The Great Diversity of HMX Conformers - American Chemical Society

Article pubs.acs.org/JPCA

The Great Diversity of HMX Conformers: Probing the Potential Energy Surface Using CCSD(T) Robert W. Molt, Jr., Thomas Watson, Jr., Alexandre P. Bazanté, and Rodney J. Bartlett* Quantum Theory Project, Gainesville, Florida 32611, United States S Supporting Information *

ABSTRACT: The octahydro-1,3,5,7-tetranitro-1,3,5,7-tetraazocine (HMX) molecule is a very commonly studied system, in all 3 phases, because of its importance as an explosive; however, no one has ever attempted a systematic study of what all the major gas-phase conformers are. This is critical to a mechanistic study of the kinetics involved, as well as the viability of various crystalline polymorphs based on the gas-phase conformers. We have used existing knowledge of basic cyclooctane chemistry to survey all possible HMX conformers based on its fundamental ring structure. After studying what geometries are possible after second-order many-body perturbation theory (MBPT(2)) geometry optimization, we calculated the energetics using coupled cluster singles, doubles, and perturbative triples (CCSD(T))/cc-pVTZ. These highly accurate energies allow us to better calculate starting points for future mechanistic studies. Additionally, the plethora of structures are compared to existing experimental data of crystals. It is found that the crystal field effect is sometimes large and sometimes small for HMX.

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INTRODUCTION The HMX molecule is formally known as octahydro-1,3,5,7tetranitro-1,3,5,7-tetraazocine. The original etymology of this acronym is Her Majesty’s Explosive, in reference to the nominal British head of state. It is a heterocyclic cyclooctane, shown in Figure 1, along with related members of its chemical family,

yield) can be made in changing the most fundamental properties (chemical), rather than bulk phase. The HMX literature is quite extensive, spanning 60 years. There have been numerous kinetic,1−24 structural,25−40 explosive,41−45 and physical properties46−54 studies. Experiments done on the solid-state have been careful to distinguish which crystalline polymorph was used; however, the same cannot always be said for the study of the gas-phase with respect to conformers. Some computational kinetic studies do acknowledge that there is more than one form of HMX, but choose only one or two conformers for study;18,19 it would be most systematic and complete to first consider what all the conformers are. “All” is mathematically difficult to guarantee, but subject to our procedure below, it is hard to imagine other gas-phase conformers. This is the primary effort of this study. Once the conformers are known, one may study the kinetics more carefully, as well as consider new crystalline polymorphs. To study the reaction kinetics, it is critical that one know all of the germane conformers. If one wishes to be accurate to within even an order of magnitude in the relative populations of conformers/products-to-reactants/any two comparative states, one must have an accuracy of 1.4 kcal/mol according to the Boltzmann distribution. Consequently, one may not meaningfully talk about the kinetics of the process unless one has such accuracy. The energy differences between conformers of related nitramine molecules are easily smaller than this, suggesting the importance of considering all the possible HMX conformers.55,56 Additionally, there is a literature history

Figure 1. The three major nitramines.

RDX and CL-20. The tell-tale feature of all of these molecules is the nitramine group. This functional group is the seat of the basic explosive properties of this molecule. Clearly, factors such as crystalline density, phonon magnitude, and many others contribute toward the overall explosive quality, but all of these properties are secondary. The nitramine groups are sine qua non for these explosives. As such, a clear understanding of reaction kinetics at the chemical level is necessary to appreciate and improve upon the explosive utility of these molecules. The greatest gains in improving the material properties (explosive© 2013 American Chemical Society

