Bimolecular Reactions between Dimethylnitramine and Its Radical

Article pubs.acs.org/JPCA

Bimolecular Reactions between Dimethylnitramine and Its Radical Decomposition Products Igor V. Schweigert* and Sharon E. Koh-Fallet†,‡ Code 6189, Theoretical Chemistry Section, U.S. Naval Research Laboratory, Washington, D.C. 20375, United States S Supporting Information *

ABSTRACT: Bimolecular reactions between intact nitramines and their radical decomposition products can accelerate thermal decomposition, yet the detailed mechanisms of such reactions are not well understood. We have used density functional theory at the M06/6-311++G(3df,3pd) level to locate transition structures and compute 0 K activation barriers for various gas-phase reactions that may contribute to radical-assisted decomposition of dimethylnitramine (DMNA, (CH3)2NNO2). Our calculations indicate that H abstraction from DMNA is the lowest-barrier mechanism for most radicals and a subsequent N−N β-scission in the alkyl radical 3 leads to an imine intermediate and NO2. H abstraction is thus responsible for conversion of most radicals to NO2. Also, among the nine radicals considered, NO is found to be least reactive and its reactions with DMNA yield dimethylnitrosoamine (DMNSA, (CH3)2NNO), a known product of DMNA decomposition. Melius18 as one such reaction. This was the only bimolecular reaction included in his detailed mechanism,18 and it remained the only bimolecular reaction in the subsequent versions.30,31 Recently, Irikura19,20 took a first step toward systematic identification of other possible bimolecular reactions involving RDX. He found that H transfer between RDX and the aminyl radical product of the initial homolysis can lead to an early autocatalytic cycle,14 similar to the one proposed by Melius. He also found that bimolecular reactions can lead to aminoxyl radicals with nitrosoamines and NO as byproducts.14 In this work, we used density functional theory (DFT) to investigate bimolecular reactions between dimethylnitramine (DMNA) and its radical decomposition products. DMNA was selected as a simpler model of larger nitramines to facilitate calculations. In section 2, we describe our computational approach based on the M06/6-311++G(3df,3pd) level of DFT. In section 3, we first discuss unimolecular reactions that are responsible for radical production and decomposition of larger radicals. We then discuss bimolecular reactions between DMNA and nine radicals deemed to be important for radicalassisted decomposition of DMNA. When possible, we compare them to previously reported calculations on DMNA or other nitramines. In section 4, we summarize our findings and discuss what reactions can accelerate the rate of DMNA decomposition.

1. INTRODUCTION Energetic molecular solids can rapidly transition from slow thermal decomposition to rapid, self-sustained reactions that lead to thermal runaway and explosion (“cook off”).1,2 Because the initial decomposition reactions are endothermic, the internal energy release and increased violence of reaction are delayed until the onset of secondary, exothermic reactions. Secondary reactions are thus of paramount importance to the safety of energetic compounds, yet their mechanisms are not well understood. Experimental measurements of thermal decomposition of nitramines,3−16 including dimethylnitramine (DMNA), hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX), and octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX), have provided evidence of multiple, competing reactions. The observed rate increase with the extent of decomposition10,17 or due to extraneous NO2,12 as well as accelerating effects of sample confinement7−9 indicate that reactions between the intact material and its decomposition products can lead to acceleration of decomposition and possible autocatalytic effects. However, theoretical calculations have so far (with a few notable exceptions18−20) focused on unimolecular reactions responsible for the initial bond breaking18,21−27 and unimolecular reactions in the resulting fragments.18,24,28 As a result, the available detailed mechanisms29−31 do not explain some of the observed intermediates of condensed-phase decomposition.24 Bimolecular reactions between intact nitramines and their radical decomposition products are likely candidates for secondary reactions that can accelerate decomposition. Radical addition of H atoms to unreacted RDX was suggested by © XXXX American Chemical Society

Received: October 25, 2016 Revised: January 31, 2017 Published: February 1, 2017 A

DOI: 10.1021/acs.jpca.6b10773 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

