Research Article Uniform versus Nonuniform Scaling …downloads.hindawi.com/journals/ijs/2014/649268.pdfResearch Article Uniform versus Nonuniform Scaling of Normal Modes Predicted

Research ArticleUniform versus Nonuniform Scaling ofNormal Modes Predicted by Ab Initio Calculations A Test on2-(26-Dichlorophenyl)-N-(13-thiazol-2yl) Acetamide

Ambrish K Srivastava1 Anoop K Pandey2 Saurabh Pandey1 Prakash S Nayak3

B Narayana3 B K Sarojini3 and Neeraj Misra1

1 Department of Physics University of Lucknow Lucknow Uttar Pradesh 226007 India2Department of Physics Govt D P G College Dantewada Chhattisgarh 494449 India3 Department of Studies in Chemistry Mangalore University Mangalagangotri Karnataka 574199 India

Correspondence should be addressed to Neeraj Misra neerajmisra11gmailcom

Received 22 February 2014 Revised 14 May 2014 Accepted 14 May 2014 Published 10 July 2014

Academic Editor Rolf W Berg

Copyright copy 2014 Ambrish K Srivastava et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

A test on calculated vibrational modes of 2-(26-dichlorophenyl)-N-(13-thiazol-2yl) acetamide using ab initio density functionalmethod has been performed The calculated harmonic vibrational frequencies are scaled via two schemes uniform ]scaled =09648]calculated and nonuniform ]scaled = 221 + 09543]calculated Scaled vibrational modes are compared with experimental FTIRbands A good correlation is shown between scaled frequencies with the correlation coefficient 1198772 = 099638-099639 This clearlyshows that both schemes efficiently reproduce observed spectrum However a close investigation of individual normal modesreveals that nonuniform scaling performs much better than uniform scaling especially in the high frequency region

1 Introduction

Ab initio quantum chemical methods are reliable tools forextracting valuable information about any chemical systemCurrently available ab initio methods are capable of repro-ducing experimental IR spectra of rigid and small- as well asmedium-size molecules In many chemical systems the the-oretically calculated frequencies and intensities of vibrationalmodes closely resemble the experimentally observed valuesHence it may be expected that the normal modes analysisfrom theoretically predicted force field reflectswell themodesof vibrations in a real molecule Normal-mode analysis iscommonly employed in the interpretation of the vibra-tional spectra of molecules [1ndash4] However there are somelimitations of the model used to calculate the vibrationalfrequencies These limitations include the effect of electroncorrelation [5] and basis set deficiencies as well as inter- andintramolecular interactions It needs to be emphasized thatthe calculated frequencies represent vibrational signature ofthe molecule in its gas (isolated) phase unlike experimental

spectra which are recorded in liquid or solid phase of samplewith impurity This is experimentally verified that ]gas gt]liquid gt ]solid [6] On comparing the vibrational spectrait is observed that at places where calculated frequenciescome out to be lower than the experimental frequenciesweak intermolecular interactions may be taking place Froma practical point of view themain disadvantage of vibrationalspectroscopy is the lack of a direct spectra-structure relationAb initio calculations follow the approximation that thechemical bonds are elastic but it is not the case especiallyat higher range of frequencies due to anharmonicity ofvibrations [7] Thus the computed frequencies within thisBorn-Oppenheimer approximation [8] need to be properlyscaled These anharmonic vibrations mainly include torsionsand inversions such as the umbrella modes of halomethylradicals [9] Similarly in lower range of frequencies (wherenearly all modes are rotational) the interaction of modes ofvibration as well as molecular interaction takes place verystrongly which certainly affect the calculated frequencies

Hindawi Publishing CorporationInternational Journal of SpectroscopyVolume 2014 Article ID 649268 7 pageshttpdxdoiorg1011552014649268

2 International Journal of Spectroscopy

The motivation for predicting or simulating vibrationalspectra is to make vibrational spectroscopy a more practicaltool [10ndash12] In this respect it is not only desirable but alsoessential to have calculated frequencies very close to theirobserved values This can usually be expected by appropriatescaling of calculated frequencies Appropriate scalingmethodis still a fundamental problem existing in the literature eventoday Merrick et al had calculated some scale factors usingharmonic approximation but these factors did not work wellin the region where mixing of several bands occurred [13]Later on Alecu et al have calculated new scale factors withinharmonic approximation for a number of theoretical meth-ods [14] They tested a lot of functional systems for exam-ple electronic model chemistries single-level wave doublyhybrid density neglect-of-diatomic-differential-overlap andso forth On the other hand Mauricio Alcolea Palafoxderived some scaling equations by statistical correlation andsuggested that these scaling equations give more satisfactoryresult as compared to constant scale factors [15ndash17]

