7699
J . Phys. Chem. 1991, 95, 7699-7702
Conclusion
are pointed out. In addition, a relation between the a-ionization potentials and protonation energies of azole molecules is established. The nature of the protonation energy is analyzed on the basis of Mulliken's resonance structure theory. It has become quite evident that the stability of the protonated systems of azoles is mainly due to polarization, charge-transfer, and exchange energies. The electrostatic energy, at the equilibrium structure, plays a rather small and destabilizing (repulsive) role. It is also found that the trend in basicity is mainly determined by the u-ionization potentials of the bases considered. This, of course, suggests the use of the a-ionization potentials of the heterocyclic azole compounds as a measure of their relative basicities.
Three approximate methods based on Koopmans, perturbation, and many-body Green function theories for calculating the ionization potentials of electrons from the upper occupied valence-shell molecular orbitals are compared at the INDO level of approximations. Different characteristics and limitations of these methods
Acknowledgment. I gratefully acknowledge the generous support from the Computer Centre of the UAE University, where this research was carried out. Registry No. Imidazole, 288-32-4; pyrazole, 288-1 3- 1; 4H- 1,2,4-
mainly determined by ion-multipole interactions", while the covalent interactions in H+-azoles must be practically constant. The analysis of the protonation energy based on Mulliken's theory, presented above, shows, however, that the trend of basicities is determined mainly by the a-ionization potential rather than by the electrostatic interaction. Besides, the example of pyrazole given above points out the importance of polarization and charge transfer in the formation of the protonated azoles. This conclusion is consistent with what has been found in a previous study on the stability of iodine complexes with ammonia and pyridine.19
(19) Jano, 1. Theor. Chim. Acta 1987, 71, 305
triazole, 63598-7 1-0; lH-I,2,4-triazole, 288-88-0; 2H-tetrazole, 100043-29-6; IH-tetrazole, 288-94-8; 1H-pentazole, 289-1 9-0; pyrazole conjugate acid, 17009-91-5.
Computational Study of the Concerted Gas-Phase Triple Dissociations of 1,3,5-Triasacyclohexane and Its 1,3,5-Trinitro Derivative (RDX) Dariush Habibollahzadeh, Michael Grodzicki, Jorge M. Seminario, and Peter Politzer* Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148 (Received: March 7, 1991)
Concerted triple dissociation reactions of 1,3,5-triazacyclohexane (I) and 1,3,5-trinitro-1,3,5-triazacyclohexane(11, RDX) were investigated by using semiempirical, ab initio, and local density functional (LDF) methods. Gaseous phase structures and energies for the ground and the transition states of I and I1 are presented and analyzed. The activation barriers for both processes are predicted to be in the range 72-75 kcal/mol. The LDF results are comparable to those obtained by the highest level ab initio procedure [MW(SDTQ)/6-31G*//3-21G]. The dipole moments and the electrostatic potentials associated with the amine nitrogen lone pairs have been computed and are used to interpret the structural and electronic factors involved in the formation of the transition states.
Introduction
As part of a continuing study of the thermal decomposition mechanisms of energetic m ~ l e c u l e s , we ' ~ have calculated the activation energy barriers for the concerted ring decompositions of 1 and 11 in the gaseous phase.
investigate the concerted gas-phase ring fragmentations of I and 11, as given in eqs 1 and 2.
I
+
(2)
3H,C=NH
Methods and Procedure
We optimized geometries through a b initio SCF-MO (Hartree-Fock, HF) calculations with GAUSSIAN 88 and at the 9
1,3,5-lriazacyclohexane,I
1,3,5-trinilro-1,3,5-triaracyclohexane, I1 (RDX)
Several experimental studies of the decomposition of RDX (11) have been reported.s-'O On the basis of these experiments, several competing primary dissociation channels have been suggested, including the scission of N-N02 bonds and the concerted symmetric ring-fragmentation shown in eq 1. In an earlier study of
I1
+
3H$=N-N02
(1)
diazacyclobutane and its dinitro derivative, the energetic requirements for N-N02 bond rupture and for ring decomposition (both in the gaseous phase) were found to be approximately comparab1e.I~~It is accordingly of interest to determine the situation in the case of RDX. Our present objectives are to To whom correspondence should be addressed.