2. COMPUTATIONAL METHODS All calculations reported here were performed with the M06 meta-hybrid functional32 combined with the 6-311++G(3df,3pd) set33,34 of atom-centered Gaussian-type orbitals, as implemented in Gaussian09.35 All open-shell diradical species were calculated in their spin-singlet state using the unrestricted Kohn−Sham equations. Unless noted otherwise, each structure was optimized without constraints until the maximum (rootmean-square) force was below 15 × 10−6 (10 × 10−6) Hartree/ Bohr or Hartree/radian and the maximum (root-mean-square) displacement was below 60 × 10−6 (40 × 10−6) Bohr or radian. Pruned grids with 99 radial shells around each atom and 590 angular points in each shell were used in these calculations. Each structure was confirmed as a local minimum or a firstorder saddle point using the eigenvalues of analytically computed Hessian matrices. Each saddle point was further confirmed as a transition structure using a Hessian-based predictor-corrector implementation36 of the intrinsic reaction coordinate (IRC) method. 37 In some cases, the IRC calculations revealed reactants and products different from those envisioned from just visualizing the imaginary-frequency normal mode. In each such case, the reaction mechanism was assigned on the basis of the IRC calculations. In some cases, IRC calculations led to weakly bound complexes, on either the reaction or product side. Unless noted otherwise, the energies of the prereaction or product complexes were found to be within a few kJ/mol of the combined energies of the corresponding fully separated reactants or products. Vibrational zero-point energies (ZPEs) for species and transition structures were computed using unscaled frequencies. Electronic energies and ZPEs were used to compute the 0 K activation energies and reaction enthalpies reported below.

Scheme 1. Unimolecular Decomposition Reactions of DMNA

transition structure of H abstraction by one of oxygens of NO2 (1−5), also with a 0 K barrier a few kJ/mol above the asymptote. The subsequent IRC calculations showed that the first transition structure leads to a complex of 2 and HNO2 and the second one leads to a complex of 2 and HONO. Other unimolecular reactions such as nucleophilic O insertion into a C−N bond and concerted scission of multiple C−N bonds have been previously considered for cyclic nitramines (see ref 28 and references therein). In DMNA, the nucleophilic O insertion into a C−N bond (not shown) has a 0 K barrier of 285 kJ/mol and leads to a high-energy N-oxide educt that requires an additional barrier to dissociate. We also found a transition structure for H insertion in DMNA (not shown) with a 0 K barrier of 303 kJ/mol that leads to a relatively stable isomer of DMNA, H3CNHCH2ONO. Given the high barriers, neither of the two insertion reactions is expected to have a significant contribution to unimolecular decomposition of DMNA. We also considered homolytic fissions of C−N, C−H, and N−O bonds but found that the corresponding barriers exceed 350 kJ/mol. These reactions and their products were not considered further. Unimolecular Reactions of Various Radicals Relevant to DMNA Decomposition (Scheme 2). The dimethylamino radical 1 is formed in N−N homolysis in DMNA (1−1). Aminyl radicals are known to undergo facile β-scissions of either C−N or C−H bonds as well as H shifts leading to their alkyl isomers.44 We found a transition structure for C−H βscission in 1 (2−1, 162 kJ/mol) that leads to 2 and a free H radical. We also found a transition structure to H shift (2−2, 167 kJ/mol) that leads to an alkyl radical (1′). It should be noted that the H shift proceeds via a tight three-atom transition structure and therefore is expected to be entropically unfavorable. The alkyl radical 1′ can undergo a facile C−N β-scission (2−3, 127 kJ/mol), leading to methanimine and

