Investigation on the Thermal Dissociation of Vinyl Nitrite with a Saddle Point Involved.

Hybrid and double-hybrid density functionals are employed to explore the O-NO bond dissociation mechanism of vinyl nitrite (CH2=CHONO) into vinoxy (CH2=CHO) and nitric monoxide (NO). In contrast to previous investigations, which point out that the O-NO bond dissociation of vinyl nitrite is barrierless, our computational results clearly reveal that a kinetic barrier (first-order saddle point) in the O-NO bond dissociation is involved. Furthermore, a radical-radical adduct is recommended to be present on the dissociation path. The activation and reaction enthalpies at 298.15 K for the vinyl nitrite dissociation are calculated to be 91 and 75 kJ mol-1 at the M062X/MG3S level, respectively, and the calculated reaction enthalpy compares very well with the experimental result of 76.58 kJ mol-1. The M062X/MG3S reaction energetics, gradient, Hessian, and geometries are used to estimate vinyl nitrite dissociation rates based on the multistructural canonical variational transition-state theory including contributions from hindered rotations and multidimensional small-curvature tunneling at temperatures from 200 to 3000 K, and the rate constant results are fitted to the four-parameter Arrhenius expression of 4.2 × 109 (T/300)4.3 exp[-87.5(T - 32.6)/(T 2 + 32.62)] s-1.

Introduction

Nitroethylene (CH2=CHNO2) as the simplest member of the nitro-olefin series was usually considered to be a useful surrogate for understanding the behavior of nitro groups in the insensitive high energetic material 1,1-diamino-2,2-dinitro-ethylene (DADNE). Due to the fact that the experimental interpretations of decomposition processes of energetic materials are very complicated, quantum chemical calculations have been performed by Gindulytė et al.,[1] Shamov et al.,[2] and Khrapkovskii et al.[3] to investigate the unimolecular decomposition mechanism of nitroethylene. Four distinct thermally initiated gas-phase decomposition pathways have been identified: direct C–NO2 bond fission (R1), nitro to nitrite rearrangement with subsequent O–NO bond fission to yield CH2CHO and NO (R2), which is a result of the weak O–NO bond, HONO elimination reaction with formation of acetylene (R3), and 1,3-H shift with generation of CH2=CN(O)OH (R4). Furthermore, the nitro to nitrite rearrangement (R2) was found to be energetically favored by the decomposition of nitroethylene.[1−3]The theoretical studies above concerned with the C–NO2 bond rupture of nitroethylene proposed that there was no maximum on this reaction pathway, as will be confirmed in this work. With respect to the NO release of vinyl nitrite in the ground state, it was also assumed to be barrierless in the same manner,[1−4] i.e., the absence of a saddle point based on the similarity of thermal destruction of aliphatic nitrites. In this respect, it was interesting to note that a maximum in energy was observed from our potential energy surface scan for the O–NO bond cleavage of vinyl nitrite in this work. However, experimental information on the detailed mechanisms of the title reaction was still insufficient, and no experimental evidence of an activation barrier has been observed for the decomposition of vinyl nitrite.[5,6] In this connection, elucidation of whether the transition state exists for the radical decomposition of vinyl nitrite becomes an important issue that will be addressed below.

If the activation barrier exists, it would produce a remarkable effect on the decomposition rate constant and a critical difference in understanding experimental measurements. Unimolecular pre-exponential factors for loose bond dissociations are very high, whereas pre-exponential factors for the well-defined transition-state saddle points would be much lower, which would increase the lifetimes of intermediate species and in turn slow down the dissociation. Furthermore, quantum kinetics near the transition state, e.g., reaction path curvature, plays a crucial role in the state-to-state reaction dynamics. Therefore, understanding the fundamental reactivity of vinyl nitrite is a key component for improving the decomposition chemistry model of nitroethylene.

To describe this abnormal dissociation behavior, quantum chemical calculations have been performed on the vinyl nitrite dissociation to characterize the potential surface with the aim of proving whether the reaction has a well-defined transition state. Furthermore, high-pressure-limit rate constants are calculated at temperatures between 200 and 3000 K relevant for pyrolysis chemistry by means of multistructural canonical variational transition-state theory with multidimensional tunneling correction.

Results and Discussion

Potential Energy Surface for the O–NO Bond Rupture

The potential energy surface for CH2=CHONO → CH2=CHO + NO, as shown in Figure , is calculated at the M062X/MG3S level to cover the O–N bond with separation from 1.404 to 4.104 Å using an interval step of 0.1 Å with other geometric parameters fully optimized and taking the spin multiplicity as 1. The M062X/MG3S dissociation curve for CH2=CHNO2 → CH2=CH + NO2 with the distance between the bonding C and N atoms is also depicted in Figure for comparison. One can observe that the energy of the system [CH2=CH···NO2] first increases with the increasing bond length and then reaches a plateau, appearing without a tight transition state along the reaction coordinate. The relative energy of CH2=CH + NO2 to CH2=CHNO2 is calculated to be 314.1 kJ mol–1 without ZPE correction. When ZPE correction and thermal correction to enthalpy are taken into account, this energy value is reduced to 298.5 kJ mol–1, which is in excellent agreement with the experimental result[7] of 299.2 kJ mol–1. Nevertheless, the homolytic cleavage process of the O–NO bond of vinyl nitrite involves a maximum point in energy, as mentioned in the Introduction, and the structure with peak potential energy is most likely a transition state. In addition, CH2=CHONO immediately dissociates via O–NO bond scission to form CH2=CHO + NO upon CH2=CHONO formation. This is a result of the much weaker O–NO bond relative to the C–N bond of CH2=CHNO2.

