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Enthalpies of Formation of Hydrazine and Its Derivatives Olga V. Dorofeeva, Oxana N. Ryzhova, and Taisiya A. Suchkova J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b04914 • Publication Date (Web): 21 Jun 2017 Downloaded from http://pubs.acs.org on June 23, 2017

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The Journal of Physical Chemistry

Enthalpies of Formation of Hydrazine and Its Derivatives

Olga V. Dorofeeva,* Oxana N. Ryzhova, and Taisiya A. Suchkova Faculty of Chemistry, Lomonosov Moscow State University, 1-3 Leninskie Gory, Moscow, 119991, Russia

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ABSTRACT: ° , both in the gas and condensed phase, and enthalpies of sublimation or Enthalpies of formation, ∆

vaporization have been estimated for hydrazine, NH2NH2, and its 36 various derivatives using quantum chemical calculations. The composite G4 method has been used along with isodesmic reaction schemes to derive a set of self-consistent high accuracy gas-phase enthalpies of formation. To estimate the enthalpies of sublimation and vaporization with reasonable accuracy (5-20 kJ/mol), the method of molecular electrostatic ° potential (MEP) has been used. The value of ∆ (NH NH , g) = 97.0 ± 3.0 kJ/mol was determined from ° 75 isogyric reactions involving about 50 reference species; for most of these species, the accurate ∆ (g)

values are available in Active Thermochemical Tables (ATcT). The calculated value is in excellent agreement with the reported results of the most accurate models based on coupled cluster theory (97.3 kJ/mol, the average of six calculations). Thus, the difference between the values predicted by high-level ° (NH theoretical calculations and the experimental value of ∆ NH , g) = 95.55 ± 0.19 kJ/mol

recommended in the ATcT and other comprehensive reference sources is sufficiently large and requires further investigation. Different hydrazine derivatives have been also considered in this work. For some of them, both the enthalpy of formation in condensed phase and enthalpy of sublimation or vaporization are available; for other compounds, experimental data for only one of these properties exist. Evidence of accuracy of experimental data for the first group of compounds was provided by the agreement with ° (g) value. The unknown property for the second group of compounds was predicted using theoretical ∆

MEP model. This paper presents a systematic comparison of experimentally determined enthalpies of formation and enthalpies of sublimation or vaporization with the results of calculations. Because of relatively large uncertainty in the estimated enthalpies of sublimation, it was not always possible to evaluate the accuracy of the experimental values; however, this model allowed us to detect large errors in the experimental data, as in the case of 5,5'-hydrazinebistetrazole. The enthalpies of formation and enthalpies of sublimation or vaporization have been predicted for the first time for ten hydrazine derivatives with no 2 ACS Paragon Plus Environment

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experimental data. A recommended set of self-consistent experimental and calculated gas-phase enthalpies of ° formation of hydrazine derivatives can be used as reference ∆ (g) values to predict the enthalpies of

formation of various hydrazines by means of isodesmic reactions.



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INTRODUCTION Hydrazine and its derivatives are the compounds with wide range of uses. They are used in the manufacture of foam plastics, agricultural chemicals (herbicides, pesticides, fungicides, and plant growth regulators), and pharmaceutical chemicals. Hydrazine and some of its derivatives have found an extensive use as the components of high-energy fuels, rocket propellants, pyrotechnics, and explosives.1,2 Although the hydrazine and its methylated derivatives are used until now in aerospace applications, the new hydrazinebased energetic materials have received increasing attention during the past decades. Among them, the hydrazine-derived ionic liquids are considered especially important because of their potential applications as propellants.3–6 Another group of promising energetic compounds are the endocyclic hydrazines (heterocycles in which at least one of the two nitrogens in the hydrazine is also found within a ring); numerous pharmaceuticals, pesticides, explosives, and dyes are based on these rings.2,7 In order to better understand and accurately model the reactions of hydrazine-based energetic ° compounds, the knowledge of enthalpy of formation (∆ ) is necessary. Enthalpy of formation is a very

important property, which is required to assess potential performance of an energetic compound.8 However, the calorimetric determination of enthalpy of combustion of hydrazines often presents challenges, and the experimental enthalpies of formation for a large number of organic derivatives of hydrazine are unknown or only known with relatively large uncertainties. It is interesting that even for hydrazine itself, there is some ° uncertainty about its exact value of enthalpy of formation. The experimental values of ∆ (g),

recommended in the most comprehensive sources of thermochemical data, such as Active Thermochemical Tables (ATcT),9 NIST Chemistry Webbook,10 JANAF,11 and Gurvich et al.,12 differ insignificantly from each other (95.2 – 95.6 kJ/mol). However, the experimental value is obviously lower than those obtained from the most reliable theoretical calculations. The values calculated by Simmie13 using the popular composite methods (CBS-QB3, CBS-APNO, G3, and G4) are from 3.7 to 8.1 kJ/mol higher than the experimental value. This disagreement was identified as outlier because such large deviations from the experimental values 4 ACS Paragon Plus Environment