In present paper we perform a critical survey on thescaling of vibrational frequencies of 2-(26-dichlorophenyl)-N-(13-thiazol-2yl) acetamide by using two different schemesThe first scheme is based on a constant scale factor assuggested by Alecu et al which we call ldquouniform scalingrdquoThe second scheme is based on a scaling equation as recom-mended by Palafox et al which we refer to as ldquononuniformscalingrdquo

2 Computational Methods

Our ab initio calculations employ a hybrid form of densityfunctional B3LYP in conjunction with 6ndash31+G(dp) basisset for geometry optimization of the test molecule TheB3LYP combines Beckersquos three-parameter exchange term[18] with the functional devised by Lee-Yang-Parr to treatelectron correlation [19] Vibrational frequency calculationsare performed using optimized geometry at the same level oftheory The calculated frequencies are scaled by two differentschemes as below

For uniform scaling [13]

]scaled = 09648]calculated (1)

For nonuniform scaling [15]

]scaled = 221 + 09543]calculated (2)

Gaussian 09 package [20] is used to perform all computationsand assignments of calculated vibrational modes are madewith the help of visual animation generated by GaussView 50program [21]

3 Results and Discussion

First we discuss some salient features of test molecule incondensed as well as isolated (gas) phase The single crystalof 2-(26-dichlorophenyl)-N-(13-thiazol-2-yl) acetamide isgrown by slow evaporation method (melting point = 489ndash491 K) [22] A photograph of this crystal along with X-ray

spectrum can be found in supplementary information (seeFigures S1 and S2 in Supplementary Material available onlineat httpdxdoiorg1011552014649268) In crystal phasemolecules are linked by pairs of NminusHsdot sdot sdotN hydrogen bondsas shown in Figure 1

ThemeasuredX-ray crystallographic parameters are usedto model an initial structure of isolated molecule for theprocess of geometry optimization After optimization wefind a sofa shaped structure in which the mean planeof dichlorophenyl ring is almost perpendicular to that ofthiazole ring as shown in Figure 2

In Figure 3 we have shown a linear correlation betweencalculated and observed bond-lengths Note that CndashH bond-lengths are not included here We find a good correlationwith correlation coefficient (1198772) of 09991 which suggests thatour computational scheme is fully capable of reproducing theexperimental geometry

FTIR spectrum of test molecule is recorded by usingShimadzu-Model Prestige 21 spectrometer in the region 400ndash4000 cmminus1 with the sample (purity of 98) in KBr pelletThe vibrational analysis of isolated molecule (Figure 2) isperformed at the same level of theory asmentioned earlier InFigure 4 we plot calculated IR and observed FTIR spectra forwavenumber region of 1800 cmminus1ndash600 cmminus1 The calculatedwavenumbers are scaled by using (1) and (2)The assignmentsof all vibrational modes have been made along with theirdirections of polarization Table 1 lists calculated and scaledwavenumbers of all vibrational modes as well as their assign-ments For the sake of comparison FTIR values of the mostprominent modes are also included

In Figures 5 and 6 we have shown the correlationbetween experimentally observed wavenumbers and theoret-ically scaledwavenumbersWe find the correlation coefficientof 099638-099639 which ensures that both scaling schemesare equivalently appropriate at least in the present case Inorder to compare these two scaling schemes for particularvibration mode we divide our vibrational analysis into twocategories

31 Higher Frequency Region (above 1400 cmminus1) This regioncovers CndashH stretching vibrations of phenyl ring and methy-lene group along with NndashH as well as C=O stretching modesof amide group NndashH stretching mode is observed experi-mentally at 3203 cmminus1 and corresponding scaled frequenciesare calculated at 3475 cmminus1 and 3459 cmminus1 by uniform scalingand nonuniform scaling respectively The apparent discrep-ancy between experimental and theoretical frequencies is aconsequence of intermolecular hydrogen bonding present incondensed phase (see Figure 1) but absent in case of isolatedmolecule The most prominent CndashH mode associated withphenyl ring vibrations is seen at 3045 cmminus1 in FTIR whichis scaled at 3090 cmminus1 and 3078 cmminus1 by our theoreticalschemes

The C=O stretching observed at 1687 cmminus1 is scaled at1684 and 1688 cmminus1 respectively Similarly CndashC stretchingof phenyl ring at 1550 cmminus1 corresponds to scaled values of1546 cmminus1 and 1551 cmminus1TheCndashH stretching associated with

