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J. phys. Chem. 1980, 84, 1376-1380
Analysis of Intra- and Intermolecular Interactions Relating to the Thermophyslcal Behavior of a-,6-, and b-Octahydro-l,3,5,7-tetranltro-1,3,5,7-tetraazocIne T. B. Brill' and C. 0. Reese Department of Chemlstty, University of Delaware, Newark, Dekware 19711 (Received December 3, 1979) Publicatbn costs assisted by the Air Force Office of Sclentitic Research
The relative stabilities of the p, a,and 6 polymorphs of HMX (octahydro-l,3,5,7-tetranitro-1,3,5,7-tetraazocine) were analyzed in terms of Coulombic forces. The internal contacts in the molecule show the feasibility of formation of HONO, CH20,and N20during pyrolysis. Intramolecular interactions cause the chair conformation adopted by /3-HMX to be more stable than the chair-chair form of a-and CHMX. It was found that the total electrostatic energy of the heavy-atom intermolecular interactions in a shell of radius 3.75A around each atom follows the experimentally observed trend in polymorph stability at room temperature. Intermolecular interactions are dominated N.-0 and C-.O attractions combined with O-.O and Ne-0 repulsions. Hydrogen bonding does not play an important role in determining the crystal structures adopted by HMX. The intermolecular forces are illustrated by use of computer graphics plots from ORTEP.
Introduction The purpose of this paper is to elaborate on the internal and crystal lattice interactions which might contribute to some of the known properties of the polymorphs of octahydro-l,3,5,7-tetranitro-l,3,5,7-tetraazocine (HMX). HMX is an important monopropellant material. It exists in four polymorphs labeled a-,p-, y-, and 6-HMX. The crystal structures of /3, a,and 6 are a~ailable.l-~A chair ring conformation is found in P-HMX but a chair-chair conformation exists in a-and 6-HMX. The trend in stability of these forms is p > a > 6 at room tern~erature.~ The reverse stability trend exists toward pressure, B 2 a > 6.6 Brief discussions of crystal lattice interactions in the and short range are made in the crystal structure studie~l-~ elsewhere on CX-HMX,~ but no comparative structural or energy analyses have appeared. Hence, the interactions that occur between atoms and lead to the stability trend in the polymorphs have not been sorted out, In this project the atomic parameters of a-,p-, and 6-HMX were used to generate Coulombic energies in order to identify the important atom-atom interactions. The relative trend in stability of the polymorphs can be rationalized from these energies. Some mechanistic suggestions about decomposition arise from the interaction distances, although more data on product distributions are needed before a thorough analysis of this factor can be made. The Model When atomic coordinates7 from the crystal structures of a-,p- and 6-HMX are used, the bond distances are readily calculated with ORTEP.~ A series of alternating positive- and negative-charged atoms comprise the HMX molecule. The relative charges on these atoms were taken from semiempirical MO-SCF calculations by Stals on HMX? In the NOz groups the charges were taken as N = +0.76 and 0 = -0.35. The charge on the ring nitrogen was N = -0.57 and that on the ring carbon was C = +0.41. The hydrogen atoms are approximately neutral. A small difference exists in the charges depending on the position of the atom in the molecule, but it does little to affect the total electrostatic energy. Although HMX is an organic molecule, the motif of alternating positive- and negativecharged atoms produces electrostatic forces which are responsible for cohesion in the solid. We can imagine that the structure adopted is a result of the interactions of a complicated potential energy surface defined by these 0022-3654/80/2084-1376$0 1.OO/O
charges. The fact that four polymorphs of HMX are known is indicative of the many potential energy minima that are possible. Quantitative calculation of the actual potential energy surface or even components of it is beyond the limit of the available parameters. However, it was pointed out many years ago by Feynmann that interactions in atoms and molecules could be treated by Coulombic forces? It should be possible to make a qualitatively informative study of HMX polymorphs using the Coulombic electrostatic potentials, E(r) = q1qZ/rl2. Atomic forces are basically electrical and therefore electrostatic energies are responsible in large part for the crystal structure adopted. The Coulombic potentials are balanced to a degree by the Born repulsive potential, e-rlp. We do not know how to parameterize the repulsive potential in these systems. However, it is well known that, except at very close contact, the repulsive potential makes a contribution of less than 10% to the total energy.1° This fact has led us to consider only the Coulombic terms in the evaluation of important interactions in HMX crystals. The Coulombic calculation in the crystal lattice was divided into two parts. The intermolecular interactions were calculated in a shell around each non-hydrogen atom to a radius of 3.2 A and again in a shell of 3.2-3.75 A. The 3.2-A radius was chosen after considering the van der Waals contact distances. The sum of the van der Waals radii leads to contact distances of C-.N = 3.07 A, C-0 = 2.97 A, N-N = 3.00 A, N--0 = 2.90 A, and 0-0 = 2.80 A. Only a few intermolecular contacts in HMX occur at these distances and so a slightly expanded shell of contact distances seems called for. The choice of 3.2 A as a shell of contacts is arbitrary but rational. Electrostatic interaction energies from contacts in this shell may contain contributions from the Born repulsion potential, polarizations, and higher multipole terms, which, of course, are not represented in the point charge model. Hence Coulombic energies calculated in this short-range shell are probably less representative of the true potentials than those calculated in a larger shell. The larger shell of radius between 3.20 and 3.75 A about each non-hydrogen atom is outside the van der Waals domain. Interaction energies in this shell should be dominated by the Coulombic potential because of Gauss' law. We neglected the hydrogen atoms in these analyses. The sum of the H and 0 van der Waals radii is 2.60 A. There 0 1980 American Chemical Society
Thermophysical Behavior of a-,
p-, and 8-HMX
The Journal of Physical Chemktry, Vol. 84, No. 11, 1980 1377
ALPHFI-HMX
Flgure 3. a-HMX. Figure 1. &HMX.