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did not occur for other compounds. The disagreement with the experiment has decreased to 1.7-1.9 kJ/mol when more accurate methods like W4,14 CCSD(T)-F12b,15 or W3X-L16 were used. However, Karton et al.14 consider such a difference between the W4 and ATcT as unusually large. Thus, the discrepancy between theory and experiment for hydrazine needs a further explanation. As for the hydrazine derivatives, the experimental data have been reported for a relatively limited ° (g) were performed mainly for methyl number of compounds. The theoretical calculations of ∆

hydrazines,13,17–21 and in general, these calculations supported the experimental data for mono- and both dimethylhydrazines and gave a reasonable estimation for tri- and tetramethylhydrazine. In the present work, we have decided to check the accuracy of the experimental data for other hydrazine derivatives taking into account the many difficulties that have been encountered working with these compounds. Among these compounds are alkyl and phenyl hydrazines, nitrosohydrazines, hydrazides of the type –C(=O)NHNH2 and – C(=S)NHNH2, diacylhydrazides, and endocyclic hydrazines. Also, the enthalpies of formation of four energetic compounds with promising properties (1-amino-1-hydrazino-2,2-dinitroethylene, 3,6-dihydrazino1,2,4,5-tetrazine, 5,5'-hydrazinebistetrazole, and 1,4-diamino-3,6-dinitropyrazolo[4,3-c]-pyrazole) have been estimated. To calculate the gas-phase enthalpies of formation, we use the composite quantum chemical G4 method22 in combination with isodesmic reactions approach.23 In our recent publications, we have shown that the G4 method applied to atomization reaction could resulted in large errors for nitrogen containing compounds,24–26 while the use of isodesmic reactions allowed to achieve an accuracy comparable with that obtained from the experimental measurements. The same picture is observed for other composite methods:27 the average of CBS-QB3, CBS-APNO, G3, and G4 methods obtained for hydrazine using isodesmic reactions (97.7 ± 2.0 kJ/mol) is in close agreement with results of high-level W4, CCSD(T)-F12b, and W3XL calculations (97.3, 97.4, and 97.5 kJ/mol, respectively),14–16 whereas the average value calculated using atomization reactions (100.8 ± 2.0 kJ/mol)13 is substantially higher. This result for hydrazine gives grounds 5 ACS Paragon Plus Environment


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to assume that the G4 method combined with isodesmic reactions will be able to obtain the accurate ° ∆ (g) values for hydrazine derivatives.

The condensed-phase enthalpies of formation needed to investigate the thermodynamic stability and performance of energetic compounds can be determined using the gas-phase enthalpy of formation and enthalpy of phase transition (either sublimation or vaporization). In this study, to predict the enthalpies of ° ° sublimation (∆ ) or vaporization (∆ ), we use their correlation with the statistical descriptors of

the molecular electrostatic potential (MEP) established by Politzer and coworkers.28,29 This method has found wide application for prediction of enthalpies of sublimation and vaporization.30–34

COMPUTATIONAL DETAILS All ab initio and density functional theory (DFT) calculations were performed using the Gaussian 03 package of programs.35 Geometry optimization, vibrational frequency calculation, and conformational analysis of hydrazine and its derivatives were carried out at the B3LYP/6-31G(d,p) density functional level. The optimized geometries of the most stable conformers were used as inputs for further G422 calculations. The G4(MP2) method36 was used instead of G4 for some large molecules. The G4 enthalpies of formation were calculated using both the atomization37 and isodesmic reaction23 approaches. The calculation via the 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 ATcT9 and reference book by Gurvich et al.12 The experimental ° (g) values for reference species involved in the isodesmic and other balanced reactions are given in ∆

Table S1 of the Supporting Information. The enthalpies of formation calculated from atomization reactions and the full list of isodesmic reactions for each compound studied in this work are given in Table S2 of the ° Supporting Information. The uncertainty of the ∆ (g) values calculated from isodesmic reactions is

defined as two times the root-mean-square deviation from the average for all reactions. 6 ACS Paragon Plus Environment

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The modified equation of Politzer34 ° = (SA) + σ υ + + Π ∆

(SA is the molecular surface area, σ indicates the variability of the potential on the molecular surface, υ is the degree of the balance between positive and negative regions, and Π is a measure of local polarity) was applied to estimate the enthalpies of sublimation. The DFT B3LYP/cc-pVTZ method was used to optimize geometries and determine the densities for generating the electrostatic potentials. The surface electrostatic potential quantities, SA, σ , υ, and Π, were calculated using the program Multiwfn.38 The regression coefficients a, b, c, and d were determined from least-squares fitting to reliable values of enthalpies of sublimation of 36 compounds. These compounds, including four hydrazines, were selected due to their structural similarity to the compounds under study. The similar equation was used for enthalpies of ° vaporization; the coefficients a, b, c, and d were obtained using the experimental ∆ values for six

liquid hydrazines. Using these coefficients and calculated values for SA, σ , υ, and Π, the theoretical values ° ° and ∆ were obtained. Comparison between the experimental and calculated enthalpies of of ∆

sublimation and vaporization, as well as the molecular electrostatic potential parameters and coefficients a, b, c, and d for enthalpies of sublimation and vaporization are given in Table S3 of the Supporting Information.

