Aminoxyl (Nitroxyl) Radicals in the Early Decomposition of the

Article pubs.acs.org/JPCA

Aminoxyl (Nitroxyl) Radicals in the Early Decomposition of the Nitramine RDX Karl K. Irikura* Chemical Informatics Research Group, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, United States S Supporting Information *

ABSTRACT: The explosive nitramine RDX (1,3,5-trinitrohexahydro-s-triazine) is thought to decompose largely by homolytic N−N bond cleavage, among other possible initiation reactions. Density-functional theory (DFT) calculations indicate that the resulting secondary aminyl (R2N·) radical can abstract an oxygen atom from NO2 or from a neighboring nitramine molecule, producing an aminoxyl (R2NO·) radical. Persistent aminoxyl radicals have been detected in electron-spin resonance (ESR) experiments and are consistent with autocatalytic “red oils” reported in the experimental literature. When the O-atom donor is a nitramine, a nitrosamine is formed along with the aminoxyl radical. Reactions of aminoxyl radicals can lead readily to the “oxy-s-triazine” product (as the s-triazine N-oxide) observed mass-spectrometrically by Behrens and co-workers. In addition to forming aminoxyl radicals, the initial aminyl radical can catalyze loss of HONO from RDX.

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height (ΔH⧧) shown with each reaction are those calculated in the present study (ideal gas at T = 298.15 K and p = 1 bar). In the present study, a popular method of quantum chemistry is used to investigate secondary reactions that may occur early during the thermal decomposition of RDX. There have been many ab initio calculations of nitramine chemistry focusing upon unimolecular initiation and unimolecular decay of the initial products. However, bimolecular reactions are certainly important in the heated solid or the melt, which are of greater practical interest than the gas-phase or dilute solutions. Bimolecular reactions have received little theoretical attention since the pioneering work by Melius.16,17 Thus, they are emphasized in the present work. Moreover, pressures are elevated under many conditions of interest, such as shocks. Molecular volumes, including activation volumes, are estimated here to facilitate future consideration of pressure effects, which probably affect the reaction mechanism. Since loose transition states are expected to have larger volumes than tight transition states, the effects of temperature and pressure may oppose each other under violent conditions.1,8 The purpose here is to investigate the possibility that aminoxyl (R2NO·) radicals are important in the early stages of the decomposition of RDX. In the Results section, entry into aminoxyl chemistry and a pathway to “oxy-sym-triazine” (OST, m/z 97)6,18 are considered first, followed by major competing reactions: unimolecular decomposition and H-atom transfer. Direct and indirect experimental evidence for aminoxyl radicals is collected from the literature on RDX, then experimental reports of aminoxyl radicals in other nitramine systems. All assertions of new chemistry are based primarily upon the present calculations.

INTRODUCTION Nitramines are important high-energy materials. The most important is RDX, also commonly known as hexogen, cyclonite, or 1,3,5-trinitrohexahydro-s-triazine. Much has been learned from decades of experimental and theoretical studies; no review will be attempted here.1−3 Despite this effort, the detailed chemical mechanism of RDX decomposition is only partly known. As in any decomposition process, the chemistry is complicated and dynamical. Interplay between condensed-phase and gas-phase processes causes the product distribution, and presumably the dominant reaction pathways, to depend upon experimental conditions such as sample geometry, heating rate, pressure, temperature, and confinement.4−9 Experimental elucidation of reaction mechanisms, or even identification of the initial reaction products, is hindered by the great speed of subsequent reactions. Usually it is only the final decomposition products that are identified clearly. Many reactions have been suggested as the initial step(s) in the decomposition of RDX.10 Among the possibilities, reaction 1,

homolytic N−N bond cleavage,11 has no barrier in excess of its endothermicity.12 This is the initiation step indicated by thin-film laser-pyrolysis studies13,14 and is believed to predominate for nitramines generally.3,15 The alternative reaction 2, 1,2-elimination

Received: October 16, 2012 Revised: January 29, 2013

of HONO, has a similar enthalpic barrier12 but is less favorable entropically. The values for enthalpy change (ΔH) and barrier This article not subject to U.S. Copyright. Published XXXX by the American Chemical Society

