Vibrational and Thermodynamic Properties of 2,2′,4,4′,6,6′-Hexanitroazobenzene and Its Derivatives: A Density Functional Theory Study

FULL PAPER

* E-mail: [email protected] Received March 23, 2009; revised August 14, 2009; accepted September 22, 2009. Project supported by the National Natural Science Foundation of China (No. 10576016), Key Foundation (No. 10576030) and Beforehand Research

Foundation of Weapon Equipment (No. 9140A05090108BQ0208).

Chin. J. Chem. 2010, 28, 149—158 © 2010 SIOC, CAS, Shanghai, & WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 149

Vibrational and Thermodynamic Properties of 2,2',4,4',6,6'-Hexanitroazobenzene and Its Derivatives:

A Density Functional Theory Study

Liu, Yan(刘彦) Gong, Xuedong*(贡雪东) Wang, Guixiang(王桂香) Wang, Lianjun(王连军) Xiao, Heming(肖鹤鸣)

School of Chemical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China

HNAB (2,2',4,4',6,6'-hexanitroazobenzene) and its derivatives have been optimized to obtain their molecular geometries and electronic structures by using density functional theory at the B3LYP/6-31G* level. Their IR spectra have been computed and assigned by vibrational analysis. The strongest peaks are attributed to the N—O asymmet-ric stretching of nitro groups. Its central position moves towards higher frequency as the number of nitro groups in-creases. It is obvious that there is hydrogen-bonding between amino and nitro groups in amino derivatives. Based on the frequencies scaled by 0.96 and the principle of statistical thermodynamics, the thermodynamic properties have been evaluated, which are linearly related with the temperature, as well as the number of nitro and amino groups, respectively, obviously showing good group additivity. And the thermodynamic functions for the nitro de-rivatives increase much more than those for the amino derivatives with the increase of the number of substituents. The values of heat of formation (HOF) for the nitro derivatives increase gradually with n, while those of the amino derivatives decrease smoothly with n.

Keywords 2,2',4,4',6,6'-hexanitroazobenzene (HNAB) derivative, density functional theory, IR spectra, heat of formation, thermodynamic function

Introduction

Recently, there is a great deal of interest in the study of efficient energy sources. Nitrogen-rich compounds, well known for their ability to store energy, have been the subjects of intense and sustained theoretical and ex-perimental studies owing to their potential as high en-ergy density materials (HEDM) for possible military application.1-5 They derive most of their energy from their high positive heats of formation and oxidation of the carbon backbone.6-8 The higher the nitrogen content of a material, the higher the heat of formation and thus the performance.9

As a kind of nitrogenrich compounds, HNAB (2,2',4, 4',6,6'-hexanitroazobenzene) is a very powerful high explosive.10 However, up to the present, there is little theoretical investigation on it. So, our primary interest in HNAB is quantum chemistry study on its structure and properties in order to look for potential high explo-sives in its derivatives.

IR spectrum, as well known, is not only the basic property of compounds, but also an effective measure to analyze substances. Vibrational spectroscopic investiga-tion with the help of the quantum chemistry calculation has attracted much research interest in recent years.11-14

However, to the best of our knowledge, the IR spectra of HNAB and its derivatives have been not explored theoretically and experimentally. Therefore, it is of great significance to predict IR spectra for both theo-retical and practical reasons by a theoretical method.

The heat of formation (HOF) is essential for ener-getic materials in many applications, because the heat release upon decomposition or combustion is a radical factor to determine detonation or propellant perform-ance.15 For stable compounds, of course, their HOF data can be obtained from experiments, but sometimes it is difficult to measure HOF via experiments due to the danger and difficulty. To solve this problem quantum chemical calculation has been widely used. Previous studies have showed that the theoretically predicted values of HOF were in good agreement with experi-ments.16

Thermodynamic properties, such as heat capacity, entropy and enthalpy, are important parameters for compounds and necessary in predicting reactive proper-ties of chemical reactions. Considerable interest exists in the prediction of these properties of materials in many processes, particularly those involving energetic materials.17-21 Accurate prediction of thermodynamic

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values is critical in developing models for chemical re-actions in which the experimental properties are incom-plete or inaccurate,22 and allows for the efficient use of resources, minimization of waste, and better screening in synthetic efforts to produce new and advanced mate-rials. For example, accurate prediction of f mH∆ � can aid us in quantitatively assessing detonation properties of explosives.23 To date, we have not found any ex-perimental thermodynamic properties of HNAB and its derivatives.