Received: November 8, 2012 Revised: March 8, 2013 Published: March 11, 2013 3467

dx.doi.org/10.1021/jp311073m | J. Phys. Chem. A 2013, 117, 3467−3474

The Journal of Physical Chemistry A

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geometries. However, it considers only two types of boats and one type of chair. It is possible that there are multiple matches to each crystal structure, given the sheer number of cyclooctane conformers. We have to walk before we can run. No one has the ability to figure out the mechanism rigorously in condensed phases. Interpreting the experiments is hard, and different experiments contradict one another. What we can offer is an unambiguous description of what is going on in the gas phase at STP. Once established, experimental groups can try to see whose methods match to this simpler system (gas, STP) to help sort out whose experiment is correct for the condensed phase (assuming it starts from the condensed phase at all; some of the literature argues that vapor from the condensed phase IS the starting point of the mechanism). Additionally, a computational estimate of condensed phase mechanism would benefit from a comparison to a closely similar system for corroboration (the gas phase).

of most gas-phase conformers corresponding to a structural “monomer” for some crystalline polymorph unit cell, subject to the crystalline field.57−64 Given that the crystalline field effect has been observed to be small in related nitramines,55,56 we might expect HMX crystalline field effects to be modest, all the more speaking to the importance of the gas phase conformers toward the discovery of new possible HMX crystalline polymorphs. The literature of HMX is inherently also tied to the literature of RDX and CL-20; we shall endeavor to focus on what has been specifically proven for HMX and the most key points about RDX and CL-20 pertinent to HMX. Lea concluded that liquid-phase RDX and HMX follow first-order kinetics with activation energies of 47.5 and 52.7 kcal/mol, respectively.1 Cosgrove and Owens disagreed with the analysis of Lea for RDX and instead thought that it was merely the vapor of the solid or liquid which began the reaction, and thus produces enough energy to begin a liquid-or-solid phase reaction.65 Rauch and Fanelli, again working with RDX, believed that the mechanisms were fundamentally different between gas and liquid phases, above and beyond just differing activation energies.66 From these original papers, great controversy arose as to what the mechanisms were, as noted in the above kinetics study references. Crystal structures of HMX were first reported in 1950;25 more crystalline polymorphs followed over time, showing the immense diversity of structures possible from this flexible cyclooctane in the solid phase.26−28,47,67−69 It has been observed that the δ crystal form has 4 coplanar carbon atoms with a C2 axis; α HMX has a C2 axis; β HMX has a center of inversion symmetry.28 The stabilities of the crystalline forms at room temperature are β > α > γ > δ, the same as the order of the densities.67 In addition to collecting Raman spectra of the polymorphs, Brill and Goetz established that the β crystalline form has a different ring structure compared to the α, γ, δ forms. They believed that the β form was more chairlike and the α and δ forms are more boat-like, as well as observing greater anharmonicity in the γ form.68 The first significant computational study on gas-phase HMX found four conformers and estimated the energies via MP2/6-311G(d,p).18 The first computational study of the reaction mechanism studied only two forms (a “boat” and a “chair”) without reference to the fact that there are indeed multiple boats or chairs in cyclooctanes.19 Additionally, this study relied on energies from Kohn−Sham density functional theory (KS-DFT) functionals which are known to be less accurate than the energy differences between the two conformers in their study.70−75 This is also problematic given that the study of nitramine geometries has shown that these functionals fail to predict nitramine lattice vectors accurately.76 This is a good example of how a parametrized method can fail outside of its parametrized scope, despite stellar success in other arenas.77 A similar kinetic study was conducted using many-body methodologies again known to be insufficiently accurate for comparing energy levels or kinetics comparing structural differences on the order of a kcal/mol,78 albeit thorough and effective in finding relevant geometric structures. There are many reactions such that small differences in geometry are the difference between exergonicity and endergonicity.79 The most thorough structural quantum chemistry study was performed by Lippert et al.34 This work closely examined the relationship between gas-phase conformers and solid-state structures. Their work showed careful examination of lengths and angles in crystals vs KS-DFT

