Use of G4 Theory for the Assessment of Inaccuracies in Experimental

Article pubs.acs.org/jced

Use of G4 Theory for the Assessment of Inaccuracies in Experimental Enthalpies of Formation of Aliphatic Nitro Compounds and Nitramines Marina A. Suntsova and Olga V. Dorofeeva* Department of Chemistry, Lomonosov Moscow State University, Moscow 119991, Russia S Supporting Information *

ABSTRACT: The gas-phase enthalpies of formation (ΔfHo298) of 57 aliphatic nitro compounds and nitramines (mono- and polynitro compounds including cyclic compounds and well-known explosives such as hexogen, octogen, and CL-20) were calculated using the Gaussian-4 (G4) theory applied to the atomization and isodesmic reaction energies. The ΔfHo298 (g) values calculated from the atomization reactions were underestimated by an average of 10 kJ·mol−1, and they could not be used for the assessment of inaccuracies in the experimental enthalpies of formation. Much better agreement between theory and experiment was obtained using the isodesmic reaction procedure. Several isodesmic reactions were investigated for each compound. Evidence of high accuracy of most experimental data was provided by the agreement with theoretical results. The differences between the calculated and the experimental enthalpies of formation in the range from (8 to 53) kJ·mol−1 were assigned to possible errors in the experimental values for 17 compounds. The theoretical ΔfHo298 (g) values were recommended for these compounds as being more reliable than the experimental values. As a result, a reference data set of internally consistent gas-phase enthalpies of formation of nitro compounds and nitramines was provided. Both experimental and calculated values are included in this data set. The enthalpies of sublimation or vaporization were evaluated for some compounds by taking into account the literature data on the condensed phase enthalpies of formation and the ΔfHo298 (g) values recommended in our work. Thus, a set of self-consistent values of the enthalpy of formation in both condensed and gaseous phases and the enthalpy of sublimation or vaporization is presented for most of nitro compounds studied. compounds with the results of calculations. The G4 theory4 combined with isodesmic reaction scheme5,6 was used to calculate the enthalpies of formation of different aliphatic nitro compounds with high accuracy. The enthalpies of formation of nitro compounds were calculated earlier by different composite and DFT methods using the standard atomization reaction procedure.7−11 The accuracy of the available experimental data was not analyzed in these works. In our previous work,12 it was revealed that the G4 method,4 one of the most successful and widely used composite methods, underestimates the ΔfHo298 (g) values for the most nitro compounds by up to 20 kJ·mol−1. However, a good agreement with the experiment was obtained when the isodesmic reactions were used instead of the atomization reaction. The applying the isodesmic reactions to nitro compounds would be successful if the accurate experimental ΔfHo298 (g) values for the key nitro compounds are available. However, until recently, the enthalpies of formation of even nitromethane and nitrobenzene were not known with certainty. Because of this, a special attention in our previous work was paid to these two key nitro compounds.13 There was some discrepancy

1. INTRODUCTION Nitro compounds are one of the fundamental classes of substances in organic chemistry. They play an important role in the synthesis of dyes, polymers, perfumes, agrochemicals, and pharmaceutical drugs. The versatility of nitro compounds in organic synthesis is largely due to their easy availability and transformation into a variety of diverse functionalities.1 Many nitro compounds are highly energetic materials and used as explosives and propellants. The nitro group is present in many currently existing explosive compounds and in new energetic materials.2 An accurate determination of enthalpy of formation (ΔfHo298) of nitro compounds is of prime importance because it is closely related to their stability and sensitivity.3 Reliable experimental data are also critical for developing the parameters of empirical and semiempirical predictive methods which are widely used to estimate the thermochemical properties of new perspective energetic compounds. Although the enthalpies of formation of many nitro compounds were determined experimentally, their accuracy is not always sufficient. The problems in determining the enthalpy of formation of nitro compounds arise from their instability and sensitivity to moisture. Today, the accuracy of the experimental enthalpies of formation can be validated by using the quantum chemical methods. In the present paper, a systematic comparison was made of a large number of experimentally determined enthalpies of formation of aliphatic nitro © 2014 American Chemical Society

Received: May 19, 2014 Accepted: July 30, 2014 Published: August 6, 2014 2813

dx.doi.org/10.1021/je500440y | J. Chem. Eng. Data 2014, 59, 2813−2826

Journal of Chemical & Engineering Data

Article

Table 1. Enthalpies of Formation of Nitro Compounds Calculated by the G4 Method atomization reaction

compound 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 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55