3. RESULTS Unimolecular Reactions of DMNA (Scheme 1). Due to weak N−N bonds and the nucleophilicity of nitro oxygens, several unimolecular reactions are energetically accessible in nitramines.23,25,26,31,38 Homolytic fission of N−N bonds is generally considered to be the dominant decomposition pathway, whereas concerted elimination of nitrous acid (HONO) has a comparable 0 K barrier but much lower activation entropy. For DMNA, the present level of theory predicts that the 0 K barrier to N−N fission (1−1, 198 kJ/mol) is slightly lower than that to HONO elimination (1−2, 201 kJ/ mol). Further details are provided in the Supporting Information. Possible unimolecular routes to nitro-nitrite rearrangement in DMNA have previously been considered, but the 0 K barriers for tight and loose transition structures were reported to be much higher than that to N−N homolysis.23,39 In contrast to these results, we found a roaming-radical reaction pathway (1−3) with a 0 K barrier slightly below the N−N fission asymptote. This reaction is mediated by a radical−radical complex that connects DMNA to the cis conformer of the nitrite isomer (dimethylaminonitrite, DMAN). Further details are provided in the Supporting Information. The possibility of H abstraction by a roaming NO2 radical has not been discussed for DMNA, but similar reactions have been reported for hydrocarbons.40−43 We found a loose transition structure describing a H atom abstraction from 1 by the nitrogen of NO2 (1−4) with a 0 K barrier a few kJ/mol above the N−N fission asymptote. We also found a loose B


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The Journal of Physical Chemistry A Scheme 2. Unimolecular Reactions of Various Radicals Relevant to DMNA Decomposition

CH3, and N−H β-scission in 1′ (2−4, 168 kJ/mol), leading to 2 and H. The alkyl radical 3 can be formed in radical H abstraction from DMNA as discussed below. 3 is thermally unstable and can undergo facile N−N β-scission (2−5, 35 kJ/mol). We also found a transition structure to C−N β-scission (not shown) with a much higher 0 K barrier of 165 kJ/mol. The difference between the barriers is consistent with N−N β-scissions being energetically favorable over C−N β-scissions in the alkyl radical products of N−N homolysis in RDX.28 A radical adduct of DMNA and H (4) can be formed in radical addition of H to DMNA and in a nucleophilic attack of the nitro oxygens of DMNA on a methyl group of another DMNA (not shown). 4 can undergo both O−H β-scission (2− 6, 24 kJ/mol), yielding DMNSA and OH, and N−N β-scission (2−7, 49 kJ/mol), yielding 1 and HONO. The dimethylaminoxyl radical 5 can be formed in O−N fission in DMAN. 5 can undergo N−C β-scission (2−8, 198 kJ/mol), with H3CNO and CH3 as the products, and H shift from a methyl group to O (2−9, 237 kJ/mol), with 2 and OH as the products. The methylaminomethoxy radical 6 can be formed in radical addition of 1′ to DMNA. 6 can undergo C−H β-scission (2− 10, 40 kJ/mol), leading to N-methylformamide (NMF) and H radical, and C−N β-scission (2−11, 54 kJ/mol), leading to H3CNH and H2CO. The methoxy radical (CH3O) can be formed in radical addition of CH3 to the nitro oxygens of DMNA. Previous theoretical and experimental studies45,46 have shown that unimolecular C−H β-scission (2−12, 104 kJ/mol), yielding

H2CO and H, is both energetically and entropically favorable to H shift. Unimolecular Reactions of Various Molecular Intermediates of DMNA Decomposition (Scheme 3). NMethylmethanimine (2) can be formed in the concerted elimination of HONO from DMNA (1−2) and unimolecular C−H β-scission of radicals 1 and 1′ (2−1 and 2−4), as well as H abstraction from DMNA by most radicals (via 3, see below). We found transition structures for H shift (3−1, 273 kJ/mol), yielding aziridine, and homolytic fission of the C−N single bond (3−2, 289 kJ/mol), yielding H2CN and CH3. Both reactions have 0 K barriers well exceeding the barrier to the initial homolysis in DMNA; thus 2 is thermally more stable than DMNA. We note that although the cyclization (3−1) has a lower barrier than the C−N fission (3−2), it proceeds via a tight three-atom transition structure and is expected to be entropically unfavorable. Nitrous acid (HONO) is formed in the concerted elimination of HONO from DMNA (1−2), in a roamingradical reaction in DMNA (1−5), and in H abstraction from DMNA by NO2 (see below). Isonitrous acid (HNO2) is also formed in H abstraction reactions by NO2. Unimolecular reactions of HONO and HNO2 have recently been reviewed.47 The dominant unimolecular decomposition channel for HONO is homolytic fission of the N−O bond leading to OH and NO radicals (3−5, 216 kJ/mol), whereas O−H homolysis (not shown) has a substantially higher barrier. The dominant unimolecular reaction for HNO2 is H shift (3−6, 196 kJ/mol) leading to HONO, whereas H−N bond homolysis (not shown) has a much higher barrier.47 C