Density functional theory (DFT) has been widely used for computation of molecular structure and vibra-tional frequencies.24 Many studies25-27 have shown that the DFT-B3LYP method28,29 in combination with the 6-31G* basis set is able to give the accurate energies, molecular structures, and infrared vibrational frequen-cies.

In this study, we are interested in azobenzene-based energetic materials with respect to our ongoing interest in nitrogen-rich compounds as ingredients for propellant and explosive formulations.30-35 A series of nitro and amino derivatives of HNAB (see Figure 1 for the struc-tural diagrams of these compounds) have been designed. At the DFT-B3LYP/6-31G* level, they were optimized and their IR spectra were obtained by vibrational analy-sis. Subsequently, thermodynamic properties from 200 to 800 K were evaluated based on the calculated vibra-tional frequencies using the statistical thermodynamic method, and their relationships with the number of nitro and amino groups as well as the temperature were stud-ied. We hope these results will be helpful for further studies on other physical, chemical and energetic prop-erties of these compounds.

Computational Methods

The structures of HNAB and its derivatives are illus-trated in Figure 1. Using the DFT-B3LYP/6-31G* method incorporated in the Gaussian 03 program pack-age,36 they were fully optimized to obtain the molecular geometries and electronic structures. Vibrational analy-ses were performed thereafter at the same level. Since the DFT-calculated harmonic vibrational frequencies are usually larger than those observed experimentally, they were scaled using an empirical factor of 0.96 as was done before.37

Based on the principle of statistical thermodynam-ics,38 the standard molar heat capacity ( , mpC� ), entropy ( mS∆ � ), and enthalpy ( mH∆ � ) from 200 to 800 K were derived using the scaled frequencies and a self-compiled program.

The isodesmic reactions were applied to calculate the HOF of the title compounds at 298.15 K. For nitro derivatives of HNAB, reaction (1) was used; while for amino derivatives, reaction (2) was used.

C12H4－nO12＋2nN8＋n＋(8＋n)CH4→2C6H6＋

(6＋n)CH3NO2＋CH3N＝NCH3 (n＝0—4) (1)

C12H4＋nO12N8＋n＋(8＋n)CH4→2C6H6＋6CH3NO2＋

nCH3NH2＋CH3N＝NCH3 (n＝0—4) (2)

For the isodesmic reactions (1) and (2), the standard enthalpy change of reaction ( r mH∆ � ) at 298.15 K can be calculated from the following expression:

Figure 1 Illustration of the molecular structures of HNAB and its derivatives (ring hydrogen atoms are omitted for clarity).

Vibrational and Thermodynamic Properties of 2,2',4,4',6,6'-Hexanitroazobenzene

Chin. J. Chem. 2010, 28, 149—158 © 2010 SIOC, CAS, Shanghai, & WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.cjc.wiley-vch.de 151

r m f m,P m,RH H H∆ ∆∑ ∑＝－

� � �

(3)

where f m,PH∆∑� is the sum of experimental standard

HOF data of products, which are known from Refs. 39 and 40; f m,RH∆∑

� is the sum of the standard HOF of reactant.

The standard HOF of title compounds can be com-puted out if the standard enthalpy change of reaction

r mH∆ � at 298.15 K is known. On the other hand, r mH∆ � can also be calculated from DFT calculation

using the following equations:

r m 298.15 298( )H E pV E nRT∆ ∆ ∆ ∆ ∆＝＋＝＋� (4)

0298.15 0 T 0,P 0,R

0 0P R T,P T,R

ZPE

ZPE ZPE

E E H E E

H H

∆ ∆ ∆ ∆ ∑ ∑

∑ ∑ ∑ ∑

＝＋＋＝－＋

－＋－ (5)

where ∆E298.15 is the energy change of reactions (1) and (2) at 298.15 K; ∆E0 is the change in total energy be-tween the products and the reactants at 0 K, ∆ZPE is the difference in the zero-point energies (ZPE) between the products and the reactants; and 0

TH∆ is the difference of thermal correction to energy from 0 to 298.15 K. These can be obtained when the same DFT analysis has been performed on CH4, C6H6, CH3NO2, CH3NH2 and CH3N＝NCH3. The ∆(pV) value is the difference of pV work term, which equals ∆nRT in the reactions of ideal gas. For the isodesmic reactions (1) and (2), ∆n is 0, so ∆(pV) equals 0.