nitromethane nitroethane 1-nitropropane 2-nitropropane 1-nitrobutane 2-nitrobutane 2-methyl-2-nitropropane 1-nitropentane 2,4,4-trimethyl-2-nitropentane dinitromethane 1,2-dinitroethane 1,1-dinitroethane 1,3-dinitropropane 1,1-dinitropropane 2,2-dinitropropane 1,4-dinitrobutane 1,1-dinitrobutane 2,3-dimethyl-2,3-dinitrobutane trinitromethane 1,1,1-trinitroethane 1,1,1-trinitropropane 1,1,1-trinitrobutane tetranitromethane 1,1,1,3-tetranitro-2-methylpropane 1,1,1,4-tetranitrobutane 1,1,3,3-tetranitrobutane 2,2,3,3-tetranitrobutane 1,1,1,2,2-pentanitropropane hexanitroethane nitrocyclohexane 1-nitrospiro[2.3]hexane 1,1-dinitrocyclopropane 1-nitroadamantane 2-nitroadamantane 2,2-dinitroadamantane 1,3-dinitroadamantane dimethylnitramine diethylnitramine dipropylnitramine N,N′-dimethyl-N,N′-dinitromethanediamine N,N′-dimethyl-N,N′-dinitroethane-1,2-diamine 1-nitropiperidine 1,4-dinitropiperazine 1,3-dinitroimidazoline 1,3,5-trinitro-1,3,5-triazocyclohexane (hexogen, RDX) 1,3,5-trinitro-1,3,5-triazacycloheptane 1,3,5,7-tetranitro-1,3,5,7-tetraazocyclooctane (octogen, HMX) 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (HNIW, CL-20) 1,3,3-trinitroazetidine (TNAZ) methyldinitramine ethyldinitramine n-propyldinitramine n-butyldinitramine methylnitramine methylenedinitramine

isodesmic reactions

ΔfHo298

ΔfHo298

kJ·mol−1

kJ·mol−1

number of reactions

(max− min)a

reference nitro compoundsb

−78.1 −107.8 −129.4 −145.1 −151.5 −169.4 −181.2 −173.2 −273.1 −52.7 −108.7 −101.8 −148.1 −124.7 −151.5 −174.1 −147.0 −252.9 −9.1 −69.9 −88.2 −111.9 65.6 −92.4d −99.8d −166.8 −111.3d −0.3d 118.3d −164.4 89.5 37.6 −197.8 −184.4 −193.2 −242.4 −9.3 −66.2 −110.9 27.8 3.3 −42.7 51.5 102.5 170.9 125.5 253.9d

−102.4 −123.7 −139.5 −146.5 −164.3 −175.9 −167.7 −265.3 −40.4 −96.8 −89.5 −137.3 −111.6 −139.0 −161.7 −134.3 −240.6 10.2 −50.9 −69.7 −93.8 91.5 −89.7d −95.1d −142.2 −109.6d 3.0d 122.1d −160.1 94.5 51.0 −189.9 −176.8 −179.0 −228.2 −4.9 −60.8 −105.6 37.8 14.9 −38.9 61.6 108.6 182.1 136.3 235.5d

6 7 7 7 8 7 8 13 8 8 6 7 8 13 7 8 9 14 13 14 9 10 14 12 13 8 16 14 9 7 14 9 8 9 11 10 8 9 12 6 9 6 8 12 11 9

8.3 4.7 4.2 1.7 1.7 1.7 3.0 7.7 1.5 3.2 2.8 3.9 4.6 5.1 4.7 5.1 10.4 4.0 2.5 4.0 4.0 5.5 9.2 9.9 5.5 8.9 6.5 14.4 6.3 2.5 4.4 4.6 4.3 10.3 4.5 7.5 5.3 9.3 9.7 8.0 5.7 6.8 2.2 8.1 5.9 7.1

1 1,2 1,2,3 1,2,3,4 1,2,3,4 1,2,4 1,2,3,5 1,2,4,5,6,7,8 1,2,3,4 1,2,3,4 1,2,10,11 1,2,3,11 1,10,11,12 1,2,3,4,6,10,11,12,14 1,2,3,5,11,13,17 1,2,10,11,12,14,15c 4,7,9c,11,13,16 1,2,3,4,10,11,12 1,3,4,10,11,12,19c 1,2,3,4,10,11,12,19c,20c 1,2,10,12,19c,20c,21c,23 1,2,10,12,19c,20c 1,2,3,4,5,11,12,14,19c,20c 1,2,3,5,10,11,12,14,19c,24c 1,2,3,6,10,11,12,23 1,2,3,6,10,11,12,23 1,2,3,4,10,11,12,13,19c,20c,27 1,2,10,11,12,14,19c,20c, 23,27,28c 1,2,4,6,8 1,2,4,6,30 1,4,10,11,12,13,14,30 1,2,3,5,6,7,30,31 1,2,3,4,6,7,30 1,4,10,11,12,14,30,33,34 1,2,3,4,6,7,11,13,30,33,35c 1,2,4,10,12 1,2,4,37 1,2,4,37,38 1,2,37,38,39,41,42,43 1,37,38,39 1,2,37,38,39,41 37,38,39,41,42 37,39,40c,42,43 37,42,43,44c 37,42,43,44c,45 37,42,43,44c,45,46c

523.1d

500.9d

10

12.9

37,42,43,44c,45,46c,47

92.1 95.8 67.9 45.8 22.7 −3.8 35.8

111.3 106.4 76.6 54.1 32.2 0.3 46.2

11 18 16 13 15 9 9

6.9 6.2 6.6 6.8 7.0 5.1 7.1

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1,10,12,37,38,42,43 1,2,3,10,12,30,37,41,42,43 1,2,4,10,30,37,41,42,43,50c 1,2,6,10,30,37,42,43,50c,51c 1,2,6,12,37,38,42,43,50c,51c,52c 1,2,7,37,38,42,43 1,2,37,38,39,42,43,54