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dx.doi.org/10.1021/jp310247z | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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experimental values) is ⟨Edif⟩ = −21.7 kJ/mol, which represents the bias in the calculated atomization enthalpies. This bias is assumed to be similar for the reactants and products of a typical reaction (they have the same stoichiometry), so that it cancels out of the reaction enthalpy. Assuming a normal distribution of biases, the variance of the difference between two uncorrelated samples is equal to twice the variance of the distribution. Thus, the standard uncertainty for a reaction enthalpy may be estimated as σdif√2, where σdif is the standard deviation of the values of Edif about their mean. (This is a conservative estimate because the reactants and products usually have chemical similarities, meaning that their biases will be positively correlated.) The standard deviation may be evaluated as σdif2 = ⟨Edif2⟩ − ⟨Edif⟩2, where the rms (root-meansquare) difference is ⟨Edif2⟩1/2 = 27.7 kJ/mol. This gives σdif√2 = 24 kJ/mol as the estimated standard uncertainty for any B3LYP/ 6-31G(d) reaction enthalpy involving molecules composed only of the elements C, H, N, and O (at least one atom of each). This precision is adequate for some purposes but clearly inadequate for the computation of reaction rates or equilibria. Restricting the analysis to nitramines and related molecules would probably lead to smaller estimated uncertainties because it is a narrower classification,38 but the appropriate definition of “related molecules” is itself uncertain. Molecular Conformations. Many of the molecules considered here,39 including RDX itself,12,40−42 exist in multiple conformations. The energy differences between conformers can affect reaction rates.43 However, in the present study, the emphasis is on qualitative chemistry, not quantitative thermochemistry or kinetics. Moreover, conformational energy differences are generally small compared with the uncertainties discussed above. All results presented here correspond to the most stable conformer investigated for each molecule.

COMPUTATIONAL METHODS19 To augment chemical intuition, qualitative reactions were sought by using isopotential searching (IPS)20 on a potential energy surface defined by the semiempirical PM3 method,21 denoted as IPS//PM3. PM3 was used for its efficiency; ab initio IPS is tediously slow.22 IPS performs best for unimolecular reactions with loose transition states; tight transition states occupy only small volumes in coordinate space and consequently are less probably encountered during a search. This is analogous to the “rare event” problem in molecular dynamics simulations. The Gaussian 98,23 GAMESS,24,25 and PC-GAMESS26 software packages were used at various times for the PM3 calculations. Interesting results from the IPS//PM3 explorations were always verified or refuted by using more reliable calculations. IPS trajectories were analyzed both visually and by using an automated procedure that produces preliminary minimumenergy and saddle-point structures. Subsequently, gas-phase properties were computed using density functional theory (DFT) with the hybrid functional B3LYP27−29 and the 631G(d) basis sets (Cartesian polarization functions, “6D”). The Gaussian 9823 and Gaussian 0330 program packages were used for the DFT calculations, but all results reported here were obtained using Gaussian 03, for consistency. All structures were fully optimized and characterized by vibrational analysis as either energy minima or first-order saddle points. When the vibrational mode associated with the imaginary frequency was ambiguous, the reactants and products corresponding to transition structures were verified by intrinsic reaction coordinate32 (IRC) calculations. Vibrational zero-point energies (ZPEs) were computed as one-half the sum of the harmonic frequencies and then multiplied by 0.9757; the ZPEs have relative standard uncertainties of about 2%.33,34 Thermodynamic functions were computed by using the rigid rotor/harmonic oscillator approximation and unscaled frequencies. There are some very low vibrational frequencies, which are probably anharmonic. The entropy and heat capacity are less reliable in such cases. For atoms, partition functions are based upon experimental energy levels.31 For computing bond dissociation energies, calculations on polyradicals were usually done with high spin to discourage isomerization. Molecular volumes were computed at the 0.001 a0−3 density contour using the “tight” option for Monte Carlo integration, without any vibrational corrections. These volumes are only approximate, both because of arbitrariness and error in the calculations and because effective volumes depend upon the solvating environment, sometimes dramatically.35,36 The atomic unit of energy, the hartree, is Eh ≈ 2625.5 kJ/mol. The symbol Ee denotes an electronic energy that does not include ZPE. The symbol E0 denotes an electronic energy to which ZPE has been added. All energy differences reported here, including barrier heights, include ZPE. When not otherwise stated, all reaction energies (including barrier heights) are ideal-gas enthalpy changes at the temperature 298.15 K. High-spin configurations are noted with appropriate left superscripts, e.g. 3 29 emphasizes that structure 29 is a spin triplet. Low-spin biradicals, such as transition states involving two radicals, were computed as spin-unrestricted singlets. Uncertainties. To estimate the uncertainty associated with the B3LYP/6-31G(d) reaction enthalpies, consider the results for atomization enthalpies. Data (at 298 K) for 38 CHNO molecules were taken from the Computational Chemistry Comparison and Benchmark Database37 (accessed 9/14/2011). The mean value of Edif (difference between theoretical and