Results and Discussion

Geometric structures

The optimized geometry parameters including bond

lengths and dihedral angles between two phenyl ring planes are listed in Table 1. In order to better compare and test the reliability of the calculated results, available experimental geometric parameters of HNAB have also been given in Table 1, which were measured from the X-ray diffraction. On the whole, the optimized struc-tures agree well with the experimental observations, and the calculated C—H bond lengths are slightly longer than the experimental results due to the large uncer-tainty of the position of H in X-ray diffraction.

As can be seen evidently, the C—C bond lengths in nitro derivatives of HNAB are approximately close, while there are obvious changes for those in amino de-rivatives. For example, the shortest length in II-1 is 0.1383 nm while that in II-5 is 0.1400 nm. The reason is that there exist intermolecular hydrogen bonds between the oxygen atom of nitro and the hydrogen of amino in amino derivatives, in which the amino and nitro groups substitute for the hydrogen atoms alternately. With the increase of the amino substituting numbers, the C—C bond length elongates gradually. As for the N＝N bond length, gradual increase in nitro derivatives and little gradual decrease in amino derivatives have been found due to the withdrawing electron effect of a nitro group and the pushing electron effect of an amino group. The most significant variation of molecular structures is found in the dihedral angles between two phenyl rings. They vary from 71.9° to 114.4° gradually and regularly with the increase of the number of nitro groups in nitro derivatives because of the repulsion of the adjacent nitro groups, while because of hydrogen bonds between the nitro and amino, the corresponding dihedral angles in amino derivatives vary slightly from 74.6° to 79.8°.

Infrared spectra

Vibrational analysis is necessary as a part of theo-retical prediction of thermodynamic properties and can

Table 1 Optimized geometry parameters for HNAB and its derivatives

Bond length/nm Compd.

C—C N＝N C—N N—O N—H C—H Dihedral angle/(°)

I-1 0.1387—0.1410 0.1243 0.1417—0.1482 0.1225—0.1227 — 0.1082—0.1083 71.9

I-2 0.1388—0.1412 0.1244 0.1417—0.1486 0.1219—0.1229 — 0.1082—0.1083 77.2

I-3 0.1386—0.1410 0.1244 0.1418—0.1487 0.1218—0.1226 — 0.1083 82.0

I-4 0.1387—0.1409 0.1247 0.1419—0.1489 0.1216—0.1228 — 0.1082—0.1083 74.6

I-5 0.1388—0.1406 0.1250 0.1415—0.1488 0.1218—0.1225 — 0.1083 112.5

I-6 0.1388—0.1405 0.1251 0.1415—0.1487 0.1219—0.1222 — — 114.4

II-1 0.1383—0.1438 0.1242 0.1418—0.1480 0.1225—0.1241 0.1013 0.1082 74.6

II-2 0.1382—0.1441 0.1241 0.1334—0.1472 0.1225—0.1243 0.1013 0.1082 76.4

II-3 0.1386—0.1443 0.1242 0.1331—0.1480 0.1224—0.1246 0.1013—0.1015 0.1082—0.1083 81.6

II-4 0.1382—0.1443 0.1240 0.1332—0.1471 0.1227—0.1246 0.1013—0.1015 0.1082 81.7

II-5 0.1400—0.1445 0.1237 0.1332—0.1456 0.1227—0.1248 0.1012—0.1016 — 79.8

exp.a 0.1383—0.1397 0.1244 0.1426—0.1487 0.1209—0.1232 0.1000—0.1010 a exp. means the experimental values for I-1 (HNAB) taken from Ref. 41.



provide the motions responsible for the vibrational modes.

For HNAB, the energy-minimized structure of molecule has a C2h symmetry and 102 normal vibra-tional modes. The vibrational representation found from the calculation includes both infrared and Raman active modes. In the present paper, only the IR vibrations are discussed. Due to the complexity of vibrational modes, as well as no experimental data are available for com-parison, the vibrational spectra of the title compounds are difficult to assign, therefore, only some typical vi-brational modes were analyzed and discussed. Figure 2 provides the simulated IR spectra of HNAB and its de-

rivatives. For HNAB and its nitro derivatives (I-1—I-6), it is

remarkable that there are four to six main characteristic regions in their IR spectra. The frequencies in 3128.6— 3143.4 cm－1 can be assigned to C—H symmetry and asymmetry stretching vibrations, and in this region, the number of bands equals to that of C—H bonds. For example, HNAB has four C—H bonds, there are four bands of 3134.3, 3136.2, 3140.4 and 3143.4 cm－1 in its spectrum. The strongest peak in 1601.6—1630.4 cm－1 range is attributed to the N—O asymmetric stretch of nitro groups. Its central position moves towards higher frequency as the number of nitro groups increases. For



