Conformers of CL-20 Explosive and ab Initio Refinement Using

Nov 8, 2012 - Molt , R. W.; Watson , T.; Lotrich , V. F.; Bartlett , R. J. J. Phys. Chem ...... Cramer , C. Essentials of Computational Chemistry, 2nd...
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Conformers of CL-20 Explosive and ab Initio Refinement Using Perturbation Theory: Implications to Detonation Mechanisms Robert W. Molt, Jr.,* Rodney J. Bartlett, Thomas Watson, Jr., and Alexandre P. Bazanté Quantum Theory Project, University of Florida, Gainesville, Florida 32611, United States S Supporting Information *

ABSTRACT: We have identified the major conformers of CL-20 explosive, otherwise known as 2,4,6,8,10,12-hexanitrohexaazaisowurtzitane, more formally known as 2,4,6,8,10,12-hexanitrohexaazatetracyclo[5.5.0.0]-dodecane, via Monte Carlo search in conformational space through molecular mechanics and subsequent quantum mechanical refinement using perturbation theory. Our search produced enough conformers to account for all of the various forms of CL-20 found in crystals. This suggests that our methodology will be useful in studying the conformational landscape of other nitramines. The energy levels of the conformers found are all within 0.25 eV of one another based on MBPT(2)/6-311G(d,p); consequently, without further refinement from a method such as coupled cluster theory, all conformers may reasonably be populated at STP in the gas phase. We also report the harmonic vibrational frequencies of conformers, including the implications on the mechanism of detonation. In particular, we establish that the weakest N−N nitramine of CL-20 is the cyclohexane equatorial nitramine. This preliminary mapping of the conformers of CL-20 makes it possible to study the mechanism of detonation of this explosive rigorously in future work.

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INTRODUCTION CL-20 (shown in Figure 1, along with its chemical brethren) has been referred to as “the densest and most energetic

demolition explosive (RDX), many conformers discovered in the gas phase were eventually discovered to be the basis for a crystalline polymorph.3−10 A gas-phase description of a molecule gives a zeroth-order description of crystal structure molecular basis. The knowledge of the various crystalline polymorphs is important; many aspects of bulk chemical reaction (namely, detonation, in this case) are dependent on crystalline properties (for example, the notion of hot spots; the propagation of initial bond breaking through phonons, etc.).11,12 Additionally, the chemical kinetics require great accuracy to study meaningfully. If one wishes to be correct in the relative population distribution between products and reactants or conformers of 2 types, one needs to be accurate to within 1.4 kcal/mol at STP to be correct to within even an order of magnitude (based simply on the Boltzmann distribution). It is thus necessary to know all the conformations from which a reaction may begin to get an accurate estimate of the activation energies required. All research performed on related nitramine (N−NO2 groups) compounds are inherently worthy of comparison. What is chemically true of CL-20s chemical cousins may be true of it; however, others dispute the seeming similarities in detonation mechanism based on various kinetic studies.13,14 In particular, CL-20 has been studied far less than its RDX and HMX cousins. This is partly due to the fact that its existence has not been known as long as RDX and HMX; partly due to

Figure 1. RDX, HMX, and CL-20 chemical structures. Note the nitramine functional group common to all.

explosive known;” this statement inherently prefaces the importance of the study of this molecule.1,2 The value of improving chemical explosives is of paramount importance in many applications. The thermodynamics of the detonation are of relevance for the design of new explosives with greater explosive yield. The kinetics of detonation are critical to the shock-sensitivity, important for application in the field. The relevant conformers of CL-20 are an important question to be studied. In chemically similar explosives, such as royal © 2012 American Chemical Society

Received: June 4, 2012 Revised: September 25, 2012 Published: November 8, 2012 12129

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chose one particular CL-20 conformer at random, without thought to the other conformers, and with a computational methodology insufficient to be trustworthy a priori. One of these papers attempted to study the mechanism of CL-20 from an arbitrary conformer25 (unwise, given the sensitivity of kinetic studies to small energy differences, as well as relying on B3LYP/6-31G(d,p) energies to be accurate to within 1 kcal/ mol, which is known to be untrue.26−31 As such, we seek to enter the fray to answer questions of the conformers of CL-20 using methodologies from the bottom to the top. We seek to use parameterless, ab initio methods in the final step of our analysis to confirm our studies and experimental checks to confirm the validity of specific properties calculated (like crystal polymorphs, lattice constants, etc.) when using highly parametrized methods. The value of using force-fields in early steps, because of their computational cheapness, is not to be underestimated but checked in subsequent steps. From such methodologies, we may know the potential energy surface of all conformers of CL-20 and thereby predict new crystal structures as well as predict the chemical mechanism of detonation.