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RESULTS Initiation is assumed to occur by reaction 1, which produces NO2 and a nitrogen-centered aminyl radical, here designated RDR.3,14,15,44 (However, reaction 2 dominates at kilobar pressures.7) The present computations yield ΔH = 156 kJ/mol, which is close to other literature values using similar theoretical methods.12,40,45,46 However, higher-level calculations predict a stronger N−N bond, requiring about 176 kJ/mol for dissociation.39 This is a reminder that the present calculations are of modest quantitative reliability; they were selected for their good computational efficiency. Molecular data needed for computing reaction energetics are collected in Table 1. Reaction energetics are collected in Table 2. Entry into Aminoxyl Chemistry. The RDR radical becomes an aminoxyl radical, denoted here as RDRO, if it abstracts an oxygen atom from a neighboring molecule. Early in decomposition, the most abundant neighbor is probably RDX, suggesting the O-atom transfer reaction 3. (In the equations, the number above the arrow is the barrier height, ΔH⧧, the number below the arrow is the enthalpy change, ΔH, and both values are in kJ/mol.) The calculated barrier is ΔH⧧ = 102 kJ/mol. This is lower than that for initiation by reaction 1, making it energetically reasonable. Moreover, the reaction is predicted to be exothermic, ΔH = −54 kJ/mol, which will help to drive further reactions. An alternative to direct O-atom transfer is formation of an intermediate RDR_RDX adduct, followed by dissociation to RDRO and a nitrosamine. The first step, reaction 4, is endothermic by 66 kJ/mol with a barrier of 92 kJ/mol. The second step, reaction 5, is exothermic by 120 kJ/mol and has a computed barrier of −2 kJ/mol (the small negative value arises from ZPE differences and may be considered as zero). Thus, B



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Table 1. Energy, Enthalpy Content, Entropy, and Volume for Molecules and Transition Structures molecule RDX RDR RDRO ONDNTA RDR_RDX RDRONO RDROH RDRH RDX-H RDXH (RDR)2NO OSTN OSTC OSTK H atom O atom (3P)b N2 NO NO2 HONO NO3 HONO2 N2O OH H2O H2CN HCN MN (methylenenitramine) 26 3 29 34 36 38 41 42 50 52 53 54 57 59 62 75 106 109 110 122 125 126 131 TS(2) a

Δ298 S298 ° V 0 H° E0 (hartree)a (kJ/mol) (J/(mol K)) (10−30 m3) −897.269316 −692.148119 −767.345138 −822.092583 −1589.392037 −897.247157 −767.958241 −692.797867 −896.635078 −897.823155 −1514.246211 −355.452147 −355.532519 −355.533829 −0.500273 −75.060623 −109.518668 −129.883730 −205.063596 −205.675392 −280.206486 −280.852736 −184.649325 −75.715352 −76.388303 −93.957669 −93.406552 −299.065301

35.4 29.9 31.3 33.7 65.0 36.9 31.7 28.5 37.2 37.8 60.4 15.3 15.4 15.8 6.2 6.7 8.7 8.7 10.2 10.9 13.2 11.7 9.5 8.7 9.9 10.2 9.1 14.9

478.1 438.3 447.5 462.0 735.9 489.5 439.1 419.9 500.8 501.4 682.5 297.7 304.5 308.1 114.7 161.1 191.7 211.2 240.2 248.0 266.4 266.1 219.8 184.2 189.0 224.1 201.4 303.5

207 168 195 185 377 212 183 196 195 207 357 115 102 104 15 18 39 31 48 49 57 54 47 24 23 44 40. 72

−692.158701 −562.223869 −561.686129 −356.019242 −486.492362 −767.287193 −766.753328 −486.493797 −692.128586 −692.166962 −767.316870 −393.036021 −691.607246 −561.095291 −767.291647 −280.833194 −616.430658 −692.156365 −410.762244 −280.847659 −486.454203 −767.310102 −897.206618

31.4 25.7 24.0 17.0 24.1 37.6 30.7 22.4 33.9 29.4 33.0 21.2 28.4 23.7 35.1 14.9 26.4 29.8 19.4 15.4 26.8 33.7 36.1

447.5 402.8 386.0 323.7 385.0 511.6 438.4 370.3 485.0 430.8 455.6 365.0 421.2 378.0 488.4 297.4 400.9 431.6 337.7 304.0 417.9 463.3 481.1

172 148 142 104 145 190. 182 143 188 166 173 121 178 137 191 95 165 165 134 93 150 168 222

Δ298 S298 ° V 0 H° E0 (hartree)a (kJ/mol) (J/(mol K)) (10−30 m3)

molecule TS(3) TS(4) TS(5) TS(6) TS(7) TS(8) TS(9) TS(10) TS(12) TS(15) TS(16) TS(17) TS(18) TS(19) TS(RDRO + NO2 = 42 + HONO) TS(RDROH = 59 + H2O) TS(20) TS(21) TS(22) TS(23) TS(24) TS(25) TS(26) TS(27) TS(28) TS(29) TS(31) TS(32) TS(33) TS(35) TS(36) TS(37) TS(38) TS(40) TS(41) TS(42) TS(43) TS(44) TS(45) TS(46) TS(48) TS(49) TS(52 = 57 + MN) TS(57 = MN + H2CN) TS(H2CN = HCN + H) TS(RDRO + NO2 = 42 + HONO) TS(RDXH = RDX + H)