Figure 2 IR spectra of the title compounds calculated at the B3LYP/6-31G* level.

instance, the most intense signals in this region for I-1 (HNAB), I-2, I-3, I-4, I-5 and I-6 are at 1603.9, 1607.1, 1605.4, 1628.3, 1618.8 and 1621.3 cm－1, respectively. This is mainly caused by the strong induction effect of nitro groups. The N＝N stretching frequency is local-ized in 1563.4—1613.8 cm－1. Another intense band locates in 1329.9—1350.7 cm－1 range, in which the most intense signal of I-1 to I-6 corresponds to the N—O symmetric stretch of nitro groups. The frequen-cies of bands in 1150—1550 cm－1 are attributed to the skeletal stretching modes of the aromatic ring. The bands at about 900 and 870 cm－1 are attributed to the

out-of-plane and in-plane deformations of the nitro groups and aromatic ring, respectively. The other weak peaks at less than 1000 cm－1 located at the fingerprint region are mainly raised from the torsion of nitro groups and ring and can be used to identify isomers.

For the amino derivatives of HNAB (II-1—II-5), there are some different regions from the nitro deriva-tives. In the range of 3340.0—3499.7 cm－1, the modes are associated with the symmetric and asymmetric stretch of N—H and the higher one is an asymmetrical mode. The number of frequencies equals to that of N—H bonds as for C—H. Compared to the corre-



sponding frequencies at 3440 and 3360 cm－1 in ani-line,36 it is obvious that there is hydrogen-bonding be-tween amino and nitro groups. The strong IR active modes locating in 1251.9—1620.5 cm － 1 range are raised from the NH2 symmetric angle deformation, the N—O asymmetric and symmetric stretch of nitro groups, the N＝N stretch and the ring skeletal stretch, in which the N＝N stretching frequency is localized at about 1583 cm－1. In this region, with the increase of the number of NO2 groups, the N—O asymmetric and symmetric stretches of nitro groups move to lower fre-quencies. The fingerprint region can be similarly used to identify isomers, and the weak peaks in this region are mainly caused by the out-of-plane and in-plane defor-

mations of amino groups. The bands in 1031.8—1055.4 cm－1 are attributed to C—H rock of the rings. The vi-brations in 507.5—563.9 cm－1 are associated with the out-of-plane deformation of amino moieties, and the number of bands equals to that of NH2 groups, taking II-5 as an example, it has four NH2 groups and there are four bands (533.3, 542.7, 547.2 and 563.1 cm－1) in its spectrum.

Thermodynamic properties

Thermodynamic properties of the title compounds ranging from 200 to 800 K were calculated and listed in Table 2.

Table 2 Thermodynamic properties of the title compounds at different temperatures

T Compd. Therm. prop.

