yash Shukla2,

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