−1589.378285 −1589.382393 −1589.392427 −1027.108254 −1027.106841 −951.941840 −1514.227221 −1644.113158 −1102.256449 −897.175727 −692.091024 −1534.680461 −1459.492517 −1459.487762 −972.400330

64.0 64.7 64.0 44.4 41.7 41.0 61.4 68.7 46.4 36.7 27.1 63.0 61.2 61.4 41.0

709.1 737.3 729.7 559.8 533.1 525.5 695.1 751.7 569.9 488.6 414.9 719.5 711.2 707.3 534.2

358 350. 390. 236 214 228 360 392 245 211 180. 384 349 352 228

−767.867068

32.6

449.7

182

−766.741550 −766.709468 −766.729865 −561.064026 −561.075640 −561.054898 −692.106093 −692.086503 −692.095103 −692.098876 −692.150826 −486.444252 −486.447072 −486.478258 −280.759190 −767.279648 −767.286827 −767.284607 −767.298681 −767.258398 −897.825208 −897.209143 −1589.405789 −1589.389515 −897.809693 −1384.267608 −692.091315 −393.015948

31.6 32.5 34.5 24.1 26.4 24.6 30.2 29.0 28.1 28.1 30.7 22.9 20.6 23.5 14.9 32.8 35.2 32.5 29.4 31.2 39.6 39.5 65.4 66.0 37.6 59.0 34.1 21.1

446.8 453.6 483.5 376.5 415.9 387.3 438.8 429.2 421.1 419.0 443.3 376.8 354.1 383.9 301.5 464.4 478.5 454.9 430.7 445.5 530.4 530.2 735.9 745.1 503.1 685.6 481.1 359.3

195 192 182 148 157 154 177 186 171 183 161 154 134 147 102 198 200 183 171 178 235 224 369 373 221 342 191 113

−93.901644

11.0

236.9

49

−972.400330

41.0

534.2

228

−897.763409

37.7

498.2

210.

1 hartree ≈ 2625.5 kJ/mol. bPartition function computed using experimental energy levels from ref 31.

the RDR_RDX adduct, although not stable as a proper intermediate, is a slightly easier pathway for O-atom transfer. The nitrosamine coproduct of reactions 3 and 5, labeled here ONDNTA (other labels in the literature are MNX and MRDX), has been observed as a major product of RDX thermolysis.1,6,47−49

The most-suggested mechanism for its formation is by recombination of RDR with NO, which is another product of decomposition.6 This reaction is exothermic by 164 kJ/mol. Another possible mechanism is displacement of NO2 by NO in RDX, reaction 6.48 The enthalpic barrier for this reaction is C



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Table 2. Molar Reaction Enthalpies (kJ/mol), Entropies (J/(mol K)), Volumes (cm3/mol), Activation Enthalpies, Activation Entropies, and Activation Volumesa ΔH298

ΔS298

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 RDRO + NO2 → 42 + HONO RDRO + NO3 → 42 + HONO2 RDRO + OH → 42 + H2O RDROH → 59 + H2O 20 21 22 23 24

156 −31 −54 66 −120 −8 −8 0 −18 0 −96 60 60 51 −91 −50 −56 −191 −154 −52

200. 191 −7 −181 174 13 13 0 −218 0 −189 11 11 169 180 −8 −17 −26 −27 −1

−145

−9

−9.5

unk

−212

−4

−8.2

unk

−91 13 −42 −55 36 −118

171 188 188 0. 186 −18

10.9 3.5 2.5 −1.0 7.2 9.2

240 32 117 52 58 18

a

ΔV

ΔH⧧298

reaction

ΔS⧧298

ΔV⧧

reaction

3.9 NB 12.3 165 3 9.3 3.2 102 −207 −9.4 1.7 92 −179 −14.4 1.5 −2 −6 7.7 −4.5 118 −129 −1.0 −4.5 119 −156 −14.2 0 89 −148 7.4 3.0 33 −205 4.6 0 190 −172 22.1 −0.8 unk. 3.1 202 −148 −4.5 3.1 two-step (ref 59) 8.5 NB 9.2 187 −1 −0.3 −1.0 147 −23 7.5 −14.6 26 −175 −3.4 −0.8 2 −175 −7.9 9.3 15 −179 −6.5 −5.4 22 −154 −7.4

11 8 15 −143 10 −148

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 52 → 57 + MN 57 → MN + H2CN MN → NO2 + H2CN H2CN → HCN + H RDX + H → RDXH

