Accurate Prediction of Enthalpies of Formation of Organic Azides by

Article pubs.acs.org/JPCA

Accurate Prediction of Enthalpies of Formation of Organic Azides by Combining G4 Theory Calculations with an Isodesmic Reaction Scheme Olga V. Dorofeeva,* Oxana N. Ryzhova, and Marina A. Suntsova Department of Chemistry, Lomonosov Moscow State University, Moscow 119991, Russia S Supporting Information *

ABSTRACT: Accurate gas-phase enthalpies of formation (ΔfH298 ° ) of 29 azides are recommended by combining G4 theory calculations with an isodesmic reaction approach. The internal consistency over a set of ΔfH°298 values was achieved by sequential adjustment of their values through the isodesmic reactions. The HN3 was chosen as a key reference compound. Of the experimental data available for 16 compounds, our predictive values agree well with 9 of them, while the deviations from 25 to 55 kJ/mol are observed for 7 compounds; possible systematic errors in the experimental data for phenyl azide, 2-azidoethanol, azidocyclopentane, azidocyclohexane, 3-azido-3-ethylpentane, 2-azido-2-phenylpropane, and 1-azidoadamantane are discussed. The recommended enthalpies of formation of organic azides were used as reference values to estimate the enthalpy of formation of four nitrogen-rich carbon nitrides. The calculations do not support the high value of the solid-state enthalpy of formation of TAAT (4,4′,6,6′-tetra(azido)azo-1,3,5-triazine); its value is estimated to be 300−400 kJ/mol lower than that measured experimentally.

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INTRODUCTION Organic azides are energy-rich molecules that are widely used as explosives, components of propellants, and pyrotechnics.1,2 The azido group (−N3) is one of the most energetic functional groups; the introduction of the azido group into an organic compound increases its energy content by approximately 300 kJ/mol.3 Organic azides are also considered as powerful precursors for nitrogen-rich compounds such as carbon nitride nanomaterials.2,4,5 Important characteristics of explosives and propellants may be calculated from the enthalpy of formation (ΔfH°298), which is closely related to the stability of these compounds.6 However, the experimental investigation of azides can present great challenges due to their extreme sensitivity to spark, friction, and impact. That is why the experimental enthalpies of formation for the vast majority of organic azides are unknown or only known with relatively large uncertainties. To satisfy the need of energetic materials chemists for reliable thermochemical data, the enthalpies of formation of organic azides can be predicted by theoretical calculations. Direct quantum chemical computation of a molecular enthalpy of formation from the atomization energies requires the high-accuracy energy methods. Because of their computational expense, these methods can be applied now only to small molecules. To make accurate predictions of thermochemical data for larger molecules, a number of composite methods have been developed over the past two decades. Among the widely used and successful composite methods are the Gaussian-n (Gn) family methods.7 The latest version of these methods, Gaussian-4 (G4) theory,8 achieves an overall accuracy of © 2013 American Chemical Society

3.3 kJ/mol for the test set of 270 accurate experimental enthalpies of formation. The G4 method was found to be accurate in calculating the enthalpies of formations of different classes of compounds including nitrogen-containing organic compounds.9,10 However, as it was found in our previous works,11,12 the G4 theory ° values of most nitro compounds by underestimates the ΔfH298 up to 20 kJ/mol. A good agreement with experiment was obtained only when the isodesmic reactions were used instead of the atomization reaction. In isodesmic reactions, the number and types of bonds are conserved on each side of the reaction, and this leads to cancellation of the inherent errors associated with the computation.13−15 It should also be noted that the isodesmic reactions approach is the only way to calculate the enthalpies of formation for large energetic molecules with 15 and more heavy atoms because of the increasingly large computational cost of the atomization energy calculation by G4 theory in this case. Compared to nitro compounds, experimental data on enthalpies of formation of organic azides are scanty and not always reliable. ° values should Therefore, a set of azides with reliable ΔfH298 be established before using the isodesmic reaction with these compounds. Otherwise, errors in reference enthalpies of formation can lead to large overall errors in the predicted enthalpies of formation, especially when the differing values are used to Received: May 6, 2013 Revised: July 8, 2013 Published: July 8, 2013 6835

dx.doi.org/10.1021/jp404484q | J. Phys. Chem. A 2013, 117, 6835−6845

The Journal of Physical Chemistry A

Article

Figure 1. Most stable conformations of the studied organic azido compounds: hydrogen azide (1), triazide radical (2), methyl azide (3), phenyl aizde (4), benzyl azide (5), 4-nitrophenyl azide (6), cyanogen azide (7), 2-azido-acetonitrile (8), 1-azido-2-nitro-2-azapropane (9), 1-azido-1,1dinitroethane (10), azidotrinitromethane (11), 2-azidoethanol (12), 1-azido-2-ethoxyethane (13), ethyl-(2-azide)-ethanoate (14), azidocyclopentane (15), azidocyclohexane (16), 1,2-diazidobenzene (17), 1,3-diazidobenzene (18), 1,4-diazidobenzene (19), 1,3,5-triazidobenzene (20), 4-azidopyridine (21), triphenylmethyl azide (22), 3-azido-3-ethylpentane (23), 2-azido-2-phenylpropane (24), 1-azidoadamantane (25), 2,4,6-tri(azido)-1,3,5-triazine or TAT (26), 2,5,8-tri(azido)-s-heptazine or TAH (27), 4,4′,6,6′-tetra(azido)azo-1,3,5-triazine or TAAT (28), and 3,6-di(azido)-1,2,4,5-tetrazine or DiAT (29).