Article

Table 1. continued atomization reaction

compound 56 57

ethylenedinitramine 1,5-dinitrobiuret

isodesmic reactions

ΔfHo298

ΔfHo298

kJ·mol−1

kJ·mol−1

number of reactions

(max− min)a

reference nitro compoundsb

18.7 −264.0

27.7 −255.2

10 15

15.3 5.2

1,2,37,38,39,42,43,54,55c 1,2,3,4,10,13,37,38,41,54,55c,56c

a

Difference between maximum and minimum values obtained from isodesmic reactions. bNumbers of nitro compounds used as the reference species to estimate the enthalpy of formation of a given compound. cCalculated ΔfHo298(g) value was used for this compound. dG4(MP2) value.

on the basis of theoretical gas-phase enthalpy of formation and experimental condensed phase enthalpy of formation.

regarding the gas-phase enthalpy of formation of nitromethane. A value of −74.7 ± 0.6 kJ·mol−1 has been reported by McCullough et al.;14 this value was based on the unpublished results and recommended in Pedley’s reference book.15 The other value of −80.8 ± 1.3 kJ·mol−1 has been reported by Knobel et al.;16 this value was listed in the NIST Chemistry WebBook.17 Our isodesmic reaction calculations13 have provided a strong support for the first value. However, when we used this value in the isodesmic reactions designed to estimate the enthalpy of formation of nitrobenzene, we could not achieve the thermochemical consistency between the available experimental enthalpies of formation of nitromethane (−74.7 ± 0.6 kJ·mol−1)14 and nitrobenzene (65.8 ± 0.4 kJ· mol−1).18 Because of this, it was suggested that either the experimental enthalpy of nitrobenzene was overestimated by (2 to 3) kJ·mol−1 or the enthalpy of formation of nitromethane was underestimated by the same value. Our assumption was confirmed by new experimental measurements by Verevkin et al.,19 from which the values of −71.5 ± 0.4 kJ·mol−1 and 65.6 ± 1.6 kJ·mol−1 were determined for the enthalpy of formation of gaseous nitromethane and nitrobenzene, respectively. These values, as is shown from isodesmic reaction calculations,19 are in internal consistency with each other and with reliable experimental enthalpies of formation of 38 different aliphatic and aromatic compounds used as the reference species in these isodesmic reactions. It should be noted that although the two reported experimental ΔfHo298 (g) values of nitromethane differ by only 3.2 kJ·mol−1, a large difference in theoretical predictions occurs when these differing values are used to estimate the enthalpies of formation of polynitro compounds. Our predictions regarding the accuracy of experimental data for nitromethane and nitrobenzene13 and previous studies of organic azides20 and amino acids21 suggest that the computational method of isodesmic reactions is sufficiently accurate to reliably assert that there exists any anomaly with the experimental values of the gas-phase enthalpy of formation. This paper describes the results of systematic comparison of calculated and experimental enthalpies of formation of 57 aliphatic nitro compounds and nitramines. Among these are the different mono- and polynitro compounds, primary and secondary nitramines including cyclic compounds and wellknown explosives such as hexogen, octogen, and CL-20. Evidence of the accuracy of most experimental data was provided by the agreement with theoretical results. The large differences between experimental and calculated values were assigned to the errors in the experimental data. For these compounds, the theoretical enthalpies of formation were recommended as being more reliable than the experimental values. In this case, a new value of enthalpy of vaporization (ΔvapHo298) or sublimation (ΔsubHo298) was sometimes suggested

2. COMPUTATIONAL DETAILS All ab initio and density functional theory (DFT) calculations were performed using the Gaussian 03 package of programs.22 Potential energy profiles for internal rotations, geometry, and vibrational frequencies were calculated at the B3LYP/631G(d,p) density functional level. The optimized geometries of the most stable conformers were used as inputs for further G44 or G4(MP2)23 calculations. The G4(MP2) method was used instead of G4 for seven large molecules (see Table 1); this modification of G4 theory is designed to shorten computational times with some loss of accuracy. The G4 enthalpies of formation were calculated using both the atomization24,25 and isodesmic reaction5,6 approaches. The calculation via 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.26 For isodesmic reaction, the resulting enthalpy of formation was calculated combining the G4 enthalpy of reaction with the enthalpies of formation of reference molecules. The experimental ΔfHo298 values for 55 reference species involved in isodesmic and other balanced reactions are given in Table S1 of the Supporting Information; their accuracy is supported by G4 calculations applied to atomization reactions. Table 1 compares the G4 enthalpies of formation calculated from atomization reaction with those obtained from isodesmic reactions. For each species, the number of isodesmic reactions designed is given; the ΔfHo298 value in the column “isodesmic reactions” corresponds to the average of all reactions. The full list of reactions is presented in Table S2 of Supporting Information. The nitro compounds used as the reference species in the isodesmic reaction calculations are also listed in Table 1. If the experimental ΔfHo298 (g) values were reproduced well by the isodesmic reaction calculations, their values were used as the reference enthalpies of formation in all further calculations. These experimental values are designated as “recommended” values and are given in Table 2 together with appropriate references. The possible errors in the experimental enthalpies of formation were identified by the large difference between the calculated and the experimental values. For these compounds, the theoretical ΔfHo298 (g) values were used as the reference enthalpies of formation in the further calculations. In this case, the theoretical values are designated as “recommended” in Table 2; these values are given without references. The recommended ΔfHo298 (g) values of nitro compounds from Table 2 were used in isodesmic reaction calculations. For the 2815