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The Journal of Physical Chemistry A Scheme 3. Unimolecular Reactions of Molecular Intermediates of DMNA Decomposition

Methanimine (H2CNH) is formed in unimolecular C−N βscission in 1′. We found that it is very thermally stable with two possible unimolecular decomposition pathways, N−H fission (3−5, 356 kJ/mol) and H2 elimination (3−6, 385 kJ/mol), having very high barriers. Dimethylaminonitrite (DMAN) is formed in the roamingradical isomerization of DMNA (1−3) and in a radical recombination between 1 and NO2 (not shown). Homolytic fission of Oa−Nn bond (3−7) in DMAN has a 0 K barrier of 48 kJ/mol. We have also found a transition structure for HONO elimination from DMAN (not shown), but its 0 K barrier is much higher, 176 kJ/mol. Dimethylnitrosoamine (DMNSA) can be formed in the N− O β-scission of radical adducts 4 (2−6), a NO2 displacement from DMNA by NO (see below), and in a radical recombination between 1 and NO (reverse of 3−8). DMNSA is a known product of DMNA decomposition and is expected to be thermally more stable than its parent nitramine. We found that the 0 K barrier to N−N bond fission in DMNSA (3−8, 201 kJ/mol) is comparable to that in DMNA, whereas the barrier to HNO elimination is higher (3− 9, 243 kJ/mol) and the barrier to C−N bond fission is much higher (not shown, 321 kJ/mol). We note that the differences in the 0 K barriers to N−N fission in DMNSA and DMNA,

estimated at the present level of theory to be about 3 kJ/mol, do not explain the thermal stability of DMNSA compared to DMNA. Dimethylnitramine (DMA) can be formed in H abstractions from DMNA by 1, NO2 displacements by H, and radical recombinations of 1 with H. By analogy with propane (C3H8), DMA is expected to have considerable barriers toward unimolecular decomposition. We found that all three possible unimolecular reactions of DMA have exceedingly large barriers: N−C bond fission (3−10, 328 kJ/mol), concerted elimination of H2 (13−11, 369 kJ/mol), and N−H bond fission (13−12, 375 kJ/mol). Dimethylhydroxylamine (DMHA) can be formed in a NO2 displacement in DMNA by OH (see below) and by a radical recombination of 1 and OH (not shown). Unlike other Nsubstituted dimethylamines, DMHA undergoes facile H2O elimination (3−13, 226 kJ/mol), which is energetically favored over N−O bond fission (3−14, 237 kJ/mol) and C−N bond fission (not shown, 278 kJ/mol). Trimethylamine (TMA) can be formed in a NO2 displacement in DMNA by CH3 (see below) and by a radical recombination of 1 and CH3 (not shown). Similar to that in DMA, the barrier to C−N fission in TMA (3−15, 314 kJ/mol) is very high. D


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The Journal of Physical Chemistry A Bimolecular Reactions of DMNA with 1 (Scheme 4). The dimethylaminyl radical 1 is formed in the initial homolysis