DELTFI-HMX
Figure 2. A projection of &"X of CyN, attractlons.
showing the transannular arrangement
are many H-0 distances in this range in HMX. However, it has been argued that an H.-O contact greater than 2.2 A in a C-H...O unit is a dubious hydrogen bondall In HMX only a few H-00 contacts less than 2.2 A exist. Given the nearly neutral charge on H, the nonlinear C-He-0 angles present, the many IH-0 distances greater than 2.2 A, and the fact that NOz is only a borderline proton acceptor,12 hydrogen bonding is not an important component in the crystal structures of HMX. Instead heavy atom electrostatic interactions iilre the controlling feature. Some evidence exists that hydrogen bonding might play a role, albeit small, in the internal stabilization of a-and 6-HMX conformation. The evidence will be noted shortly.
Intramolecular Interactions The stable form of HMX at room temperature, 8-HMX, has been studied by both X-ray13and neutron diffracti0n.l The neutron diffraction data were used in this work. The ring conformation of P-HMX is best described as a chair conformation as shown in Figure 1. This particular conformation leads to minimal internal repulsions between NO2 groups and maximal transannular attractions in the ring. Only four of the eight oxygen atoms in neighboring NO2 groups are in cllose repulsive interaction (3.10 A). Two
Flgure 4. 6-HMX.
transannular attractions between C1 and N3 occur at 2.78
A as projected in Figure 2. This strong attraction is artly
1,
offset by a transannular N3-N3 repulsion at 2.77 but is aided by an elongation of the ring which increases the distance of the N2-.N2transannular repulsion to 3.94 A. In contrast, the progressively less stable HMX polymorphs at room temperature, a-and 8-HMX, exist in the chakchair conformation shown in Figures 3 and 4. This ring conformation forces all eight oxygen atoms into close approach at a distance of 3.0-3.2 A. When 8-HMX is used as the example, the transannular attractions of C2.-N2 and C4-.N2 are lengthened to 3.14 A while the distances of the N-.N repulsions are lengthened to 3.07 A in the case of N2--N5and shortened in the case of N3-Ns to 3.73 A. The
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The Journal of Physical Chemistry, Vol. 84, No. 11, 1980
TABLE I: The Number of Intermolecular Heavy Atom Interactions per Moleculeu
p CY
6
0 CY
6
8(3.02-3.13) 4(3.05) lO(2.89-3.15)
4(3.13) 4(2.83) 2(3.16)
6. The trend in energy also follows the trend of decreasing density of these forms, but the rate of change in energy is greater than that of density. While it is possible to generalize intermolecular interactions in the three polymorphs as is done above, it is difficult to visualize all of the directional types of interactions. Hence only what appear to be the most important interactions will be outlined for each polymorph. Figure 5 illustrates the dominating close-range attractions which occur between O3 and C1 and O3 and C2 in P-HMX. These attractions are offset to some extent by an O3.-N3 repulsion. This interaction with the C1N3C2 ribbon brings on same cooperative electrostatic pairing between O3and N4 when viewed from the top looking along the chains as shown in Figure 6. However, the N4”’03 distances involved are quite large (3.7 A). The other dominant close-range interaction in P-HMX is a crosswise
+ 0.02 + 0.29
+0.26 +0.54 +0.38
+ 0.06 + 0.64
+0.38
+ 0.09
- 1.48 -1.50 - 1.03
+0.52 +0.68 +0.38
+ 0.64
-1.46 -1.21 -0.97
+0.52 t 0.68
t0.09
BETA-HMX
Flgure 6. The longer range cooperative attractions between O3and N, along “chains” in 8-HMX.
BETFI-HMX
Flgure 7. The cbe-range interactions between the “chains” in P-HMX.
interaction between the chains in Figure 6. This is an 02.**N4attraction combined with an 02.-04repulsion as shown in Figure 7. In a-HMX, Figure 8 shows the cooperative electrostatic attraction involving O3 and N4 in the equatorial NO2 groups along the chains. However, this forces close repulsive contact between O3 and N2 which both carry a negative charge. Across the chains O4 engages in a repulsive interaction with N1 and an attractive interaction with Cz. The distance between O4 and the atoms in the
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The Journal of Physical Chemistry, Vol. 84, No. 1 I, 1980
fit PHfi-HMX
Flgure 8. The intermolecular contact distances of short range in aHMX.