the fact that it is an even more dangerous explosive than its counterparts (and thus undesirable experimentally); partly due to its restrictions in information as a classified weapon; and partly due to its larger size (inhibiting easy computational study). Pace and co-workers first studied the change in the concentration of nitro groups in the three major nitramines (RDX, HMX, and CL-20) through EPR experiments.15 They concluded that nitro groups become trapped and stabilized within the CL-20 crystal structure. Oxley and co-workers studied thermal decomposition of CL-20 in dilute solution.16 Their studies of dilute solutions had the advantage that it inherently avoids autocatalysis and multiphase decomposition, and the samples could be kept isothermal. Indeed, one of the greatest challenges in the study of RDX and HMX is the ability to generalize a mechanistic study of a single-phase to a multiphase system, or the ability to discriminate reactions of one phase amidst data from a multiphase experimental system. Oxley’s work shows that the rate constant under the aforementioned conditions for CL-20 decomposition is about 3.5 times greater than for RDX and about 35 times greater than HMX. The activation energies observed, in each case, are between 40 and 50 kcal/mol. This is suggestive of a common mechanism; the slight variations in activation energy could be a result of structural differences endemic to RDX, HMX, and CL20, rather than a different mechanism. Other experimental studies, referenced above,14 disagree; some evidence implies that the RDX and HMX mechanisms differ significantly. In all instances, however, we emphasize that different experimental conditions may mean that the results do not contradict one another; the interpretation of the data differs widely in various cases. Ryzhkov and McBride also performed EPR studies of CL-20 crystals and came to a similar conclusion as Oxley and co-workers.17 Rice, Thompson, and Sorescu performed constant particle number, pressure, temperature molecular dynamics calculations (NPT-MD) on CL-20 in the crystalline phase using MD parameters associated with RDX.18 This work demonstrated that the essential qualities of the basic crystal structures could be replicated for CL-20 from the basic physical chemistry of RDX, i.e., that CL-20 is essentially RDX, chemically speaking. Further extensions of their work were able to replicate pressure−temperature (PT) curves of all of the nitramines, further validating their MD calculations.19 However, Kohn−Sham density functional theory (KS-DFT) calculations on the solid state of nitramines showed drastic failures20 in predicting lattice vectors. This is a good example of the subtle nuance of computational modeling: success in modeling one property by no means implies successful prediction of other properties. Additionally, this is a good example of where common wisdom that KS-DFT is better than molecular mechanics is far from true. This is a usual phenomenon in highly parametrized methodologies, such as many (but far from all) KS-DFT functionals and MD calculations. Three B3LYP computational studies have been performed on gas phase conformers.21−23 The first such paper identified four conformers.21 In chemically similar compounds, the harmonic vibrational frequencies are known to be quite small.10 It would be unwise to use a numerical grid for gradients or Hessians, as is required by KS-DFT. Numerical grids play havoc with the sign of harmonic vibrational frequencies, and the correct sign is needed to determine energetic minima vs maxima. As such, the conformers interpreted to be minima in that paper cannot be known to be minima rigorously.24,25 The other two papers