Figure 1

Fully optimized M062X/MG3S potential energy curves for the O–NO bond rupture of vinyl nitrite to form CH2=CHO + NO (in squares) and the C–N bond rupture of nitroethylene to produce CH2=CH + NO2 (in circles).

Geometries and Energies

This work employs the BB1K,[8,9] MPWB1K,[10] and M062X[11] hybrid density functionals coupled with the MG3S basis set[12] and the B2PLYP,[13] B2PLYPD,[14] B2PLYPD3,[15,16] mPW2PLYP,[17] and mPW2PLYPD[14] with the TZVP basis set[18] to conclusively prove whether the vinyl nitrite dissociation has a well-defined transition-state saddle point via the “TS” and “QST3” calculations with the “Guess = Mix” keyword to break the spin symmetry. Figure depicts the optimized geometries of the stationary points, and selected geometrical parameters obtained with the various DFT-based electronic model chemistries used in this study are compared in Table and the agreement is good. The detailed geometries, rotational constants, and vibrational frequencies obtained at various levels for all species involved in the title reaction are documented in the Supporting Information.

Figure 2

Geometries of the lowest-energy conformers of the reactant, transition state (TS), intermediate (IM), and products for the O–NO bond dissociation of vinyl nitrite to form CH2=CHO + NO. Color coding of atoms: red, oxygen; blue, nitrogen; green, carbon; and white, hydrogen.

Table 1

Selected Geometric Parameters for CH2CHONO, Transition State (TS), Intermediate (IM), CH2CHO, and NO

species	parametera	BB1K	MPWB1K	M062X	B2PLYP	B2PLYPD	B2PLYPD3	mPW2PLYP	mPW2PLYPD
CH2CHONO	R(C1–C2)	1.312	1.310	1.318	1.326	1.326	1.326	1.323	1.323
	R(C2–O1)	1.361	1.360	1.373	1.374	1.374	1.374	1.374	1.374
	R(O1–N)	1.387	1.382	1.404	1.493	1.493	1.492	1.468	1.468
	R(N–O2)	1.152	1.151	1.158	1.161	1.161	1.161	1.160	1.160
	R(C1–H1)	1.075	1.074	1.080	1.080	1.080	1.080	1.078	1.079
	R(C1–H2)	1.073	1.072	1.078	1.079	1.079	1.079	1.077	1.078
	R(C2–H3)	1.077	1.076	1.082	1.083	1.084	1.083	1.081	1.082
	D(C1–C2–O1–N)	180.0	180.0	180.0	180.0	180.0	180.0	180.0	180.0
	D(C2–O1–N–O2)	180.0	180.0	180.0	180.0	180.0	180.0	180.0	180.0
TS	R(C1–C2)	1.357	1.355	1.375	1.367	1.368	1.368	1.363	1.363
	R(C2–O1)	1.274	1.274	1.270	1.286	1.287	1.286	1.288	1.288
	R(O1–N)	2.063	2.053	2.063	2.058	2.058	2.062	2.036	2.036
	R(N–O2)	1.112	1.111	1.117	1.136	1.136	1.136	1.132	1.132
	R(C1–H1)	1.076	1.075	1.081	1.081	1.082	1.081	1.080	1.080
	R(C1–H2)	1.075	1.074	1.080	1.080	1.081	1.080	1.079	1.079
	R(C2–H3)	1.089	1.088	1.095	1.095	1.095	1.095	1.093	1.093
	D(C1–C2–O1–N)	–85.3	–85.2	–56.4	–90.6	–89.7	–90.1	–88.6	–87.7
	D(C2–O1–N–O2)	178.6	178.5	140.3	179.2	178.7	178.7	178.8	178.3
IM	R(C1–C2)	1.410	1.409	1.425	1.429	1.429	1.428	1.426	1.426
	R(C2–O1)	1.220	1.220	1.224	1.229	1.229	1.229	1.227	1.227
	R(O1–N)	3.259	2.939	2.833	2.998	2.924	2.942	2.947	2.904
	R(N–O2)	1.130	1.128	1.136	1.154	1.154	1.154	1.150	1.150
	R(N–H1)	3.115	2.871	2.743	2.938	2.749	2.830	2.859	2.743
	R(C1–H1)	1.076	1.075	1.080	1.080	1.081	1.080	1.079	1.079
	R(C1–H2)	1.075	1.075	1.080	1.080	1.081	1.080	1.079	1.080
	R(C2–H3)	1.096	1.095	1.101	1.102	1.102	1.102	1.100	1.101
	D(C1–C2–O1–N)	–2.6	–1.9	–4.0	–10.7	–14.3	–14.2	–11.4	–14.1
	D(C2–O1–N–O2)	177.8	177.5	175.7	167.4	168.8	168.4	167.8	169.1
CH2CHO	R(C1–C2)	1.410	1.409	1.426	1.429	1.430	1.429	1.426	1.427
	R(C2–O1)	1.220	1.219	1.223	1.228	1.228	1.228	1.226	1.226
NO	R(N–O2)	1.130	1.129	1.136	1.155	1.155	1.155	1.151	1.151

Bond lengths are in Å and dihedral angles are in degrees.