DELTA-HMX
Flgure 9, The Intermolecular contacts of short range in 6-HMX.
axial NO2 group bonded to N2 are all greater than 3.40 A. Hence the equatorial NN02 groups dominate in the heavy atom interactions in (U-HMX.~ In 6-HMX the principal intermolecular interactions occur in a complex network of staggered HMX molecules as shown in Figure 9. The principal interactions exist between an equatorial NO2 group and a neighboring ring and its equatorial NO2 group. O2of one molecule interacts with a C1-N8-N1-07 ribbon of a second molecule above, while O7 of that second molecule interacts with the C3Ns-N7 ribbon of a third molecule above the second and so forth. The axial oxygen (06) of the first molecule interacts repulsively with O1 of the second molecule. As in a-HMX, the main intermolecular attractions are found in
Brill and Reese
the equatorial NNOz groups of the molecule. In summary, there are N.-O and C-0 attractions in all HMX polymorphs. These attractions demand a number of O-.O and O-.N repulsions because of the symmetry of the charges in the molecule. Beyond this description, each polymorph is unique in the direction and number of these interactions. However, the equatorial groups of a- and 6-HMX engage in more intermolecular interactions than do the axial NO2 groups. Electrostatic effects, although complex in HMX, can be seen to control the relative stabilities of these polymorphs and probably play an important role in the thermal decomposition. Acknowledgment. We are grateful to the Air Force Office of Scientific Research for support (AFOSR-76-3055) of this work. References and Notes (1) C. S. Chol and H. P. Boutin, Acta Crystallogr., Sect. B , 26, 1235 (1970). (2) H. H. Cady, A. C. Larson, and D. T. Cromer, Acta Crysfallogr., 16, 617 (1963). (3) R. E. Cobbledick and R. W. H. Small, Acta Crystallogr., Sect. 6, 30, 1918 (1974). (4) A. S. Teetsov and W. C. McCrone, Microsc. Cryst. Front, 15, 13 (1965). (5) F. Goetz, T. B. Brlll, and J. R. Ferraro, J . Phys. Chem., 82, 1912 (1978). (6) J. Stals, Aust. J. Chem., 22, 2505 (1969). (7) The x, y , and L coordinates for each atom In the crystal structures of a-,@-, and 6-HMX were used as published except that the x coordinate of N, in ref 2 should be -0.018 k 5 rather than the positlve value given. (8) C. K. Johnson, ORNL-3795, Oak Ridge National Laboratoty, Oak Ridge, TN, June, 1970, (9) R. P. Feynmann, Phys. Rev., 56, 340 (1939). (10) M. P. Tosl, SolM State Phys., 16, 1 (1964). (11) J. Donohue in “Structural Chemistry and Molecular Biology”, A. Rich and N. Davidson, Ed., W. H. Freeman, San Francisco, CA, 1968, p 443. (12) S. N. Vinogradov and R. H. Linnell, “Hydrogen Bonding”, Van Nostrand-Rhelnhok!, New York, 1970. (13) P. R. Eiland and R. Peplnsky, Z. Kristaliog., 106, 273 (1955). (14) F. Goetz and T. B. Brlll, J . Phys. Chem., 83, 340 (1979). (15) L. Pauling, “The Nature of the Chemlcal Bond”, Cornell University Press, Ithaca, NY, 1960. (16) A. J. B. Robertson, Trans. Faraday SOC.,45, 85 (1949). (17) J. J. Rocchio and A. A. Juhasz, “Proceedings of 11th JANNAF Combustion Meeting”, Vol. I, CPIA Publication uo. 261, CPIA, 1974. (18) B. B. Goshgarian, AFRPL-TR-78-76, Air Force Rocket Propulsion Laboratory, Edwards AFB, CA, 1978. (19) R. A. Beyer, ARBRL-MR-02816, Aberdeen Proving Ground, MD, 1978. (20) K. P. McCarty, AFRPL-TR-7659, Air Force Rocket Propulsion Laboratory, Edwards AFB, CA, 1976. (21) R. Shaw and F. E. Walker. J . Phvs. Chem.. 81. 2572 (1977). (22j B. Suryanarayana, R. J. Graybush,and J. R. Autera, Cheh. Ind. (London), 2177 (1967). (23) . . J. Stals, A. S. Buchanan, and C. G. Barraclough, Trans. Faraday Soc., 67, 1756 (1971). (24) B. Suryanarayana, T. Axenrod, and G. W. A. Milne, Org. Mass Spectrom., 3, 13 (1970). (25) J. J. Batten, Aust. J. Chem., 24, 945 (1971).