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METHODOLOGY We began by assembling a structure of the CL-20 molecule from a rudimentary guess of common bond lengths and angles. This form was then optimized using second-order many-body perturbation theory (MBPT(2))/6-311G(d,p)).32−35 Manybody perturbation theory is Möller−Plesset perturbation theory (MP) if the reference chosen happens to be Hartree−Fock. Indeed, there are many instances in which the use of nonHartree−Fock references is advantageous to circumnavigate issues of degeneracy; as such, we keep an open mind to the general formulation of applying perturbations atop an arbitrary reference state. We chose a triple-ζ basis set, as MBPT(2) is known to be accurate to within ±0.01 Å for single-reference molecules.36 We emphasize the value of choosing perturbation theory; as this is an ab initio method (ab initio here meaning a parameterless methodology, which is systematically correctable), we can expect it to work equally well on any singlereference molecule. This is in contrast with Kohn−Sham density functional theory (KS-DFT),37−40 which can be highly dependent on the choice of functional (especially since many functionals are heavily parametrized and thus cannot be expected to give unbiased results beyond the parametrized set).31,41,42 We use the ACES III software for our calculations, as it is optimally designed to be a massively parallelized software for calculations using MBPT(2).43 From this optimized molecular geometry, we began a Monte Carlo force-field based search for other CL-20 conformers. From the aforementioned initial CL-20 conformer, we varied bond lengths, angles, and dihedrals in a Metropolis Monte Carlo fashion using the PCModel92 software and the MMX force-field. The standard MMX force-field does not have parameters for the nitramine functional group, as the nitramine functional group is somewhat exotic to standard organic chemistry. We substituted an amine group in place of the nitro group; for the sake of finding a rough estimate of the conformers, this is similar in size and bond length, such that the sterics of what is possible is preserved. This is a trivial assumption for the conformational search. All aspects of the search are left at default parameters except for the following. The duration of the searches is indefinite until either 10 000 minima structures are found or a minimum structure is found 12130

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shows the differences in axial vs equatorial positions in the bridging cyclohexane base. The bottom of Figure 3 illustrates the differences in how the cyclopentane nitramines orient with respect to one another. The conformers are so named based on CL-20 crystal structures. The actual crystal structures have varying availability publicly.18 The basic lattice constants and other bulk properties are available for four of the five polymorphs (α, β, γ, and ε, but not ζ).18,45−49 Refined data, such as molecular-level data, however, are not available for the α anhydrous crystals or β crystals as a matter of restricted information.18,45−48 The hydrated α crystal data is incomplete.18 The γ and ε crystal structures, including molecular-level properties, are public knowledge and well-known.49 The ζ form exists only at high pressures, and no data exists beyond its basic zeta crystalline assignment.46 From the myriad of sources referred to above, we have endeavored to establish which of our conformers belong to which crystalline polymorph, if any. The first conformer has the cyclopentane nitramine orientation and axial/equatorial combination consistent with the β crystal and is thus named the β conformer.18 The α and γ crystals are known to have a cyclopentane nitramine orientation consistent with both of the next two conformers.18,49 The γ crystal has a form of CL-20, which is diequatorial, indicating that the third conformer ought to be designated the γ conformer.18,49 The α crystal structure is not so resolved that we can claim that the second conformer is the basis for the α crystal structure; nonetheless, it is known to be different than the γ but still have the same cyclopentane nitramine orientation.18 We thus propose the second conformer based on our evidence is likely the α form. To emphasize that this is a reasonable interpretation of data but not experimentally confirmed, we call the second conformer α?. It would be of great interest for our experimental colleagues to investigate this conjecture. The α? and γ conformers differ with respect to one another only in that α has an axial and an equatorial pair of nitramines on the cyclohexane, whereas the γ conformer has two equatorial nitramines. The next pair of conformers, ζ and ε, again only differ in cyclohexane nitramines; the ζ? conformer has one axial and one equatorial, with the ε conformer being diequatorial. The ε conformer matches the ε crystal structure in nitramine cyclopentane orientation and diequatorial nature.18,49 The ε conformer is of Cs symmetry. That the ζ? conformer has a relationship to the ζ crystal is very speculative; we offer this purely based on the fact that there is one remaining crystal structure not accounted for. It is more than possible that the ζ crystal basis is one of the other conformers again or a completely unstable conformation in the gas phase alone (for example, the γ RDX crystal is actually the transition state between the diaxial, equatorial to triple axial conformations, completely unstable in the gas phase on its own).6 However, no nomenclature has existed before this point in previous CL-20 work; we offer this first attempt at taxonomy to help organize previous data in terms of our own more complete survey of the conformational landscape of CL20, as well as to better relate our data to the solid-state community. The transition state conformer is so-named because it is the only conformer that is an energetic maximum via harmonic frequency analysis. It is also of Cs symmetry. We emphasize the success of our methodology for finding the crystalline polymorphs’ molecular bases. Our Monte Carlo force-field search combined with MBPT(2) discriminating against the false positives has produced 5 minima, in accordance with 5 crystal structures. It is suggestive (albeit