International Journal of Spectroscopy 3

a

b

c0

Figure 1 Crystal geometry of 2-(26-dichlorophenyl)-N-(13-thiazol-2yl) acetamide Intermolecular interactions are shown by broken lines

Cl(25)

Cl(24)

C(8)H(10)

H(9)

C(5)

C(15)

C(21)

C(16)

C(11)

O(12)

N(13)

H(14)

N(20)

S(19)H(17)

H(18)

H(7)H(23)

H(22)

C(6)

C(4)

C(3)

C(1)C(2)

Figure 2 Molecular geometry of 2-(26-dichlorophenyl)-N-(13-thiazol-2yl) acetamide optimized at B3LYP6ndash31+G(dp) level


Table 1 Normal modes assignments and scaled frequencies for 2-(26-dichlorophenyl)-N-(13-thiazol-2yl) acetamide For comparisonobserved FTIR bands are also given

Calculatedfreq cmminus1

Scaled freq(1) cmminus1


FTIR freqcmminus1

IR intensityau Assignment of vibrational modes Direction of

polarization3602 3475 3459 3203 68 ](13Nndash14H) Along 13Nndash14H3272 3156 3144 1 ]

119904(15Cndash18H) + ]

119904(17Cndash21H) Along 13Hndash11C

3233 3119 3107 878 ]as(15Cndash18H) + ]119904(17Cndash21H) Per R1

3228 3114 3102 169 ]as(3Cndash2H) + ](2Cndash23H) +](1Cndash7H) Along 6Cndash5H

3224 3110 3098 023 ](3Cndash2H) + ](1Cndash7H) Per R13203 3090 3078 3045 332 ](3Cndash2H) + ](2Cndash23H) + ](1Cndash7H) Along 2Cndash23H3137 3026 3015 009 ]as(9Hndash8Cndash10H) Per R13093 2984 2973 343 ](9Hndash8Cndash10H) Along 11Cndash12O1746 1684 1688 1687 26685 ](11C=12O) Along 13Nndash14H1627 1569 1574 920 ](CndashC)R2 Along R21603 1546 1551 1550 3768 ](CndashC)R2 Per R1

1582 1526 1531 43027 ](CndashC)R2 + ](CndashN)R2 +](6Cndash13C) + 120573(15ndash18H) Per R2

1525 1471 1477 10734 120573(15Cndash21H) + 120573(15Cndash18H) +120573(13Nndash14H) Along 11Hndash12O

1474 1422 1428 1436 900 Scissoring (9Hndash8Cndash10H) +120573(13Nndash14H) Along 11Hndash12O

1468 1416 1423 6364 120573(CndashH)R2) Along R2

1465 1413 1420 1652 120573(1Cndash7H) + 120573(3Cndash22H) +120573(13Nndash14H) + ](5Cndash8C) Per14H plane

1459 1407 1414 2622 Scissoring (9Hndash8Cndash10H) +120573(13Nndash14H) Containing 13Nndash14H

1349 1301 1309 6292 120573(21Cndash7H) + 120573(15Cndash18H) Along 13Nndash16C1335 1288 1296 425 Rocking (9Hndash8Cndash10H) + 120573(CndashH)R1 Along 8Cndash5C1334 1287 1295 1286 105 120591(9Hndash8Cndash10H) + 120573(CndashH)R1 Per R1

1306 1260 1268 11291 120573(13Nndash14H) + ](16Cndash19S) Plane containing 17Ndirected along R1

1251 1206 1215 141 120573(CndashN)R2 + 120591(9Hndash8Cndash10H) Per R1

1226 1182 1192 5376120573(1Cndash7H) + 120573(3Cndash22H) +120573(15Cndash18H) + rocking

(9Hndash8Cndash10H)Along 8Cndash11C

1220 1177 1186 4398120573(15Cndash8H) + 120573(13Nndash14H) +120573(3Cndash22H) + rocking

(9Hndash8Cndash10H)Along 17Nndash16C

1196 1153 1163 949 120573(CndashH)R2 + 120591(9Hndash8Cndash10H) Per R11181 1139 1149 3016 120573(15Cndash18H) + 120573(13Nndash14H) Along 13Nndash14H1172 1130 1140 1141 1673 120591(9Hndash8Cndash10H) + 120573(2Cndash23H) Per R11101 1062 1072 1316 120573(CndashH)R2 Along 11Cndash12O1088 1049 1060 984 Scissoring (18Hndash15Cndash21Cndash17H) Along R2

1086 1047 1058 896 120573(3Cndash22H) + 120573(1Cndash7H) + rocking(9Hndash8Cndash10H) + ](6Cndash25Cl) Along R1