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Table 2. Enthalpies of Formation (ΔfHo298) in Both Condensed and Gaseous Phases and Enthalpies of Sublimation (ΔsubHo298) or Vaporization (ΔvapHo298) of Aliphatic Nitro Compounds

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Table 2. continued

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Table 2. continued

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Table 2. continued

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Table 2. continued

a

Values calculated from isodesmic reactions are given. bCalculated in this work using the relationships between condensed and gas phase enthalpies of formation: ΔfHo298 (l) + ΔvapHo298 = ΔfHo298 (g) or ΔfHo298 (cr) + ΔsubHo298 = ΔfHo298 (g). cReference 31. dReference 34. eEstimated on the basis of experimental ΔvapHo298 values for nitromethane and trinitromethane. f(323 to 353) K. gEstimation. hReference 35. iReference 36. jG4(MP2) energies were used in the isodesmic reaction calculations. kReference 37. lThe value of ΔfHo298 (cr) = 83.7 kJ·mol−1 is given by the authors, however, a different value, 108.0 kJ·mol−1, is obtained from the enthalpy of combustion given in ref 52. mEstimated from empirical equation. nReference 54. o Reference 56. pReference 42. qReference 64. rReference 71. sThe enthalpy of sublimation at 373.7 K (ref 74) was recalculated to 298.15 K using the Cop,298 (cr) = 218.0 J·K−1·mol−1 (ref 77) and Cop,298 (g) = 171.7 J·K−1·mol−1 calculated in this work. tInterpolated from the enthalpies of formation of methyldinitramine (50) and n-butyldinitramine (53). uReference 87. vObtained using MP2/cc-pVTZ calculations and the estimated value of ΔsubHo298; this value leads to reasonable agreement with the experimental enthalpy of combustion determined in ref 60. wAssumed to be equal to the enthalpy of sublimation of biuret. xEstimated by comparison with related compounds, see ref 76.

Figure 1. Deviations between the experimental enthalpies of formation and those calculated using the G4 atomization energies (open circles are used for species with estimated rather than experimental ΔfHo298 (g) values); the positive deviations are marked with the compound’s number (see Table 1). The dashed lines represent the expected uncertainty limits of the G4 results. Numerical values of deviations can be found in Table S3 of the Supporting Information.

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Figure 2. Deviations between the experimental enthalpies of formation and those calculated via the isodesmic reaction procedure (open circles are used for species with estimated rather than experimental ΔfHo298 (g) values). The compound’s numbers are given for species with possible errors in the experimental data (see text). The dashed lines represent the expected uncertainty limits of the isodesmic reaction results. Numerical values of deviations can be found in Table S3 of the Supporting Information.

of 50 and 53 (the ΔfHo298 (g) values for 51 and 52 were estimated by the interpolation of enthalpies of formation of 50 and 53) are of questionable accuracy. N,N-dinitramines are very sensitive explosives, and their experimental investigation provides many challenges, and therefore, a large error in the experimental values is not surprising. The calculated enthalpy of formation of 47 is about 18 kJ·mol−1 too high compared to the experimental value. In this case, the computational method may be insufficiently accurate to reliably determine the nature of deviation. As to the remaining compounds, most of the calculated values are from (1 to 25) kJ·mol−1 less than the experimental enthalpies, and the calculated values for 11 compounds are too low by (25 to 60) kJ·mol−1. Thus, the G4 theory, when applied to atomization reactions, exhibits a marked trend to underestimate the enthalpies of formation of nitro compounds. This trend is clearly shown in Figure 1. The use of isodesmic reactions provides an altogether different picture (Figure 2). For most of the compounds shown in Figure 2, the deviations between the calculated and the experimental values are within the error limits expected from the computational method. Only compounds for which the deviations are greater than (5 to 7) kJ·mol−1, may be regarded as having an error in the experimental data. In Figure 2, these compounds are labeled by their numbers in accordance with Table 1; the numbers are not given for some species with estimated values of ΔsubHo298 (48, 57) or ΔfHo298 (g) (51, 52). The analysis of the deviations between the experimental and calculated values and the detection of possible errors in the experimental data is given in Section 3.2. 3.2. Analysis of Experimental Data. The reported experimental data on enthalpies of formation in both condensed and gaseous phases and enthalpies of sublimation or vaporization are given in Table 2 together with the average values calculated from isodesmic reactions. The experimental value of −71.5 ± 0.4 kJ·mol−1 of the enthalpy of nitromethane (1) determined recently by Verevkin et al.19 is accepted in the

most effective error compensation, the structurally similar nitro compounds were used as the product and reactant in all isodesmic reactions. The errors in the calculated enthalpies of formation (Table 2) were evaluated from the spread of isodesmic reaction values (Table S2 of Supporting Information) and the uncertainties in the reference values. These errors are approximately equal to two mean absolute deviation (MAD) of the calculated enthalpies of formation from the experimental values. In evaluating the MAD for each of molecules, they have also included the uncertainties in the enthalpies of formation of reference species.

