J. Phys. Chem. 1995, 99, 187-194
187
Theoretical Prediction of the Structures and Stabilities of Azidamines H. Harvey Michels,*J John A. Montgomery, Jr.,l Karl 0. Christe,*2 and David A. Dixon*S United Technologies Research Center, East Hartford, Connecticut 06108, Rocketdyne, A Division of Rockwell Intemational Coporation, Canoga Park, Califomia 91309, and The DuPont Company, Central Research and Development, Experimental Station, Wilmington, Delaware 19880-0328 Received: September 23, 1994@
Ab initio molecular orbital and density functional theory calculations show that azidamines, a new family of polynitrogen compounds, are minima on their respective potential energy surfaces. The geometries, vibrational frequencies, and heats of formation are predicted for N(N3)3, HN(N3)2, the N(N3)2- anion, and the N(N3)4+ cation. All of these compounds are highly energetic materials with large positive heats of formation. The results suggest that these polynitrogen compounds could be synthetically accessible, and potential methods for their syntheses are proposed.
Introduction The recent discovery of new allotropic forms of carbon and the rich and fascinating chemistry that it has produced has also stimulated a renewed search for new allotropic forms of nitrogen?-'' Although nitrogen and the CH group are pseudoelements'* and numerous stable (CH,) compounds, such as benzene or polyacetylene, are well-known, the analogous polynitrogen compounds, N,, where n exceeds 3, have so far not been prepared. The main reasons for this difference are the relative energies of their triple, double, and single bonds. For nitrogen, the average thermochemical bond energy of the triple bond (946 kJ mol-') is 368 kJ mol-' larger than the sum of those for a double (418 kJ mol-') and a single (160 kJ mol-') bond.19 Thus, dinitrogen, Nz, is by far the most stable polynitrogen compound. For carbon the situation is reversed. The bond energy of a triple bond (813 kJ mol-') is 141 kJ mol-' smaller than the sum of those for a double (598 kJ mol-') and a single (356 kJ mol-') bond.I9 Thus, acetylene, (CH)2, is thermodynamically unstable with respect to its higher homologues. In view of the above energetic considerations, it is not surprising that the polynitrogen compounds with n > 2 are highly energetic and, thus, are of interest for halogen-free highenergy-density materials (HEDM). The obvious challenge to their use is their thermodynamic instability, which renders their syntheses and handling very difficult. Most publications dealing with polynitrogen compounds have been limited to theoretical predictions of their behavior, and experimental studies, such as the one by Vogler,20 are rare. Previously calculated but presently still unknown polynitrogen (n > 3) compounds include N4,' N4+,13-17Ng-,' N,5,5-739 N8,5969'2N12," and N ~ O . * ~ 'Most ~J' of these compounds are cyclic or polycyclic and, hence, would require synthetically very difficult ring-closing methods. In order to avoid this difficulty, we are searching for stable polynitrogen structures which would be more amenable to an actual synthesis. As an aid to the synthetic chemist, we have calculated energies, stabilities, and vibrational spectra of a set of polynitrogen compounds, the azidamines.
Computational Methods Ab initio molecular orbital (MO) calculations were carried out by using the Gaussian 92 programs.21 RHF/6-31G* and @
Abstract published in Advance ACS Abstracts, December 1, 1994.
0022-3654/95/2099-0187$09.00/0
MP2/6-3 lG* geometry optimizations were performed for all species; additonal calculations with the 6-3 lG* set augmented with diffuse functions (lU-IF/6-3 1+G*) were performed for the anion. The density functional theory" calculations were done with the program DGau~s,2~ which employs Gaussian basis sets on a Cray YMP computer. The basis sets for N and H are triple-c in the valence space augmented with a set of polarization functions (TZVP) with the form (71 11/411/1) for N and (31 1/ 1) for H.24 The auxiliary fitting basis set for the electron density and the exchange-correlation potential has the form [8/4/4] for N and [4/1] for H. The calculations were done at the self-consistent gradient-corrected (nonlocal) level (NLDFT) with the nonlocal exchange potential of Becke2' together with the nonlocal correlation functional of Perdew26 (BP). The local potential of Vosko, Wilk, and NusaiS7 was used. Geometries were optimized by using analytical gradient^?^ Second derivatives were calculated by numerical differentiation of the analytic first derivatives. A two-point method with a finite difference of 0.01 a.u. was used.
The MO electronic structure calculations for N(N3)z- were carried out in both CZand C, symmetries. The dinitramide28 analogue structure, A, of C, symmetry was not vibrationally
r
I"-"-'"
I
1-
N
2
A
stable, exhibiting two imaginary vibrational frequencies at the RHF/6-31G* level of theory. This is in accord with our inability to find a satisfactory electronic structure which possesses eight valence electrons on each nitrogen atom. In contrast, the open chain, diazidamide structure, (N3-N-N3)-, was a minimum at the RHF/6-31G* level and exhibited all real frequencies. Additional calculations including diffuse functions (=/63 1+G*) and electron correlation (MP2/6-31G*) also yielded true minima on the potential energy surface (PES). The results are given in Tables 1 and 2, and the stable Cz conformation is shown in Figure 1. At the MP2/6-31fG* correlated level of theory, the central Nl-N2 bond distance (1.44 A) is only slightly longer than that of 1.38 A previously reported for the 0 1995 American Chemical Society
188 J. Phys. Chem., Vol. 99, No. 1, 1995
Michels et al.