987 952 963 033 120574(CndashH)R2 Plane containing 13Ndirected to R1

975 940 952 931 778 120596(9Hndash8Cndash10H) + 120573(CndashH)R1939 905 918 4174 Rocking (9Hndash8Cndash10H) Per R1909 877 889 006 120574(1Cndash7H) + 120574(3Cndash22H) Along R2


Table 1 Continued




FTIR freqcmminus1


polarization897 865 878 326 120591(18Hndash25Cndash21Cndash17H) Per R1882 850 863 856 668 In plane R1 bending Along R1855 824 838 310 Ring R2 breathing (9Hndash8Cndash10H) Along R2787 759 773 785 3864 120574(CndashH)R3 In between 13Nndash14H

783 755 769 761 2320 120574(CndashH)R2 + R1 breathing Plane containing 13Ndirected to R1

767 740 754 6740 In plane R2 bending +120591(9Hndash8Cndash10H) Per R1

718 692 707 692 3909 120574(15Cndash18H) + 120574(21Cndash17H) Per R1661 637 652 1108 120573(R1) + R(9Hndash8Cndash10H) Along 16Cndash21H631 608 624 2947 120574(13Nndash14H) + 120574(16Cndash20Nndash15C) Per R1

624 602 617 592 867 120574(CndashH)R1 + 120574(19Sndash15Cndash20C) +Rocking (9Hndash8Cndash10H) Per R1

563 543 559 216 120574(R1) + 120574(13Nndash14H) + rocking(9Hndash8Cndash10H) Per R1

559 539 555 1284 Twisting R1 + rocking(9Hndash8Cndash10H) Per R2

511 493 509 1114 120574(R1) + 120574(13Nndash14H) Per R1

486 468 485 855 120574(1Cndash2Cndash3C) + 120574(CH)R2 +120596(9Hndash8Cndash10H) Per R2

478 461 478 474 120573(R2) + R(9Hndash8Cndash10H) Per R2424 409 426 428 120574(4Cndash24Cl) + 120591(1Cndash2Cndash3C) Along 10Cndash11O

404 389 407 509 120573(CH)R2 + R(9Hndash8Cndash10H) +120573(CndashCl)R2 Per R1

Note ] stretching ]119904 symmetric stretching ]as asymmetric stretching 120573 in-plane-bending 120574 out-of-plane bending 120596 wagging 120591 torsion

dcalculated = 1040dexperimental minus 0051

R2= 09991

Experimental bond-lengths (A)

18

16

14

12

161412

Calc

ulat

ed b

ond-

leng

ths (

A)

Figure 3 Correlation between calculated and experimental bond-lengths of 2-(26-dichlorophenyl)-N-(13-thiazol-2yl) acetamide

methylene group is found to be coupled with NndashH stretchingmode at 1436 cmminus1 which is theoretically scaled at 1422 cmminus1and 1428 cmminus1 by uniform scaling and nonuniform scalingschemes respectively

32 Lower Frequency Region (below 1400 cmminus1) In thisregion the bending modes associated with ring systems and

various groups are generally observed The in-plane bendingof methylene group observed at 1286 cmminus1 and 1141 cmminus1 iscoupledwith phenyl ring vibrationThe uniform scaling givesthese modes at 1287 cmminus1 and 1130 cmminus1 while nonuniformscaling calculates at 1295 cmminus1 and 1140 cmminus1 respectivelySimilarly out of plane bending of methylene coupled withphenyl ring at 931 cmminus1 in FTIR is scaled at 940 cmminus1 and952 cmminus1 by our theoretical schemes

The in-plane bending of thiazole ring is observed at856 cmminus1 against scaled values of 850 cmminus1 and 863 cmminus1On the other hand the bending of phenyl ring observed at785 cmminus1 is scaled at 759 cmminus1 and 773 cmminus1 Furthermorethe coupling of vibrations of both rings is observed at761 cmminus1 corresponding to scaled values of 755 cmminus1 and769 cmminus1 Moreover even lower normal modes at 692 cmminus1and 592 cmminus1 associated with bending of thiazole rings arescaled at 692 cmminus1 and 602 cmminus1 by uniform scaling methodwhereas at 707 cmminus1 and 617 cmminus1 by nonuniform scalingscheme

The above discussion suggests that scaled wavenumbersby both schemes successfully explain observed bands in caseof title molecule giving a good correlation with experimentalfrequencies (see Figures 5 and 6) The comparative responseof two scaling schemes is given in terms of wavenum-ber difference between observed and scaled bands plottedin Figure 7 A close investigation on Figure 7 reveals that


T(

)

(a)

T(

)