Scheme 5. Bimolecular Reactions of DMNA with NO2

Scheme 4. Bimolecular Reactions of DMNA with 1

Scheme 6. Bimolecular Reactions of DMNA with H in DMNA (1−1). Irikura20 suggested that the aminyl radical product of N−N homolysis in RDX can readily react with unreacted RDX molecules. He reported transition structures for O abstraction by Na (eq 3 in ref 20), radical addition at a nitro O (eq 4 in ref 20), H abstraction by Na (eq 45 in ref 20), and nucleophilic abstraction (eq 46 in ref 20), with the H abstraction having the lowest barrier. For DMNA + 1, we found four transition structures: H abstraction by 1 from a methyl group of DMNA (4−1, 44 kJ/ mol), H abstraction by a nitro O of DMNA from a methyl group of 1 (4−2, 109 kJ/mol), NO2 displacement by 1 at the amino N of DMNA (4−3, 125 kJ/mol), and O transfer from the nitro group of DMNA to the amino N of 1 (4−4, 126 kJ/ mol). As discussed above, 3 and 4 can undergo facile β-scissions leading to, respectively, 2 + NO2 and DMNSA + OH. Reactions (4−1) and (4−3) thus convert 1 to NO2 and reactions (4−2) and (4−3) convert 1 to, respectively, OH and 5. We also note that although Irikura reported separate transition structures for O abstraction from and radical addition to a nitro O of RDX (eq 3 and 4 in ref 20), we found only one transition structure that leads to O abstraction (4−4) according to the IRC calculation. This was confirmed by attempting to optimize the radical adduct of DMNA and (CH3)2N and finding the Nn−O bond to be unstable. Bimolecular Reactions of DMNA with NO2 (Scheme 5). For RDX + NO2, Irikura reported two transition structures: O abstraction leading to the mononitroso analogue of RDX and NO3 (ref 19) and isoergic radical displacement of NO2 (eq 12 in ref 20). For DMNA + NO2, we found four transition structures: H atom abstraction (5−1, 81 kJ/mol), isoergic radical displacement of NO2 (5−2, 133 kJ/mol), O abstraction (5−3, 149 kJ/mol) leading to dimethylnitrosamine (DMNSA) and NO3, and radical displacement of NO2 leading to DMAN (5−4, 186 kJ/mol). We also found a transition structure to radical displacement of CH3 at Na, but the corresponding 0 K barrier is much higher than that to NO2 displacement. Bimolecular Reactions of DMNA with H (Scheme 6). H radicals can be formed in β-scissions of C−H bonds in aminyl radicals such as reaction (2−1) in 1. Melius estimated reactions of free H radicals with methylnitramine, both radical addition

and H abstraction, to proceed with barriers below 40 kJ/mol.18 For DMNA + H, we found three transition structures: H atom abstraction (6−1, 30 kJ/mol), radical addition at a nitro O (6− 2, 38 kJ/mol), and NO2 displacement (6−3, 40 kJ/mol). Radical addition is thus not the lowest-barrier reaction; however, all three reactions have similar 0 K barriers. Bimolecular Reactions of DMNA with OH (Scheme 7). OH radicals are formed in unimolecular N−O fissions in Scheme 7. Bimolecular Reactions of DMNA with OH

HONO, N−O β-scissions in the radical adduct 4, and possibly in reactions48 of H2O with NO2 and other radicals (not discussed here). Reactions of small nitramines and photolytically generated OH radicals are of interest to atmospheric chemistry, and Maguta et al.49 recently reported a detailed experimental and theoretical study of DMNA + OH. They showed that OH can abstract H from DMNA via a barrierless reaction mediated by a prereaction complex and transition structure whose 0 K energies are below the reactant asymptote. E


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The Journal of Physical Chemistry A At the present level of theory, we also found that DMNA and OH form a prereaction complex with the 0 K energy of 22 kJ/ mol below the reactant asymptote. H transfer from a methyl group of DMNA to OH has a 0 K barrier of only 4 kJ/mol and leads to a product complex that requires an additional 9 kJ/mol to dissociate to 3 and H2O (7−1). Additionally, we found a transition structure to NO2 displacement at Na (7−2, 74 kJ/ mol). Bimolecular Reactions of DMNA with NO (Scheme 8). NO radicals are formed in the unimolecular N−O fissions in