3. RESULTS AND DISCUSSION 3.1. Comparison of G4 Results Based on Atomization and Isodesmic Reactions. Figure 1 compares the experimental ΔfHo298 (g) values of aliphatic nitro compounds with those calculated by the standard method using the G4 atomization energies. The G4 theory achieves an overall accuracy of 3.3 kJ·mol−1 for the test set of 270 accurate experimental enthalpies of formation.4 This method was found to be accurate in calculating the enthalpies of formations of different classes of compounds including nitrogen-containing organic compounds. For 63 nitrogen-containing compounds, the G4 method was found to perform with the mean absolute deviation of 2.6 kJ·mol−1.27 The experimental enthalpies of formation of 32 amides were reproduced with the mean absolute deviation of 3.7 kJ·mol−1.28 It is reasonable to assume that the accuracy of G4 method for nitro compounds is comparable with the accuracy found for the other compounds. However, Figure 1 shows, that the G4 method underestimates the enthalpies of formation of all compounds except for HMX (47) and four N,N-dinitramines, 50−53 (hereinafter, the compound’s numbers are given according to Table 1). The large deviations of about 40 kJ·mol−1 observed for 50−53 are inconsistent with the errors expected from the computational method, and hence, the experimental enthalpies of formation58 2821



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Among the seven cyclic and polycyclic nitro compounds (3036), the largest difference of 47 kJ·mol−1 is revealed between the experimental and calculated ΔfHo298 (g) values of 1,1dinitrocyclopropane (32). Evidence of experimental error for 32 was derived from the results of isodesmic reaction calculations (see Table S2 of Supporting Information). The 14 isodesmic reactions with 8 reference nitro compounds, including nitrocyclohexane (30), give the values consistent with one another within 4.4 kJ·mol−1. The average of all reactions is recommended in Table 2 for the enthalpy of formation of gaseous 32. It is also worth noting that the experimental and calculated values agree well for other structurally similar compound (31) studied by the same authors53 and for species with two nitro groups on one carbon atom of cyclobutane ring (49, see below). The enthalpies of vaporization of 31 and 32 were estimated in ref 53 using the empirical equation. Assuming that this equation estimates well the enthalpy of vaporization of 31, we can estimate the enthalpy of formation of liquid 32 to be about −12 kJ·mol−1. Thus, the experimental value of ΔfHo298 (l) may be overestimated by about 45 kJ·mol−1. The computed and experimental enthalpies of formation of two mononitroadamantanes (33 and 34) are in good agreement, whereas the calculated values for two dinitroadamantanes (35 and 36) are ∼18 kJ·mol−1 more negative than the experimental values. That the experimental enthalpies of formation of 35 and 36 are inconsistent with those of closely related nitro compounds, including mononitroadamantanes (33 and 34), is shown by comparison with the results of isodesmic reaction calculations (see Table S2 of the Supporting Information). A good agreement with the existing literature data is obtained for four noncyclic secondary nitramines, 37−39 and 41, whereas the calculated value is 13 kJ·mol−1 less than the experimental one for 40. The calculated ΔfHo298 (g) value, which is in internal consistency with the experimental data for noncyclic and cyclic nitramines, is recommended in Table 2. There are no recommendations of ΔfHo298 (cr) and ΔsubHo298 for this compound because it is difficult to assign the possible experimental error to one of these quantities. The next nitro compounds considered in this work are the cyclic nitramines (42−49). Among these, hexogen (45), octogen (47), and CL-20 (48) are well-known explosives. Although a good agreement with the experimental values is found for the cyclic mono- and dinitroamines (42−44), the theoretical value is recommended in Table 2 for 1,3dinitroimidazoline (44). Our calculated value (108.6 ± 4.0 kJ·mol−1) is only 4.8 kJ·mol−1 higher than the experimental one (103.8 ± 2.9 kJ·mol−1).58 However, it is reproduced by eight well balanced reactions (Table S2 of Supporting Information) within 2.2 kJ·mol−1, and thus, is particularly reliable. Furthermore, this value, when used to estimate the enthalpies of formations of cyclic polynitramines (45−48), leads to more consistent ΔfHo298 (g) values. Rather conflicting results have been reported by several authors (Table 2) concerning the enthalpies of formation and sublimation of hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX, hexogen, 45) and octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX, octogen, 47). The value calculated in the present work, ΔfHo298 (RDX, g) = 182.1 ± 5.0 kJ·mol−1, is in the best agreement with the results of earlier investigations,62,63 ΔfHo298 (RDX, cr) = 70.4 kJ·mol−1 and ΔsubHo298 (RDX) = 112.1 ± 2.0 kJ·mol−1, that are recommended in Table 2. The selected ΔfHo298 (cr) value agrees well with the later results58,65 (71.1 ±