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COMPUTATIONAL METHODOLOGY We would like to approach chemical accuracy as best we can in this work. Refinement of our work for chemical accuracy will be the subject of future computational efforts. KS-DFT80−83 methods can be accurate to 1 kcal/mol when they are parametrized to some specific set of molecules, but not beyond the “parametrization space.”70−75 Whether one is in the parametrization range or not is always an open question; the accuracy decreases easily outside of the specific set of particles studied. General purpose, nonempirically parametrized functionals, such as PBE,84 LDA,85 VWN,86 PBEmolβ0,87 typically do not offer accuracy as high as 3 kcal/mol for an arbitrary molecule, despite their more physically grounded quality compared to highly parametrized functionals.88−92 Nitramines are a somewhat exotic functional group, and thus we cannot be sure which functional to trust. Consequently, we opt for ab initio coupled cluster singles, doubles, and perturbative triples (CCSD(T))93−98 in a triple-ζ basis set. Its accuracy is established99 for even more stringent energetic demands than the raw electronic energy (it has chemical accuracy for even the enthalpy of formation). This assumes that one has the geometries to a proper accuracy. Second-order many-body perturbation theory (MBPT(2)), or MP2 if one uses a canonical Hartree−Fock reference,100 provides bond-length geometries as accurate as 0.01 Å for single-reference systems with a triple-ζ basis set.101 One of the best software for massively parallelized calculations using MBPT(2) and CCSD(T) is ACES III,102 and was thus used. We wished to use a basis set with some diffuse functions as needed, but not an excessive amount, as in the augmented Dunning style.103,104 We thus performed our geometry optimizations using MBPT(2)/6311++G(d,p),105,106 as well the calculation of harmonic vibrational frequencies to establish energetic maxima vs minima. Single-point energies were performed using CCSD(T)/cc-pVTZ.104 We wish to perform extrapolated energies eventually, and thus choose the Dunning basis sets. However, given the aforementioned excess of diffuse functions present, we opt for the nonaugmented form.

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SEARCHING OVER THE POTENTIAL ENERGY SURFACE Now that we have established how we wish to optimize and understand the energy differences, we must establish what to 3468



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Figure 2. Examples of cyclooctane conformers, hydrogens omitted. (a) Boat-Boat, (b) Chair, (c) Chair-Chair, (d) Crown.

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optimize and study. There has been great success in predicting the possible RDX conformers in terms of basic cyclohexane chemistry;55,57 analogously, so too do we look to cyclooctane chemistry for the basic HMX conformers. Previous work on cyclooctane chemistry shows that there are 10 conformers: boat-chair, twist-boat-chair, crown, chair-chair, twist-chair-chair, boat-boat, twist-boat, boat, chair, and twist-chair.105 This nomenclature of cyclooctanes derives from looking at each side of 6 carbons on either end and concluding whether it is a boat, chair, twist-boat, or twist-chair from cyclohexane chemistry. If the two sides have a perpendicular mirror plane and are either boat-boat or chair-chair, we call it boat-boat or chair-chair. If such a mirror plane does not exist perpendicular to the ring, it is simply a chair or a boat. An exception to this is the crown conformer, which is a distinct concept of cyclooctane chemistry. Together, the two ends give the two-part name (except the crown). For visual aid, in Figure 2, we have examples of the HMX forms of boat-boat, chair, chair-chair, and crown. We constructed each of these conformers out of the heterocyclic cyclooctane of HMX (accounting for all the additional conformers possible because nitrogens in the ring introduces more variations). Beyond this, we constructed every possible combination of axial/equatorial positions of the NO2 coming off of the ring nitrogens for each of the ring conformers. From this large set of possible conformers, we calculated the optimal geometry via Newton−Raphson optimization.107 Many optimizations went nowhere, with large RMS values persisting (greater than 1 mHart/Bohr persisting over at least 10 cycles, with no real downward trend in value). These conformers were thus discarded as unviable. The default convergence criterion was 0.1 mHart/Bohr. Many others simply converged toward one of the other stationary states found. The remaining conformers were subject to an energy Hessian with respect to normal coordinates to determine if the conformer was a minimum or maximum. All of these were then subject to a single-point calculation of energy using CCSD(T)/cc-pVTZ. We believe this technique to have been a rather exhaustive search of the potential energy surface (PES) of HMX.