Reasonably similar tight transition-state structures have been identified. The optimized separation distances between the O and N atoms of the transition state are quite consistent across all adopted levels of theory, as presented in Table , which correspond to the first-order saddle points characterized by only one imaginary frequency, confirming the process of the combination and separation of the CH2=CHO and NO fragments. In addition, the IRC calculations confirm that the transition state connects to the CH2=CHONO minimum-energy geometry on the reactant side, and on the product side, the IRC path did not dissociate into the free products but instead led via a movement of the NO moiety to a hydrogen-bonded OC(H)C(H)H···NO radical–radical complex (IM). See Figure for schematic structures of the stationary points. This represents quite a mechanistic oversight to assume the CH2=CHONO → CH2=CHO + NO reaction to be barrierless. The transition state has a biradical character, and the geometrical parameters of the CH2=CHO and NO fragments in the transition structure are almost the same as those in their equilibrium structures obtained at the same theoretical level.

The O–NO bond dissociation of singlet vinyl nitrite proceeds via a spin-flip process to yield two doublet radicals, where two electrons initially paired in the O–NO bonding orbital become separated into two different orbitals, introducing evident problems associated with spin contamination. At the equilibrium geometry, the two electrons in the O–NO bonding orbital are correlated, but this correlation energy disappears once the bond is broken. Furthermore, the vinoxy radical is stabilized between the CH2=CH–O• and •CH2–CH=O conformations (the dot • denotes the radical center) with the latter being predominant. Therefore, it is necessary to assess whether single-reference methods are suitable for accurate investigations of this system. In this work, the T1 diagnostic of Lee and Taylor[19] was employed to measure the multireference character for the M062X/MG3S- and B2PLYPD3/TZVP-optimized geometries by the CCSD[20,21]/cc-pVnZ and aug-cc-pVnZ (n = D, T)[22−24] calculations, and the T1 diagnostic results are presented in Table .

Table 2

T1 Diagnostics for Species Involved in the O–NO Bond Dissociation of Vinyl Nitrite

	CCSD/cc-pVDZ		CCSD/cc-pVTZ		CCSD/aug-cc-pVDZ		CCSD/aug-cc-pVTZ
species	B2PLYPD3	M062X	B2PLYPD3	M062X	B2PLYPD3	M062X	B2PLYPD3	M062X
CH2CHONO	0.021	0.019	0.021	0.019	0.022	0.020	0.021	0.019
transition state (TS)	0.025	0.027	0.026	0.028	0.026	0.028	0.027	0.028
intermediate (IM)	0.032	0.028	0.031	0.028	0.031	0.028	0.031	0.028
CH2CHO	0.032	0.032	0.032	0.031	0.032	0.032	0.032	0.031
NO	0.030	0.021	0.030	0.021	0.030	0.022	0.030	0.022

As can be seen in Table , T1 parameters <0.045 are evaluated for the open-shell systems,[25] despite the severe problems associated with TS, IM, and CH2=CHO. In addition, those for the spin-restricted geometry (CH2=CHONO) are calculated to be lower than the threshold of 0.02,[19] suggesting that the decomposition reaction of vinyl nitrite can be correctly characterized using the above-mentioned single-reference methods. Furthermore, our calculated values of the vibrational frequencies for vinyl nitrite and vinoxy radicals are in good agreement with the MP2/6-31G(d,p), MP2/6-31G(d), and B3LYP/6-311G(2d,d,p) results,[1,26,27] as compared in the Supporting Information. Thus, previously computed single-reference reaction energies for the overall reaction CH2=CHONO → CH2=CHO + NO are likely to be reasonable, and the DFT methods employed in this work are applicable for the direct dynamics calculations.

Table presents the activation energies for the O–NO bond dissociation of vinyl nitrite. One can see that gratifying results are achieved by different single-reference methods, especially at the double-hybrid density functionals with the TZVP basis set and the M062X/MG3S level, for estimating the transition-state energies (barrier heights calculated by taking the energy difference between the reactant and transition-state structures).

Table 3

Activation Energies, Enthalpies, and Free Energies [ΔE≠, ΔH≠ (298 K) and ΔG≠ (298 K) in kJ mol–1] for the O–NO bond Dissociation of Vinyl Nitrite

electronic model chemistry	ΔE≠	ΔE≠ + ZPEa	ΔH≠	ΔG≠
B2PLYP/TZVP	97.0	89.4	90.2	86.2
B2PLYPD/TZVP	96.5	89.1	89.9	85.8
B2PLYPD3/TZVP	96.9	89.5	90.3	86.2
mPW2PLYP/TZVP	93.6	85.4	86.4	81.8
mPW2PLYPD/TZVP	93.3	85.1	86.1	81.5
BB1K/MG3S	91.8	81.0	82.8	75.4
MPWB1K/MG3S	93.5	82.6	84.5	77.2
M062X/MG3S	100.8	89.9	91.0	86.6

ZPEs are scaled.