−0.8 7.4 5.8 −3.5 6.5 4.7

ΔH298

ΔS298

ΔV

ΔH⧧298

ΔS⧧298

ΔV⧧

−82 55 −22 −42 −26 37 −26 108 5 43 −41 −38 144 158 156 −39 94 76 −102 −187 −40 −33 45 2 −289 74 38 121 139 −144

168 47 −7 −1 9 138 171 48 15 137 160 7 41 64 196 187 16 8 −26 −9 4 6 145 185 −36 183 163 161 92 −91

16.4 12.0 −1.7 4.0 2.4 10.5 12.0 4.8 1.4 8.0 −0.5 −1.0 −2.2 −3.1 −0.7 −2.0 −16.1 −13.2 14.8 8.4 9.7 6.3 1.4 6.0 23.1 3.5 −3.1 10.3 7.1 −9.2

107 111 161 137 128 N.B. 20 131 121 NB 36 194 173 157 NB 160 120 228 −6 6 31 74 NB 35 75 98 53 NB 148 12

9 1 −9 −17 −19

10.3 5.4 10.8 2.1 9.1

−4 6 −16

−6.5 7.1 −5.0

−1 4 17 31

1.4 3.9 2.0 3.4

7 −17 −2 −156 −148 −181 −171

−7.0 −14.4 −10.1 11.2 6.6 −3.2 −0.6

2 −191 −4 −6

8.6 4.2 1.8 −4.7

13 −95

3.0 −7.5

NB indicates that no barrier was found higher than all educts; unk indicates that no transition structure calculations were done.

ΔH⧧ = 118 kJ/mol and the enthalpy change is ΔH = −8 kJ/mol. The formally equivalent reaction 7, O-atom abstraction from RDX by NO, has an equal barrier height, 119 kJ/mol. Seemingly in contradiction to the chemistry proposed here, isotope crossover experiments show complete N−NO bond scrambling, suggesting that ONDNTA does not arise from O-atom abstraction.18 However, isotopic scrambling in ONDNTA may be subsequent to its formation.50 Three possible scrambling mechanisms are degenerate NO displacement [reaction 8], reversible formation of bis(RDR)aminoxyl radical [reaction 9], and symmetric NO exchange as proposed by Suryanarayanan and Bulusu51 for dimethylnitrosamine [reaction 10]. If NO-exchange reactions are significant, then observing isotopic crossover provides no information about the mechanism for ONDNTA formation. Another likely neighbor is NO2, the coproduct of the initiation reaction.52 Recombination of RDR and NO2 can lead back to RDX or to an N-nitrite, reaction 11.16,53 This reaction

is exothermic, ΔH = −96 kJ/mol. As a radical recombination process, it is not expected to have any significant kinetic barrier. Bimolecular formation of the nitrite (RDRONO) from RDX through displacement of NO2 by another molecule of ONO, reaction 12, is also conceivable, ΔH = 60 kJ/mol, but the

barrier (202 kJ/mol) is too high for this to be an important route to RDRONO. Unimolecular nitro-nitrite isomerization, reaction 13, has been proposed for other nitramines,10,54−57

D



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although with some disagreement.58 In the present study, I was unable to find a corresponding spin-unrestricted transition structure. This is consistent with the conclusion by Soto et al. that the nitro-nitrite isomerization of the parent compound, NH2NO2, proceeds by dissociation followed by recombination.59 Thus, isomerization probably cannot compete with dissociation in the absence of cage effects.16 Dissociation of RDRONO to RDRO and NO,53,60,61 reaction 14, requires only

also can abstract hydrogen from RDRO exothermically to form 42, including NO2 (ΔH = −52 kJ/mol, barrier of 22 kJ/mol), NO3 (−157 kJ/mol), and OH (−212 kJ/mol). The hydroxylamine product of reaction 17 is relatively stable. For example, dehydration of RDROH is exothermic by 91 kJ/mol but has a high barrier of 240 kJ/mol. In contrast, the nitrone 42 has an exceptionally weak N−NO2 bond; the dissociation reaction 20 is

ΔH = 51 kJ/mol and has no additional barrier. The competing loss of HONO from RDRONO, reaction 15, has ΔH = −91 kJ/mol

but ΔH⧧ = 187 kJ/mol. The net enthalpy change for O-transfer from NO2 to RDR is therefore −45 kJ/mol. As a point of reference, the computed aminoxyl N−O bond dissociation enthalpy in RDRO is 363 kJ/mol. Thus, many oxygen donors can be considered. For example, oxidation of RDR to RDRO by NO3,62,63 HNO3, and N2O is exothermic by 144, 51, and 174 kJ/mol, respectively. In addition to bimolecular sources of aminoxyl radicals, intramolecular O-atom transfer, reaction 16, is exothermic by

endothermic by only 13 kJ/mol, with a barrier of 32 kJ/mol. (In contrast, 3,4-loss of HONO, reaction 21, is exothermic by