0
~
~
9
~
( I ) Grodzicki, M.; Seminario, J. M.; Politzer, P. Theor. Chim. Acta 1990, 77, 359. (2) Murray, J. S.;Politzer. P. Chemistry and Physics of Energetic Materials; Bulusu, S. N., Ed.; Kluwer: Dordrecht, The Netherlands, 1990; Chapter 9. (3) Grodzicki. M.; Seminario, J. M.; Politzer, P. J . Chem. Phys. 1991, 94, 1668. (4) Seminario, J . M.; Grodzicki, M.; Politzer, P. Density Functional Methods in Chemistry; Labanowski, J. K., Andzelm, J. W., Eds.; SpringerVerlag: New York, 1991. ( 5 ) Farber, M.; Srivastava, R. D. Chem. Phys. feu. 1979.64, 307. (6) Dubovitskii, F. I.; Korsunskii, B. L. Russ. Chem. Reu. 1981,50,958. (7) Zuckermann, H.; Greenblatt, G.D.; Haas, Y. J . Phys. Chem. 1987, 91, 5159. (8) Zhao, X.;Hintsa, E. J.; Lee, Y. T. J . Chem. Phys. 1987. 88, 801. (9) Oyumi, Y.;Brill, T. B. Propellants, Explos., Pyrotech. 1988, 13.69. (IO) Capellos, C.; Papagiannakopoulos,P.; Liang. Y.-L. Chem. Phys. Lett. 1989, 164, 533.
( I I ) Frisch, M. J.; Head-Gordon, M.; Schlegel, H. B.; Raghavachari, K.; Binkley, J . S.;Gonzalez, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R.; Kahn, L. R.; Stewart, J . J . P.; Fluder, E. M.; Topiol, S.; Pople, J. A. GAUSSIAN 88; Gaussian Inc.: Pittsburgh, PA, 1988.
0022-3654/91/2095-7699%02.50/00 I99 1 American Chemical Society
~
Habibollahzadeh et al.
7700 The Journal of Physical Chemistry, Vol. 95, No. 20, 1991 TABLE I: Calculated and Experimental Structures molecule 1,3,5-triazacyclohexane
ground
HA-NH I
state
\
HN\
/CHz
HF-NH
IA
bond length, A/ bond angle, deg
AMI 1.47 1.13
C-N C-H N-H CNC NCN HCN HNC NCCN C-N C-H N-H CNC NCN HCN HNC NCCN
1 I8 106-109 Ill 142 1.32, 1.96 1.11 0.99 1 I4 109 116-122 112 133
C-N C-H N-N N-0 CNC NCN HCN NNC ONN NCCN C-N C-H N-N N-0 CNC NCN HCN NNC ONN NCCN
1.47 I . 13-1.14 1.42 1.20 I I3 1 I6 105-1 11 118 1 I8 140 1.34, 1.95 1.11, 1.12 1.40 1.20 116 107 114-122 I I4 116-120 131
1.oo 111
STO-3G
3-21G
1.49 1.09 1.03
1.47 1.08 1.01
1 IO 1 I5
111 1 I4
108-109 107 134 1.31, 2.06 1.09 1.04 117
107-1 IO 112 135 1.30, 2.05 1.07 1.01 I I4 112 118-123 113 137
110
118-123 112 139
expt
1,3,5-trinitro-1,3,5-triazacyclohexane ground
IIA
transition
a
Reference 20.
115 115 107-108 1 I3 1I 7 142 1.32, 2.07 1.09
1.44-1.47,” 1.4646 1.06-1.09,” 1.089’ 1.35-1.40,” 1.4136 1.20-1.23,” 1.213’ 114.6-1 15.1,” 123.76 107.8-1 11.7,” 109.4’ 106.9-1 11.3’ 115.6-120.9,0 116.3’ 116.8-117.8,” 117.2’
1S O
1.27 120 108 117-121
115 1 15-1 19 138
’Reference 21.