As can be seen in Table , the vinyl nitrite dissociation reaction is calculated to be an endothermic process. The M062X/MG3S level provides a reaction enthalpy of 75.14 kJ mol–1 with ZPE correction included at 298.15 K, concurring with the determination of 76.58 kJ mol–1 using the involved species enthalpies of formation: experimentally based ΔHf,298o(NO) = 91.120 ± 0.065 kJ mol–1 and ΔHf,298o(CH2CHO) = 15.58 ± 0.77 kJ mol–1 taken from ref (28) and theoretically well-established ΔHf,298o(CH2CHONO) = 30.12 kJ mol–1 via a variety of homodesmic and isodesmic reactions by Snitsiriwat et al.[27] Other theoretical calculations all underestimate the reaction enthalpy, i.e., at the B2PLYPD3/TZVP and mPW2PLYPD/TZVP levels, this value is calculated to be 63.75 and 58.38 kJ mol–1, respectively, which is about 13 and 18 kJ mol–1, respectively, lower than the experimentally based value. In view that the M062X/MG3S level performs well to predict thermochemistries of species, it will be selected for the anharmonic torsion and kinetics calculations to be carried out in the next sections.

Table 4

Reaction Energies, Enthalpies, and Free Energies [ΔE, ΔH (298 K) and ΔG (298 K) in kJ mol–1] for the O–NO Bond Dissociation of Vinyl Nitrite

electronic model chemistry	ΔE	ΔE + ZPEa	ΔH	ΔG
B2PLYP/TZVP	70.6	57.3	60.9	13.8
B2PLYPD/TZVP	72.3	58.9	62.5	15.5
B2PLYPD3/TZVP	73.5	60.2	63.8	16.7
mPW2PLYP/TZVP	67.3	53.5	57.2	9.9
mPW2PLYPD/TZVP	68.6	54.7	58.4	11.1
BB1K/MG3S	70.7	55.0	59.2	10.8
MPWB1K/MG3S	73.9	58.1	62.3	13.8
M062X/MG3S	85.2	71.1	75.1	26.9

ZPEs are scaled.

Multistructural and Torsional Anharmonicities

Two internal rotations about the O–NO and C–ONO bonds in the trans-vinyl nitrite and TS structures are involved, which are denoted τ-i and τ-ii, respectively, and ϕ1(O–N–O–C) and ϕ2(N–O–C–C) correspond to the two torsional angles specified above. The total energies as functions of torsion angles are calculated by scanning the torsion angles between 0° and 360° with the step size of 5°. At every step, we constrain the dihedral angle corresponding to a specific torsion, and then a minimum or a saddle point is obtained by the full optimizations of the remaining degrees of freedom. The M062X/MG3S-based one-dimensional τ-i and τ-ii potentials are pictured in Figure for the lowest-energy conformers (trans configuration) of vinyl nitrite.

Figure 3

One-dimensional potentials for the (a) τ-i internal rotation about the O–NO bond and (b) τ-ii internal rotation around the C–ONO bond in the trans-vinyl nitrite structure calculated at the M062X/MG3S level. Data in the figure denotes the energy differences between the jth conformer and trans-vinyl nitrite.

As can be found in Figure a, two different minima are observed on the τ-i potential plot, leading to the number of distinguishable minima (P) for τ-i of trans-vinyl nitrite equal to 2 with στ-i being unity. The deep minimum (trans configuration of the nitrite group) is predicted to be more stable than the shallow one (cis isomer) by about 7 kJ mol–1 without ZPE included. The O–NO internal rotation in vinyl nitrite exhibits a symmetric twofold significantly high barrier of 49 kJ mol–1, which is not corrected for ZPEs. It can be argued that the rotation of the NO moiety about the O–NO bond seems very difficult. The τ-ii torsional potential profile in Figure b involves the locations of three minima from 0 to 360°. Except for the most stable trans conformer of vinyl nitrite, the other two minima, which are isoenergetic, correspond to the mirror-image structures; therefore, they are distinguishable. The connectivity between these two mirror-image structures (labeled as Reactant-3 and Reactant-4) exhibits a low torsional barrier height of 1.2 kJ mol–1, whereas the transformation of trans-vinyl nitrite to Reactant-3 or Reactant-4 structures requires to surmount a high zero-point-exclusive barrier height of about 15 kJ mol.

In the relaxed scan of the τ-i torsion of the TS structure, the transformation between the CH2=CH–O• and •CH2–CH=O fragments with large bond length changes is involved. Chuang and Truhlar’s approach[29] is employed to treat the torsional anharmonicity of τ-i of TS. Figure depicts the M062X/MG3S-based τ-ii potential for the lowest-energy TS conformer. Two different minima are observed on the τ-ii potential plot. These two isoenergetic minima correspond to the mirror-image structures (TS-1 and TS-2), leading to P equaling 2 with στ-ii being unity. The connectivity between TS-1 and TS-2 requires to get over a significant zero-point-exclusive barrier height of about 26 kJ mol.