RESULTS AND DISCUSSIONS Enthalpy of Formation of Hydrazine. The results of quantum chemical calculations carried out at different levels of theory are presented in Table 1 together with the experimental values recommended in the most reliable sources of thermochemical data.9–12 As can be seen, the different versions of composite ccCA method40,41 give the values both less and more than the experimental one, whereas the composite CBS-QB3, CBS-APNO, G3, and G4 methods13,42 lead to the values overestimated by up to 8 kJ/mol. The average of these four methods, 100.8 ± 2.0 kJ/mol,13 is about 5 kJ/mol higher than the experimental enthalpy of formation. 7 ACS Paragon Plus Environment


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Table 1. Experimental and Theoretical Enthalpies of Formation, Enthalpy of Vaporization, and Total Atomization Energy of Hydrazine (in kJ/mol) ° ∆ (liq)

50.82 ± 0.19 50.63 50.38 ± 0.30

° ∆

44.73 44.73 44.8 ± 0.4

∆ %° (g)

∑ '%

95.55 ± 0.19 95.35 95.18 ± 0.33 94.3 78.0 102.0 109.2 93.7 90.4 101.7 98.3 101.7 99.7 100.5 99.3 100.0 103.7 100.3

109.71 109.43 109.34

1695.6 ± 0.2

100.8 ± 2.0 96.7 96.8a 98.1a 97.3a 97.4 99.3a 97.5

115.4 ± 2.0 111.3 111.3a 112.6a 111.8a 111.9 113.8a

° ∆ (g)

97.7 ± 2.0 97.0 ± 3.0 a

113.8 114.6 118.2 114.8 1689.9 ± 2.0 1694.0 1692.7 1693.5 1693.9 1691.5

comments

ref

exp exp exp W1 B3LYP/6-311+G(3df,2pd) G2MP2 ccCA-aTZ ccCA-CBS-1 ccCA-CBS-2 ccCA-P/6-31+G(d) ccCA-P/6-31G(2df,p) ccCA-P/cc-pVTZ CBS-QB3 CBS-APNO CBS-QB3 CBS-APNO G3 G4 average of four methods (CBS-QB3, CBS-APNO, G3, G4) CCSD(T)/CBS extrapolations CCSD(T)b CCSD(F12) W4 CCSD(T)-F12b CCSD(T)+F12+INT/cc-pVQZ-F12 W3X-L average of four methods (CBS-QB3, CBS-APNO, G3, G4) with 45 isodesmic reactions G4 with 75 isodesmic reactions

9 10,11 12 39 17 17 40 40 40 41 41 41 42 42 13,43 13,43 13,43 13,43 13,43 19 44 45 14 15 46 16

27 this work

Calculated in this work using experimental enthalpies of formation of gaseous atoms at T = 0 K and thermal corrections for

elements in their standard states from refs 9 and 12, respectively. bCCSD(T)/cc-pCVQZ//CCSD(T)/cc-pCVTZ with several corrections.

However, as mentioned above, this average value decreases to 97.7 ± 2.0 kJ/mol when these four composite methods are used in combination with isogyric reactions.27 In this study, the enthalpy of formation of hydrazine is estimated by G4 method combined with 75 isogyric reactions which can be divided into three groups depending on reference species used. The first group of 35 reactions is constructed using radicals 8 ACS Paragon Plus Environment

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•NH2, •CH2NH2, •NHCH3, •NHNH2, and •NHOH as the reference species; the accurate, reliable, and ° internally consistent ∆ (g) values for these radicals and all other species used in the reactions were

taken from the ATcT.9 The second group of 20 reactions contains only small molecules whose enthalpies of formation are recommended in ATcT,9 and the third group of 20 reactions contains larger molecules with reliable enthalpies of formation from different experimental studies. As can be seen from Table S2 of the ° Supporting Information, the average ∆ (g) values for the three groups of reactions (97.0, 96.9, and 97.3

kJ/mol) are in close agreement with each other, and the average value of all 75 reactions (97.0 ± 3.0 kJ/mol) agrees well with the six results of new developed composite models based on coupled cluster theory (from 96.7 to 97.5 kJ/mol, the average is 97.3 kJ/mol; see Table 1).14–16,19,44,45 Although the value obtained in this work is in agreement with the experimental one when the uncertainty of calculation is taken into account, the values from CCSD calculations14–16,19,44,45 are much more accurate, and therefore one can assume that the experimental value is underestimated by about 2 kJ/mol. Because of this, the hydrazine was not used as a reference molecule in our further calculations. The results of calculations for methylhydrazine, 1,1-, and 1,2dimethylhydrazine are in support of this: Table S2 of the Supporting Information shows that the use of ° (g) values underestimated by ~3.3 kJ/mol compared to hydrazine in isodesmic reactions leads to the ∆

reactions without hydrazine. Thus, the experimental value of gas-phase enthalpy of formation of hydrazine is not consistent with the experimental data for a large number of compounds used in the isodesmic reactions for hydrazine, methylhydrazine, 1,1-, and 1,2-dimethylhydrazine. It is also interesting to note that the largest discrepancy between the enthalpy of formation calculated from atomization and isodesmic reactions occurs for the unsubstituted hydrazine itself (the only exceptions are species with nitro groups, large molecules, and some heterocycles for which a large uncertainty in the values obtained from atomization reaction was mentioned earlier).24,47 The addition of substituents results in a decrease of this discrepancy, as it is shown in Figure 1 for methyl-substituted hydrazines.


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° (at) ° (isodes), ∆ * ∆ kJ/mol


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Figure 1. Difference between the enthalpies of formation of methyl-substituted hydrazines calculated from atomization and isogyric reactions depending on the number of methyl groups.