Scheme 10. Bimolecular Reactions of DMNA with 1′

Bimolecular Reactions of DMNA with CH3 (Scheme 11). Methyl radicals can be formed in C−N β-scissions in

Scheme 8. Bimolecular Reactions of DMNA with NO

Scheme 11. Bimolecular Reactions of DMNA with CH3

radicals 1′ and 5. H abstraction is the lowest-barrier reaction for DMNA + CH3 (11−1, 41 kJ/mol). Radical addition to a nitro oxygen has a higher barrier (11−2, 62 kJ/mol) and leads to a radical adduct that readily undergoes N−O β-scission (not show, 11 kJ/mol) leading to DMNSA and methoxy radical. Bimolecular Reactions of DMNA with CH3O (Scheme 12). Methoxy radicals are formed in radical additions of CH3 to

HONO (3−3), DMAN (3−7), and DMNSA (3−8). To our knowledge, reactions between nitramines and NO have not been previously considered. For DMNA + NO, we found three transition structures: radical displacement of NO2 (8−1, 115 kJ/mol), O transfer (8−2, 140 kJ/mol), and H abstraction (8− 3, 163 kJ/mol). Unlike the other radicals, the radical displacement of NO2 is the lowest-barrier pathway, whereas H abstraction has a higher barrier. Overall, NO is found to be least reactive among the nine radicals considered. Bimolecular Reactions of DMNA with 5 (Scheme 9). Aminoxyl radicals (5) are formed in unimolecular N−O fissions

Scheme 12. Bimolecular Reactions of DMNA with OCH3.

Scheme 9. Bimolecular Reactions of DMNA with 5

DMNA. H abstraction is the lowest-barrier reaction for DMNA + CH 3 (12−1, 19 kJ/mol), yielding 3 and CH3 OH. Nucleophilic attack of a nitro O of DMNA on a methyl H of CH3O (12−2, 47 kJ/mol) has a higher barrier and yields 4 and CH2O as the products. We also found a transition structure to NO2 displacement (not shown), but the barrier of 158 kJ/mol is too high for this reaction to have an appreciable branching ratio.

in DMAN and bimolecular O abstraction from DMNA by 1. Irikura has recently reviewed possible reactions of aminoxyl radicals with RDX.20 For DMNA + 5, we found that H abstraction is monotonically uphill (9−1, 87 kJ/mol) and NO2 displacement has a much higher 0 K barrier (9−2, 155 kJ/mol). Bimolecular Reactions of DMNA with 1′ (Scheme 10). The alkyl radical 1′ can be formed in the unimolecular isomerization of 1 (2−2). We found that, unlike 1, the lowestbarrier mechanism of DMNA + 1′ is a radical addition to one of the nitro oxygens of DMNA (10−1, 26 kJ/mol). The resulting radical adduct readily undergoes N−O β-scission (not shown, 9 kJ/mol), yielding DMNSA and (methylamino)methoxy radical 6. H abstraction has a higher barrier (10−2, 53 kJ/mol).

4. DISCUSSION Using the reactions mechanisms discussed in the previous section as the reference, we have drawn preliminary conclusions (Scheme 13) about which bimolecular reactions can compete with unimolecular pathways and accelerate DMNA decomposition. The dominant unimolecular pathway is N−N fission in DMNA, followed by C−H β-scission in the dimethylamino radical 1, ultimately leading to N-methylmethanimine 2, H, and NO2 (13−1) as the stable products. Additional unimolecular pathways include concerted HONO elimination and roamingradical reactions in DMNA, as well as H shift in 1, and the F


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Using the B2PLYP/jun-cc-pVTZ geometries, we also computed electronic energies with the CCSD(T) coupled-cluster method56 and the same basis set. The resulting 0 K activation energies that combine the CCSD(T)/jun-cc-pVTZ energies at the B2PLYP/jun-cc-pVTZ geometries and the ZPE corrections with the unscaled B2PLYP/jun-cc-pVTZ frequencies are provided in Table 1.