STO-3G and 3-21G levels for I and STO-3Gfor 11. We have also calculated the structures with the semiempirical AMI method, in order to explore the dependence of the activation energies on different procedures for geometry optimization. Both the ST03G and the 3-21G basis sets generally provide quite reliable struct u r e ~ ,although ’~ the former sometimes has problems with conjugated systems, while split valence basis sets may overestimate bond angles on heteroatoms having lone pairs, e.g., nitrogen and oxygen.I4 For both 1 and 11, the transition state was determined by choosing as the reaction coordinate either three alternate C-N distances or the central angles a that are defined by these distances and then performing a full geometry optimization at each fixed value of the reaction coordinate. Both procedures lead to virtually identical transition-state geometries. We also took the approach of starting at the dissociation limit, with a = 30° (corresponding to a C-N distance of 3.48 A), and again arrived at the same state. To verify that this is a transition state, we performed a frequency calculation and did obtain a single imaginary frequency. Since a b initio SCF methods are known to overestimate activation barriers,l*’.I3we computed these by means of a local density functional (LDF) procedure, DMol,15J6with a double numerical (12) Frisch, M. J.; Head-Gordon, M.; Trucks, G . W.; Foreman, J . 9.; Schlegel, H. 9.; Raghavachari, K.;Robb, M. A.; Binkley, J. S.; Gonutlez, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Topiol, S.; Pople, J. A. GAUSSIAN 90: Gaussian, Inc.: Pittsburgh, PA, 1990. (13) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbiral Theorv: John Wilev and Sons: New York. 1986. (14) Pulay. P.; Fogarisi, G.;Pang,’F.; Boggs, J. E. J . Am: Chem. SOC. 1979, 101, 2550.
1.49 1.09 1.48 1.27
(DN) basis set, using the AMI- and HF-optimized geometries. For I, we also applied Moller-Plesset perturbation methods to the calculation of the barrier (MP2/6-31G*, MP3/6-31G*, and MP4/6-3 1G*) . I 3 The electrostatic potential V(r) that is created in the space around a molecule by its nuclei and electrons is expressed rigorously by eq 3. ZAis the charge on nucleus A, located at RA,
and p(r) is the electron density at r, obtained from the molecular wave function. V(r) is a real physical property, which can be determined experimentally as well as computationally,” it will be used here primarily as an indication of the degrees of delocalization of the amine nitrogen lone pair^.'^,^^ We have computed V(r) at the STO-5G level, using the A M I , STO-3G and 3-21G optimized structures. Results and Discussion Structures and Energies. Table I summarizes the optimized geometries of the ground and transition states of 1 and 11. The calculated structures are in reasonably satisfactory agreement with (15) Delley, 9. J. Chem. Phys. 1990, 92, 508.
( I 6) DMol, commercially available from Biosym Technologies, Inc. (1 7) Chemical Applicafions oJ Atomic and Molecular ElecfrosfaficPofenfials;Politzer, p., Truhlar, D. G., Eds.; Plenum Press: New York, 1981. (18) Murray, J. S.; Redfern,P. C.;Seminario, J . M.; Politzer, P. J. Phys. Chem. 1990.. 94..~ 2320. (19) Murray, J . S.:Redfern. P. C.; Lane, P.; Politzer, P.; Willer, R. L.J. Mol. Srrucf. (THEOCHEM) 1990, 207, 177. ~
The Journal of Physical Chemistry, Vol. 95, No. 20, 1991 7701
Concerted Gas-Phase Triple Dissociations
TABLE Ik Calculated Properties of 1,3,5-T1lamcyclobexa11e a d 1,3,5-Tridtro-l,3,5-triazacyclohexnne(RDX)and Their Triple Dissociation Transition States dipole moment, D Vmin(N)+ kcal/mol methods/ geometry calcd activation ground transition ground transition molecule basis set optimization energy, kcal/mol state state state state CIH9Nl (1)
AM1 HF/STO-3G HF/STO-SG HF/3-21G 6-31G*: HF MP2 MP3 MP4(DQ) MP4(SDQ) M P4( SDTQ) LDF/DN
HFjSTO-5G HF/3-2 1G LDF/DN
AM1 AM 1 STO-3G 3-21G AM 1 STO-3G 3-21G AM 1 STO-3G 3-21G 3-21G
99.9 158.9 168.2 168.6 157.1 167.0 167.3 86.0 93.2 93.0
2.06 2.37 1.70 1.95 2.35 1.70 1.93 2.66 1.79 2.10
0.8 16 1.21 1.46 1.45 1.21 1.47 1.46 1.39 1.52 1S O
2.01
1.30
AM 1 STO-3G 3-21G
90.1 77.7 85.4 85.6 81.2 74.7 64.0 72.1 74.9
AM 1 STO-3G AMI STO-3G AMI STO-3G AM 1 STO-3G
73.9 142.6 135.5 141.7 78.3 79.4 62.5 72.2
6.96 5.89 5.86 6.04 7.71 8.24
9.91 7.68 8.30 7.84 10.5 10.4