200 298.15 300 400 500 600 700 800

,mpC� 314.59 417.70 419.51 508.85 580.33 635.75 678.43 711.54

m∆S� 652.93 798.16 800.75 934.09 1055.63 1166.56 1267.90 1360.75 I-1

m∆H � 38.33 74.37 75.14 121.71 176.31 237.24 303.04 372.61

,mpC� 348.24 456.60 458.50 551.52 625.83 683.39 727.62 761.78

m∆S� 705.81 865.53 868.36 1013.45 1144.84 1264.25 1373.07 1472.55 I-2

m∆H � 42.66 82.28 83.12 133.78 192.80 258.39 329.03 403.58

,mpC� 381.67 495.56 497.53 594.37 671.55 731.26 777.02 812.22

m∆S� 748.60 922.78 925.85 1082.72 1223.99 1351.95 1468.26 1574.41 I-3

m∆H � 46.69 89.88 90.79 145.56 209.01 279.28 354.80 434.33

,mpC� 382.59 496.00 497.97 594.59 671.66 731.31 777.03 812.21

m∆S� 749.79 924.24 927.32 1084.28 1225.58 1353.55 1469.87 1576.03 I-4

m∆H � 46.85 90.11 91.03 145.82 209.29 279.57 355.09 434.63

,mpC� 415.46 534.31 536.36 636.84 716.88 778.77 826.10 862.37

m∆S� 788.45 977.11 980.42 1148.98 1300.05 1436.47 1560.23 1673.02 I-5

m∆H � 50.85 97.61 98.60 157.44 225.29 300.21 380.55 465.06

,mpC� 449.23 573.26 575.39 679.61 762.51 826.55 875.41 912.71

m∆S� 834.67 1037.85 1041.40 1221.73 1382.66 1527.60 1658.85 1778.29 I-6

m∆H � 55.10 105.45 106.51 169.45 241.72 321.32 406.53 496.02

,mpC� 327.58 438.33 440.26 534.60 609.62 667.67 712.39 747.16

m∆S� 658.22 810.18 812.90 952.94 1080.63 1197.14 1303.57 1401.06 II-1

m∆H � 39.13 76.85 77.66 126.57 183.94 247.93 317.03 390.07

,mpC� 340.41 458.88 460.92 560.33 638.93 699.63 746.40 782.83

m∆S� 666.67 825.31 828.15 974.88 1108.72 1230.81 1342.33 1444.47 II-2

m∆H � 40.01 79.40 80.25 131.49 191.62 258.68 331.08 407.61

,mpC� 339.60 458.00 460.05 559.78 638.64 699.50 746.38 782.89

m∆S� 669.38 827.65 830.49 977.01 1110.76 1232.81 1344.32 1446.46 II-3

m∆H � 40.11 79.40 80.25 131.42 191.51 258.55 330.94 407.48

,mpC� 352.54 478.68 480.84 585.61 668.01 731.51 780.42 818.57

m∆S� 676.88 841.88 844.85 998.09 1138.00 1265.66 1382.26 1489.06 II-4

m∆H � 40.96 81.94 82.83 136.34 199.20 269.32 345.02 425.04

,mpC� 363.97 498.11 500.39 610.72 697.03 763.38 814.47 854.36

m∆S� 687.02 858.17 861.26 1020.93 1166.89 1300.10 1421.78 1533.25 II-5

m∆H � 41.76 84.27 85.20 140.97 206.54 279.71 358.71 442.23 a Units: T, K; ,mpC� , J•mol－1•K－1; m∆S� , J•mol－1•K－1; m∆H � , kJ•mol－1.



From Table 2, it can be seen that all thermodynamic functions increase evidently with the rise of temperature. The reasonable interpretation of this result is that trans-lational, vibrational and rotational movements strengthen gradually as the temperature increases, so the thermodynamic functions mH∆ � and mS∆ � , contrib-uted from these three movements, increase evidently with the rise of temperature. As for translational ,mpC� and rotational ,mpC� , they are constant under some approximations. Only vibrational heat capacity depends on temperatures. The vibrational movement is weak when temperature is low, so the main contributions to

,mpC� come from the translation and rotation of mole-cule, while with the rise of the temperature, the vibra-tional movement is intensified and therefore makes more contributions to ,mpC� , which leads to the increase of ,mpC� values. As for isomers, no significant differ-ences can be observed between their three thermody-namic functions owing to their similar geometric and electronic structures. Figure 3 shows the temperature- dependent relations of ,mpC� , mS∆ � and mH∆ � in the range 200—800 K for HNAB. For the derivatives of HNAB, similar relationships are found too. It is evident that, as the temperature increases, the gradients of ,mpC� and mS∆ � to the temperature decrease, while that of

mH∆ � increases gradually.

Coefficients of the relationships between the ther-modynamic functions and the temperature (T) for the title compounds were calculated and listed in Table 3.

Moreover, the three thermodynamic functions in-crease with the addition of the number of nitro and amino substituent groups. The reason is that the more the number of atoms the molecule has, the more vibra-tional modes there are, then the greater the correspond-ing thermodynamic functions are.

Figure 4 presents the plots of the calculated thermo-dynamic functions versus the substituent number of ni-tro (n1) and amino (n2) groups at 298.15 K, respectively.

It can be found from Figure 4 that, for the nitro and amino derivatives of HNAB (I-1－I-6 and II-1－II-5), the thermodynamic functions increase linearly along with the number of nitro (n1) or amino (n2) groups.

The linear relationships between the thermody-namic functions and the number of nitro groups (n1) are

,mpC�＝184.51＋38.88n1

mS∆ �＝448.18＋59.10n1

mH∆ �＝27.96＋7.75n1

Figure 3 Relationships between the thermodynamic functions and the temperature (T) for HNAB.



Table 3 Coefficients of the relationships between the thermodynamic functions and the temperature (T) for the title compounds

,mpC� /(J•mol•K－1) m∆S� /(J•mol－1•K－1) m∆H � /(kJ•mol－1) Compd.