Information. The enthalpies of formation calculated by different composite methods from atomization energy are summarized in Table S2 (Supporting Information). The G4 enthalpies of formation were calculated using both the atomization18,19 and isodesmic reaction13−15 procedures. The calculation through atomization reaction involves the use of experimental enthalpies of formation of gaseous atoms at T = 0 K and thermal corrections for elements in their standard states; the corresponding values were taken from the reference book by Gurvich et al.20 For isodesmic reaction, the resulting enthalpy of formation was calculated combining the G4 enthalpy of reaction8 with the enthalpies of formation of reference molecules. For three large molecules (22, 27, and 28), the G4(MP2) method21 was used instead of G4. This modification of G4 theory is designed to shorten computational times with some loss of accuracy. The experimental ΔfH°298 values for reference species involved in isodesmic and other balanced reactions are given in Table S3 of the Supporting Information. In Table 1, the G4 enthalpies of formation calculated from atomization reaction are compared with those obtained from isodesmic reactions. For each species, the number of isodesmic reactions designed is given; the ΔfH°298 value in the column “isodesmic reactions” corresponds to the average of all reactions. The full list of reactions is presented in Table S4 (Supporting Information). The number of reference azido compounds used

calculate the enthalpy of formation of compounds with several azido groups. In this study, the enthalpies of formation of 29 azides (Figure 1) were calculated using the G4, G4(MP2), G3, and G3(MP2)// B3LYP methods.7 For five small molecules, the calculations by W1U theory16 were also performed. The reliable internally self° values were recommended combining the G4 or consistent ΔfH298 G4(MP2) theory calculations with an isodesmic reaction scheme. The species considered contain from 3 to 26 non-hydrogen atoms and include several synthesized heterocyclic carbon nitrides like 2,4,6-tri(azido)-1,3,5-triazine (TAT), 2,5,8-tri(azido)-s-heptazine (TAH), 4,4′,6,6′-tetra(azido)azo-1,3,5-triazine (TAAT), and 3,6di(azido)-1,2,4,5-tetrazine (DiAT). First of all, the compounds with reported experimental data were included in this study.

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COMPUTATIONAL DETAILS All ab initio and density functional theory (DFT) calculations were performed using the Gaussian 03 package of programs.17 Geometry optimizations and frequency and potential energy calculations were performed for all of the molecules using the DFT/B3LYP/6-31G(d,p) method. The optimized geometries of the most stable conformers were used as inputs for further G4, G4(MP2), G3, G3(MP2)//B3LYP, and W1U calculations. The optimized Cartesian coordinates of the most stable conformers of all compounds are collected in Table S1 of the Supporting 6836



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Table 1. Enthalpies of Formation of Azido Compounds Calculated by the G4 Method (in kJ/mol) atomization reaction 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

isodesmic reactions

compounda

ΔfH°298

ΔfH°298

number of reactions

number of reference azides

(max−min)b

HN3 •N3 CH3N3 C6H5N3 C6H5CH2N3 1,4-NO2−C6H4−N3 NCN3 NCCH2N3 CH3N(NO2)CH2N3 CH3C(NO2)2N3 C(NO2)3N3 HOCH2CH2N3 CH3CH2OCH2CH2N3 N3CH2C(O)OC2H5 azidocyclopentane azidocyclohexane 1,2-diazidobenzene 1,3-diazidobenzene 1,4-diazidobenzene 1,3,5-triazidobenzene 4-azidopyridine (C6H5)3CN3 (CH3CH2)3CN3 (CH3)2(C6H5)CN3 1-azidoadamantane TAT TAH TAAT DiAT

289.0 445.5 293.9 409.5 400.9 384.3 495.4 453.3 330.5 246.0 337.8 112.5 93.5 −83.2 256.5 208.0 746.6 736.7 739.1 1064.9 463.8 592.6c 126.1 326.5 170.1 1120.8 1418.1c 1936.0c 1116.8

291.9 449.9 297.9 414.7 404.7 393.9 501.1 457.4 336.1 262.7 357.2 114.7 99.6 −79.0 256.2 210.0 756.1 745.7 748.0 1077.4 470.1 610.4c 132.0 332.7 182.8 1137.0 1408.7c 1924.6c 1125.0

10 20 50 38 23 25 16 29 10 20 26 21 50 28 16 21 16 18 19 12 21 29 25 27 18 17 14 7 8