Figure 4

One-dimensional potentials for the τ-ii hindered rotation in the structure of the transition state (TS) involved in the O–NO bond dissociation process of vinyl nitrite calculated at the M062X/MG3S level.

Figure depicts the four distinguishable conformations of vinyl nitrite due to the strong coupling between the τ-i and τ-ii torsional motions, and TS-1 and TS-2 geometries are also included. Then, the same relaxed scan procedure is also carried out on all uncoupled torsions for the cis conformer and Reactant-3 geometries of vinyl nitrite. The information about the fully optimized geometries, rotational constants, harmonic vibrational frequencies, and Fourier series for one-dimensional τ-i and τ-ii potentials of all conformers for vinyl nitrite is summarized in the Supporting Information.

Figure 5

Four structures of vinyl nitrite and two geometries of transition-state TS. A vertical dashed line is used to separate the mirror-image structures.

Table presents the torsional information for all structures of vinyl nitrite and TS related to its partition function approximations. U denotes the energy difference between the jth structure and the most stable conformer, and U for the global minimum conformations is zero by definition. The reduced moments of inertia (I) are calculated by the Pitzer method[30,31] by assuming that no coupling between internal rotations is at structure j. W represents the uncoupled torsional barrier, and ω is the harmonic frequency based on the internal coordinate at the jth structurewherewith k being the force constant for a given torsion τ, V the torsional potential along ϕτ, ϕτ,eq, its equilibrium torsional angle at the jth structure, and M the local periodicity of torsion, given byTable illustrates the temperature-dependent multistructural anharmonic factors for the species involving torsions and overall reaction-specific multistructural torsional anharmonicity factor FMS-T, and their data are extended to a broad temperature range 50–3000 K.

Table 5

Information Used for the Vinyl Nitrite and TS Partition Functions Using the Multistructural Treatmenta

torsion	ωj,τ	Ij,τ	Wj,τ	Mj,τ	Pj,τ
Vinyl Nitrite
trans-vinyl nitrite (Uj = 0)
τ-i	117	18.74	49.41	1.93	1.93
τ-ii	42	50.90	14.99	2.05	2.05
cis-vinyl nitrite (Uj = 7.09 kJ mol–1)
τ-i	112	17.69	42.03	1.95	1.95
τ-ii	12	96.52	14.05	0.81	0.81
Structures Reactant-3 and Reactant-4 (Uj = 8.35 kJ mol–1)
τ-i	103	18.83	43.66	1.81	1.81
τ-ii	32	48.64	3.92	3.04	3.04
Transition State
structures TS-1 and TS-2 (Uj = 0)
τ-ii	29	151.64	15.97	2.35	2.35

The M062X/MG3S level of theory is used for this table. The units are cm–1 for uncoupled harmonic frequency obtained using internal coordinates (ω), amu·Å2 for internal moments of inertia (I), and kJ mol–1 for uncoupled torsional barrier heights (W) of the τ torsion in the jth structure. The local periodicity of torsion (M) and the number of distinguishable minima (P) for torsional coordinate τ of structure j are unitless.

Table 6

Species-Specific and Reaction-Specific Multistructural Factors for the O–NO bond Dissociation of Vinyl Nitritea

T (K)	Fvinyl nitriteMS-LH	Fvinyl nitriteT	Fvinyl nitriteMS-T	FTSMS-LH	FTST	FTSMS-T	FMS-T
50	1.000	1.000	1.000	2.000	1.000	2.000	2.000
100	1.001	1.001	1.001	2.000	0.999	1.998	1.995
150	1.016	1.003	1.019	2.000	0.997	1.994	1.957
200	1.070	1.006	1.077	2.000	0.994	1.987	1.845
250	1.172	1.009	1.182	2.000	0.989	1.979	1.673
298.15	1.307	1.009	1.318	2.000	0.984	1.969	1.494
400	1.658	1.002	1.662	2.000	0.973	1.946	1.170
600	2.389	0.978	2.336	2.000	0.947	1.894	0.810
800	3.021	0.950	2.870	2.000	0.919	1.839	0.641
1000	3.534	0.921	3.257	2.000	0.892	1.784	0.548
1200	3.949	0.894	3.529	2.000	0.865	1.730	0.490
1400	4.286	0.867	3.716	2.000	0.839	1.679	0.452
1600	4.565	0.841	3.841	2.000	0.815	1.629	0.424
1800	4.798	0.817	3.919	2.000	0.791	1.582	0.404
2000	4.996	0.793	3.963	2.000	0.768	1.537	0.388
2200	5.166	0.771	3.982	2.000	0.747	1.494	0.375
2600	5.442	0.729	3.967	2.000	0.707	1.415	0.357
3000	5.656	0.691	3.909	2.000	0.671	1.343	0.344

Fvinyl nitriteMS-LH and FTSMS-LH, multistructural harmonic factors of vinyl nitrite and transition state, respectively; Fvinyl nitriteT and FTST, torsional anharmonicity factors of vinyl nitrite and transition state, respectively; Fvinyl nitriteMS-T and FTSMS-T, ratios of the MS-T partition functions to the single-structure, rigid-rotor harmonic-oscillator ones for vinyl nitrite and transition state, respectively; FMS-T, the reaction-specific multistructural torsional anharmonicity factor.