50 kJ/mol and has a barrier of 147 kJ/mol. The product, 53, probably has reactivity similar to that of RDRO, discussed below. Pathways to OST. Besides ONDNTA, Behrens and Bulusu detected another large-molecule product at m/z 97, corresponding to C3H3N3O and labeled oxy-sym-triazine, or OST.6,18 Three plausible structures have been suggested,6,64 all based upon 1,3,5-triazine: the N-oxide (OSTN), the 2-hydroxide (OSTC), and the keto tautomer of the 2-hydroxide (OSTK). The last two of these isomers are of nearly equal stability, while the N-oxide is about 212 kJ/mol less stable (H298). Only routes to OSTN were investigated during the present study. 42 kJ/mol but has a higher barrier of 117 kJ/mol.) The weakness of the N−NO2 bond may be attributed to resonance stabilization of radical 34; its spin density indicates that the forms shown in Scheme 1 are important. Like RDRO, 34, is susceptible to H-atom Scheme 1. Important Resonance Forms of Radical 34, As Indicated by Its Spin Density

In general, disproportionation is facile for aminoxyl radicals with alpha C−H bonds, producing a hydroxylamine and a nitrone.65 In the case of RDRO, reaction 1753 is exothermic by

abstraction. For example, reaction 22 is exothermic by 55 kJ/mol and has a barrier of only 52 kJ/mol. The conjugated nitrone 62 also can lose NO2 easily, reaction 23; ΔH = 36 kJ/mol and the barrier is 58 kJ/mol. The product radical, 36, has a weak C−H bond (180 kJ/mol) and can be converted to OSTN by any H-atom scavenger. For example, reaction 24 is exothermic by 118 kJ/mol and has a barrier of only 18 kJ/mol. Alternatively, 62 can lose HONO in one step, reaction 25; this is exothermic by 82 kJ/mol, has a barrier of 107 kJ/mol, and also results in OSTN.

56 kJ/mol and has a barrier of only 26 kJ/mol. RDRO may react analogously with RDR, reactions 18 and 19, which are

exothermic by 191 and 154 kJ/mol, respectively. The corresponding barriers are 2 and 15 kJ/mol. Other radicals E



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Competing Unimolecular Reactions. Experimentally, different products are found from neat RDX and from RDX in dilute solution,15 presumably because dilution suppresses bimolecular reactions (because of their quadratic dependence upon concentration). Similarly, laser thermolysis (IRMPD) produces OH radicals from isolated RDX molecules but not from RDX clusters.66 Unimolecular reactions of RDR compete with bimolecular processes such as those discussed above and can prevent the formation of RDRO. Schroeder considered beta-cleavage of the ring and unzipping to methylenenitramine (H2CNNO2), and 1,2-migration of an H atom from carbon to nitrogen.1 For the ring-opening reaction 26, Chakraborty et al.

without additional barrier), but loss of HONO is again marginally more favorable (ΔH = −41 kJ/mol, barrier = 36 kJ/mol), as shown in reaction 35. In 106, the CH bond dissociation enthalpy is only 89 kJ/mol, so s-triazine, a major product in some experiments,49 results readily from H-atom abstraction. H-atom 1,2-migration, to give a carbon-centered radical, is exothermic by 38 kJ/mol but has a barrier of 194 kJ/mol. Unimolecular reactions of RDRO could compete with the OST formation mechanism described above. However, none of the obvious reactions has a particularly small barrier. The ring-opening reactions, 37 and 38, are endothermic by 144 and

computed a barrier of 110 kJ/mol.12 The present calculations, using essentially the same methods, yield 111 kJ/mol (with ΔH = 55 kJ/mol; thus, the reverse barrier is 55 kJ/mol). The H atom migration, reaction 27, is exothermic by 22 kJ/mol with a barrier of 161 kJ/mol. The analogous 1,4-migration, reaction 28, is exothermic by 42 kJ/mol and has a barrier of 137 kJ/mol. An alternative 1,4 H-atom migration is from carbon to oxygen, reaction 29. This is computed to have ΔH = −26 kJ/mol and a 158 kJ/mol, respectively, with corresponding barriers of 173 and 157 kJ/mol (the latter is lowered by ZPE effects). Reactions 39 and 40, which are analogous to the RDX initiation

reactions, have ΔH = 156 and −39 kJ/mol, respectively. Reaction 39 has no barrier beyond endothermicity, but reaction 40 has a barrier of 160 kJ/mol. The lowest unimolecular barrier found here is 120 kJ/mol for the 1,5 H-migration, reaction 41, which is endothermic by 94 kJ/mol. The 1,3 H-migration, reaction 42, is uncompetitive (ΔH = 76 kJ/mol, ΔH⧧ = 228 kJ/mol).

