Quasiclassical Trajectory Study of CH3NO2 Decomposition via

The PES harmonic D0 for the first path is 53.04 kcal mol–1, which is 6.76 kcal .... (27). Figure 9. Potential energy relative to the CH3NO2 global m...
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Quasiclassical Trajectory Study of CH3NO2 Decomposition via Roaming Mediated Isomerization Using a Global Potential Energy Surface Zahra Homayoon and Joel M Bowman* Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States ABSTRACT: We report a global potential energy surface (PES) for CH3NO2 based on fitting roughly 114 000 density functional theory (UB3LYP/6311+g(d,p)) electronic energies. The PES is a precise, permutationally invariant fit to these energies. Properties of the PES are described, as are some preliminary quasiclassical trajectory calculations. An isomerization-roaming pathway to the CH3ONO isomer and then to the CH3O + NO products is found. Although the pathway occurs at larger distances than a related loose saddle-point on the PES, the pathway supports the supposition of such a pathway based on locating a loose first-order saddle point and associated IRC, reported previously by Zhu and Lin [Zhu, R. S.; Lin, M. C. Chem. Phys. Lett. 2009, 478, 11].

points to cis- and trans-CH3ONO have been reexamined by Zhu and Lin15 with higher levels of theory in 2009. They located a loose isomerization saddle point (SP) to cisCH3ONO at 59.2 kcal mol−1 (“zero-point corrected”) above the nitromethane zero-point energy (ZPE) and 0.6 kcal mol−1 below the CH3 + NO2 asymptote at the UCCSD(T)/CBS level of theory. This is roughly 4 kcal mol−1 above the experimental estimate. They also calculated an intrinsic reaction coordinate (IRC) profile from this SP, at which the C−N bond distance is 3.58 Å, at the UCCSD(T)/6-311+G(d) level of theory. Statistical rate constant calculations were also done using the energies computed at the UCCSD(T)/CBS level to determine the energy dependence of the branching ratio for reactions R1 and R2. The calculations were redone using the barrier of 55 kcal mol−1 from experiment7 and with their calculated structures. On the basis of that calculation the experimental branching ratio of 0.6 was found at around 61 kcal mol−1, about 2 kcal mol−1 above their calculated isomerization barrier. They also suggested that the isomerization through this loose saddle point-transition state might be an isomerization-roaming pathway, somewhat analogous to the roaming pathway reported in the photodissociation of H2CO.17−19 Quoting from that paper “Determination of the relative contribution to the dissociation products from the roaming channel versus the conventional product channels needs to carry out (sic) a full dimensional calculation on a complete potential surface, which

I. INTRODUCTION Nitromethane (NM) is the simplest organic-nitro compound as well as an important energetic material. Its importance has led to numerous studies both experimental and theoretical.1−16 Experimentally, the decomposition products CH3 + NO2 were reported by most studies as the major channel of NM photodissociation1−7 CH3NO2 + hv → CH3 + NO2

(R1)

In 1986, infrared multiphoton dissociation studies in a molecular beam by Lee’s group7 revealed the first experimental evidence of NO from the direct decomposition of NM. They suggested a mechanism whereby NM isomerizes to CH3ONO followed by decomposition to CH3O + NO CH3NO2 + nhv → CH3ONO* → CH3O + NO

(R2)

They reported a branching ratio of 0.6 for reaction R1 under the conditions of their experiment. Using the calculated preexponential factor by Dewar et al.8 they predicted the barrier height of the isomerization channel to be about 55.5 ± 1.5 kcal mol−1. Theoretically, the isomerization paths of NM are challenging. In 1989 Mckee11 found a loose transition state with a long C− N bond distance (3.62 Å) for the isomerization process, CH3NO2 → cis-CH3ONO, at the CAS (4,4)/6-31G(d) level of theory, 10.0 kcal mol−1 above CH3 + NO2 at the MRCI/631G(d)//CAS/6-31G(d) level of theory. This was later confirmed by Saxon et al.12 at the MRCI(7,7)/6-31G(d)// CAS(4,4)/4-31G level of theory. However, they calculated the saddle point to lie 56.7 kcal mol−1 above NM, 0.4 kcal mol−1 below reaction 1 (57.1 kcal mol−1) in much better agreement with the estimate from experiment. The isomerization saddle © 2013 American Chemical Society

Special Issue: Curt Wittig Festschrift Received: December 7, 2012 Revised: January 16, 2013 Published: January 17, 2013 11665

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is outside of the scope of this work”.15 Roaming is a recently verified unusual pathway to molecular products from unimolecular dissociation of an energized molecule.17−19 In these processes, two incipient radicals may spend several hundred femtoseconds at separations of 3−4 Å before sampling an orientation that leads to an internal abstraction leading to other products. A recent study of nitrobenzene decomposition20 suggested that roaming may play an important role in the process to make C6H5O + NO. To conclude this brief review, we note in 1958 Brown and Pimentel16 observed the HNO radical as one of the primary products from the photolysis of nitromethane in a matrix in the range 240−360 nm. They suggested that the photolysis to the products proceeds in two steps, CH3NO2 + hv → CH3ONO* → CH 2O + HNO