A B C

A B C

A B C

I-1 66.25 1.40 －7.43×104 333.20 1.72 －5.43×104 －24.40 0.24 3.24×104

I-2 88.59 1.47 －7.83×104 355.32 1.89 －6.20×104 －27.04 0.27 3.37×104

I-3 110.23 1.53 －8.26×104 367.32 2.06 －6.96×104 －29.99 0.30 3.51×104

I-4 111.95 1.53 －8.22×104 368.13 2.07 －6.98×104 －29.94 0.30 3.50×104

I-5 133.01 1.60 －8.63×104 376.55 2.24 －7.73×104 －32.76 0.33 3.63×104

I-6 155.38 1.67 －9.03×104 391.96 2.41 －8.50×104 －35.49 0.37 3.77×104

II-1 64.00 1.49 －7.99×104 322.80 1.80 －5.67×104 －26.70 0.25 3.41×104

II-2 61.40 1.58 －8.56×104 315.64 1.88 －5.91×104 －28.88 0.26 3.58×104

II-3 59.98 1.59 －8.57×104 319.06 1.88 －5.87×104 －28.54 0.26 3.59×104

II-4 57.53 1.68 －9.14×104 310.84 1.96 －6.11×104 －30.79 0.27 3.76×104

II-5 52.31 1.78 －9.74×104 306.30 2.04 －6.30×104 －32.76 0.28 3.95×104

Figure 4 Relationships between the thermodynamic functions and the number of NO2 (n1, left) and NH2 (n2, right) groups at 298.15 K.

respectively, and the corresponding correlation coefficients are 1.0000, 0.9992 and 1.0000, all being larger than 0.99. In this condition, ,mpC� , mS∆ � , and

mH∆ � increase by 38.88 J•mol－1•K－1, 59.10 J•mol－1• K－1 and 7.75 kJ•mol－1 on average respectively when one more nitro group is introduced, which indicates good group additivity of the thermodynamic functions.

As for the amino derivatives of HNAB (II-1－II-5), the correlation equations are as follows:

,mpC�＝418.51＋19.96n2

mS∆ �＝794.44.20＋15.92n2

mH∆ �＝74.42＋2.48n2

The corresponding correlation coefficients are 0.9999, 0.9989 and 0.9998, respectively. Similarly,

,mpC� , mS∆ � , and mH∆ � increase on average by 19.96 J•mol－1•K－1, 15.92 J•mol－1•K－1 and 2.48 kJ•mol－1, respectively when one more amino group is introduced, which are much smaller than those of nitro groups.

From those mentioned above it can be concluded evi-dently that the thermodynamic functions for nitro de-rivatives increase much more than those for amino de-rivatives with the increase in the number of substituents. It is also the result of hydrogen-bonding between amino and nitro groups.

Table 4 presents the total energies, zero-point ener-gies, the values of thermal correction and standard HOF for the title compounds and five reference compounds being enlisted in the isodesmic reactions.

It is evident that the nitro and amino derivatives of HNAB both have quite large positive HOF, which is useful for high energy density materials, and the values of HOF for the nitro derivatives are larger than those for the amino ones. In addition, the values of standard HOF relate to the number of substituent groups for the title compounds. Figure 5 shows the plots of the calculated HOF versus the number of substituents (n), in which the lowest HOF data of isomers with the same kind and number of substituting groups have been adopted.

It is obvious that the plots all have a good linear re-lationship with correlation coefficients (R) larger than 0.99, which indicates good group additivity on the HOF of HNAB derivatives. At the same time, it can be seen



Table 4 Energies and heats of formation for the title com-pounds and five reference compounds

Compd. E0 a ZPE a m∆H � a f m∆ H � b

C6H6 －232.25 0.10075 0.10514 82.9c

CH3NO2 －245.01 0.05018 0.05455 －80.8c

CH3NH2 －95.85 0.06443 0.06781 －22.5c

CH3N＝NCH3 －189.28 0.08494 0.09007 148.8d

CH4 －40.52 0.04522 0.04809 －74.6c

I-1 －1799.68 0.20368 0.23029 346.4

I-2 －2004.14 0.20508 0.23465 401.2

I-3 －2208.60 0.20648 0.23888 461.0

I-4 －2208.60 0.20642 0.23891 446.8

I-5 －2413.07 0.20804 0.24333 502.6

I-6 －2617.53 0.20943 0.24764 556.2

II-1 －1855.05 0.22118 0.24868 304.2

II-2 －1910.41 0.23860 0.26702 265.7

II-3 －1910.41 0.23842 0.26684 271.7

II-4 －1965.77 0.25586 0.28519 234.5

II-5 －2021.14 0.27311 0.30327 201.0 a E0, ZPE, m∆H � in a.u.; b

f m∆ H � in kJ•mol－1; c from Ref. 35; d from Ref. 36.