barrier of 128 kJ/mol. The resulting aci radical can lose OH, reaction 30 (ΔH = 37 kJ/mol with no additional barrier) or HONO, reaction 31 (ΔH = −26 kJ/mol, barrier = 20 kJ/mol). This can be followed by beta-cleavage to open the ring, reaction 32. Ring-opening is endothermic (ΔH = 108 kJ/mol) with a barrier of 131 kJ/mol. The ring-opened product appears poised to unzip to methylenenitramine (H2CNNO2), HCN, and H2CN16,67 radical. Alternatively, formation of a second aci radical by another 1,4-migration, reaction 33, is thermoneutral (ΔH = 5 kJ/mol) and has a barrier of 121 kJ/mol. This aci radical can also lose OH by reaction 34 (ΔH = 43 kJ/mol

Competing Bimolecular Reactions. The RDR radical can be trapped by H-atom sources, preventing the formation of RDRO. For example, reaction 43 with HONO is exothermic by 102 kJ/mol and has a barrier of −6 kJ/mol (negative because F



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(170 °C) solution of RDX in sulfolane (0.1 mol/L concentration).53 The lifetime of RDRO was about 30 min, after which it was replaced by a radical with a more complicated, unassigned spectrum. The more complicated spectrum was observed immediately in a 1 M solution. Since the NO coproduct was not observed, the authors suggested that it reacts with the solvent, preventing RDRO from being destroyed by the reverse of reaction 14.53 However, as pointed out by a reviewer, solutionphase NO would not be observed by ESR because of severe line-broadening.70−72 The nascent NO/aminoxyl radical pair was observed by Toscano after UV photolysis of crystalline RDX under cryogenic conditions.61 This radical pair was destroyed upon annealing to 45 K, presumably by radical recombination. In addition to the direct ESR evidence, there is qualitative, indirect evidence for the formation of aminoxyl radicals during the decomposition of RDX. Persistent aminoxyl radicals are typically red, yellow, or orange.65 For example, di-t-butylaminoxyl is a red liquid that is air-stable up to 120 °C,65 and the archetypal TEMPO radical, (2,2,6,6-tetramethylpiperidin-1-yl)oxyl, can be purified by vacuum sublimation to form dark red crystals that melt at 35 °C.65 Several studies of RDX decomposition have noted the formation of red, orange, or yellow liquids that accelerate decomposition when added to a fresh sample of RDX. In the earliest such report, Robertson observed that the residual solvent (molten TNT) “had a dark red colour and drops of a red liquid could also be seen.”73 Most recently, Maharrey and Behrens published photographs showing the spread of an orange−red, nonvolatile residue (“NVR”) across the surface of heated samples of RDX.48 In thermolysis of other cyclic nitramines, corresponding aminoxyl radicals have been detected by ESR.74 For dimethylnitramine (DMNA), the analog of reaction 3 has been reported in the gas phase.54,58 Reaction was initiated by infrared thermolysis54 or photolysis,58 and dimethylnitrosamine was observed as the major product. In a clever variation, a mixture of ordinary and isotopic d6-DMNA was subjected to infrared photolysis. Although the d6 isotopologue does not absorb the radiation and therefore does not dissociate, d6nitrosamine was formed in proportion to the concentration of d6-DMNA. This demonstrates that the nitrosamine product is formed by O-atom abstraction, not by recombination of an aminyl radical with NO.58 A later study showed that the aminyl radical can also abstract an oxygen atom from NO2, analogously to reactions 11 and 14.75 Formation of OST. The product known as oxy-sym-triazine (OST) has been detected only by mass spectrometry, which does not provide structural information.18,64 It has been suggested to form unimolecularly, by loss of HNO and two HONO molecules,12,18 or by reaction of OH with triazine (to give OSTC),76 although this is not competitive with H-atom abstraction.77 In their landmark isotopic study, Behrens and Bulusu concluded that OST is a product of strictly unimolecular chemistry.18 In constrast, the reactions presented here provide a bimolecular route. However, closer examination shows that only the oxygen atom originates in a different molecule of RDX. Thus, only the 18O labeling experiment (experiment no. 4 in ref 18) bears on the mechanism presented here. The 18O enrichment was only 3.7%, so the expected fraction of OST at m/z 99 is 4.5% in the limit of no scrambling and 3.6% in the limit of complete oxygen scrambling (see the Supporting Information for statistical analysis). The difference between these values is too small to be measured convincingly (the fraction observed mass spectrometrically was