0 1 2 3 5 7 5 12 4 7 8 8 13 7 9 10 7 8 9 6 10 9 7 7 5 8 6 5 5

12.2 7.3 12.0 9.3 7.6 12.4 7.9 9.9 10.4 9.4 10.2 7.4 7.4 11.4 6.3 6.9 11.2 8.9 10.0 12.3 10.4 12.7 10.1 8.6 10.6 16.6 28.4 14.0 7.8

a

The compound’s number according to Figure 1 is given for each molecule. bDifference between maximum and minimum values obtained from isodesmic reactions. cG4(MP2) values.

diagnostic tool to identify experimental data that may require re-examination.

in the isodesmic reaction calculations is also given in Table 1. The selection of these reference species requires some explanations. Hydrogen azide HN3 was chosen as a key reference compound. The accepted value of ΔfH°298(HN3, g) = 292.5 ± 1.5 kJ/mol was calculated from the reference value of the atomization energy recommended in the Active Thermochemical Tables (ATcT).22 This value is in good agreement with the experimental value of 294 ± 4.0 kJ/mol20 and results of the most precise calculations;22,23 it was used in all further calculations. The enthalpy of formation of the next compound, radical •N3, was accepted to be equal to the average of isogyric reactions with HN3 involved as a reference molecule (Table S4, Supporting Information). After that, the new compound, CH3N3, was considered; its ΔfH°298 value was estimated from isodesmic reaction calculations (Table S4, Supporting Information) using the earlier accepted enthalpies of formation of HN3 and •N3. The ΔfH298 ° values for remaining species were obtained in the same way; the compounds with previously estimated enthalpies of formation were used as reference compounds in the isodesmic reaction calculations for new molecules. In other words, in each step, a new reference species was added while all values determined in previous steps were frozen. Table 2 shows the reference species that were used in isodesmic reactions for each of 29 compounds studied in this work. The proposed sequential approach was used to assess the internal consistency over the ΔfH298 ° values and as a

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RESULTS AND DISCUSSION Comparison with Experimental Data and Results of Previous Calculations. The ΔfH298 ° values calculated in this study from isodesmic reactions and other types of balanced reactions are compared with available experimental data and results of previous calculations in Table 3. As mentioned above, the enthalpy of formation of HN3 (1) accepted in this work, 292.5 ± 1.5 kJ/mol, is based on the ATcT reference value of the atomization energy.22 As seen from Table 3, this value agrees well with the experimental value and results of high-level fc-CCSD(T)/cc-pCVQZ//ae-CCSD(T)/cc-pCVTZ22 and W423 calculations, while the CCSD(T)/CBS value25 is significantly larger (297 kJ/mol). It should be noted that although the isogyric and other balanced reactions give the ΔfH°298(HN3, g) values in the range of 287−299 kJ/mol (Table S4, Supporting Information), the average of 10 reactions (292 kJ/mol) is very close to the recommended value. Thus, the use of the large number of reactions, even if they are not well balanced, leads to reliable estimation of the enthalpy of formation. Conflicting experimental results for the enthalpy of formation of the •N3 radical (2) are reported in the literature (Table 3). The value recommended in this work, ΔfH°298(•N3, g) = 450 ± 4 kJ/mol, is the average of 20 isogyric reactions with HN3 and different radicals involved in these reactions as reference species 6837



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Table 2. Use of Azido Compounds as Reference Species in Isodesmic Reaction Calculationsa

Species used as the reference in isodesmic reaction calculations are marked by a solid circle symbol. For example, HN3, •N3, and CH3N3 species were used in isodesmic reactions for C6H5N3.

a

recommended in this study, ΔfH298 ° (C6H5N3, g) = 415 ± 5 kJ/mol, is the mean of the values derived from 38 reactions with •N3, HN3, and CH3N3 used as the reference species (Table S4, Supporting Information). The ΔfH298 ° values obtained from these reactions vary from 410 to 419 kJ/mol, and thus, none of the reactions give the value close to the experimental one (389 kJ/mol). All composite methods (Table S2, Supporting Information) also predict values higher than 409 kJ/mol. Therefore, the theoretical results show that the experimental enthalpy of formation of liquid C6H5N3 or/and its enthalpy of vaporization may be underestimated by 25 kJ/mol in total. An additional argument in support of inaccuracy of the experimental value for C6H5N3(g) comes from comparison with the reported gas-phase enthalpy of formation of its nitro derivative, 1,4-NO2−C6H4−N3 (389.7 kJ/mol),35 which is practically the same as that for phenyl azide, while usually, the addition of a nitro group to phenyl derivatives decreases the enthalpy of formation from 15 to 30 kJ/mol. Because the experimental ΔfH298 ° (1,4-NO2−C6H4−N3, g) value agrees well with that calculated in this study (Table 3), one can suggest that the experimental enthalpy of formation of C6H5N3 is not reliable enough.