Figure 5 Relationship between HOF and the number of sub-stituents.

that different groups exert different influence on the values of HOF. The HOF increases by 52.1 kJ•mol－1 if one more nitro group is introduced; while for amino derivatives, one more amino group leads to the decrease of HOF by 36.05 kJ•mol－1.

Furthermore, for the isomers with the same kind and number of substituting groups, the values of HOF of the isomers are lightly different, indicating that the HOF is also influenced by the position of the substituting groups. Taking nitro derivatives for example, the HOF of I-3 is higher than that of I-4. This is because there are six adjacent nitro groups in I-3, while only five ones in I-4, which leads to more repulsion energy in I-3, thus the higher HOF. As far as the isomers II-2 and II-3 are concerned, the effect of hydrogen bonds in II-2 is larger than that in II-3, so the HOF of II-2 is lower than that of II-3. The thermodynamic functions and correlation

equations obtained here would be helpful for further studies on the other physical, chemical and explosive properties of the derivatives of HNAB.

Conclusion

From the above theoretical calculation and analysis on the IR spectra and thermodynamic properties of the derivatives of HNAB at the B3LYP/6-31G* level, the following conclusions can be drawn:

(1) The calculated IR spectra have four to six main characteristic regions. Two of them are very strong. One corresponds to the N—O asymmetric stretch, NH2 sym-metric angle deformation and skeletal vibration, and the other is associated with the N—O symmetric stretch. The N＝N stretching frequency is localized in 1563.4— 1613.8 cm－1. The band in the range greater than 3000.0 cm－1 is due to the symmetric and asymmetric stretch of C—H or N—H. The peaks at less than 1000 cm－1 are mainly raised from the torsion of nitro groups and ring or out-of-plane deformation of amino moieties that lo-cate in the fingerprint region.

(2) Thermodynamic functions ( ,mpC� , mS∆ � and mH∆ � ) in the range from 200 to 800 K were evaluated

and the relationships with temperature were found. As the temperature increases, ,mpC� , mS∆ � , and mH∆ � increase, the gradients of mH∆ � to the temperature in-crease gradually too, while those of ,mpC� and mS∆ � decrease. At the same time, thermodynamic properties increase quantitatively with the increase in the number of nitro and amino groups, reflecting good group addi-tivity. And the thermodynamic functions for the nitro derivatives increase much more than those for the amino derivatives with the increase in the number of substitu-ents.

(3) The nitro and amino derivatives of HNAB both have quite large positive HOF, which is useful for high energy density materials, and the values of HOF for the nitro derivatives are larger than those for the amino ones. The calculated HOF data have a good linear relationship with the number of groups, indicating good group addi-tivity. Different substitutent groups exert different in-fluence on the values of HOF. The values of HOF for the nitro derivatives increase gradually with n, while those of the amino derivatives decrease smoothly with n. For the isomers, the values of HOF are slightly differ-ent.

References

1 Li, Q.-S.; Cheng, L.-P. J. Phys. Chem. A 2003, 107, 5561. 2 Petrie, M. A.; Sheehy, J. A.; Boatz, J. A. J. Am. Chem. Soc.

1997, 119, 8802. 3 Ye, C.-F.; Shreeve, J. M. J. Chem. Eng. Data 2008, 53, 520. 4 Mulinax, R. L.; Okin, G. S.; Coombe, R. D. J. Phys. Chem.

1995, 99, 6294. 5 Qiu, L.; Gong, X.-D.; Xiao, H. M. Chin. J. Chem. 2008, 26,

2165. 6 Klapötke, T. M.; Sabaté, C. M. Chem. Mater. 2008, 20,



3629. 7 Chavez, D. E.; Hiskey, M. A.; Gilardi, R. D. Angew. Chem.,

Int. Ed. 2000, 39, 1861. 8 Hammerl, A.; Klapötke, T. M.; Nöth, H. Inorg. Chem. 2001,

40, 3570. 9 Ostrovskii, V. A.; Pevzner, M. S.; Kofman, T. P.; Tselinskii,

I. V. Heterocycl. Syst. 1999, 3, 467. 10 Rodriguez, M. A.; Campana, C. F.; Rae, A. D. Acta Crys-

tallogr. C 2005, 61, 127. 11 Huang, Z.; Chen, B.; Gao, G.-Q. J. Mol. Struct. 2005, 752,

87. 12 Wang, G.-X.; Shi, C.-H.; Gong, X.-D.; Xiao, H.-M. Chin. J.