RESULTING CONFORMERS AND NOMENCLATURE

There were 13 stationary states discovered from this analysis; they are given in Table 1. We shall explain our proposed nomenclature of these states. Clear nomenclature will help future efforts between solid-state studies of crystals and gas-phase conformers. The bridgehead atom is always given the number “1” in assigning numbers to the ring atoms. We then classify each nitro group as either axial, Table 1. Stationary States of the HMX Molecule; CCSD(T)/ cc-pVTZ Energies, MBPT(2)/6-311++G(d,p) Harmonic Frequencies

conformer 1,7-diaxial-3,5-dipseudo-boat chair 1,5-diaxial-3,7-diequatorial-chair 2,4,8-tripseudo-6axial-twist boatchair 1,3,5,7-tetraaxialtwist boat 2,4-diaxial-6,8-dipseudo-boat chair 2,8-dipseudo-4,6-diaxial-boat chair 1,3-diaxial-5,7-diequatorial-boatboat 1,5-diaxial-3,7-diequatorial-crown 2,6,8-tripseudo-4axial boat-chair 2,4,6,8-tetrapseudotwist-boat 1,5-diaxial-3,7-diequatorial-chairchair 2,4-diequatorial-6,8dipseudo-twist boat 3469

electronic E + ZPE (kcal/mol)

electronic E (kcal/mol)

smallest 2 frequencies (cm−1)

ZPE (kcal/mol)

0

+28, +61

122.5

0

0.7

+26, +61

122.3

0.5

1.1

+21, +52

122.3

0.9

1.2

+64, +73

122.4

1.2

2.1

−9, +50

122.2

1.8

2.2

+16, +41

122.3

2.01

2.3

+29, +37

122.2

2.1

4.2

+39, +50

122.1

3.9

5.7

−43, −22

121.8

5.01

11.9

+26, +43

122.6

12.01

13.5

−9, −7

121.5

12.6

15.1

−22, −9

122.3

15.01



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across an enantiomeric pair, and thus only list 2,8-dipseudo-4,6diaxial boat chair in Table 1’s physical properties. The enantiomer is given in the Supporting Information. The energy levels of the conformers show that most conformers are energetically accessible at STP, excepting 1,5diaxial-3,7-diequatorial-chair chair, 2,6,8-tripseudo-4-axial-boat chair, 2,4-diequatorial-6,8-dipseudo-twist boat, and 2,4,6,8tetrapseudo-twist boat. The use of CCSD(T) typically accounts for 99% of the correlation energies in a single-reference system in a triple-ζ basis; the only consequential approximation is thus the number of functions in the expansion of basis vectors.110,111 The use of our triple-ζ basis set makes it plausible that 1,5diaxial-3,7-diequatorial chair might yet lower in energy to be in the thermally populated range. This is of importance, given that certain proposed mechanisms (such as HONO elimination) are likely to be sterically sensitive. This disproves the previous assertions that there are only 2 gas phase conformers;19 there are certainly more than two. We now proceed to correlate our gas-phase conformers with known solid-state results. Some conformers feature significant symmetry; this is important for the sake of matching to observed experimental spectra. The 1,3,5,7-tetraaxial-twist boat is approximately S4 in point group. This is of particular interest, in that no HMX species with this symmetry has been observed experimentally; the nitramine orientation is unlike that of α, β, or δ.30 Moreover, the energy of this conformer is quite low with stable harmonic frequencies; one would expect its observation. It is conceivable that rapid gas-phase interconversion of different forms makes the observation of this distinct species difficult; this has been shown for RDX.112 We nonetheless would be interested to see if experimental identification is yet possible. The 1,5-diaxial-3,7-diequatorial crown features C2v symmetry. In the past, the literature has cited that both the α and δ phases as having C2v symmetry30,33,34,78 when the gasphase conformer is optimized starting from either α crystal monomer or δ crystal monomer. However, all of these references describe the α and δ conformers as being types of boats. This is probably due to a fast-and-loose comparison to cyclohexane chemistry rather than cyclooctane chemistry. When one examines the gas-phase version of the α and δ crystal monomers, one sees the same nitramine orientation as is present in the 1,5-diaxial-3,7-diequatorial crown. The nomenclature used in describing HMX should change to reflect this fact (cyclohexane chemistry should not be used to describe cyclooctane chemistry; this is a crown, not a boat). There is general agreement between our proposed crown structure’s geometry and the crystalline α and δ forms.34 We confirm the conclusion of Brand and co-workers34 that the most logical geometric assignment of lengths/angles is such that the C2v structure corresponds to the α and δ crystalline monomers; we thus do not lengthily repeat our geometric data confirmation. We do submit that our geometries are more trustworthy by nature of MBPT(2)/6-311++G(d,p) calculations compared to B3LYP/6-31G(d) calculations, but the chemistry conclusion is the same. Given that the crystalline forms of α and δ distort monomers down to C2 and C1, respectively, we agree with the inference the crystal-field effect is strong in these cases. The β crystal’s monomer is known to have Ci symmetry, consistent with the 1,5-diaxial-3,7-diequatorial chair form; the bond lengths also very closely match the crystalline geometry.26 This also speaks to the relatively weak intermolecular forces of the crystal that the gas phase geometries match the crystal to within 0.01 Å. It is interesting to see such contrast in the