(Table S4, Supporting Information). This value is between two experimental values (469 ± 2126 and 436 ± 15 kJ/mol20) and is close to the results of the most accurate calculations (449−454 kJ/mol).24,27,28 The enthalpy of formation of CH3N3 (3) was not derived experimentally, while its accurate value is required in the ° values of different energetic compounds prediction of ΔfH298 with an azido group. The value recommended in this study, ΔfH°298(CH3N3, g) = 298 ± 4 kJ/mol, is the mean of the values derived from 50 reactions with •N3 and HN3 used as reference species (Table S4, Supporting Information). The root-meansquare deviation of the calculated values from this value is 2.4 kJ/mol. The recommended value is in good agreement with the W1U value (Table S2, Supporting Information) and the value accepted by Chen and McQuaid24 based on isodesmic reaction calculations (Table 3). As for the value calculated at the CCSD(T)/CBS level,25 it seems to be overestimated as well as the value for HN3 (Table 3). The literature value of the enthalpy of formation of gaseous C6H5N3 (4) is based on the enthalpy of formation of the liquid phenyl azide determined in 1929 by Roth and Muller31 and enthalpy of vaporization derived later from the temperature dependencies of the vapor pressures33 (Table 3). The value 6838



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Table 3. Enthalpies of Formation (ΔfH298 ° ) in Both Condensed and Gaseous Phases and Enthalpies of Sublimation (ΔsubH298 ° ) or Vaporization (ΔvapH°298) of Azido Compounds (in kJ/mol) experiment compounda

ΔfH298 ° (l) or ΔfH298 ° (cr)

calculation

° or ΔvapH298 ΔsubH298 °

ΔfH298 ° (g)

ΔfH298 ° (g)

reference this workb

294 ± 4 469 ± 21 436 ± 15 414 ± 21

1 2

HN3 (g) •N3 (g)

3 4

CH3N3 (l) C6H5N3 (l)

344.3

5

C6H5CH2N3 (l)

368.2 ± 1.3

6 7

1,4-NO2−C6H4−N3 (cr) NCN3 (l)

308.7 ± 4.3

8 9 10

NCCH2N3 (l) CH3N(NO2)CH2N3 (l) CH3C(NO2)2N3 (l)

196.2 ± 2.9

11 12

C(NO2)3N3 (l) HOCH2CH2N3 (l)

306.3 ± 5.4 94.0 ± 1.6

13 14

CH3CH2OCH2CH2N3 (l) N3CH2C(O)OC2H5 (l)

15

azidocyclopentane (l)

16

azidocyclohexane (l)

22

(C6H5)3CN3 (cr)

23 24 25

(CH3CH2)3CN3 (l) (CH3)2(C6H5)CN3 (l) 1-azidoadamantane (cr)

26 27 28

TAT (cr) TAH (cr) TAAT (cr)

−139.3 179.0 108.4 486.2 ± 1.3

44.8 47.1 48.1 51.8 81.0

52.6 39.7 56.5 59.6 46.0

± ± ± ± ±

± ± ± ± ±

46.0o 67.4p 62.2 ± 46.6 ± 48.1p 56.3 ± 41.8q 41.3 ± 46.0q 49.2 ± 120.5 ± 122.8 ±

0.8 0.8 0.4 0.4 3.0j

389.1 416.3 ± 1.7 389.7 ± 5.2 452 ± 21 484 ± 15k

0.2 0.8m 0.8 0.8 2.2

252.7 ± 3.8 255.8 352.3 ± 6.3 140.0 161.5

0.3 0.5 0.4

−91.2 −83.0 220.8

0.4 154.4 0.5 1.3 1.3

606.7 ± 2.5 169.9 ± 11.7 365.7 ± 10.0 215.9 ± 10.9 202r

1053.0

31−33 34 32, 33 34 35 36 34 38 32 34 32 39 40 32 34 34 31, 32 34 42, 32 34 42, 32 34 33 34 43 43 43 45

2171 ± 10

47 48

178.7u 29

20 26 20 29

DiAT (cr)

292 450

298 415

297.9,h 297,i 304 f

405 394 501 457 336 263

506l

337n

357 115

100 −79 256 210 610 132 333 183 1137 1409 1925 1125

a

other works 292.5,c 291.4,d 293.3,e 297 f 449−454g

1187.3s 2298t 1112− 1135,v 1080.5,w 1075x

b

The compound’s number according to Figure 1 is given for each molecule. Values calculated from isodesmic reactions are given. cCalculated from the ATcT reference value of the atomization energy, ref 22. dCalculated from the atomization energies computed at the fc-CCSD(T)/cc-pCVQZ// ae-CCSD(T)/cc-pCVTZ level (ref 22) and by the W4 method (ref 23). eThe mean of the values derived from the reaction HN3 + CH2N• → CH2NH + •N3 using different CBS and Gn composite methods, ref 24. fCCSD(T)/CBS, ref 25. gThese values were obtained by different composite methods (ref 24), different ab initio methods (ref 27), and CCSD(T)/aug-cc-pVQZ calculations (ref 28). hThe mean of the values derived from the reaction CH3N3 + CH2N• → CH2NCH3 + •N3 using different CBS and Gn composite methods, ref 24. iG2 value, ref 30. j Assumed by analogy with 1,3-dinitrobenzene. kRecalculated in this study using D(NC−N3) = 401.4 ± 9.6 kJ/mol (ref 36), ΔfH°0 (CN, g) = 437 ± 5 kJ/mol (ref 20), and ΔfH0°(N3, g) = 453 ± 5 kJ/mol (this work). lThis value corresponds to ΔfH0°(NCN3, g) = 511 kJ/mol calculated by the G3 method (ref 37). mEstimated from the boiling temperature. nMP2/aug-cc-pVDZ, combustion reaction, ref 38. oAssumed to be the same as that in azidocyclohexane. pEstimated in accordance with ref 41. qEstimated from an empirical correlation of the surface tension with the heat of vaporization. rRecalculated in this work using the experimental enthalpy of formation of 1-aminoadamantane, ref 44. sB3LYP/6-31G(d), isodesmic reaction, ref 46. tB3LYP/aug-cc-pVDZ, isodesmic reaction, ref 48. uEstimated using the Politzer approach, refs 49 and 50. vB3LYP, HF, and MP2 calculations, isodesmic reaction, ref 51. wB3LYP/6-31G(d), isodesmic reaction, ref 52. xB3LYP/6-311++G(3d,3p), isodesmic reaction, ref 53.