Chem. 2009, 27, 687. 13 Qiu, L.-M.; Gong, X.-D.; Wang, G.-X.; Zheng, J.; Xiao,

H.-M. Chin. J. Chem. 2009, 27, 455. 14 Wang, G.-X.; Gong, X.-D.; Xiao, H.-M. Chin. J. Chem.

2008, 26, 357. 15 Wang, F.; Xu, X.-J.; Xiao, H.-M.; Zhang, J. Acta Chim.

Sinica 2003, 61, 1939 (in Chinese). 16 Zhang, J.; Xiao, H.-M. J. Chem. Phys. 2002, 116, 10674. 17 Gutowski, K. E.; Rogers, R. D.; Dixon, D. A. J. Phys. Chem.

B 2007, 111, 4788. 18 Schmidt, M. W.; Gordon, M. S.; Boatz, J. A. J. Phys. Chem.

A 2005, 109, 7285. 19 Zorn, D. D.; Boatz, J. A.; Gordon, M. S. J. Phys. Chem. B

2006, 110, 11110. 20 Gutowski, K. E.; Holbrey, J. D.; Rogers, R. D.; Dixon, D. A.

J. Phys. Chem. B 2005, 109, 23196. 21 Gutowski, K. E.; Rogers, R. D.; Dixon, D. A. J. Phys. Chem.

A 2006, 110, 11890. 22 Miller, J. A.; Kee, R. J.; Westbrook, C. K. Annu. Rev. Phys.

Chem. 1990, 41, 345. 23 Rice, B. M.; Hare, J. Thermochim. Acta 2002, 384, 377. 24 Parr, R. G.; Yang, W. Density-functional Theory of Atoms

and Molecules, Oxford University Press, New York, 1989. 25 Xu, X.-J.; Xiao, H.-M.; Gong, X.-D.; Ju, X.-H.; Chen, Z.-X.

J. Phys. Chem. A 2005, 109, 11268. 26 Qiu, L.; Xiao, H.-M.; Gong, X.-D.; Ju, X.-H.; Zhu, W.-H. J.

Phys. Chem. A 2006, 110, 3797. 27 Zhang, J.; Xiao, H.-M. J. Chem. Phys. 2002, 116, 10674. 28 Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785. 29 Becke, A. D. J. Chem. Phys. 1992, 97, 9173. 30 Chavez, D. E.; Hiskey, M. A. J. Energy Mater. 1999, 17,

357. 31 Chavez, D. E.; Hiskey, M. A.; Naud, D. L. Propell. Explos.

Pyrotech. 2004, 29, 209. 32 Hammerl, A.; Holl, G.; Kaiser, M.; Klapötke, T. M.; Mayer,

P.; Nöth, H.; Piotrowski, H.; Warchhold, M. Eur. J. Inorg. Chem. 2002, 4, 834.

33 Hammerl, A.; Holl, G.; Klapötke, T. M.; Mayer, P.; Nöth, H.; Piotrowski, H.; Suter, M. T. Z. Naturforsch. B 2001, 56, 857.

34 Geith, J.; Klapötke, T. M.; Weigand, J. J.; Holl, G. Propell. Explos. Pyrotech. 2004, 29, 3.

35 Klapötke, T. M.; Mayer, P.; Shulz, A.; Weigand, J. J. Pro-pell. Explos. Pyrotech. 2004, 29, 325.

36 Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.; Vreven, J. T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scal-mani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochter-ski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Sal-vador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Ste-fanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, Gaussian, Inc., Pittsburgh, PA, 2003.

37 Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502. 38 Hill, T. L. Introduction to Statistic Thermodynamics, Addi-

son-Wesley, New York, 1960. 39 Lide, D. R. CRC Handbook of Chemistry and Physics,

Internet Version 2005, CRC Press, Boca Raton, FL, 2005. 40 Dean, J. A. LANGE’S Handbook of Chemistry, 15th ed.,

McGraw-Hill, Inc., New York, 1999, Chapter 6. 41 Graeber, E. J.; Morosin, B. Acta Crystallogr. 1974, B30,

310.

(E0903232 Zhao, C.; Fan, Y.)

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