equatorial, or pseudo. Axial and equatorial are familiar to chemists; we use the word “pseudo” to indicate a nitro group whose position is halfway between being a full axial or a full equatorial. As is seen in Table 1, this is common, a result of the conformational flexibility of the cyclooctane ring. Finally, we add the basic cyclooctane conformer label of the ring (crown, chair chair, etc.). The activation barriers in RDX are very small indeed, based on research of Vladimiroff and Rice.112 RDX chemistry is based on the cyclohexane. Cyclohexanes are more rigid than cyclooctanes; qualitatively, we would thus expect that the barriers in HMX would also be small, if not smaller. The barriers to conformer interconversion are themselves not relevant to the detonation mechanism. The energetic barriers we calculate in a mechanistic study, however, may be off significantly if we start from the wrong conformer. For example, even within RDX conformers, N−N homolysis varies by about 5 kcal/mol depending on the conformation.55 The N−N homolysis would presumably be less sensitive, mechanistically speaking, compared to say the HONO elimination mechanism (which requires sterics to be just right). This highlights the importance of the right conformer as a starting-point. The energy levels feature several very closely lying states, beyond the resolution of CCSD(T)/cc-pVTZ to guarantee. We are aware of this, and thus emphasize that the energetic ordering of states above is NOT meant to be taken as the true ordering of states except when the differences are greater than 2 kcal/mol of one another. Future work performing basis-set extrapolation will hopefully resolve this issue, as well as taking into account the anharmonicity. Four of these states are transition states/saddle points according to MBPT(2)/6-311++G(d,p) harmonic frequencies. We list the first two harmonic vibrations in each case due to the presence of very small harmonic frequencies. Our Hessian calculations are done analytically, not requiring a grid as KSDFT does; this is a significant advantage for small frequencies (we do not suffer issues of numerical instability in the same manner). We emphasize that the absolute values of MBPT(2) frequencies are not more accurate in magnitude than previous studies done using B3LYP; only in cases of numerical sensitivity to small values is MBPT(2) more reliable.108,109 However, small differences in energy curvature may or may not be accurately resolved with the MBPT(2) estimate of the correlation energy (or anything less than CCSD(T), for that matter). The PES curvature is quite small. Beyond just the basis set and correlation, anharmonic effects are important for such small frequencies. The presence of two negative frequencies makes it seem more plausible for a stationary state to be a genuine saddle point or at least transition state, as is the case for 2,4-diequatorial-6,8-dipseudo-twist boat and 2,6,8-tripseudo-4axial-boat chair. It is less clear whether 2,4-diaxial-6,8-dipseudoboat chair and 1,5-diaxial-3,7-diequatorial-chair chair are genuine transition states/saddle points, especially the boat chair given that the next harmonic vibrational frequency is solidly positive (+50 cm−1). Further refinement of basis set, correlation, and anharmonicity are needed. For the sake of simplicity of analysis below, we say “conformer” in reference to these twelve states, given our agnosticism about some of the harmonic frequencies’ sign. However, clearly, if it is a saddle point or energetic maximum, it is not a true “conformer.” One may notice that there are, in fact, only 12 states listed in Table 1, despite the claim of 13 distinct stationary states. There is no contradiction; rather, in our conformer searches, we came 3470



