4788
J. Phys. Chem. B 2007, 111, 4788-4800
Accurate Thermochemical Properties for Energetic Materials Applications. II. Heats of Formation of Imidazolium-, 1,2,4-Triazolium-, and Tetrazolium-Based Energetic Salts from Isodesmic and Lattice Energy Calculations† Keith E. Gutowski, Robin D. Rogers,* and David A. Dixon* Department of Chemistry and Center for Green Manufacturing, The UniVersity of Alabama, Box 870336, Tuscaloosa, Alabama 35487-0336 ReceiVed: September 29, 2006; In Final Form: December 22, 2006
A computational approach to the prediction of the heats of formation (∆Hf°’s) of solid-state energetic salts from electronic structure and volume-based thermodynamics (VBT) calculations is described. The method uses as its starting point reliable ∆Hf°’s for energetic precursor molecules and ions. The ∆Hf°’s of more complex energetics species such as substituted imidazole, 1,2,4-triazole, and tetrazole molecules and ions containing amino, azido, and nitro (including methyl) substituents are calculated using an isodesmic approach at the MP2/complete basis set level. On the basis of comparisons to experimental data for neutral analogues, this isodesmic approach is accurate to 14r -38.7 ( 2.2s 16.2 ( 2.2t 24.6 ( 2.3u 47.9 ( 3.1V
a Reference 59. b Reference 60. c Reference 61. d Reference 62. Reference 28. f Reference 63. g Reference 64. h Including a -2.1 kcal/ mol higher-order correction (ref 28). i Reference 65. jReference 66. k Reference 78. l Reference 67. m Reference 68. n Reference 84a. o From ∆Hf° of 1H-imidazole (ref 69b), ∆Hf° of H+ (ref 78), and proton affinity of 1H-imidazole (ref 69a). p From ∆Hf° of 1H-1,2,4-triazole (ref 70), ∆Hf° of H+ (ref 78), and proton affinity of 1H-1,2,4-triazole (ref 69a). q From ∆Hf° of HNO3 (ref 78), ∆Hf° of H+ (ref 78), and deprotonation enthalpy of HNO3 (ref 71). r From ∆Hf° of HClO4 (ref 28), ∆Hf° of H+ (ref 78), and deprotonation enthalpy of HClO4 (ref 72). s From ∆Hf° of phenol (ref 73), ∆Hf° of H+ (ref 78), and deprotonation enthalpy of phenol (ref 74). t From ∆Hf° of 1H-imidazole (ref 69b), ∆Hf° of H+ (ref 78), and deprotonation enthalpy of 1H-imidazole (ref 74). u From ∆Hf° of 1H-1,2,4-triazole (ref 70), ∆Hf° of H+ (ref 78), and deprotonation enthalpy of 1H-1,2,4-triazole (ref 75). V From ∆Hf° of 1H-tetrazole (ref 70), ∆Hf° of H+ (ref 78), and deprotonation enthalpy of 1-Htetrazole (ref 74). e
volumes were calculated by using Gaussian 03. The volume was taken as that inside the 0.001 a.u. contour of the B3LYP/ TZVP electron density.58 With the default parameters (100 points), the volume is calculated to a numerical accuracy of approximately 10%, so a larger number of points (2500) were used in the Monte Carlo integration to obtain the desired level of accuracy, a reproducible calculated volume to better than 1%. Results and Discussion Isodesmic Reaction Energies. Table 1 contains the calculated ∆Hf°’s of the neutral molecules, cations, and anions used to calculate the ∆Hf°’s of the cations and anions shown in Figure 1 using an isodesmic approach. The cations and anions shown in Figure 1, including NO3- and ClO4-, are then paired later to predict the thermochemistry of a variety of energetic salts. The calculated ∆Hf°’s in Table 1 are taken from previous studies (CH4,59 NH3,60 C2H6,59 N2H4,61 CH2CHCH3,62 1,3-H-imidazolium,63 and NO3- 64) or were calculated in the first part of this study.28 In nearly all cases, the agreement between the calculated and the experimental values (CH4,65 NH3,66 C2H6,65 N2H4,78 CH2CHCH3,67 CH2CHNO2,68 CH3NO2,84a CH3NH2,67 1,3-Himidazolium,69,78 1,4-H-1,2,4-triazolium,69a,70,78 NO371,78 ClO4-,28,72,78 C6H5O-,73,74,78 imidazolate,69b,75,78 1,2,4-triazolate,70,74,78 and tetrazolate28,74,78) is