As can be seen in Table , deviations between the torsional partition functions and the harmonic ones for vinyl nitrite grow more significant with temperature and the anharmonic ones approach the high-temperature limit of the free rotor. However, the harmonic ones rise steadily and cannot characterize the torsions reliably. The FTST factor for the transition state exhibits the same behavior, as outlined in Table . Since trans-vinyl nitrite accounts for the global minimum conformer, the approximation of the MS-LH factor of vinyl nitrite leads to 1.000 at 50 K with the f and Z factors in eq being unity. With the elevated temperature, the three less stable conformations begin to contribute to the overall partition functions of vinyl nitrite, and the Fvinyl nitriteMS-LH values rise significantly to 5.656 at 3000 K. The FTSMS-LH component of the species-specific F-factor for the transition state in Table is equal to 2 at all temperatures since TS has only one additional structure, its isoenergetic mirror image. Here, this leads to the conclusion that, for vinyl nitrite and transition state, the multiple-structural anharmonicity (FαMS-LH) predominates at low temperatures compared to the torsional effect (FαT) and makes a pronounced contribution to FαMS-T, and with the increasing temperature, the torsional anharmonicity factors (FαT) of the vinyl nitrite and transition state appear more remarkable.

Rate Constants

The M062X/MG3S-calculated minimum-energy path potential (VMEP), local zero-point vibrational energy (ZPE), and vibrationally adiabatic ground-state potential energy (VaG) with respect to the reaction coordinate (s) for the O–NO bond dissociation of vinyl nitrite are depicted in Figure . Location s corresponds to the distance along the MEP with s = 0 at the first-order saddle point. MEP terminates on the reactant side for negative s and on the product side for positive s. VMEP(s) value represents the potential energy at location s relative to trans-vinyl nitrite (VMEP(s → −∞) = 0). ZPE(s) is computed with the M062X/MG3S-based Hessian results scaled by 0.97, and VaG(s) is obtained through adding VMEP(s) to VMEP(s). Note that at high energies, very small amounts of points with large T1 parameters are exhibited, and they have been omitted from VMEP.

Figure 6

M062X/MG3S minimum-energy path potential VMEP(s), ZPE(s), and vibrationally adiabatic ground-state potential VaG(s) profiles for the O–NO bond dissociation of vinyl nitrite.

For the O–NO bond dissociation of vinyl nitrite, the notable geometry changes primarily occur in the reaction coordinate range from −3.69 to 1.55 bohr, as seen from VMEP(s) in Figure , and then they proceed by the rearrangement of heavy atoms to approach the vinyl nitrite or IM structures. A lower concave can be observed ranging from −0.59 to 0.52 bohr on the ZPE(s) profile, which leads to that VaG(s) gets its maximum in energy at s = −0.15 bohr, indicating that the variational effect should be taken into consideration in the kinetic modeling.

This work employs various levels of theory including TST, CVT, ICVT, and MS-CVT to calculate the high-pressure-limit rate constants using the M062X/MG3S-based gradients, force constants, geometries, and energetics. Tunneling probabilities are taken into account by utilizing the ZCT and SCT approximations. Here, it should be noted that the overall rotational symmetry number for a given species has been included in its partition function approximations, and the chiral effect of Reactant-3 or TS based on the fact that the two isoenergetic mirror-image structures make equivalent influence to the total partition function has been taken into consideration in the MS-CVT approximations by the multistructural factor, FαMS-LH.

The TST, CVT, ICVT, CVT/ZCT, CVT/SCT, and MS-CVT/SCT rate constants at various temperatures are outlined in Table , where /ZCT or /SCT denotes that ZCT or SCT tunneling estimates are included in the rate constants.

Table 7

Thermal Rate Constants in s–1 for the O–NO Dissociation of Vinyl Nitrite

T (K)	kTST	kCVT	kICVT	kCVT/ZCT	kCVT/SCT	kMS-CVT/SCT
200	1.85 × 10–7	3.75 × 10–8	3.75 × 10–8	1.33 × 10–7	3.06 × 10–7	5.65 × 10–7
250	2.38 × 10–3	6.09 × 10–4	6.09 × 10–4	1.34 × 10–3	2.29 × 10–3	3.83 × 10–3
298.15	1.12	0.33	0.33	0.57	0.83	1.24
400	4.15 × 103	1.44 × 103	1.44 × 103	1.95 × 103	2.40 × 103	2.81 × 103
600	1.42 × 107	5.52 × 106	5.52 × 106	6.31 × 106	6.91 × 106	5.60 × 106
800	8.80 × 108	3.13 × 108	3.13 × 108	3.37 × 108	3.55 × 108	2.28 × 108
1000	1.07 × 1010	3.47 × 109	3.47 × 109	3.64 × 109	3.76 × 109	2.06 × 109
1200	5.75 × 1010	1.73 × 1010	1.73 × 1010	1.79 × 1010	1.83 × 1010	8.99 × 109
1400	1.92 × 1011	5.48 × 1010	5.48 × 1010	5.61 × 1010	5.70 × 1010	2.58 × 1010
1600	4.76 × 1011	1.30 × 1011	1.30 × 1011	1.32 × 1011	1.34 × 1011	5.68 × 1010
1800	9.66 × 1011	2.54 × 1011	2.54 × 1011	2.58 × 1011	2.61 × 1011	1.05 × 1011
2000	1.70 × 1012	4.36 × 1011	4.36 × 1011	4.41 × 1011	4.44 × 1011	1.72 × 1011
2200	2.72 × 1012	6.77 × 1011	6.77 × 1011	6.84 × 1011	6.88 × 1011	2.58 × 1011
2600	5.57 × 1012	1.33 × 1012	1.33 × 1012	1.34 × 1012	1.35 × 1012	4.81 × 1011
3000	9.44 × 1012	2.19 × 1012	2.19 × 1012	2.20 × 1012	2.21 × 1012	7.60 × 1011