1800 1600 1400 1200 1000 800 600

Wavenumber (cmminus1)(b)

Figure 4 Calculated (a) and experimental (b) vibrational IR spectra of 2-(26-dichlorophenyl)-N-(13-thiazol-2yl) acetamide in the region1800ndash600 cmminus1

1000 2000 3000

Scal

ed w

aven

umbe

r (cm

minus1)

Experimental wavenumber (cmminus1)

scaled = 106757experimental minus 7284346

R2= 099639

1000

2000

3000

Figure 5 Correlation between calculated (scaled) and experi-mental wavenumbers of 2-(26-dichlorophenyl)-N-(13-thiazol-2yl)acetamide Scaling is performed by a scale factor (equation (1))

1000 2000 3000

Scal

ed w

aven

umbe

r (cm

minus1)



R2= 099638

1000

2000

3000

Figure 6 Correlation between calculated (scaled) and experi-mental wavenumbers of 2-(26-dichlorophenyl)-N-(13-thiazol-2yl)acetamide Scaling is performed by a scaling equation (equation (2))

3000

2500

2000

1500

1000

500

minus250 minus200 minus150 minus100 minus50 0

By scaling equationBy scale factor

Wavenumber difference (cmminus1)

Expe

rimen

tal w

aven

umbe

rs (c

mminus1)

Figure 7 The difference between scaled and experimental wave-numbers for 2-(26-dichlorophenyl)-N-(13-thiazol-2yl) acetamide

nonuniform scaling performs much better than uniformscaling especially in the high frequency region Thus thecalculated vibrational modes should be scaled by appropriatescaling equation to account for anharmonicity in vibrationsFor lower frequency region where discrepancies betweencalculated and observed wavenumbers are observed mainlydue to mixing of vibrational modes and the effect of electroncorrelation both scaling schemes perform equally well

4 Conclusions

We have performed a test on the scaling of calculatedvibrational bands in case of 2-(26-dichlorophenyl)-N-(13-thiazol-2yl) acetamide adopting two different scalingschemes namely scale factor and scaling equation Scalednormal modes are compared with observed vibrationalbands The validity of both schemes is established by thecorrelation between theoretically scaled frequencies andexperimentally observed frequencies with the coefficient of09964 The analysis of individual modes has revealed thatboth schemes perform equally well for the lower range offrequencies below 1400 cmminus1 (torsion wagging etc) In case


of high frequency region (above 1400 cmminus1) where most ofthe stretching modes occur scaling equation provides moreaccurate vibrational bands as compared to scale factor To bespecific CminusHstretching of phenyl ring observed at 3045 cmminus1(in present case) is better represented by 3078 cmminus1 (byscaling equation) rather than by 3090 cmminus1 (by scale factor)at B3LYP6ndash31+G(dp) theoryThus the present assessment issupposed not only to assist further studies on the predictionor simulation of vibrational spectra of new molecules butalso to assign more accurate vibrational modes for previouslyreported molecules in the literature

Conflict of Interests

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

Acknowledgment

Ambrish K Srivastava wishes to thank Council of Scientificand Industrial Research (CSIR) New Delhi India for pro-viding a research fellowship

References

[1] N Misra O Prasad L Sinha and A Pandey ldquoMolecularstructure and vibrational spectra of 2-formyl benzonitrile bydensity functional theory and ab initio Hartree-Fock calcula-tionsrdquo Journal of Molecular Structure THEOCHEM vol 822no 1ndash3 pp 45ndash47 2007

[2] S A Siddiqui A Dwivedi N Misra and N Sundaragane-san ldquoComputational note on vibrational spectra of Tyraminehydrochloride DFT studyrdquo Journal of Molecular Structure vol847 no 1ndash3 pp 101ndash102 2007

[3] A K Srivastava B Narayana B K Sarojini and N MisraldquoVibrational structural and hydrogen bonding analysis ofN1015840-[(E)-4-Hydroxybenzylidene]-2- (naphthalen-2-yloxy)acetohydrazide-combined density functional and atoms-in-molecule based theoretical studiesrdquo Indian Journal of Physicsvol 88 pp 547ndash556 2014

[4] A K Srivastava A K Pandey B Narayana B K Sarojini P SNayak and N Misra ldquoNormal modes molecular orbitals andthermochemical analyses of 2 4 and 3 4 dichloro substitutedphenyl-N-(1 3-thiazol-2-yl) acetamides DFT study and FTIRspectrardquo Journal of Theoretical Chemistry vol 2014 Article ID125841 10 pages 2014

[5] J A Pople H B Schlegel R Krishnan et al ldquoMolecularorbital studies of vibrational frequenciesrdquo International Journalof Quantum Chemistry vol 15 pp 269ndash278 1981