For the next compound (9), the accepted value of ΔfH°298[CH3N(NO2)CH2N3, g] = 336 ± 5 kJ/mol is based on 10 reactions, in which •N3, HN3, CH3N3, and C6H5N3 are taken as reference molecules (Table S4, Supporting Information). This value

agrees well with the value obtained by Klapötke et al.38 from MP2/ aug-cc-pVDZ calculations applied to the combustion reaction. The species 1−4 and 9 serve as reference molecules to determine the enthalpy of formation of C6H5CH2N3 (5) from a 6839



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obtained in this study and experimental enthalpies of vaporization,34 we estimate the values of the enthalpy of formation of liquid azidocyclopentane and azidocyclohexane to be 215 and 161 kJ/mol, respectively. The enthalpy of formation of 22, ΔfH°298[(C6H5)3CN3, g] = 610 ± 5 kJ/mol, is calculated from 29 reactions with nine azido compounds (1−5, 7, 10, 15, and 16) used as reference species (Table S4, Supporting Information). This value agrees well with the experimental one (Table 3). Good agreement with experiment is also obtained for 14; the recommended value, ΔfH°298[N3CH2C(O)OC2H5, g] = −79 ± 5 kJ/mol, deviates insignificantly from the experimental value based on the enthalpy of vaporization determined recently by Verevkin et al.34 The enthalpies of formation of liquids 8 and 13 were not derived experimentally. The gas-phase enthalpies of formation of these compounds, ΔfH298 ° (NCCH2N3, g) = 457 ± 5 kJ/mol ° (CH3CH2OCH2CH2N3, g) = 100 ± 5 kJ/mol, are and ΔfH298 obtained in this study using a large number of isodesmic reactions (Table S4, Supporting Information) with more than 10 reference azides whose internally consistent ΔfH298 ° values were estimated as described above. Using these values and experimental enthalpies of vaporization,34 the liquid-phase enthalpies of formation of 8 and 13 are estimated to be 404 and 53 kJ/mol, respectively. The gas-phase enthalpies of formation of three azides (23−25) were determined by Wayne et al.43 based on the experimentally measured enthalpies of hydrogenation (ΔhydH°298) for the reaction RN3 + H2 → RNH2 + N2 and the enthalpies of formation of corresponding amines estimated by group additivity methods or molecular mechanics calculations. As is seen from Table 3, these ΔfH°298 values are 33−38 kJ/mol higher than those calculated in this study. For 25, the deviation is reduced to 19 kJ/mol if the experimental enthalpy of formation of 1-aminoadamantane is used (see Table 3). However, the use of the experimental value for amine does not improve the agreement for 24. Because such large deviations exceed the expected error range of the G4 method, it is very likely that the uncertainty in the experimental enthalpies of hydrogenations is greater than the stated error of 10−12 kJ/mol. This suggestion is supported by calculations of the enthalpy of hydrogenation for different compounds including some azides for which reliable experimental data are available both for the azide and corresponding amine (Table S5, Supporting Information). It should be also mentioned that the authors of the experimental work indicate that the experimental determination of ΔhydH298 ° is difficult and may suffer ° values of 23−25 systematic error.30 Therefore, the ΔfH298 calculated in this work (Table 3) seem to be more reliable estimations of the enthalpies of formation than the experimental values reported by Wayne et al.43 The deviations between results of different isodesmic reactions for 26−28 are somewhat larger than those for the above compounds because it is difficult to design reactions with good group balance for these nitrogen-rich carbon nitrides. Nevertheless, the constructed reactions can yield rather reliable estimates of ΔfH298 ° values for 26−28. For TAT (26), the recommended value of ΔfH°298(TAT, g) = 1137 ± 8 kJ/mol combined with the experimental value of the enthalpy of formation of solid TAT (Table 3) allows us to estimate the enthalpy of sublimation of this compound as 84 kJ/mol. This value looks quite reasonable compared to ΔsubH°298 values for 6 and 22. Thermochemical properties of TAH (27) were not derived experimentally; however, the gas-phase enthalpy of formation