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(5) Okamoto, Y.; Croce, M. Cationic Micellar Catalysis of the Aqueous Alkaline Hydrolyses of 1,3,5-Triaza-1,3,5-trinitrocyclohexane and 1,3,5,7-Tetraaza-1,3,5,7-tetranitrocyclooctane. J. Org. Chem. 1979, 44, 2100−2103. (6) Brill, T. B.; Goetz, F. Laser Raman Spectra of α-, β-, γ-, and δOctahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine and Their Temperature Dependence. J. Phys. Chem. 1979, 83, 340−346. (7) Brill, T. B.; Landers, A. G. Pressure-Temperature Dependence of the β-δ Polymorph Interconversion in Octahydro-1,3,5-7-tetranitro1,3,5,7-tetrazocine. J. Phys. Chem. 1980, 84, 3573−3577. (8) Karpowicz, R. J.; Brill, T. B. The β-δ Transformation of HMX: Its Thermal Analysis and Relationship to Propellants. J. Phys. Chem. 1982, 86, 4260−4265. (9) Ebinger, M. H.; Janney, J. L.; et al. Deuterium Isotope Effects in Condensed-Phase Thermochemical Decomposition Reactions of Octahydro-1,3,5-7-tetranitro-1,3,5,7-tetrazocine. J. Phys. Chem. 1985, 89, 3118−3126. (10) Velicky, R. W.; Autera, J. R.; Weinstein, D. I.; Bulusu, S. Deuterium Kinetic Isotope Effect in the Thermal Decomposition of 1,3,5-Trinitro-1,3,5-triazacyclohexane and 1,3,5-7-tetranitro-1,3,5,7tetracyclooctane: Its Use as an Experimental Probe for Their ShockInduced Chemistry. J. Phys. Chem. 1986, 90, 4121−4126. (11) Haas, Y.; Greenblatt, G. D.; Zuckermann, H. OH Formation in the Infrared Multiphoton Decomposition of Jet-Cooled Cyclic Nitramines. J. Phys. Chem. 1987, 91, 5159−5161. (12) Miller, P. J.; Block, S.; Piermarini, G. J. Effects of Pressure and Temperature on the Thermal Decomposition Rate and Reaction Mechanism of β- Octahydro-1,3,5-7-tetranitro-1,3,5,7-tetrazocine. J. Phys. Chem. 1987, 91, 3872−3878. (13) Behrens, R. Thermal Decomposition of Energetic Materials: Temporal Behaviors of the Rates of Formation of the Gaseous Pyrolysis Products from the Condensed-Phase Decomposition of Octahydro-1,3,5-7-tetranitro-1,3,5,7-tetrazocine. J. Phys. Chem. 1990, 94, 6706−6718. (14) Bulusu, S.; Behrens, R. Thermal Decomposition of Energetic Materials. 2. Deuterium Isotope Effects and Isotopic Scrambling on Condensed-Phase Decomposition of Octahydro-1,3,5-7-tetranitro1,3,5,7-tetrazocine. J. Phys. Chem. 1991, 95, 5838−5845. (15) Brower, K. R.; Naud, R. L. Pressure Effects on the Thermal Decomposition of Nitramines, Nitrosamines, and Nitrate Esters. J. Org. Chem. 1992, 57, 3303−3308. (16) Williams, G. K.; Gongwer, P. E.; Brill, T. B. Thermal Decomposition of Energetic Materials. 66. Kinetic Compensation Effects in HMX, RDX, and NTO. J. Phys. Chem. 1994, 98, 12242− 12247. (17) Zheng, W.; Szekeres, R.; Kooh, A. B.; Oxley, J. C. Mechanisms of Nitramine Thermolysis. J. Phys. Chem. 1994, 98, 7004−7008. (18) Bharadwaj, R. K.; Smith, G. D. Quantum Chemistry Based Force Field for Simulations of HMX. J. Phys. Chem. B 1999, 103, 3570−3575. (19) Voth, G. A.; Opdorp, K. V.; Glaesemann, K. R.; Lewis, J. P. Ab Initio Calculations of Reactive Pathways for α- Octahydro-1,3,5-7tetranitro-1,3,5,7-tetrazocine (α-HMX). J. Phys. Chem. A 2000, 104, 11384−11389. (20) Goddard, W. A.; Dasgupta, S.; Muller, R. P.; Chakraborty, D. The Mechanism for Unimolecular Decomposition of RDX (1,3,5Trinitro-1,3,5-triazine), an ab Initio Study. J. Phys. Chem. A 2001, 105, 1302−1314. (21) Lewis, J. P. Energetics of intermolecular HONO formation in condensed-phase Octahydro-1,3,5-7-tetranitro-1,3,5,7-tetrazocine (HMX). Chem. Phys. Lett. 2003, 371, 588−593. (22) Bernstein, E. R.; Greenfield, M.; Guo, Y. Q. Decomposition of nitramine energetic materials in excited electronic states: RDX and HMX. J. Chem. Phys. 2005, 122, 244310−244315. (23) Bernstein, E. R.; Bhattacharya, A. B.; Greenfield, M.; Guo, Y. Q. On the excited electronic state dissociation of nitramine energetic materials and model systems. J. Chem. Phys. 2007, 127, 154301− 154310.