present study. As mentioned in the Introduction, this value is consistent with the reported enthalpy of formation of nitrobenzene. The use of this value in the isodesmic reactions designed to estimate the enthalpy of formation of nitroethane (2) leads to the value which is in excellent agreement with the experimental enthalpy of formation of 2 reported by Miroshnichenko et al.35,36 (see Table 2 and Table S2 of the Supporting Information). Thus, the evidence of the accuracy of the experimental ΔfHo298 (g) value for 2 was provided by the agreement with the theoretical results, and this value is recommended in Table 2 as belonging to a reference data set. In going from nitroethane (2) to 1-nitropropane (3), two model nitro compounds, 1 and 2, were used to construct the isodesmic reactions. In other words, the new model nitro compounds were added in calculations after their experimental ΔfHo298 (g) values were confirmed by theoretical calculations. If the difference between the experimental and calculated values was considerably larger than the error assigned to the computational method (usually larger than 8 kJ·mol−1), the theoretical value was recommended for this compound. Continuing in this way, the accuracy of the experimental enthalpies of formation was confirmed for all mononitroalkanes (2−8) except for 2,4,4-trimethyl-2-nitropentane (9). The values of enthalpy of formation of 9 calculated from 13 reactions using 7 reference nitro compounds agree within 7.7 kJ·mol−1. However, the average value obtained from these reactions, 265.3 ± 7.0 kJ·mol−1, is 16 kJ·mol−1 lower than the experimental value by Verevkin.39 The theoretical value is recommended for 9 in Table 2 because it is in internal consistency with the ΔfHo298 (g) values of closely related nitroalkanes (1−8). It is significant also to note that, of seven nitro compounds studied by Verevkin,39 the experimental and calculated values agree well for two aliphatic (8, 30) and four aromatic nitro compounds. The inaccuracy in the experimental gas-phase enthalpy of formation of 9 is difficult to assign to either ΔfHo298 (l) or to ΔvapHo298, and because of this, there are no recommendations for these properties in Table 2. The experimental and calculated enthalpies of formation of all dinitroalkanes (10−18) agree well. A large number of deviations are revealed for the polynitroalkanes with 3−6 nitro groups (19−29). The calculated values are from (10 to 20) kJ· mol−1 less than the experimental enthalpies of formation of 19−22, 26, 28, and 29. At first glance it might appear that these deviations display the systematic errors in the computational model associated with the increase of the number of nitro groups. However, the calculated enthalpies of formation agree with the experimental values for species with four (23) and three (24, 25) nitro groups on one carbon atom and for compound with two adjacent C(NO2)2 groups (27). The calculated ΔfHo298 (g) values for 19−22, 26, 28, and 29 are in internal consistency with the experimental data for mononitroalkanes (1−8), dinitroalkanes (10−18), and tetranitroalkanes (23−25, 27), and thus the theoretical gas-phase enthalpies of formation are recommended for 19−22, 26, 28, and 29 in Table 2 rather than the experimental data. On the basis of these values and the experimental condensed phase enthalpies of formation, the new values of enthalpy of vaporization or sublimation are recommended in Table 2 for 19, 20, 26, 28, and 29. It is obviously that the accuracy of these values depends not only on the accuracy of the calculated ΔfHo298 (g) values but also on the reliability of the reported experimental ΔfHo298 (l) or ΔfHo298 (cr) values. 2822



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5.0 kJ·mol−1 and 66.9 ± 1.3 kJ·mol−1); however there is a significant difference with the enthalpies of sublimations (∼130 kJ·mol−1) reported later.61,64,66 The calculated value for 47 matches the experimental values66,67 of ΔfHo298 (HMX, cr) = 75.3 kJ·mol−1 and ΔsubHo298 (HMX) = 161.0 ± 0.3 kJ·mol−1, that are recommended in Table 2. However, a higher value of enthalpy of formation of crystalline 47 (∼86 kJ·mol−1)58,65 cannot be excluded, and in this case the value of about 150 kJ· mol−1 is expected for the enthalpy of sublimation of 47. It should be noted that the criteria of internal consistency was used in the selection of the recommended values for 45 and 47. We recommend the ΔfHo298 (g) values with a high degree of confidence while the recommendations for ΔfHo298 (cr) and ΔsubHo298 can be considered reliable if one of these two values is determined with high accuracy. The calculated enthalpy of formation of 46 is 18 kJ·mol−1 less than the only reported value known to us.58 Table S2 (Supporting Information) shows that this value is consistent with the enthalpies of formation of noncyclic (37) and other cyclic nitramines (42-45), and because of this it is recommended in Table 2. Since it is difficult to assign the possible experimental error either to ΔfHo298 (cr) or to ΔsubHo298, there are no recommendations for these values in Table 2. CL-20 (48) is the polycyclic nitramine belonging to one of the most interesting nitrogen-rich energetic molecules developed in recent years.2 CL-20 is referred to as a caged compound because it resembles two RDX rings joined at several carbon atoms. The strained rings of this compound cause an increase in the enthalpy of formation, which makes it powerful explosive. CL-20 exists in four different polymorphs (labeled as α, β, γ, and ε),78 from which the ε-CL-20 phase is the most stable.79 The enthalpy of formation of crystalline εCL-20 is given in Table 2. The optimized geometry of the most stable conformer in the gas phase, which corresponds to experimentally obtained crystalline β-form, was used in the G4(MP2) calculation in this work. This conformer was also defined as the most stable in the previous studies.80,81 The recommended gas-phase enthalpy of formation of CL-20 (Table 2) is the mean of the 10 reactions with aliphatic (37) and cyclic (42, 43, 44, 45, 46, and 47) nitramines involved as the reference species. The values obtained from these reactions agree within 12.9 kJ·mol−1, and this makes us confident that the calculated value (500.9 ± 10.0 kJ·mol−1) is sufficiently reliable. This value combined with the experimental enthalpy of formation of ε-CL-20 (377.4 ± 13.0 kJ·mol−1)69 leads to the value of 123.5 ± 23.0 kJ·mol−1 for the enthalpy of sublimation. This ΔsubHo298 value is significantly lower than that reported by Miroshnichenko58 (226.8 ± 4.6 kJ·mol−1) by assuming its value is equal to the experimental activation energy of the phase transition. Note that our value agrees satisfactorily with the theoretical estimations of enthalpy of sublimation (168.7 and 150.8 kJ·mol−1),82,83 taking into account the uncertainty of these values. Another potential explosive in the group of nitramines is 1,3,3-trinitroazetidine (TNAZ, 49). The solid-phase enthalpy of formation of TNAZ, 36.4 kJ·mol−1, is cited by various authors,71−73 but we were unable to find an original source for this data. A lower value of 11.8 kJ·mol−1 was measured by Simpson et al.71 from the combustion calorimetry experiments. As can be seen from Table 2, this value combined with the experimental enthalpy of sublimation,74 gives a value of ΔfHo298 (g) = 110.6 ± 4.2 kJ·mol−1, in good agreement with our theoretical result (111.3 kJ·mol−1).