each other and with crystallographicz0 and electron diffractionz* data for RDX (II), the major discrepancies being that the STO-3G procedure overestimates the N-N and N-0 bond lengths. The electron diffraction study2I confirms the axial nature of the nitro groups in the gas phase. The activation energies computed with the different methods and geometries are displayed in Table 11. The barriers obtained at any given computational level are essentially the same for the STO-3G and 3-21G structures, but 7-10 kcal/mol greater than for the AMI; this reflects the fact that the latter predicts the transition state to be at a significantly smaller value of the reaction coordinate (Table I). For both I and 11, the activation barriers calculated by a b initio techniques show a marked decrease in magnitude as we go to more sophisticated computational levels. Indeed the stepwise inclusion of many-body corrections in the case of I shows that even triple excitations have a significant effect, reducing the activation energy by almost 7 kcal/mol in going from MP4(SDQ) to MP4(SDTQ). Particularly striking is the close agreement between the MP4(SDTQ) and the LDF results, supporting our earlier findings that local density functional methods are an extremely useful tool for describing the energetics of chemical reaction^.^,^ We conclude that the activation barriers for the concerted triple dissociations of I and I1 are in the range 72-75 kcal/mol. This is in agreement with the conclusion reached in a recent experimental analysis, that the energy requirement for reaction 1 is not more than about 80 kcal/mol.* Thus we feel that the activation energy of 49.8 kcal/mol that has been determined experimentally for RDX should be attributed to N-N02 bond rupture.z2 This is indeed very close to our calculated energy requirement for breaking an N-NO, bond in dinitrodiazacyclobutane,5 1 kcal/mol.I However we believe that our present results do also support ring decomposition as a possible thermal decay mode of highly vibrationally excited RDX in the gas phase. Even though the energy required for this process is (20) Choi, C. S.;Prince, E. Acta Crysfallogr. 1972, 828, 2857. (21) Shishkov, I. F.; Vilkov, L. V.; Kolonits, M.; Rozsondai, B. Struct. Chem. 1991. 2, 57. (22) Bulusu, S.; Weinstein, D. 1.; Autera, J . R.; Velicky, R . W. J . Phys. Chem. 1986, 90,4121.
-89.1 -89.6 -89.3
-75.5 -73.4 -74.0
-18.5 -28.1
-1 1.9 -16.7
about 50% higher than for N-NOZ bond rupture, the preferred primary decay channel may also be dependent upon the type of vibrational excitation that is involved. N-N02 bond breaking is related to a normal mode with symmetry AI, implying a significantly shorter lifetime due to anharmonic coupling than for the rather isolated A2 mode that supports ring fragmentation.' Accordingly, concerted triple dissociation may well be competitive with N-NOZ bond scission as a primary decay channel. Dipole Moments and Molecular Electrostatic Potentials. The calculated dipole moments and most negative electrostatic potentials associated with the amine nitrogens, Vmi,,(N), are given in Table 11. These provide some insight into the structural and electronic changes associated with the formation of the transition states. While the dipole moments are quite sensitive to the computational procedure, they show two consistent features: In going from the ground to the transition state, the calculated dipole moment of I decreases, while that of 11 increases, quite markedly. Some understanding of this can be obtained by analyzing the Vmin(N) values in Table 11. Vmi,(N) is strongly negative in the ground state of I, reflecting the fact that the amine nitrogens are pyramidal in character, with highly localized lone pairs. In the ground state of 11, on the other hand, the strongly electron withdrawing NOz groups greatly diminish the magnitude of Vmi,(N) and also reduce the pyramidal nature of the nitrogen, through conjugation such as is shown in eq.4.
Figure 1 shows that the ground-state six-membered rings of I and I I have chair conformations, with the carbons and nitrogens in parallel planes. The ring in I I is flatter than in I, as is indicated also by the STO-3G values for the NCCN dihedral angles of I and I 1 (Table I). In I, the large magnitudes of Vm,(N) show that major factors in determining the molecular dipole moment are the amine nitrogen lone pairs. In 11, however, these are considerably delocalized, and negative charge has shifted toward the NO2 substituents. It can be seen from Figure 1 that in I1 the effect of the diminished amine lone pairs on the dipole moment is actually
7702
J. Phys. Chem. 1991,95,7702-7709
a 0
?
0I
0 i\
0
00
0
Ground state
Transition state 1,3,5-Triaracyclohexane(I)
?