[6] M Silverstein G C Basseler and C Morill SpectrometricIdentification of Organic Compounds Wiley New York NYUSA 1981

[7] J A Pople A P Scott M W Wong and L Radom ldquoScalingfactors for obtaining fundamental vibrational frequencies andzero-point energies from HF6-31Glowast and MP26-31Glowast har-monic frequenciesrdquo Israel Journal of Chemistry vol 33 pp 345ndash350 1993

[8] httpenwikipediaorgwikiBornndashOppenheimer approxima-tion

[9] P Marshall G N Srinivas and M Schwartz ldquoA computa-tional study of the thermochemistry of bromine-and iodine-containing methanes and methyl radicalsrdquo The Journal ofPhysical Chemistry A vol 109 no 28 pp 6371ndash6379 2005

[10] S A Siddiqui A Dwivedi P K Singh et al ldquoMolecularstructure vibrational spectra and potential energy distributionof protopine using ab initio and density functional theoryrdquoJournal of Structural Chemistry vol 50 no 3 pp 411ndash420 2009

[11] A K Pandey S A Siddiqui A Dwivedi K Raj and N MisraldquoDensity functional theory study on the molecular structure ofloganinrdquo Spectroscopy vol 25 no 6 pp 287ndash302 2011

[12] S A Siddiqui A Dwivedi A Pandey et al ldquoMolecularstructure vibrational spectra and potential energy distributionof colchicine using ab initio and density functional theoryrdquoJournal of Computer Chemistry Japan vol 8 no 2 pp 59ndash722009

[13] I M Alecu J Zheng Y Zhao and D G Truhlar ldquoComputa-tional thermochemistry scale factor databases and scale factorsfor vibrational frequencies obtained from electronic modelchemistriesrdquo Journal of Chemical Theory and Computation vol6 no 9 pp 2872ndash2887 2010

[14] J P Merrick D Moran and L Radom ldquoAn evaluation ofharmonic vibrational frequency scale factorsrdquo The Journal ofPhysical Chemistry A vol 111 no 45 pp 11683ndash11700 2007

[15] M Alcolea Palafox ldquoScaling factors for the prediction ofvibrational spectra I Benzene moleculerdquo International Journalof Quantum Chemistry vol 77 no 3 pp 661ndash684 2000

[16] M Alcolea Palafox and V K Rastogi ldquoQuantum chemicalpredictions of the vibrational spectra of polyatomic moleculesThe uracil molecule and two derivativesrdquo Spectrochimica ActaA Molecular and Biomolecular Spectroscopy vol 58 no 3 pp411ndash440 2002

[17] M Alcolea Palafox J L Nuez and M Gil ldquoAccurate scalingof the vibrational spectra of aniline and several derivativesrdquoJournal of Molecular Structure vol 593 pp 101ndash131 2002

[18] A D Becke ldquoDensity-functional thermochemistry IIIThe roleof exact exchangerdquoThe Journal of Chemical Physics vol 98 no7 pp 5648ndash5652 1993

[19] C Lee W Yang and R G Parr ldquoDevelopment of the Colle-Salvetti correlation-energy formula into a functional of theelectron densityrdquo Physical Review B vol 37 no 2 pp 785ndash7891988

[20] M J Frisch G W Trucks H B Schlegel et al Gaussian 09Revision B01 Gaussian Wallington Conn USA 2010

[21] R Dennington T Keith and J Millam GaussView Ver 501Semichem Shawnee Kan USA 2005

[22] P S Nayak B Narayana H S Yathirajan J P Jasin-ski and R J Butcher ldquo2-(26-Dichlorophenyl)-N-(13-thiazol-2-yl)acetamiderdquo Acta Crystallographica Section E StructureReports Online vol 69 no 4 p o523 2013

Submit your manuscripts athttpwwwhindawicom

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The motivation for predicting or simulating vibrationalspectra is to make vibrational spectroscopy a more practicaltool [10ndash12] In this respect it is not only desirable but alsoessential to have calculated frequencies very close to theirobserved values This can usually be expected by appropriatescaling of calculated frequencies Appropriate scalingmethodis still a fundamental problem existing in the literature eventoday Merrick et al had calculated some scale factors usingharmonic approximation but these factors did not work wellin the region where mixing of several bands occurred [13]Later on Alecu et al have calculated new scale factors withinharmonic approximation for a number of theoretical meth-ods [14] They tested a lot of functional systems for exam-ple electronic model chemistries single-level wave doublyhybrid density neglect-of-diatomic-differential-overlap andso forth On the other hand Mauricio Alcolea Palafoxderived some scaling equations by statistical correlation andsuggested that these scaling equations give more satisfactoryresult as compared to constant scale factors [15ndash17]