Number of CH3 groups

Enthalpies of Formation of Hydrazine Derivatives. Table 2 collects the results of theoretical calculations and the available experimental data on enthalpies of formation and enthalpies of vaporization or sublimation of various hydrazine derivatives. Of the eight alkyl substituted hydrazine compounds, 1-8 ° (g) values were (hereinafter, the compound’s numbers are given according to Table 2), the ∆

determined from the experimental measurements only for mono- (1) and dimethylhydrazines (2, 3). The values calculated in this work for 1 and 2 differ from the experimental values by just 1 kJ/mol and these two compounds were used as the main reference species in isodesmic working reactions for other hydrazines. The discrepancy for 3 is somewhat larger and because of this, and taking into account large uncertainty of the ° experimental value, the theoretical ∆ (g) value is recommended for this compound as being more

reliable due to its consistency with the experimental values for 1 and 2 and a number of other compounds (see isodesmic reactions for 3 in Table S2 of the Supporting Information). The gas-phase enthalpies of formation for 4-8 were calculated from reactions where 1, 2, and different compounds with accurate ° experimental ∆ (g) values were used as the reference species. The liquid-phase enthalpies of formation ° were also estimated for these compounds; the values of ∆ (l) are based on the available experimental


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enthalpies


of

vaporization

for

5

and

7

and



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° Table 2. Experimental and Theoretical Enthalpies of Formation (∆ ) in Both Condensed and Gaseous Phases and Enthalpies of

° ° Vaporization (∆ ) or Sublimation (∆ ) of Hydrazine Derivatives (in kJ/mol)a ° ∆ (cr) ° or ∆ (liq)

° ∆ ° or ∆

° ∆ (g)

comment

ref

CH3NHNH2 (l)

54.1

40.4

94.5 81.0 96.0 107.0 90.7 ± 2.2 108.2 99.5 ± 2.4 93.4 ± 3.0

exp calc: B3LYP/6-311+G(3df,2pd) calc: G2MP2 calc: G3 calc: composite methods with isodesmic reactions calc: G4 calc: average of CBS-QB3, CBS-APNO, G3, G4 calc: G4 with 20 reactions

10, 48, 49 17 17 18 20 21 13 this work

2

(CH3)2NNH2 (l)

48.3 ± 3.6

35.0 ± 0.2

83.3 ± 3.6 77.0 77.0 94.0 79.7 ± 2.2 83.4 84.0 ± 3.1 82.3 ± 3.0

exp calc: B3LYP/6-311+G(3df,2pd) calc: G2MP2 calc: G3 calc: composite methods with isodesmic reactions calc: G4 calc: average of CBS-QB3, CBS-APNO, G3, G4 calc: G4 with 30 reactions

10, 50, 51 17 17 18 20 21 13 this work

3

CH3NHNHCH3 (l)

52.8 ± 4.2

39.3 ± 0.1

92.1 ± 4.3 84.0 89.0 103.3 90.0 92.7 ± 2.4 95.8 97.1 ± 3.0 94.8 ± 3.0

exp calc: B3LYP/6-311+G(3df,2pd) calc: G2MP2 calc: G3MP2 calc: G3MP2 with isodesmic reactions calc: composite methods with isodesmic reactions calc: G4 calc: average of CBS-QB3, CBS-APNO, G3, G4 calc: G4 with 31 reactions

10, 52, 53 17 17 19 19 20 21 13 this work

4

CH3CH2NHNH2 (l)

65.7 ± 2.0 25.7 ± 4.0b

40.0 ± 3.0

calc: G4 with 10 reactions est: MEPc

this work this work

48.8b

33.3 ± 0.1(292 K) 78.6 ± 2.3 82.4 83.2 ± 3.7 82.1 ± 3.0

exp calc: composite methods with isodesmic reactions calc: G4 calc: average of CBS-QB3, CBS-APNO, G3, G4 calc: G4 with 47 reactions

54 20 21 13 this work

no.

compound

1

5

(CH3)2NNH(CH3) (l)


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6 7

(CH3)2CHNHNH2 (l) (CH3)2NN(CH3)2 (l)



this work this work

exp calc: composite methods with isodesmic reactions calc: G4 calc: average of CBS-QB3, CBS-APNO, G3, G4 calc: G4 with 45 reactions

55, 56 20 21 13 this work

-2.0 ± 3.0


this work this work

31.3 ± 3.0 -10.7 ± 5.0b

42.0 ± 3.0

47.9b

32.9(305 K) 76.4 ± 2.3 80.7 81.3 80.8 ± 4.0

8

(CH3)3CNHNH2 (l)

-49.6 ± 5.0b

47.6 ± 3.0

9

H2NN(CH3)NO (cr)

86.2 ± 0.8

79.5 ± 0.4

165.7 ± 0.9 161.7 ± 3.0

exp calc: G4 with 10 reactions

57 this work

10

H2NN(NO)CH2CH2N(NO)NH2 (cr)