Scheme 13. Unimolecular and Bimolecular Reactions Controlling DMNA Decomposition

Table 1. 0 K Activation Energies (ΔE≠0K) for a Selected Subset of Reactions Estimated at the M06/6-311+ +G(3df,3pd), B2PLYP/jun-cc-pVTZ, and CCSD(T)// B2PLYP/jun-cc-pVTZ Levels of Theory (All Values in kJ/ mol) 1−1 1−2 2−1 2−2 2−5 4−1 6−1 7−1 11−1 12−1

subsequent decomposition of 1′. However, although these channels have barriers comparable to the dominant pathway, they involve at least one reaction that is entropically unfavorable and thus are expected to have lower rates than (13−1). The dominant bimolecular pathway for radicals 1, 5, H, OH, CH3, and CH3O is H abstraction from DMNA (13−2) and the corresponding barriers vary from no barrier (DMNA + OH) to 87 kJ/mol (DMNA + 5). All these reactions produce a thermally unstable radical 3 that undergoes facile N−N βscission, yielding 2 + RH + NO2. Additional bimolecular reactions with these radicals include radical additions followed by β-scissions, yielding DMNSA and RO radicals, and NO2 displacement reactions, yielding N-substituted dimethylamines and NO2. The bimolecular H abstraction from DMNA by NO2 (13−3) is autocatalytic (NO2 participates as both reactant and product), and given a relatively low barrier of 81 kJ/mol, can proceed even if the temperature is lowered (e.g., due to endothermic reactions). Furthermore, HONO formed in (13− 3) can decompose either unimolecularly or bimolecularly,50−52 yielding more OH radicals to be converted to more NO2. At an early stage of DMNA decomposition when unreacted DMNA is the dominant species, reactions (13−1), (13−2), and (13−3) thus result in a growing concentration of NO2 and thus are a likely explanation of the rate dependence on the extent of decomposition and the accelerating effect of sample confinement. The unique reactivity of NO (13−4) contributes to the importance of DMNSA as a major product of DMNA decomposition. NO radicals are formed primarily in unimolecular and bimolecular reactions of HONO, which is produced in a number of reactions including (13−3). Unlike any other radical, the dominant reactions of DMNA + NO are NO2 displacement and O abstraction, both yielding DMNSA + NO2. DMNSA is also formed in radical reactions of DMNA with 1, H, and CH3 via the radical adduct 4. To test the accuracy of the estimated 0 K activation energies, we reoptimized the transition structures for 16 reactions discussed in section 4 using the double-hybrid B2PLYP functional53 combined with the correlation-consistent triple-ζ cc-pVTZ basis set54 and the “jun” set55 of diffuse functions.

5−1 5−2 5−3 8−1 8−2 8−3

B2PLYP CCSD(T)a

reaction

M06

DMNA, N−N homolysis DMNA, HONO elimination 1, C−H β-scission 1, H shift 3, N−N β-scission DMNA + 1, H abstraction DMNA + H, H abstraction DMNA + OH, H abstraction DMNA + CH3, H abstraction DMNA + OCH3, H abstraction DMNA + NO2, H abstraction, cis DMNA + NO2, NO2 displacement DMNA + NO2, O abstraction DMNA + NO, NO2 displacement DMNA + NO, O abstraction DMNA + NO, H abstraction

197.9 200.7 161.8 166.6 34.7 44.2 29.7 −17.8b 40.5 10.9

171.8 186.7 152.4 169.8 29.1 51.8 24.0 −6.3b 44.3 21.1

81.4

96.9

96.8

132.9

144.2

N/Ac

149.1

169.8

N/Ac

114.6

132.6

146.9

139.9 163.0

159.3 189.2

155.5 193.4

186.2 191.5 152.2 169.8 31.2 N/Ac 35.9 −1.3b 49.4 N/Ac

a

Electronic CCSD(T)/jun-cc-pVTZ energies computed at the B2PLYP/jun-cc-pVTZ geometries and combined with the B2PLYP/ jun-cc-pVTZ ZPE corrections. bThis reaction proceeds via a prereaction complex and the corresponding transition structure has energy below the reactant limit. cCCSD(T) energy was not computed for this reaction.