In present paper we perform a critical survey on thescaling of vibrational frequencies of 2-(26-dichlorophenyl)-N-(13-thiazol-2yl) acetamide by using two different schemesThe first scheme is based on a constant scale factor assuggested by Alecu et al which we call ldquouniform scalingrdquoThe second scheme is based on a scaling equation as recom-mended by Palafox et al which we refer to as ldquononuniformscalingrdquo

2 Computational Methods

Our ab initio calculations employ a hybrid form of densityfunctional B3LYP in conjunction with 6ndash31+G(dp) basisset for geometry optimization of the test molecule TheB3LYP combines Beckersquos three-parameter exchange term[18] with the functional devised by Lee-Yang-Parr to treatelectron correlation [19] Vibrational frequency calculationsare performed using optimized geometry at the same level oftheory The calculated frequencies are scaled by two differentschemes as below

For uniform scaling [13]

]scaled = 09648]calculated (1)

For nonuniform scaling [15]

]scaled = 221 + 09543]calculated (2)

Gaussian 09 package [20] is used to perform all computationsand assignments of calculated vibrational modes are madewith the help of visual animation generated by GaussView 50program [21]

3 Results and Discussion

First we discuss some salient features of test molecule incondensed as well as isolated (gas) phase The single crystalof 2-(26-dichlorophenyl)-N-(13-thiazol-2-yl) acetamide isgrown by slow evaporation method (melting point = 489ndash491 K) [22] A photograph of this crystal along with X-ray

spectrum can be found in supplementary information (seeFigures S1 and S2 in Supplementary Material available onlineat httpdxdoiorg1011552014649268) In crystal phasemolecules are linked by pairs of NminusHsdot sdot sdotN hydrogen bondsas shown in Figure 1

ThemeasuredX-ray crystallographic parameters are usedto model an initial structure of isolated molecule for theprocess of geometry optimization After optimization wefind a sofa shaped structure in which the mean planeof dichlorophenyl ring is almost perpendicular to that ofthiazole ring as shown in Figure 2

In Figure 3 we have shown a linear correlation betweencalculated and observed bond-lengths Note that CndashH bond-lengths are not included here We find a good correlationwith correlation coefficient (1198772) of 09991 which suggests thatour computational scheme is fully capable of reproducing theexperimental geometry

FTIR spectrum of test molecule is recorded by usingShimadzu-Model Prestige 21 spectrometer in the region 400ndash4000 cmminus1 with the sample (purity of 98) in KBr pelletThe vibrational analysis of isolated molecule (Figure 2) isperformed at the same level of theory asmentioned earlier InFigure 4 we plot calculated IR and observed FTIR spectra forwavenumber region of 1800 cmminus1ndash600 cmminus1 The calculatedwavenumbers are scaled by using (1) and (2)The assignmentsof all vibrational modes have been made along with theirdirections of polarization Table 1 lists calculated and scaledwavenumbers of all vibrational modes as well as their assign-ments For the sake of comparison FTIR values of the mostprominent modes are also included

In Figures 5 and 6 we have shown the correlationbetween experimentally observed wavenumbers and theoret-ically scaledwavenumbersWe find the correlation coefficientof 099638-099639 which ensures that both scaling schemesare equivalently appropriate at least in the present case Inorder to compare these two scaling schemes for particularvibration mode we divide our vibrational analysis into twocategories

31 Higher Frequency Region (above 1400 cmminus1) This regioncovers CndashH stretching vibrations of phenyl ring and methy-lene group along with NndashH as well as C=O stretching modesof amide group NndashH stretching mode is observed experi-mentally at 3203 cmminus1 and corresponding scaled frequenciesare calculated at 3475 cmminus1 and 3459 cmminus1 by uniform scalingand nonuniform scaling respectively The apparent discrep-ancy between experimental and theoretical frequencies is aconsequence of intermolecular hydrogen bonding present incondensed phase (see Figure 1) but absent in case of isolatedmolecule The most prominent CndashH mode associated withphenyl ring vibrations is seen at 3045 cmminus1 in FTIR whichis scaled at 3090 cmminus1 and 3078 cmminus1 by our theoreticalschemes

The C=O stretching observed at 1687 cmminus1 is scaled at1684 and 1688 cmminus1 respectively Similarly CndashC stretchingof phenyl ring at 1550 cmminus1 corresponds to scaled values of1546 cmminus1 and 1551 cmminus1TheCndashH stretching associated with


a

b

c0


Cl(25)