208.4 ± 1.7

172.4 ± 1.3

380.8 ± 2.1 343.3 ± 4.0

236.5 ± 15.0b

106.8 ± 12.0

exp calc: G4 with 11 reactions est: MEPc

57 this work this work

143.1 141.0 ± 0.8

61.5 61.9 ± 0.8

204.6 202.5 ± 1.3 208.3 ± 3.0

146.9 ± 5.0b

61.4 ± 3.0

exp exp calc: G4 with 20 reactions est: MEPc

48, 58, 59 60 this work this work

210.8 ± 1.7 207.3 ± 3.0


61 this work

316.9 ± 3.0



333.4 ± 3.0


this work this work

439.5 ± 3.0

calc: G4MP2 with 8 reactions est: MEPc

this work this work

exp calc: G4MP2 with 8 reactions est: MEPc

10, 48, 58, 62 this work this work


56 this work

est: MEPc

this work

11

C6H5NHNH2 (l)

12

C6H5N(CH3)NH2 (l)

147.6 ± 1.2

63.2 ± 0.7

13

C6H5NHNHC6H5 (cr)

221.2 ± 1.3

95.7d 108.8 ± 10.0

14 15 16

(C6H5)2NNH2 (cr) (C6H5)2NNHC6H5 (cr) (C6H5)2NN(C6H5)2 (cr)

230.2 ± 12.0b

103.2 ± 10.0

286.1 ± 12.0b

153.4 ± 10.0

457.9 ± 2.5

86.7d 544.6 ± 4.0

338.5 ± 20.0b 17

2-nitrophenylhydrazine (cr)

60.0

b

206.1 ± 15.0 124.7 184.7 ± 4.0 105.4 ± 10.0



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

18

4,4'-dinitrohydrazobenzene (cr)

109.6

168.7d 278.3 ± 4.0

exp calc: G4MP2 with 8 reactions est: MEPc


-115.1 ± 4.0



5.8 ± 3.0


this work this work

-125.9 -214.8 ± 3.0

exp exp calc: G4 with 16 reactions est: MEPc est: exp + calc (see text)

64 65 this work this work this work

-318.5 ± 3.0



exp exp calc: G4MP2 with 11 reactions est: MEPc

10, 48, 58, 62 66 this work this work


this work this work


10, 62, 67 this work this work

exp exp calc: G4 with 7 reactions

62, 68 69 this work



181.4 ± 10.0

19

H2NC(O)NHNH2 (cr)

-225.7 ± 0.6

110.6d 111.6 ± 10.0

20 21

22

H2NNHC(O)NHNH2 (cr) HC(O)NHNHC(O)H (cr)

CH3C(O)NHNHC(O)CH3 (cr)

-101.6 ± 12.0b

107.4 ± 10.0

-331.0 ± 0.7 -315.6 ± 4.0b

205.1 ± 0.7 100.8 ± 0.5

-315.6 ÷ -331.0

98.9 ± 10.0 100.8 - 116.2

-421.6 ± 5.0b

103.1 ± 1.7 97.3 ± 10.0

23

C6H5C(O)NHNHC(O)C6H5 (cr)

-213.8 ± 1.3 -201.7 ± 6.3

154.3d -47.4 ± 4.0 147.7 ± 10.0

24 25

H2NC(O)NHNHC(O)NH2 (cr) H2NNHC(O)C(O)NHNH2 (cr)

-320.5 ± 3.0 -443.7 ± 12.0b

123.2 ± 10.0

-295.2 ± 0.5

143.6d -151.6 ± 3.0 91.9 ± 20.0

26

27

H2NC(S)NHNH2 (cr)

H2NNHC(S)NHNH2 (cr)

Page 14 of 31

24.7 ± 5.0 2.4 ± 0.6

125.8 ± 1.5

128.2 ± 1.6 128.8 ± 4.0

108.1 ± 0.4

152.1 ± 3.0

260.2 ± 3.0 243.6 ± 2.0

135.6 ± 12.0b

108.0 ± 10.0


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28

2-furancarboxylic acid hydrazide (cr)

29

4-pyridinecarboxylic acid hydrazide (cr) -25.2 ± 5.0b

-205.5 ± 0.9

99.0 ± 0.7

-106.5 ± 1.1 -108.0 ± 2.0


70 this work

75.8 ± 4.0



16.2 ± 3.0


this work this work

101.0 ± 1.1 100.1 ± 10.0

30

benzoic acid hydrazide (cr) -78.6 ± 12.0b

94.8 ± 10.0

31

3-indazolinone (cr)

-57.6 ± 1.6

127.6 ± 1.5

70.0 ± 2.2 71.7 ± 3.0


72 this work

32

phthalhydrazide (cr)

-247.2 ± 2.3

139.8 ± 0.7

-107.4 ± 2.4 -98.8 ± 3.0



155.6 110.4 ± 6.0

calc: MP2/6-311++G(d,p) calc: G4 with 21 reactions est: MEPc

74–76 this work this work

exp calc: B3LYP/6-311++G(3d,3p), MEP calc: B3LYP/6-311G(d) calc: G4 with 13 reactions est: MEPc