500 times. The search is executed 3 times from various random seeds. We allow for energy ranges of 3.5, 20, 50, 100, and 400 kcal/mol energy increases for possible generated structures to be minimized relative to the conformational minimum. The search never generates more than 14 possible conformers, which generally only differ in the axial/equatorial position of the amines. This seems reasonable; the caged structure of CL20 is such that few relaxations seem possible. These 14 conformers are subject to a MBPT(2)/6311G(d,p) optimization of geometry using a Newton−Raphson algorithm.44 Of the 14, only 6 converged toward an energetic extremum. The other 8 are discarded from further analysis; their geometric optimizations do not converge, the RMS force remains quite high. The 6 that did converge did so relatively quickly for a molecule of this size. The harmonic vibrational frequencies are then calculated using the same many-body methodology. Five are energetic minima and the sixth a maximum. The energy levels are then considered from these MBPT(2)/6-311G(d,p) calculations.

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THE SIX CONFORMERS The structure of CL-20 (shown in Figure 2) is that of two cyclopentanes bridged together by one carbon in each of the

Figure 2. Side view of equatorial/axial vs diaxial forms of CL-20. Oxygen atoms are denoted as red, carbon atoms are denoted as gray, hydrogen atoms as white, nitrogen atoms as blue. Note that, as this is a side view, the two cyclopentane rings are atop one another, superimposed.

pentagons, as well as the bases of the pentagons forming a cyclohexane to form this bridged bicyclic compound. There are two major differences that distinguish the CL-20 conformers from one another: the axial vs equatorial nature of the cyclohexane nitramine groups, and the angle of the cyclopentane nitramine groups with respect to one another. Figure 2 12131

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Figure 3. Conformers of CL-20, overhead. All conformers differ only in terms of the cyclopentane nitramine orientations and cyclohexane axial/ equatorial choices.

not deterministic) that our methodology is efficient if we wish to apply it to similar chemicals to find the relevant structures. We also emphasize the extent to which these geometries are a true benchmark for the current best estimate of the gas-phase geometries of these conformers; the only method expected to produce a better geometry would be CCSD(T) or higher coupled cluster excitations.50−56 All of the geometries are available in the Supporting Information.

Table 1. Energetics of the CL-20 Conformers Based on MBPT(2)/6-311G(d,p)a β conformer α? conformer γ conformer ζ? conformer ε conformer transition state

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ENERGETICS AND GEOMETRIC SPECULATION THEREIN The energetics of the compounds are displayed in Table 1.The β conformer is of lowest energy relative to the methodology used, but we adamantly make no statement as to what conformer is the minimum. The only methodology capable of being accurate to within 0.1 eV consistently, a priori, is probably CCSD(T) with an extrapolation of single-particle

kJ/mol

eV

0 16.4 17.1 10.6 23.1 23.3

0 0.17 0.18 0.11 0.24 0.24

a

All energies are reported to one decimal in kJ/mol and two in eV for the sake of qualitative comparison. We emphatically do not claim that this method is accurate to this many decimals in energy.

basis sets or explicitly using an R12 formalism.57 We had originally intended to perform CCSD(T)/cc-pVTZ calculations on these systems, but declined in the face of the above 12132

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evidence. Short of performing a basis extrapolation, no real insight would be gained about the reaction or conformer populations from just this calculation alone. We may say that the energy levels are near-degenerate, but it is wildly speculative to read into even the qualitative ordering as being correct when the energy levels are this close. Rather, we can see from the data that all of the minima may be reasonably populated at STP; the reaction mechanism might proceed from any of these starting points. In order to consider the kinetics accurately, one must consider the activation barriers from any of these starting points. Note that this point is in sharp disagreement with previous kinetic studies.23 Rather, given that the energies are not quantitative enough to compare against one another, we attempted to find a geometric, intuitive means to judge the conformers qualitatively. We would argue that there is always significant noise in the value of bond lengths to 0.001 Å; a clear trend might be seen easily if manifest in 0.01 Å. In Table 2, we list the bond lengths of

Table 3. Lowest Four Harmonic Vibrational Frequencies Calculated Using MBPT(2)/6-311G(d,p) in cm−1

conformer

β

ζ?

α?

γ

ε

transition

1.43 1.44 1.43 1.57 1.48 1.57

1.43 1.44 1.43 1.57 1.47 1.57

1.43 1.45 1.44 1.57 1.45 1.57

N/A 1.44, 1.43 1.45, 1.40 1.57 1.47 1.57

N/A 1.43 1.43 1.59 1.47 1.58

1.42 N/A 1.41 1.57 1.46 1.57

β

ζ?