As can be seen in Table , the CVT rate constants are appreciably overestimated by the TST evaluations, and the difference between the TST and CVT rate constants first decreases with temperature and then increases with the elevated temperature, i.e., factors of kTST to kCVT are estimated to be 4.94, 2.55, 3.09, 3.91, and 4.31, respectively, at 200, 650, 1000, 2000, and 3000 K. The variational transition states move toward negative from s = −0.29 bohr at 200 K to location s = −0.38 bohr at 640 K. When the temperature is above 650 K, the generalized free energy of activation at −0.64 bohr becomes larger than that at −0.38 Å and then moves gradually to location s = −0.67 bohr at 3000 K. This clearly shows the importance of variational effects in the vinyl nitrite dissociation, and inclusion of variational approximations would provide more reasonable rate constants. Furthermore, it is found that the microcanonical effect is negligible on the rate constants of the vinyl nitrite dissociation with kCVT almost equal to kICVT and thus the tunneling effect is discussed based on the CVT rate constants.

At high temperatures, the CVT/SCT and CVT/ZCT rate constants approach the CVT ones asymptotically since more and more vinyl nitrite molecules dissociate either by the pathway above the barrier or by the vibrational tunnel very close to the barrier. With the decreasing reaction temperature, the ZCT and SCT tunneling effects in an analogous way become increasingly important in the estimations of the rate constants, and most of the vinyl nitrite molecules dissociate by the pathway through the barrier with small vibrational activation. Since the process CH2=CHONO → CH2=CHO + NO involves a fairly high activation barrier, as shown in Table , the tunneling effect is observed to be modestly significant. Due to the fact that the local reaction path curvature close to the transition state is taken into consideration in the SCT tunneling, the CVT/SCT rate constants appear generally greater than the CVT/ZCT ones at the same temperature (the factors for kCVT/SCT:kCVT/ZCT are 2.31, 1.03, 1.01, and 1.00 at 200, 1000, 2000, and 3000 K, respectively), confirming the significant role of the small-curvature effects, especially at low temperatures. Furthermore, multiple-structural anharmonicities produce a substantial effect on the rate constant evaluations at low temperatures, increasing them by factors of 1.84 and 1.17 at 200 and 400 K, respectively, whereas with the increased temperature, torsional anharmonicities become increasingly critical, and the MS-CVT rate constants are 0.81, 0.39, and 0.34 times the CVT estimates at 600, 2000, and 3000 K, respectively.

Because of the lack of experimental data for the O–NO dissociation of vinyl nitrite, it is hoped that this work will enable a more rigorous understanding of the underlying chemistry and facilitate a detailed comparison between theory and future experiments to refine the chemical kinetic mechanisms for nitroethylene pyrolysis.

This work employs the four-parameter modified Arrhenius functional to describe the temperature dependence of the MS-CVT/SCT rate constants over the temperature range 200–3000 K with a step of 50 K. These parameters in eq are obtained through minimizing the root-mean-square residual (RMSR), which is given bywith N being the total number of temperatures, k(T) the MS-CVT/SCT rate constant at T, and kM(p1, p2, p3, p4, T) the computed rate constants by eq . The four parameters are given by the frequency factor A = 4.2 × 109 s–1, E = 87.5 kJ mol–1, n = 4.3, and T0 = −32.6 K for the reaction kinetic model of vinyl nitrite dissociation.

Conclusions

Quantum chemical calculations are performed to explore the detailed kinetic mechanism for the O–NO dissociation of vinyl nitrite to produce CH2=CHO + NO. There are indications that the title reaction involves a transition state with a well-defined saddle point connected to a hydrogen-bonded complex directly instead of ultimate products (CH2=CHO + NO) from our computational results, and the activation energy at 298.15 K for the O–NO dissociation of vinyl nitrite is calculated to be 91 kJ mol–1 at the M062X/MG3S level. Direct kinetics calculations demonstrate that tunneling appears to be important at low temperatures and variational effects on the computed rate constants are observed to be evident. Torsional and multiple-structure anharmonic effects in the vinyl nitrite and transition state considerably influence the rate constants, especially at high temperatures. The M062X/MG3S rate constants in units of per second based on the MS-CVT calculations with corrections from SCT tunneling, hindered rotation, and variational effects are fitted to the four-parameter Arrhenius form for the temperature range of 200–3000 K. Note that some strong features proposed by our calculations have not been observed, thus serving as predictions.