In comparison with CCSD(T)//B2PLYP, M06 tended to overestimate the 0 K activation barriers for unimolecular reactions, with the largest difference predicted for N−N homolysis in DMNA (1−1, +11 kJ/mol). On the contrary, M06 tended to underestimate the 0 K activation barriers for radical H abstractions, with the largest difference predicted for H abstraction by NO (8−3, −30 kJ/mol). Qualitatively, the predicted 0 K activation energies given in Schemes 112 are thus expected to be accurate within about 30 kJ/mol. Ongoing calculations will compare M06 predictions to complete active space second-order perturbation theory (CASPT2) for a larger set of unimolecular and bimolecular reactions involving methylenenitramine and methylnitramine to provide better estimates of the errors associated with DFT description of radical reactions. We emphasize that the presented set of 0 K barriers provides only a qualitative picture of dominant reaction pathways. The competition between entropically favorable unimolecular reactions and energetically favorable bimolecular reactions is expected to result in the branching ratios that are strongly dependent on both the temperature and density of the reacting material. Efforts are underway to provide quantitative estimates G



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ACKNOWLEDGMENTS We thank the anonymous referees for their comments. This work was supported by the Office of Naval Research (ONR), both directly (project N0001416WX00033, Dr. Clifford Bedford) and through the U.S. Naval Research Laboratory (NRL). S.E.K.-F. acknowledges support from NRL through the American Society for Engineering Education (ASEE) Postdoctoral Fellowship Program. Computational resources were provided by the Department of Defense High Performance Computing Modernization Program.

for the activation entropies from variational transition state theory as well as the Rice, Ramspperger, Kassel, and Marcus (RRKM) analysis of the complex-mediated reactions. Ultimately, quantitative estimates of the rate constants will allow us to verify the role of the reported bimolecular reactions in DMNA decomposition. We are also investigating the effects of various condensedphase environments on the reaction mechanisms. For example, in a solvent or liquid DMNA, the radical products of the initial homolysis are trapped in the cage of spectator molecules and can undergo facile radical−radical recombination and/or disproportionation reactions, effectively shifting the dominant pathway to reactions (1−3) and (1−4). The rates of molecular diffusion responsible for product separation as well as the possibility of reactions with solvent molecules57 need to be evaluated. Furthermore, a polarizable environment may promote charge stabilization and proton (rather than radical) abstraction reactions. Calculations of small clusters of DMNA are currently being pursued to investigate the possibility of such ionic reactions.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b10773.

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REFERENCES

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5. SUMMARY We have presented the transition structures and 0 K reaction energetics computed at the M06/6-311++G(3df,3pd) level for various unimolecular and bimolecular reactions in DMNA. Our principal finding is that bimolecular H abstractions from DMNA by various radicals formed in unimolecular reactions offer a low-barrier, autocatalytic reaction pathway that can accelerate DMNA decomposition. The presented reaction mechanisms, together with mechanisms reported by Irikura20 for RDX, provide a first step toward extending the detailed models of nitramine decomposition beyond just the unimolecular mechanisms. Efforts are underway to estimate the corresponding rate constants, which will allow us to quantitatively analyze the role of these reactions in DMNA decomposition.

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Article

Results of additional calculations on N−N homolysis and roaming radical reactions in DMNA (PDF)

AUTHOR INFORMATION

Corresponding Author

*I. V. Schweigert. E-mail: [email protected]. ORCID

Igor V. Schweigert: 0000-0002-9474-7767 Present Address ‡

Strategic Analysis, Inc., 4075 Wilson Blvd Suite 200, Arlington, VA 22203. Author Contributions

The manuscript was written through contributions of all authors. Notes

The authors declare no competing financial interest. † ASEE Postdoctoral Fellow, U.S. Naval Research Laboratory. H


Article

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Bimolecular Reactions between Dimethylnitramine and Its Radical

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