strength of intermolecular forces of organic crystals of the same molecule. It is known that C2 axes are present in the α crystalline form. The 1,5-diaxial-3,7-diequatorial-chair chair form features a C2 axis of symmetry, but the N−N bond lengths do not match well, and defer to our previous conclusion that the crown C2v form most well-matches the α form. All of these conformers would be of interest in a solid-state calculation. The potential exists that these conformers, as starting geometries of a lattice vector optimization, may yield new crystalline forms. Even if not, it would be of interest to observe how the intermolecular forces mold the gas-phase conformers strongly in some cases, weakly in others, to the solid-state structure. Indeed, given how many RDX crystalline forms exist from a simple cyclohexane, it is surprising that more than four HMX crystal forms have not yet been found. Previous work exists in the literature for the opposite process: starting from the known crystal structures, new gas phase conformers were discovered at the time.34 It is a reasonable hope that the process might be fruitful in reverse.

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CONCLUSIONS Our ab initio study of HMX conformers has allowed us to begin work on the mechanism of gas-phase HMX decomposition. This comprehensive study of the potential energy surface enables us to be highly accurate to the geometric sensitivities of the kinetics. The high-accuracy of our CCSD(T) energies allow us to be confident of what conformers may be reasonably thermally populated. The variety of our thirteen stationary states geometrically is suggestive of possible new bases for crystalline forms. The lack of correspondence among some known crystalline forms our PES survey is suggestive that the intermolecular forces of some crystals are high, and the close corollary in others suggest weak intermolecular forces.

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ASSOCIATED CONTENT

S Supporting Information *

Geometries and harmonic frequencies are available in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]fl.edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are thankful for funding for this research by the Army Research Office.

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REFERENCES

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