Computational Details

Electronic Energy Calculations

The Gaussian 09 computational package was employed for the theoretical calculations.[32] The ground-state geometries on the potential energy surface were fully optimized with the hybrid density functionals BB1K,[8,9] MPWB1K,[10] and M062X[11] in combination with the MG3S basis set[12] without symmetry restrictions. In addition, a series of double-hybrid density functionals B2PLYP,[13] B2PLYPD,[14] B2PLYPD3,[15,16] mPW2PLYP,[17] and mPW2PLYPD[14] in conjunction with the TZVP basis set[18] have also been employed to characterize the vinyl nitrite dissociation. For the singlet species, CH2=CHONO, the spin-restricted method was used; otherwise, unrestricted methods were employed for the NO and CH2=CHO radicals, postreaction CH2=CHO···NO complex (IM), and transition state, with their wave function instability being checked.

Critical points were checked by counting no imaginary frequency for local minima and a single imaginary frequency for the transition state. The calculated values of vibrational frequencies are given in the Supporting Information. The transition state (TS) accounting for first-order saddle point is characterized by a single imaginary frequency, i.e., 755i cm–1 at the M062X/MG3S level, 390i cm–1 at the B2PLYP/TZVP level, and 421i cm–1 at the mPW2PLYP/TZVP level, which describe properly the desired breaking/forming process for the O–NO bond of vinyl nitrite. Minimum-energy path (MEP) is calculated using the intrinsic reaction coordinate (IRC) algorithm[33,34] with a step of 0.07 bohr to verify the connection between the transition state and the desired reactant and product. The rate constant is computed using the M062X/MG3S gradients and Hessian of 90 selected points (50 and 40 points on the reactant and product sides, respectively) on MEP.

Zero-point energies and thermal corrections to enthalpy and Gibbs free energy were computed with the same level. The HDFT energetics includes zero-point energy (ZPE) corrections. Taking the account of electronic uncertainty, the BB1K/MG3S, MPWB1K/MG3S, M062X/MG3S, and B2PLYP/TZVP ZPEs were, respectively, scaled by factors of 0.957, 0.954, 0.970, and 0.9832.[35,36] The scaling factors for the B2PLYPD, B2PLYPD3, mPW2PLYP, and mPW2PLYPD with the TZVP basis set ZPEs are taken as the same as that for the B2PLYP/TZVP ZPEs.

Rate Constant Calculations

Multistructural canonical variational transition-state theory[37,38] (MS-CVT) was employed to calculate the high-pressure-limit rate constants in the gas phase, defined as followswhere kCVT(T) is the single-structure CVT[39,40] rate constant, and the reaction-specific multistructural torsional anharmonicity factor, FMS-T, accounts for torsional and multiple-structure anharmonic effects.

Total partition functions for a given chemical species are defined as products of the electronic (Qelec), translational (Qtrans), and conformational–rovibrational (Qcon-rovib) contributionsAccording to the multistructural treatment for torsional anharmonicity[38] (MS-T), the conformational–rovibrational partition function is calculated viawith J being the number of distinguishable structures for a given species, kB Boltzmann’s constant, T the temperature, t the torsion number in structure j, and U the energy difference between the jth structure and the most stable conformer. In eq , for the jth structure, f denotes the internal coordinate torsional anharmonicity, QQH is the normal-mode harmonic-oscillator vibrational partition function, Qrot, is the classical rotational partition function, and the MS-T calculations reach the correct high-temperature limit by the Z factor. Here, it should be noted that the rotational symmetry numbers of the reactant and TS are directly included in their respective rotational partition function calculations.

The FαMS-T factor is defined as the ratio of the MS-T partition function to the single-structure, rigid-rotor harmonic-oscillator (SS-RRHO) one for the α speciesand it can be divided into two components: a multistructural harmonic factor, FαMS-LH, and a torsional factor, FαTto assess the multiple-structural and torsional anharmonicity, respectively. Qcon-rovib,αMS-LH in eq denotes the multistructural normal-mode harmonic partition function. Accordingly, the reaction-specific factor, FMS-T, is given bywhere the effect of chirality is taken into consideration.

Tunneling contributions are treated by the multidimensional zero-curvature tunneling[41] (ZCT) and small-curvature tunneling[42] (SCT) approximations. By substituting the appropriate tunneling predictions into the MS-CVT rate constants, the overall rate constants are computed byThe single-structure CVT rate constants, as well as ZCT and SCT tunneling corrections, are evaluated by the Polyrate 9.7 program[43] with the M062X/MG3S structures, energies, gradients, and force constants of the adopted points along MEP as inputs.

Discrete MS-CVT/SCT rate constants for the vinyl nitrite dissociation in the temperature range of 200–3000 K with a step of 50 K are fitted to the four-parameter modified Arrhenius expression[44]where A, n, T0, and E are the parameters of the modified Arrhenius equation.