77 32 78 this work this work

118.3 ± 20.0

33

34

(O2N)2C=C(NH2)(NHNH2) (cr) H-FOX 3,6-dihydrazino-1,2,4,5-tetrazine (cr) DHT

71.6

84.0e

-29.8 ± 20.0b

140.2 ± 15.0

535.6 535.6

129.7d 104.6

94.0 ± 20.0

640.2 1075.0 665.3 ± 7.0



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

35

36

5,5'-hydrazinebistetrazole (cr) HBT

1,4-diamino-3,6-dinitropyrazolo[4,3-c]pyrazole (cr), DADNP, LLM-119

565.4 ± 4.4 414.0

90.0

657.0 ± 20.0b

149.3 ± 15.0

495.3 ± 20.0b

130.9 ± 15.0

504.0 806.3 ± 3.0

626.2 ± 5.0

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exp calc: MP2/aug-cc-pVDZ calc: G4 with 38 reactions est: MEPc

79 80 this work this work


this work this work

° ° The recommended values are highlighted in bold. bCalculated using the given value of ∆ (or ∆ ) and the gas phase enthalpy of formation highlighted in bold.

a c

Estimated by the molecular electrostatic potential method (MEP, see text). dCalculated using the given value of condensed phase enthalpy of formation and the gas phase

enthalpy of formation highlighted in bold. eThis value was assumed to be the same as for other energetic compounds in ref 81.

° ∆ values estimated by molecular electrostatic potential (MEP) method for 4, 6, and 8. Table S3 of the Supporting Information shows that

the MEP model reproduces well the experimental enthalpies of vaporization for 1-3, 5, 7, 11, and 12, and therefore we can expect a reliable prediction for the structurally similar compounds 4, 6, and 8. Experimental values of enthalpy of formation and enthalpy of sublimation were determined for two alkylnitroso hydrazines, 9 and 10 (Table 2). We can assume that our calculations support the experimental data for 9 because the difference between the theoretical and ° (g) experimental values is within the combined errors of the two determinations. However, in the case of 10, the calculated and reported ∆

values

differ

by

about 16

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40 kJ/mol. From this it follows that any large errors in experimental data are likely to be found either in the enthalpy of combustion or in the enthalpy of sublimation, or in both. The MEP model predicts the enthalpy of sublimation of 10 to be 66 kJ/mol less than the experimental value. This difference is considerably larger than the probable error assigned to the MEP model, and therefore the experimental enthalpy of sublimation ° value with the calculated gas-phase enthalpy seems to be overestimated. Combining the predicted ∆ ° of formation, a somewhat higher ∆ (cr) value can be suggested for 10 (Table 2).

The next compounds studied are phenylhydrazines (11-18). The combustion and vapor pressure data for the parent phenylhydrazine (11) obtained by Gilbert et al.58,59 in the early forties of the last century give ° (g) the value of ∆ = 204.6 kJ/mol. A slightly smaller value (202.5 kJ/mol) has been later determined by

Lebedeva et al.60 The value calculated in the present work (208.3 ± 3.0 kJ/mol) is noticeably larger than both experimental determinations; this value, as can be seen from Table S2 of the Supporting Information, is based on twenty working reactions none of which give the value below 205.6 kJ/mol. In addition, when 11 ° (g) was used as a reference compound in the isodesmic reactions for 12, the calculated ∆ value was

significantly underestimated in comparison with the experimental one (see Table S2 of the Supporting Information). Based on these results, the theoretical gas-phase enthalpy of formation is recommended for ° (l) phenylhydrazine (11). Therefore, we can assume that the experimental value of ∆ is slightly ° (g) underestimated. The experimental and calculated ∆ values for 12 agree within the combined error

limits. Only the data on solid-phase enthalpy of formation are available for phenylhydrazines 13, 16, and 18. Using these experimental values and calculated gas-phase enthalpies of formation, the enthalpies of sublimation can be estimated for these compounds. Such estimated values for 13 and 18, as Table 2 shows, are in reasonable agreement with the enthalpies of sublimation determined by the MEP method, and therefore ° the experimental ∆ (cr) values48 for 13 and 18 can be considered as high enough quality data. On the ° ° (g, ° (cr, other hand, the same comparison for 16 (the value of ∆ = ∆ calc) * ∆ exp) = 86.7



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kJ/mol against the value of 206.1 kJ/mol calculated by the MEP method) suggests that the experimental solid-phase enthalpy of formation of 1658,62 is highly overestimated. The reported enthalpy of sublimation of 17 (which is in satisfactory agreement with that calculated by the MEP model, see Table 2) allows us to obtain an approximate value for the solid-phase enthalpy of formation. On the basis of theoretical estimates, ° (cr) values were predicted for 14 and 15 for which no experimental data are available at all. the ∆

The experimental values of both enthalpy of formation and enthalpy of sublimation were reported for only one (21) of the seven carbohydrazides (19-25) listed in Table 2. The two values of enthalpy of sublimation64,65 of 21 differ from each other by 104 kJ/mol. A large discrepancy between the calculated gasphase enthalpy of formation and that experimentally determined by Lebedeva et al.64 (Table 2) suggests an error in the experimental data. Since the enthalpy of sublimation estimated by the MEP method agrees well with the experimental value of Suzuki et al.,65 the latter value seems to be more accurate than the value in ref ° (cr) 64. On the other hand, there are no grounds for suggesting that the reported ∆ value64 is in error. ° (g) Thus, on the basis of the ∆ value calculated in this work and taking into account the experimental ° (cr)64 ° and ∆ ,65 it is reasonable to assume that the solid-phase enthalpy of formation values of ∆