TABLE 1: Calculated Geometries (A and deg) of the Diazidamide Anion [N(N&-] geometry RHF/6-31G* (C2") RHF/6-31G* (Cl) MP2/6-31G* (C2) MP2/6-31G* (Cl) R12 R23 R34
eZrl2 e123 e234
t2'123
51234
1.418 1.197 1.133 101.8 113.2 176.6 180 180
1.451 1.244 1.174 100.6 115.8 170.2 -150.9 - 144.4
1.409 1.198 1.131 102.7 112.8 177.1 -173.7 - 154.7
1.442 1.247 1.174 101.2 113.6 171.5 -156.4 -137.6
TABLE 2: Calculated Harmonic Frequencies in cm-' and Infrared Intensities [ ] in M m o l of N(N3)zmode RHF/6-31G* (C,) MP2/6-31G* (C2) MP2/6-31+G* (C2) mode RHF/6-31+G* (CzJ A
vi v2 v3 v4 V5
v6 Vl
V8
B
v9 VI0 VI1
v12 v13 VI4
v15
2388 [256] 1476 [14] 1001 [16] 629 [2] 510 [O] 465 [5] 145 [5] 107 [O] 2304 [2970] 1428 [9] 1024 [173] 796 [l59] 492 [30] 282 [23] 74 [SI
2291 [14] 1188 [9] 914 [4] 610 [7] 425 [O] 396 [O] 150 [l] 63 [OI 2280 [1197] 1162 [2] 869 [47] 743 [60] 385 [12] 218 [25] 35 131
2263 [47] 1184 [21] 911 [l] 593 [l] 408 [O] 379 [O] 145 [O] 85 to1 2255 [1422] 1159 [2] 899 [78] 737 [4] 326 [13] 227 [23] 44 [61
Figure 1. Geometry of N(N3)Z- at the MP2/6-31G* level of theory.
dinitramide anion, N(NO~)Z-.~* Other known compounds of nitrogen exhibit even larger N-N bond lengths: N2O3 (1.86 A),29N204 (1.78 A),30and N2H4 (1.45 A).29 The N2-N3 and N3-N4 bond lengths are typical of those found in other covalent azides such as hydrogen azide and the halogen The longest and weakest bonds in N(N3)2- are the central N1N2 bonds whose lengths are comparable to those in N2H429and N ( N O Z ) ~ - .Typically, ~~ N-N single bond strengths are 150180 kJ/mol. As shown below, our calculations give a much smaller value for the activation banier for N2 elimination, suggesting that N2 elimination, rather than cleavage of the N-N single bond, is the lowest energy decomposition path. The central bond angle, 0(2'12), of 101" is consistent with a simple valence bond model with sp3 hybridization on the central nitrogen atom involving two ligands and two more repulsive, sterically active, free valence electron pairs. These free electron pairs are more repulsive than the two N1 -N2 bonds, which is consistent with the N2'-N1 -N2 bond angle being somewhat smaller than the ideal tetrahedral angle of 109.5". Because of the bonding patterns in these molecules there is the possibility that, even at the MP2 level, we are not providing an adequate description of the wave function. In order to test whether this level is providing an adequate treatment, we used density functional theory, which we have shown is a good method to use in the prediction of geometries and energies for structures that are often difficult to treat with traditional ab initio MO methods.36 These results are also shown in Table 1 for the geometry parameters and in Table 2 for the frequencies. The predicted geometry is quite sensitive to the level of theory, as the RHF/6-3 lG* and NDLFTlTZVP calculations give a CzV structure, whereas the RHF/6-3 l+G* and MP2/6-31G* calculations give a CZ structure. Other than these differences, the agreement in the predicted geometry parameters between the
Ai
A2
BI
B2
2359 [190] 1473 [7] 991 [20] 622 [4] 459 [4] 140 [l] 523 [O] 72 [OI 2318 [2634] 1421 [7] 982 [114] 799 [118] 278 [24] 525 [33] 56 [5l
NLDFTRZVP (C2") 1.430 1.230 1.183 102.6 116.2 174.9 180 180
NLDFTRZVP (C2J 2069 [93] 1252 [lo] 948 [3] 552 [3] 410 [l] 137 [3] 251 [O] 107 [O] 2059 [1333] 1218 [154] 937 [59] 693 [la] 258 [23] 212 [5] 90 [31
MP2/6-3 1+G* and NLDFRTZW levels is quite good, showing that the MO calculations are predicting reasonable structures. The frequencies at the best MO and DFT levels are in qualitative agreement. Usually, the MO frequencies are higher than the experimental values whereas the DFT values are comparable or a little low. Thus it is surprising that the DFT frequencies for the weaker N-N stretches are higher than the MP2 values. This is consistent with the differences in geometry and suggests that the MP2 values for the lower frequency N-N stretches are probably too low. The lowest stretching frequency is at 937 cm-', so there are no very low-frequency modes (