The experimental enthalpies of formation of two N,Ndinitramines,58,59 50 and 53, are of questionable accuracy, as discussed above (see Section 3.1). N,N-Dinitramines are highly explosive liquids, and their combustion presents difficulties. To avoid the explosion of the sample, the substances were mixed with dimethyl phthalate and burned in terylene ampule, and this could cause an increase in the experimental error. The evidence of the inaccuracy of these data was provided by the large discrepancy with quantum chemical results (Figure 2). The recommended ΔfHo298 (g) values for 50−53 are the mean of the 13 to 18 isodesmic reactions (see Table S2 of the Supporting Information) with different combinations of reference species involved in these reactions. It is obviously that there are substantial uncertainties in the reported values of ΔfHo298 (l) and ΔvapHo298 for these compounds. The last group of compounds we are going to discuss includes three primary nitramines (54−56) and 1,5-dinitrobiuret (57) containing the −NHNO2 group adjacent to carbonyl group. The evidence of the accuracy of experimental data for (54) was provided by the agreement with isodesmic reaction results (Table 2), but the experimental and calculated values for 55 and 56 differ by 33 and 17 kJ·mol−1, respectively. These differences are considerably larger than the errors expected from the computational method, and because of this the theoretical ΔfHo298 (g) values are recommended for 55 and 56. The reported enthalpies of formation of solid 56 are in good agreement (Table 2), and therefore it can be assumed that the experimental enthalpy of sublimation87 is overestimated by o about 17 kJ·mol −1 . Note that the Δ fH 298 (g) values recommended in this work for 54−56, lead to the same value of enthalpy of formation of 57 (∼255 kJ·mol−1) when used in isodesmic reactions (see the last three reactions in Table S2 of the Supporting Information). The Table S2 also shows that the enthalpies of formation of 54−56 are in internal consistency not only with one another but also with other nitro compounds. The enthalpy of formation of solid 1,5-dinitrobiuret (57) was estimated by Geith et al.60 based on the MP2/cc-pVTZ calculations and assuming the enthalpy of sublimation of 1,5dinitrobiuret to be the same as that of biuret. The ΔfHo298 (cr) obtained in our work (Table 2) is based on the isodesmic reaction calculations and the enthalpy of sublimation evaluated from the experimental data on piperazine, 1,4-dinitropiperazine, and biuret.76 The difference between two values of ΔfHo298 (cr)60,76 is two times larger than that between the accepted ΔsubHo298 values. This is partly because of the different quantum chemical methods used in two studies and partly because the calculations in ref 60 were carried out not for the most stable conformer.

4. CONCLUSIONS The accuracy of experimental enthalpies of formation of aliphatic nitro compounds and nitramines was investigated by using the G4 theory. The enthalpies of formation were systematically underestimated at the G4 level of theory using the standard approach based on the atomization reaction (Figure 1). G4 theory has been shown to be very successful in predicting thermochemical data for a variety of molecules;4,27,28,84 however the G4 theory performs less satisfactorily for molecules containing nitro group. Thus, the accurate determination of enthalpies of formation of nitro compounds poses a challenging problem not only for experiment, but also for theory. Much better agreement between theory and 2823