set of isogyric and isodesmic (or nearly isodesmic) reactions (Table S4, Supporting Information). The values calculated from 23 reactions agree within 8 kJ/mol, and the value of ΔfH298 ° (C6H5CH2N3, g) = 405 ± 5 kJ/mol is recommended in this study. As is seen from Table 3, this value is 11 kJ/mol less than the experimental one; however, such a difference is not very significant compared to combined errors of experimental and theoretical determinations. For 7, 16 reactions with reference species 1−5 lead to the value of ΔfH°298(NCN3, g) = 501 ± 5 kJ/mol. Earlier, the enthalpy of formation of NCN3 was estimated by Okabe and Mele36 (Table 3) using the value of D(NC−N3) = 401.4 ± 9.6 kJ/mol obtained from the energy of the NCN3 photodissociation threshold and available values of ΔfH°0 (CN, g) = 423 ± 5 kJ/mol and ΔfH°0 (•N3, g) = 434 ± 19 kJ/mol. In this study, we re-estimated the ΔfH298 ° (NCN3, g) value using a more recent20 enthalpy of formation of CN and the above recommended enthalpy of formation of •N3. As can be seen from Table 3, this value agrees with our calculated value within the error limits. The enthalpy of formation of 6 is obtained from 25 reactions with 1−5, 7, and 9 used as reference molecules (Table S4, Supporting Information). This value, ΔfH°298(1,4-NO2−C6H4− N3, g) = 394 ± 5 kJ/mol, is in good agreement with the experimental one (Table 3). To compute the enthalpy of formation of 12, 21 reactions were designed (Table S4, Supporting Information). In these reactions, eight azido compounds (1−7 and 9) were taken as reference species. The results from these reactions agree within 7 kJ/mol, and the average value, ΔfH298 ° (HOCH2CH2N3, g) = 115 ± 5 kJ/mol, is recommended in this study. This value, as is seen from Table 3, is substantially lower than experimental ones. The enthalpy of vaporization of 12 was recently determined from the temperature dependence of the vapor pressures measured by the transpiration method, and this value is in internal consistency with vaporization enthalpies of similarly structured compounds,34 whereas doubt was cast on the experimental value of ° (HOCH2CH2N3, l).54 Therefore, one may suggest that ΔfH298 the liquid-phase enthalpy of formation of 12 determined by Fagley et al.39 is overestimated. In support of this suggestion, it should be noted that the enthalpy of formation of benzotriazole determined by Fagley et al. in the same work is also noticeably overestimated, as was shown later.55 Thus, the experimental measurements of Fagley et al.39 may suffer systematic error. On ° (g) obtained in the present work the basis of the value of ΔfH298 and the experimental enthalpy of vaporization,34 the enthalpy of formation of liquid 12 is predicted to be 53 kJ/mol. The recommended enthalpies of formation of 10 and 11, ΔfH298 ° [CH3C(NO2)2N3, g] = 263 ± 5 kJ/mol and ΔfH298 ° [C(NO2)3N3, g] = 357 ± 5 kJ/mol, are the average values of 20 and 26 isodesmic reactions, respectively (Table S4, Supporting Information). As is seen from Table 3, these values are in good agreement with experimental data. The isodesmic reactions give very consistent values of the enthalpy of formation of 15 and 16 (Table S4, Supporting Information), and the corresponding average values are recommended for these compounds, ΔfH°298(azidocyclopentane, ° (azidocyclohexane, g) = 210 ± g) = 256 ± 5 kJ/mol and ΔfH298 5 kJ/mol. These values, as can be seen from Table 3, are substantially higher than the experimentally derived values. However, the experimental data by Fagley and Myers42 on the liquid-phase enthalpy of formation of 15 and 16 have long been ° (g) values questioned.54 Because of this, on the basis of ΔfH298 6840



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Table 4. Enthalpies of Formation of Gaseous 4,4′,6,6′-Tetra(azido)azo-1,3,5-triazine (TAAT) Calculated from Isodesmic and Other Balanced Reactions Using G4(MP2) Energies (in kJ/mol)a

a The values of the enthalpies of reaction (ΔrH°) are given together with the enthalpies of formation (ΔfH298 ° ) for each isodesmic reaction. The experimental enthalpies of formation of all species used in isodesmic reactions are given in Table S3 (Supporting Information).

was calculated by Ghule et al.46 at the DFT/B3LYP/6-31G(d) level of theory using only one isodesmic reaction (reaction 9 in Table S4, Supporting Information) with CH3N3 as the reference compound. The ΔfH°298 value of TAH obtained by Ghule et al. from this reaction (1187 kJ/mol) is about 200 kJ/mol less than that calculated in this work not only for reaction 9 but also for the other 13 reactions in Table S4 (Supporting Information), in which 6 different reference azido compounds are used. The main reason for this large discrepancy is the use of a lower value of enthalpy of formation of CH3N3 (238 kJ/mol) by the authors.46 As can be seen from Table 3, none of the theoretical calculations give such a low ° value for CH3N3. Because three CH3N3 molecules are ΔfH298 involved in reaction 9, this leads to the large error in the enthalpy of formation of TAH calculated in ref 46. On the basis of reactions in Table S4 (Supporting Information), the value of ΔfH°298(TAH, g) = 1409 ± 15 kJ/mol is recommended in this study. The enthalpy of formation of solid TAAT (28) was determined experimentally by Huynh et al.47,56 Using this value together with available experimental data for related compounds, Slayden and Liebman57 found the reaction