Cl(24)

C(8)H(10)

H(9)

C(5)

C(15)

C(21)

C(16)

C(11)

O(12)

N(13)

H(14)

N(20)

S(19)H(17)

H(18)

H(7)H(23)

H(22)

C(6)

C(4)

C(3)

C(1)C(2)







FTIR freqcmminus1



119904(15Cndash18H) + ]








1468 1416 1423 6364 120573(CndashH)R2) Along R2















Table 1 Continued




FTIR freqcmminus1









511 493 509 1114 120574(R1) + 120574(13Nndash14H) Per R1






R2= 09991


18

16

14

12

161412

Calc

ulat

ed b

ond-

leng

ths (

A)








T(

)

(a)

T(

)

1800 1600 1400 1200 1000 800 600



1000 2000 3000

Scal

ed w

aven

umbe

r (cm

minus1)



R2= 099639

1000

2000

3000


1000 2000 3000

Scal

ed w

aven

umbe

r (cm

minus1)



R2= 099638

1000

2000

3000


3000

2500

2000

1500

1000

500




Expe

rimen

tal w

aven

umbe

rs (c

mminus1)



4 Conclusions






Acknowledgment


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


a

b

c0


Cl(25)

Cl(24)

C(8)H(10)

H(9)

C(5)

C(15)

C(21)

C(16)

C(11)

O(12)

N(13)

H(14)

N(20)

S(19)H(17)

H(18)

H(7)H(23)

H(22)

C(6)

C(4)

C(3)

C(1)C(2)







FTIR freqcmminus1



119904(15Cndash18H) + ]








1468 1416 1423 6364 120573(CndashH)R2) Along R2















Table 1 Continued




FTIR freqcmminus1









511 493 509 1114 120574(R1) + 120574(13Nndash14H) Per R1






R2= 09991


18

16

14

12

161412

Calc

ulat

ed b

ond-

leng

ths (

A)








T(

)

(a)

T(

)

1800 1600 1400 1200 1000 800 600



1000 2000 3000

Scal

ed w

aven

umbe

r (cm

minus1)



R2= 099639

1000

2000

3000


1000 2000 3000

Scal

ed w

aven

umbe

r (cm

minus1)



R2= 099638

1000

2000

3000


3000

2500

2000

1500

1000

500




Expe

rimen

tal w

aven

umbe

rs (c

mminus1)



4 Conclusions






Acknowledgment


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of






FTIR freqcmminus1



119904(15Cndash18H) + ]








1468 1416 1423 6364 120573(CndashH)R2) Along R2















Table 1 Continued




FTIR freqcmminus1









511 493 509 1114 120574(R1) + 120574(13Nndash14H) Per R1






R2= 09991


18

16

14

12

161412

Calc

ulat

ed b

ond-

leng

ths (

A)








T(

)

(a)

T(

)

1800 1600 1400 1200 1000 800 600



1000 2000 3000

Scal

ed w

aven

umbe

r (cm

minus1)



R2= 099639

1000

2000

3000


1000 2000 3000

Scal

ed w

aven

umbe

r (cm

minus1)



R2= 099638

1000

2000

3000


3000

2500

2000

1500

1000

500




Expe

rimen

tal w

aven

umbe

rs (c

mminus1)



4 Conclusions






Acknowledgment


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Table 1 Continued




FTIR freqcmminus1









511 493 509 1114 120574(R1) + 120574(13Nndash14H) Per R1






R2= 09991


18

16

14

12

161412

Calc

ulat

ed b

ond-

leng

ths (

A)








T(

)

(a)

T(

)

1800 1600 1400 1200 1000 800 600



1000 2000 3000

Scal

ed w

aven

umbe

r (cm

minus1)



R2= 099639

1000

2000

3000


1000 2000 3000

Scal

ed w

aven

umbe

r (cm

minus1)



R2= 099638

1000

2000

3000


3000

2500

2000

1500

1000

500




Expe

rimen

tal w

aven

umbe

rs (c

mminus1)



4 Conclusions






Acknowledgment


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


T(

)

(a)

T(

)

1800 1600 1400 1200 1000 800 600



1000 2000 3000

Scal

ed w

aven

umbe

r (cm

minus1)



R2= 099639

1000

2000

3000


1000 2000 3000

Scal

ed w

aven

umbe

r (cm

minus1)



R2= 099638

1000

2000

3000


3000

2500

2000

1500

1000

500




Expe

rimen

tal w

aven

umbe

rs (c

mminus1)



4 Conclusions






Acknowledgment


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of





Acknowledgment


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of










Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

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