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(4) Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. Gaussian-4 Theory. J. Chem. Phys. 2007, 126, 084108/1−084108/12. (5) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople. J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (6) Raghavachari, K.; Stefanov, B. B. Accurate Density Functional Thermochemistry for Larger Molecules. Mol. Phys. 1997, 91, 555−559. (7) Osmont, A.; Catoire, L.; Gökalp, I.; Yang, V. Ab Initio Quantum Chemical Predictions of Enthalpies of Formation, Heat Capacities, and Entropies of Gas-Phase Energetic Compounds. Combust. Flame 2007, 151, 262−273. (8) Asatryan, R.; Bozzelli, J. W.; Simmie, J. M. Thermochemistry of Methyl and Ethyl Nitro, RNO2, and Nitrite, RONO, Organic Compounds. J. Phys. Chem. A 2008, 112, 3172−3185. (9) Kiselev, V. G.; Gritsan, N. P. Theoretical Study of the Nitroalkane Thermolysis. 1. Computation of the Formation Enthalpy of the Nitroalkanes, Their Isomers and Radical Products. J. Phys. Chem. A 2008, 112, 4458−4464. (10) Khrapkovskii, G. M.; Tsyshevsky, R. V.; Chachkov, D. V.; Egorov, D. L.; Shamov, A. G. Formation Enthalpies and Bond Dissociation Enthalpies for C1−C4 Mononitroalkanes by Composite and DFT/B3LYP Methods. J. Mol. Struct.: THEOCHEM 2010, 958, 1−6. (11) Jorgensen, K. R.; Oyedepo, G. A.; Wilson, A. K. Highly Energetic Nitrogen Species: Reliable Energetics via the Correlation Consistent Composite Approach (ccCA). J. Hazard. Mater. 2011, 186, 583−589. (12) Dorofeeva, O. V.; Kolesnikova, I. N.; Marochkin, I. I.; Ryzhova, O. N. Assessment of Gaussian-4 Theory for the Computation of Enthalpies of Formation of Large Organic Molecules. Struct. Chem. 2011, 22, 1303−1314. (13) Dorofeeva, O. V.; Suntsova, M. A. Enthalpies of Formation of Nitromethane and Nitrobenzene: Theory vs Experiment. J. Chem. Thermodyn. 2013, 58, 221−225. (14) McCullough, L. P.; Scott, D. W.; Pennington, R. E.; Hossenlopp, I. A. Nitromethane: The Vapor Heat Capacity, Heat of Vaporization, Vapor Pressure and Gas Imperfection; the Chemical Thermodynamic Properties from 0 to 1500 K. J. Am. Chem. Soc. 1954, 76, 4791−4796. (15) Pedley, J. B. Thermochemical Data and Structures of Organic Compounds; Thermodynamics Research Center: College Station, TX, 1994; Vol. I. (16) Knobel, Y. K.; Miroshnichenko, E. A.; Lebedev, Y. A. Heats of Combustion of Nitromethane and Dinitromethane: Enthalpies of Formation of Nitromethyl Radicals and Energies of Dissociation of Bonds in Nitro Derivatives of Methane. Russ. Chem. Bull. 1971, 20, 425−428. (17) NIST Chemistry Webbook, NIST Standard Reference Database Number 69; Linstrom, P. J., Mallard, W. G., Eds.; National Institute of Standards and Technology: Gaithersburg MD; http://webbook.nist. gov. (18) Lebedeva, N. D.; Katin, Y. A.; Akhmedova, G. Y. Standard Enthalpy of Formation of Nitrobenzene. Russ. J. Phys. Chem. 1971, 45, 1192−1193. (19) Verevkin, S. P.; Emel’yanenko, V. N.; Diky, V.; Dorofeeva, O. V. Enthalpies of Formation of Nitromethane and Nitrobenzene: New Experiments vs Quantum Chemical Calculations. J. Chem. Thermodyn. 2014, 73, 163−170. (20) Dorofeeva, O. V.; Ryzhova, O. N.; Suntsova, M. A. Accurate Prediction of Enthalpies of Formation of Organic Azides by Combining G4 Theory Calculations with an Isodesmic Reaction Scheme. J. Phys. Chem. A 2013, 117, 6835−6845. (21) Dorofeeva, O. V.; Ryzhova, O. N. Gas-Phase Enthalpies of Formation and Enthalpies of Sublimation of Amino Acids Based on Isodesmic Reaction Calculations. J. Phys. Chem. A 2014, 118, 3490− 3502. (22) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.;

experiment was found when the calculation of the enthalpies of formation was based on the isodesmic reactions (Figure 2) rather than the atomization reaction. The isodesmic reaction approach was used in this paper to estimate the accuracy of experimental enthalpies of formation of aliphatic nitro compounds. A systematic comparison of experimentally determined enthalpies of formation with the results of calculations revealed the possible errors in the experimental values for 17 compounds. The experimental and calculated values for these species differ by more than 8 kJ·mol−1 (these compounds are labeled by their numbers in Figure 2). The theoretical ΔfHo298 (g) values were recommended for these compounds as being more reliable than the experimental values. For remaining compounds, the experimental values were recommended on the basis of an analysis of available research data (Table 2). Thus, a reference data set of gas-phase enthalpies of formation that contains both experimental and calculated values was constructed. All recommended values were used in the isodesmic reaction calculations to estimate the enthalpies of formation of various nitro compounds, and so these values constitute an internally self-consistent set. This reference data set may be useful for predicting the enthalpies of formation of different nitro compounds by isodesmic reaction method and for the development of empirical estimation methods. On the basis of recommended ΔfHo298 (g) values and the literature data on the condensed phase enthalpies of formation, the new values of enthalpy of sublimation or vaporization were suggested for some compounds. Thus, a set of self-consistent values of enthalpy of formation in both condensed and gaseous phases and enthalpy of sublimation or vaporization is presented for compounds studied.

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ASSOCIATED CONTENT

S Supporting Information *

Experimental enthalpies of formation of reference compounds used in isodesmic reaction calculations and their comparison with the values calculated by the G4 and G4(MP2) method from the atomization reaction (Table S1), enthalpies of formation of gaseous nitro compounds calculated from the isodesmic reactions using G4 energies (Table S2), and comparison of experimental enthalpies of formation with those calculated from atomization and isodesmic reactions (Table S3). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

This research was supported by the Russian Foundation for Basic Research under Grant No. 14-03-00612. Notes

The authors declare no competing financial interest.

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REFERENCES

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