α?

γ

ε

transition

v1 v2 v3 v4

48 55 59 68

48 57 59 61

48 54 56 61

49 54 57 64

46 52 59 61

41i 44 53 56

these normal modes show that all of these modes are various types of nitramine wags. Thus, the weakest bond is indeed the nitramine N−N bond. In particular, it is a nitramine wag on the cyclohexane nitramine. This implies that homolytic dissociation does not proceed from the cyclopentane nitramines and considerably reduces the number of possible reaction paths to consider. The zero-point energies are all 141 kcal/mol; the zero-point energies only vary among conformers by up to 0.6 kcal/mol. The complete list of harmonic vibrational frequencies and exact zero-point energies are available in the Supporting Information, as well as the enthalpies and entropies. We also compare the CL-20 N−N bond lengths to that of RDX. The average N−N length of RDX for the equatorial position is 1.41 Å;10 for CL-20, it is 1.44 Å. The CL-20 equatorial bond lengthens and therefore is weaker than in RDX. The average N−N length of RDX for the axial position is 1.44 Å;10 for CL-20, it is 1.42 Å. The CL-20 axial bond is shorter and therefore stronger than in RDX. We know that CL-20s rate constant in solution phase decomposition is 3.5 greater than RDX.16 Assuming the reactivity trend is qualitatively true in the gas phase (not unreasonable), something must account for this difference in reactivity. The putative mechanism considered in nitramine degredation is nitro group homolysis.1−10,12−23 If the CL-20 nitramine dissociation starts from the cyclohexane nitramines, we would infer that it is probably the equatorial nitramine bond that is breaking, given that equatorial is weaker than axial in CL-20.

Table 2. Bond Lengths of CL-20 Conformers N−N axial N−N equ. N−N penta C−C hexa C−N penta C−C bridge

conformer

various parts of the CL-20 molecule. We consider the C−C, C−N, and N−N lengths of various parts of the hexagons and pentagons in the bicyclic structure. If a given conformer did not have a certain type of nitramine, we denote this as N/A. The C−C bridge refers to the carbon atom atop the cyclopentanes, which joins together the rings. The table lists the conformers in order of increasing energy from left to right, for ease of examining a trend within the lengths. However, the data does not seem to show any clear trend. The two major qualities that distinguish the CL-20 conformers are the axial/equatorial combination and the cyclopentane nitramine orientation. We considered if equatorial is inherently more favorable in this caged structure than is axial, and vice versa. This also shows no clear trend in stability, as there are mostly axial/equatorial mixtures, rather than diequatorial or diaxial. The orientation of the nitramines does not, to our analysis, lend itself to an obvious trend. We thus infer that no simple geometric measure can give guidance on the energy minimum; given the small energy differences in the conformers (0.2 eV), this is not surprising.

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CONCLUSIONS The successful generation of the conformers of the CL-20 explosive through our combined molecular-mechanics Monte Carlo search combined with ab initio quantum mechanical refinement allows us to search among other nitramines for conformers with confidence. The five energetic minima of the CL-20 conformers have been classified in terms of the solidstate crystal structure where possible and so named. The energies of the conformers are such that any of them could reasonably be the minimum. On the basis of the harmonic vibrational frequencies, we can see that the weakest bond is the N−N nitramine on the cyclohexane, rather than the cyclopentane; on the basis of comparative bond lengths with other known nitramine explosives, we can see that it is the equatorial position that is the weakest, rather than the axial.

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IMPLICATIONS TOWARD REACTIVITY The harmonic vibrational frequencies of the CL-20 conformers lend credence to the idea that homolytic dissociation of the N− N bond in the nitramine is a major mechanism of decomposition. The harmonic vibrational frequencies are given in Table 3. We do not propose that the accuracy of the harmonic frequencies is within a wavenumber; the absolute values of MP2 frequencies are not very good compared to an IR spectrum.53 However, with an appropriate scaling factor, they do perform well.54 For our purposes, though, a qualitative insight into the mechanism is reliable from this methodology. We can see that the harmonic frequencies for all of the conformers are comparable and all quite small. Visualization of

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ASSOCIATED CONTENT

* Supporting Information S

Conformer data. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest. 12133

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

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