of ZPE). Conversely, reaction 44, H-atom transfer from RDR to NO2, is exothermic by 187 kJ/mol with a barrier of 6 kJ/mol. Similarly, RDR can react with RDX by H-atom transfer in either direction. Transfer from RDX to RDR, reaction 45, yields a secondary amine and a carbon radical that is unstable to NO2 loss (93 kJ/mol exothermic). Reaction 45 is exothermic by 40 kJ/mol and has a barrier of only 31 kJ/mol. Conversely, H-atom transfer from RDR to RDX, reaction 46, yields an imine and an aci radical. This reaction is exothermic by 33 kJ/mol and has a barrier of 74 kJ/mol. The aci radical, RDXH, figures prominently in the autocatalytic H-atom cycle proposed by Melius.16 It can lose52 OH (ΔH = 45 kJ/mol, no additional barrier) to generate ONDNTA, reaction 47, or lose52 HONO by reaction 48 (ΔH = 2 kJ/mol, ΔH⧧ = 35 kJ/mol) to generate another molecule of RDR, thus providing a short-cut catalytic cycle without free H-atoms. Two RDR radicals in proximity may also disproportionate, reaction 49. This is exothermic by 289 kJ/mol and has a barrier of 75 kJ/mol.

Pressure vs Temperature. As mentioned in the Introduction, there is an expectation that loose transition structures will have large entropies and large volumes. Thus, a reaction with a loose transition structure is expected to be favored by high temperature and by low pressure. Explosions typically correspond to high temperature and high pressure, bringing the expected effects of temperature and pressure into opposition. However, the reaction data in Table 2 do not show any meaningful correlation between ΔS and ΔV (correlation coefficient = 0.29) or between ΔS⧧ and ΔV⧧ (correlation coefficient = 0.37). To the extent that the computational data are reliable, this indicates that pressure and temperature effects do not necessarily oppose each other, and that their convenient cancellation cannot be assumed.

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DISCUSSION Aminoxyl Radicals. The first reports of the formation of RDRO from RDX (by UV photolysis) were the ESR studies by Darnez and Paviot and by Bodnar and Rowell.68,69 In both reports, the structural assignment was supported by computer simulation of the spectrum. The suggested mechanism was isomerization to the N-nitrite followed by loss of NO, reaction 14.68 In a later, thermal study, RDRO was detected in warm G



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about 80 kJ/mol lower than the initiation barrier, so represents significant catalysis. It could also cause some confusion when reaction 2 is under investigation as a direct initiation step.

2.8%, which is lower than expected in any case). For example, the observation at m/z 97 is lower than expected by at least 1.7% and the observation at m/z 100 is higher by at least 6.0%. Greater 18O enrichment is needed to determine how much oxygen scrambling occurs. Autocatalysis. H-atom transfer to RDR (e.g., reaction 45) has substantially lower barriers than O-atom transfer (e.g., reaction 3). Since O-atom transfer apparently occurs, as discussed above, it is nearly certain that H-atom transfer occurs as well. Melius suggested a branching cycle carried by H atoms,16 shown in the upper part of Figure 1 with energetics computed in the

RDX → HONO + 2NO2 + 3HCN + 2H

(50)

Another role for aci radicals, such as RDXH, is as a source of OH radicals (e.g., reaction 47). Exothermic decomposition of RDX probably requires the formation of C−O bonds. Reactions of OH radicals are a route to carbon-centered radicals and to C−O bonds, as is known from studies of the combustion of common fuels.78

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CONCLUSIONS As inferred from the present results, aminoxyl radicals are formed in the thermolysis of RDX, by reaction of the initial aminyl radical with RDX or with NO2. The coproduct is either a nitrosamine (ONDNTA) or NO, both known products of RDX decomposition. Subsequent reactions are expected to form nitrones and other N−O bonded compounds, including the N-oxide isomer of OST, another prominent product identified by mass spectrometry. Aminoxyl radicals aside, H-atom transfer provides a catalytic route for net loss of HONO, reaction 2.

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ASSOCIATED CONTENT

S Supporting Information *

Statistical analysis of 18O-labeling experiment of ref 18, atomic coordinates, electronic energies, and values of ⟨S2⟩ for all minima and saddle points (46 pages). 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]. Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS Some of the results described herein were presented at the conferences “Emerging Methods in Computational Chemistry and Materials Science” (Aberdeen, MD, June 1, 2001) and “55th JANNAF Propulsion Meeting” (Newton, MA, May 13, 2008). Some of the computations were done on the “Biowulf” computer cluster at the National Institutes of Health, Bethesda, MD.

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REFERENCES

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Figure 1. Catalytic routes to RDX decomposition. (top) Branching cycle proposed by Melius.16 (bottom) Cycle proposed here.

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Aminoxyl (Nitroxyl) Radicals in the Early Decomposition of the

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