to be exothermic by ∼700 kJ/mol. This value, according to the author’s57 opinion, is untenable. Indeed, this reaction with good group balance should be roughly energetically neutral. The calculation of the enthalpy of formation of TAAT by the isodesmic reaction approach (Table 4) helps to find the reason for an unexpected large enthalpy of the above reaction. Six reactions with five reference azido compounds (1, 3, 5, 7, and 26) and one reaction based on the reliable experimental enthalpies of formation of C2N2 and N2 (reaction 7 in Table 4) are used in this study. The fact that the ΔfH298 ° values obtained from these reactions agree within 14 kJ/mol makes us confident that the calculated value is quite accurate and consistent with enthalpies of formations of other azido compounds. The value of ΔfH298 ° (TAAT, g) = 1925 ± 10 kJ/mol is recommended in this work. We can see from Table 4 that the enthalpy of reaction 2 (this reaction is inverse to that of Slayden and Liebman) was decreased to 10 times as compared to the value obtained in ref 57. Thus, it is confirmed that the above reaction is roughly thermoneutral, whereas the experimental value of the 6841



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enthalpy of formation of solid TAAT47,56 appears to be strongly overestimated. The enthalpy of sublimation of TAAT was estimated to be 179 kJ/mol in the framework of the Politzer approach by Wang et al.48 Using the recommended ΔfH°298 value of the gas-phase enthalpy of formation of TAAT and assuming the enthalpy of sublimation to be between 80 and 180 kJ/mol, the enthalpy of formation of solid TAAT is estimated to be in the range from 1745 to 1845 kJ/mol. This value is 300−400 kJ/mol less than the reported experimental value,47,56 and it seems to be more reliable. It is also worth noting that the enthalpy of formation of TAAT was calculated earlier from isodesmic reaction 4 (see Table 4), and its value is 370 kJ/mol higher48 than that obtained in this study. A large discrepancy between results of two calculations, as in the case of TAH, arises most probably from the difference in the values accepted for the enthalpy of formation of CH3N3. Unfortunately, this value is not presented by the authors,48 while the ΔfH298 ° values for other reference compounds are close in both studies. It looks like Wang et al.48 used the ΔfH°298(CH3N3, g) value, which is too high, while Ghule et al.46 accepted the value that is too low. TAH and TAAT provide a nice example of the role of reference compounds in the results of isodesmic reaction calculations. A difference in ΔfH°298 values accepted for CH3N3 leads to large error when the differing values are used to calculate the enthalpy of formation of a compound with several azido groups. There are no experimental data on the enthalpy of formation of DiAT (29). The value recommended in this study, ΔfH298 ° (DiAT, g) = 1125 ± 8 kJ/mol, is in good agreement with those estimated by the additivity method5 and calculated

from isodesmic reactions at different levels of theory51 (see Table 3). A somewhat lower value is calculated by Ghule et al.52 As in the case of TAH,46 these authors used a rather low value of the enthalpy of formation of CH3N3, but here, it is compensated for by the higher ΔfH°298 value accepted for 1,2,4,5-tetrazine. The underestimated value is also obtained from the isodesmic reaction with unreliable reference species.53 Experimental or theoretical enthalpies of formation of di- and triazido benzenes and 4-azidopyridine (17−21) were not reported. The enthalpies of formations of (17−21) are recommended in this work based on isodesmic reaction calculations, and their values are given in Table 1; the reactions designed for each species are listed in Table S4 (Supporting Information). The uncertainty of these values is estimated to be 5 kJ/mol. Experimental gas-phase enthalpies of formation, as can be seen from Table 3, are determined for 16 azido compounds. Of these, good agreement between experimental results and calculations is obtained for nine species; the deviations do not exceed 5 kJ/mol for 1, 6, 11, 14, and 22, while the difference is within the combined errors of the two determinations (8−15 kJ/mol) for 2, 5, 7, and 10. A large difference observed for 12, 15, and 16 is, as discussed above, due to doubtful accuracy of the experimental liquid-phase enthalpies of formation derived by Fagley et al.39,42 A difference of 25 kJ/mol between experimental and calculated values for 4 may be also attributed to inaccuracy of the liquid-phase enthalpy of formation. And last, the significant difference between experimental and calculated values for 23−25 may be the result of systematic error in the experimental measurement of enthalpies of hydrogenation. Thus, we can conclude that the ΔfH°298 values recommended in this study show an internal consistency with more than half of the available experimental data.