B
Ground state
Transition state
1,3,5-Trinitro-l, 3,5-Triazacyclohexane (RDX, 11)
= CARBON = NITROGEN
-
OXYGEN
0 = HYDROGEN Figure 1. Calculated STO-3G structures.
to oppose the much stronger contribution of the NOz groups. The transition states clearly reflect the incipient formation of the products shown in eqs 1 and 2, e.g., in the short C-N distances. The Vmin(N) values for both I and I1 decrease somewhat in magnitude, which is typical of what we have found when amine nitrogens change from triply to doubly c ~ o r d i n a t e d . ~ * * ~This ~J~J~ (23) Murray, J. S.; Seminario, J. M.; Politzer, P. J. Mol. Struct. (THEOCHEM) 1989, 187,95.
is presumably indicative of more diffuse lone pairs in the transition states. In terms of our interpretation of the roles that the lone pairs play in determining the total dipole moments, this explains why the dipole moment of I decreases in going to the transition state, while that of I1 increases. Summary
Various computational methods have been used to investigate the concerted gas-phase triple dissociations of 1,3,5-triazacyclohexane, I, and its 1,3,5-trinitro derivative, I1 (eqs 1 and 2). We find the activation barriers for both processes to be in the range 72-75 kcal/mol. We conclude, in agreement with a recent infrared multiphoton dissociation study: that ring fragmentation is competitive with N-N02 bond rupture as a primary decomposition channel for RDX (11). The results obtained with a local density functional method combined with H F structure optimization are found to be comparable in accuracy to those of a high-level many-body approach [MP4(SDTQ/6-3 lG*//3-21G]; this provides support for the general strategy of combining minimal basis HF structure optimization with LDF energy calculation in studying the decomposition modes of molecules too large to be treated by more elaborate post-Hartree-Fock methods. We used dipole moments and the electrostatic potentials associated with the amine nitrogen lone pairs to help understand the structural and electronic factors involved in the formation of the transition states in reactions 1 and 2.
Acknowledgment. We thank Dr. Jane S. Murray and Dr.M. Edward Grice for very helpful discussions and Ms. Anita Hamel for preparing this article. We greatly appreciate the support of this work by the Office of Naval Research, through Contract N00014-85-K-0217, and the computer time provided by the Pittsburgh Supercomputer Center. (24) Murray, J. S.; Ranganathan, S.;Politzer, P. J. Org. Chem. 1991,56, 3134.
Computational Study of the N-N02 Rotational Energy Barriers in Some Aliphatic and Alicyclic Nitramines Dariusb Habibollabzadeb, Jane S. Murray, Paul C. Redfern, and Peter Politzer* Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148 (Received: March 4, 1991)
An ab initio self-consistent-field molecular orbital investigation of the rotational energy barriers of the N-NO2 bonds in a series of aliphatic and alicyclic nitramines has been carried out. Structures, energies, dipole moments, and electrostatic potentials of the ground and rotational transition states of these nitramines have been presented and compared, with the aim of exploring the dependence of the NO2 rotational energy barrier upon structural and electronic features of these molecules. For the mononitramines, we find that the rotational barrier is greater when the C-N(N02)-C portion of the ground-state molecule is planar (or nearly so) than when it is pyramidal. This can be viewed as a result of the amine lone pair being more highly delocalized in the former instance; more energy is then required to rotate the NO2 group and disrupt this higher degree of conjugation. Structural, electrostatic potential, and dipole moment data support this interpretation. Our results for two dinitrohydrazines indicate that the second amine nitrogen and nitro group introduce significant new factors, including a suggested competitive conjugation.
Introduction In the course of a continuing study of the structural and reactive properties of energetic nitramines,I-' we have noted that a decrease in the degree of pyramidal character of the amine nitrogen parallels a decrease in N-NO2 bond length.3*4This observation is consistent with the intuitive notion that greater delocalization of its "lone To whom correspondence should be addressed.
0022-3654/9 1/2095-7702$02.50/0
pair" into the bond oocurs as its geometry more nearly approaches Planarity. Since rotation ofthe NO2 may perturb the conjugation (1) Politzer, P.; Sukumar, N.; Jayasuriya, K.;Ranganathan, R. J. Am. Chem. Soc. 1988,110,3425. (2) Murray, J. S.; Sukumar, N.; Ranganathan, S.; Politzer, P. Int. J. Quantum Chem. 1990,37,61 I . (3) Murray, J. S.; Redfern, P. C.;Seminario, J. M.; Politzer, P. J. Phys. Chem. 1990, 94, 2320.
0 1991 American Chemical Society