and enthalpy of sublimation of 21 may vary between -316 and -331 kJ/mol and 101-116 kJ/mol, respectively. The solid-phase enthalpy of formation was determined for three acyl hydrazides (19, 23, and 25). The ° (g) ° values of ∆ calculated in this work for 19 support the experimental result63 (Table 2). and ∆ ° (cr) Of two ∆ values reported for 23, we prefer the value determined by Karyakin et al.66 because of its ° (g) ° better agreement with the values of ∆ and ∆ calculated in this work. Since the enthalpy of

sublimation of H2NC(O)C(O)NH2 estimated in this work is underestimated by 17 kJ/mol compared to experiment (see Table 3 of the Supporting Information), the same large error can be expected for related compound 25. However, even in this case the enthalpy of sublimation of 143.6 kJ/mol derived from the ° (cr) ° (g) experimental value of ∆ and calculated ∆ value (Table 2) looks somewhat overestimated;

therefore, we could not exclude that the solid-phase enthalpy of formation of 25 is less negative than the 18 ACS Paragon Plus Environment

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reported experimental value.67 For 22, the experimental data exist for only enthalpy of sublimation. As can be seen from Table 2, this value is in good agreement with that calculated using MEP model; therefore, combing ° the experimental ∆ value with calculated gas-phase enthalpy of formation gives a fairly reliable ° (cr) ° estimate of ∆ and for 22. The experimental data are not available for 20 and 24; their ∆ ° (cr) ∆ values were estimated in this work. ° (cr) Two thiocarbohydrazides (26, 27) are presented in Table 2. Two experimental values of ∆

for 26 differ by about 20 kJ/mol. Our calculations support the lower value determined by Torres Gomez and Sabbah.69 However, a large difference between the experimental and calculated gas-phase enthalpy of formation of 27 suggests that the experimental data for this compound69 are inaccurate; on the basis of ° ° (cr) theoretical results, more reasonable values of ∆ and ∆ are suggested for this compound.

The next three compounds (28-30) contain the –C(O)NHNH2 group attached to the furan, pyridine, and benzene ring. Our theoretical calculations are consistent with the reported experimental data for 28. The experimental enthalpy of sublimation is only known for 29. This value agrees well with that estimated from MEP model (Table 2), and it was used to evaluate the solid-phase enthalpy of formation of 29. No experimental data are available for 30; the enthalpies of formation and sublimation for this compound were estimated on the basis of theoretical calculations. Both the enthalpy of formation and the enthalpy of sublimation were measured for two compounds with the endocyclic hydrazine moiety (31, 32). A good agreement between the theory and experiment is obtained for 31, whereas the discrepancy of 8.6 kJ/mol is observed for 32. This difference is outside the ° combined errors of two determinations, and this implies a small error in the experimental values of ∆ ° (cr). or ∆ However, it is difficult to assume which of these two values may be in error because of large

uncertainty in the estimated enthalpy of sublimation of 32. The last four species in Table 2 (33-36) are the hydrazine-based energetic compounds. The solidphase enthalpy of formation of H-FOX (33) was estimated earlier by Gao and Shreeve74–76 using quantum 19 ACS Paragon Plus Environment


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chemical calculations. This value, as can be seen from Table 2, is about 100 kJ/mol higher than the value ° (g) estimated in this work. A large difference between the two calculated ∆ values can be attributed to

the use of the less accurate MP2 method in refs 74–76. As for enthalpy of sublimation, its value was assumed to be 84 kJ/mol in refs 74–76, just as it was done earlier for a set of energetic compounds containing pentafluorosulfanyl groups.81 To confirm the accuracy of calculated values, the solid-phase enthalpy of formation of the unsubstituted parent compound (FOX-7, (O2N)2C=C(NH2)2) was also calculated in this ° ° study. Our calculated values ∆ 7FOX-7, g= = 3.4 ± 6.0 kJ/mol and ∆ (FOX-7) = 135.0 ± 15.0 ° 7FOX-7, cr= = -131.6 ± 20.0 kJ/mol, which is in agreement with the kJ/mol give the value of ∆

experimental one (-133.9 kJ/mol,82 see also ref 83), whereas the value estimated by Gao and Shreeve75,76 (53.1 kJ/mol) is again significantly overestimated. It should be noted that FOX-7, together with other compounds, was used as a reference species in the working reactions for 33. As can be seen from Table S2 of the Supporting Information, both types of reactions lead practically to the same results. This indicates that the calculated gas-phase enthalpy of formation of H-FOX (33) is mutually consistent with the experimental value for FOX-7. Due to the lack of experimental data, the tetrazine-based compounds are not present in a calibration set of MEP model. If we assume that the MEP model noticeably underestimates the enthalpy of sublimation of tetrazines, the experimental value of solid-phase enthalpy of formation of 34 is reasonably reliable; otherwise, the value is somewhat underestimated. However, we cannot say the same for tetrazole-based compound 35, whose experimental enthalpy of formation is obviously underestimated. The experimental or theoretical data for 36 were not reported until now.