Figure 2. Deviations between enthalpies of formation calculated from isodesmic reactions and atomization reactions using different methods. The ° values computed dashed lines represent the expected uncertainty limits of the isodesmic reaction results. The mean absolute deviations of the ΔfH298 with G4, G4(MP2), G3, and G3(MP2)//B3LYP methods are 7.4, 4.0, 4.7, and 5.6 kJ/mol, respectively, when compared to isodesmic reaction values; the corresponding mean deviations are 7.4, 0.0, −3.6, and −2.1 kJ/mol, respectively. 6842



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The ΔfH°298(g) values determined in this work allowed one to predict or improve the condensed-phase enthalpies of formation for some azido compounds for which experimental investigation often presents difficulties. The liquid-phase enthalpies of formation of 8 and 13 were estimated for the first time using the experimental enthalpies of vaporization determined recently by Verevkin et al.34 The questionable ΔfH298 ° values of liquids 12, 15, and 16 were improved similarly. Special attention in this work was given to TAAT (28). The experimentally measured enthalpy of formation for TAAT is the highest ever reported for energetic materials including polynitro, high-nitrogen, and polyazido compounds.47,56 The results of the present calculations, however, show that the experimental value may be overestimated by 300−400 kJ/mol. This conclusion is supported by G4(MP2) calculations applied to both the atomization reaction (Table 1) and seven isodesmic reactions with different reference compounds (Table 4).

Comparison of Results of Different Composite Methods. The enthalpies of formation of all compounds calculated by four Gaussian-n family methods are given in Table S2 of the Supporting Information. It may be seen that the values calculated by G4, G4(MP2), G3, and G3(MP2)// B3LYP methods from atomization energies show considerable scatter (from 5 to 30 kJ/mol). Unfortunately, the insufficient amount of accurate experimental data does not allow one to choose the most reliable method by comparison with experimental values. Because the isodesmic reaction scheme brings the calculated ΔfH298 ° values very close to those of the experiment, the results from isodesmic reactions are accepted as reference values in this study. The deviations of G4, G4(MP2), G3, and G3(MP2)//B3LYP values from isodesmic reaction results are shown in Figure 2. As can be seen from Figure 2, the worst agreement with isodesmic reaction results is observed for the G4 method. When compared to isodesmic reaction values, practically all G4 values are underestimated. The largest deviations (17−19 kJ/mol) are obtained for two nitro compounds (10, 11), similarly as was observed earlier for other nitro compounds.11 Therefore, the G4 method underestimates the enthalpies of formation of azido compounds but substantially less than that for nitro compounds. Among the four methods, the G4(MP2) theory demonstrates the best agreement with reference values; the discrepancy between G4(MP2) and isodesmic reaction values exceeds 5 kJ/mol only for five molecules (9, 22, 26, 27, and 28), four of which contain 15 and more non-hydrogen atoms. Therefore, the G4(MP2) method can be recommended for reliable prediction of enthalpies of formation of organic azides with the number of non-hydrogen atoms up to 15. As for larger molecules, most likely, the accumulation of systematic errors in G4 and G3 theory is observed with an increasing number of heavy atoms. The results from isodesmic reactions in this case are expected to be more accurate.

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ASSOCIATED CONTENT

S Supporting Information *

G4 energies and Cartesian coordinates for the lowest-energy conformers of all azido compounds optimized at the B3LYP/ 6-31G(2df,p) level (Table S1). Enthalpies of formation of all compounds calculated by different composite methods (G4, G4(MP2), G3, G3(MP2)//B3LYP, and W1U) from the atomization energy (Table S2). Experimental enthalpies of formations of reference compounds used in isodesmic reaction calculations and their comparison with values calculated by the G4 method from the atomization reaction (Table S3). Enthalpies of formation of all compounds calculated from isogyric, iodesmic, and other balanced reactions using G4 energies (Table S4). Comparison of experimental enthalpies of hydrogenation with those calculated by the G4 method (Table S5). This material is available free of charge via the Internet at http://pubs.acs.org.

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CONCLUSIONS Accurate gas-phase enthalpies of formation are recommended in this study for a number of organic azides by combining G4 theory calculation with an isodesmic reaction scheme. The reference ΔfH298 ° values were determined by a sequential approach starting with a literature-derived value of the enthalpy of formation of HN3. Of the experimental data reported for 16 compounds, good agreement was obtained for nine compounds (1, 2, 5−7, 10, 11, 14, and 22). Taking into account the problems with experimental measurements of azides, a large percentage of unreliable experimental data is not surprising. The systematic error in the experimental data39,42,43 for 12, 15, 16, and 23−25 was assumed earlier,30,54 and our calculations confirm it. Therefore, the agreement with experimental data for nine compounds may be considered as convincing evidence of high accuracy and internal consistency of our recommended values. We have seen above that the difference in ΔfH298 ° values of reference compounds can lead to large errors in the predicted enthalpies of formation for a target molecule, especially if it contains several azido groups. The values obtained in this work will help to avoid large errors in isodesmic reaction calculations. A set of recommended enthalpies of formation can be used in thermochemical models to compute accurately the performance of energetic materials and select the most promising candidates for synthesis.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of this manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the Grant of President of Russian Federation for State Support of Leading Scientific Schools NSh-2724.2012.3

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REFERENCES

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Accurate Prediction of Enthalpies of Formation of Organic Azides by

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