CONCLUSIONS The gas-phase enthalpy of formation of hydrazine, 97.0 ± 3.0 kJ/mol, is determined in the present work from a large number of isogyric reactions whose enthalpies are calculated using high-level G4 method. 20 ACS Paragon Plus Environment

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This value is in excellent agreement with the results of the most accurate methods to date for predicting the enthalpy of formation (from 96.7 to 97.5 kJ/mol, the average is 97.3 kJ/mol).14–16,19,44,45 This finding shows that, even for simple small molecules like hydrazine, using the G4 theory along with isodesmic reactions can give more reliable results rather than using the atomization reactions. The biggest differences between the values calculated by isodesmic and atomization reactions are from 5 to 15 kJ/mol. Such differences are observed for compounds with nitro groups (17, 18, 33, 36) and aromatic compounds containing three and four phenyl rings (20, 21). As it was shown earlier,26 this difference also depends on the number of NH2 groups, and the addition of NH2 groups somewhat compensates for the effect of NO2 groups. Because of this, it is difficult to predict in advance how large the difference will be for different nitrogen containing compounds. ° (NH The explanation of difference between the experimental value of ∆ NH , g) = 95.55 ± 0.19

kJ/mol recommended in the ATcT9 and theoretical value of about 97.3 kJ/mol remains a challenge for further investigations. The ATcT value is based on the six experimental determinations of enthalpy of reactions which give internally consistent enthalpies of formation for all chemical species involved in these reactions. On the other hand, the coupled cluster theory calculations14–16,19,44,45 achieve subchemical accuracy on the order of or better than 1.0 kJ/mol, and therefore the difference between the experimental and theoretical ° (g) ∆ values is appreciable enough and is worthy of attention. The discrepancy between the

experimental value and that calculated in this work also requires explanation because, as it is shown by isodesmic reaction calculations, the calculated value is internally consistent with the experimental enthalpies of formation of more than 40 species recommended in ATcT.9 The gas-phase enthalpies of formation of 36 different hydrazine derivatives were calculated using the isodesmic reaction approach. The reported experimental data for 1-3, 9, 11, 12, 26, 28, and 31 are generally confirmed by calculations, while the errors in experimental enthalpies of formation for 10, 21, 27, and 32 were identified by the large difference (from 9 to 89 kJ/mol) between the calculated and experimental values. 21 ACS Paragon Plus Environment


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For the above listed compounds, both the enthalpy of formation in condensed phase and enthalpy of sublimation (or enthalpy of vaporization) are available; for other compounds (5, 7, 13, 16-19, 22, 23, 25, 29, 34, 35), experimental data for only one of these properties exist. In this case, the unknown property can be ° (cr) predicted using MEP model. Only the values of ∆ were reported for 13, 16, 18, 19, 23, 25, 34, and

35. Combining these values with calculated gas-phase enthalpies of formation gives the enthalpies of sublimation. When these values are in reasonable agreement with those estimated by MEP model (13, 18, 19, ° (cr) 23), the experimental ∆ values can be considered as reliable; otherwise they are unreliable and

more accurate values can be obtained using the estimated enthalpies of sublimation. Of course, this analysis is rather crude because of large uncertainty in the estimated enthalpies of sublimation. It is not always ° (cr) possible to conclude with certainty that the reported ∆ value is in error (as in the case with 25 and

34), but nevertheless it allows us to detect large errors in the experimental values, as it was for 16, 35. Only the values of enthalpy of sublimation are available for 17, 22, and 29. Where agreement between calculated and reported enthalpies of sublimation exists, it is reasonable to assume that the experimental value is, indeed, accurate. Thus, on the basis of good agreement between calculated and experimental values, the solid-phase enthalpies of formation of 22 and 29 can be estimated with rather high accuracy. However, the differences in enthalpies of sublimation in the range ±20 kJ/mol are difficult to assign to either experiment or to calculation (17). For compounds for which no experimental data are available, it is hoped that our calculated results will serve as reliable estimates. Both enthalpies of formation and enthalpies of sublimation or vaporization were predicted for ten hydrazine derivatives (4, 6, 8, 14, 15, 20, 24, 30, 33, and 36). The solid-phase enthalpy of formation of energetic compound H-FOX (33) was significantly improved in comparison with previous estimation.74–76 This statement is confirmed by similar calculations for related compound FOX-7 for which the experimental data were reported. ° Considering the result for NH2NH2, we find a remarkable accuracy of calculated ∆ (g) value,


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which is comparable to the results of coupled cluster methods with large basis sets.14–16,19,44,45 Therefore, a sufficiently high accuracy can be expected for hydrazine derivatives. A set of self-consistent experimental and calculated gas-phase enthalpies of formation of hydrazine derivatives recommended in this work can be ° (g) values to predict the enthalpies of formation of various hydrazines by means of used as reference ∆

isodesmic reactions.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Experimental enthalpies of formation of reference compounds used in isodesmic reactions (Table S1). Enthalpies of formation of hydrazine and its derivatives calculated from atomization, isodesmic, isogyric, and other balanced reactions using G4 energies (Table S2). Molecular electrostatic potential parameters calculated for the molecular geometries optimized at the B3LYP/cc-pVTZ level, regression coefficients a, b, c, and d for enthalpies of sublimation and vaporization, and comparison between experimental and calculated enthalpies of sublimation and vaporization. (PDF)

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected]. ORCID Olga V. Dorofeeva: 0000-0002-7362-1540 Notes The authors declare no competing financial interest.



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Enthalpies of Formation of Hydrazine and Its Derivatives - The Journal

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