Several strategies were used to generate data set. Part of the configurations were obtained by performing direct, “on the fly” classical trajectory calculations at the UB3LYP/6-311+G(d,p) level of theory. We ran trajectories initiated from the CH3NO2 global minimum (GM), cis- and trans-CH3ONO, TS1, TS2, TS3, and TS4, where the notation conforms to that given in ref 15 (also see Figure 3). The trajectories were run at different energies to sample many different configurations. The energy ranges for trajectories initiated from TSs were up to 15 kcal mol−1 above the TS energy, and higher energies were run for trajectories initiated from minima, up to 40 kcal mol−1 above these minima. In this way about 25 000 configurations were calculated covering the important reaction path regions. More data were added to the data set by focused sampling in the vicinity of stationary configurations. Fragment energies were obtained as well, using the UB3LYP/6-311+G(d,p) level of theory calculations. For products we added data with different orientation of fragments CH3 + NO2, CH3O + NO, and CH2O + HNO. These data were replicated for bond dissociation distances larger than 4 Å for CH3 + NO2 and CH3O + NO and larger than 6 Å for CH2O + HNO up to separation distances of approximately 8 Å, to ensure smooth flat dissociation limits to the PES. Some UB3LYP/6-311+G(d,p) energies in the near asymptotic region of the CH3O + NO produced a suspicious maximum in the potential and these were examined and replaced with CASSCF (8,8)/6-311+G(d,p) calculations specifically in the region where the separating N−O distance is between 2 and 4 Å. The CASSCF absolute energies were shifted by a constant amount equal to the difference in those energies and the UB3LYP/6-311+G(d,p) ones for the noninteracting CH3O(equilibrium) + NO(equilibrium) products and then added to the data set to be compatible with the data set. Initial fits (using methods described below) were used in several QCT calculations initiated from different stationary points at different energies. From results of these calculations, undersampled regions of the PES were identified and additional electronic energies were added to the database and the PES was refit. The next improvement of the PES were done by comparing the minimum energy paths of minimums to products and IRC of transition states with DFT calculations, as explained below. The final number of configurations is roughly 114 000. Figure 1 shows the energy distribution of the data set used in the fitting procedure. One can see that a large number of points are in the energy region of 30−120 kcal mol−1 above the GM, the important parts of the PES provide very good sampling needed to describe the dynamics to CH3 + NO2, CH3O + NO, and CH2O + HNO. II.B. Fitting the Potential Energy Surface. CH3NO2 is a 7-atom system with 15 degrees of freedom and 21 internuclear distances. We used the fitting procedures described in detail in ref 25 and thus the PES is represented by factored polynomials that are invariant with respect to all (12) permutations of like atoms. The variables of these polynomials are all the internuclear distances, transformed to Morse-like variables yi,j = exp(−ri,j/λ), where ri,j are the internuclear distances between atoms i and j and λ is a range parameter, which is typically between 2 and 3 bohr. In the present case it is 2 bohr. The polynomials are restricted to a maximum total order of five and this results in 7946 linear coefficients (one for each polynomial). Fitting is done by a standard linear least-squares method, with a simple weight for the energies, namely E0/(E +

(R3)

and that the nitro−nitrite isomerization is the primary process. This channel is also of interest to us. Motivated by these interesting mechanisms of NM decomposition, we have developed a global potential energy surface for CH3NO2. The main goal of the present paper is to give the details of this fitted surface with a focus on the isomerization paths and dissociation to three reaction channels given above and to assess the quality for future in-depth dynamical studies. As noted by others, this is a challenging system from the electronic structure point of view, owing to both the number of electrons and the regions of open-shell character. Zhu and Lin applied several unrestricted single reference methods successfully, including the efficient density functional method, UB3LYP. So, we based the current PES on that method, with details given below. The paper is organized as follows. In the next section we give details of the construction and properties of the PES. Tests of the PES both representing the electronic energies and structures of stationary points of given comparisons with previous, more accurate electronic structure single-point calculations are also given. Several PES IRC profiles are also presented, including one analogous to the loose one presented previously by Zhu and Lin. Section III describes preliminary quasiclassical trajectory calculations of the unimolecular dissociation using the new PES. A roaming-mediated isomerization pathway is identified in this calculations, which, however, “strays” considerably from the loose IRC pathway mentioned above.

II. CONSTRUCTION OF POTENTIAL ENERGY SURAFCE II.A. Electronic Energy Calculations. The construction of a global PES begins by considering the regions of configuration space that the PES should describe. In the present case, these regions include the three CH3NO2 isomers, three isomerization reaction paths, and paths from the isomers to the products of interest, CH3 + NO2, CH3O + NO, and CH2O + HNO. Of course all the adjoining regions must be considered, because the PES must describe large amplitude motion away from these paths. On the basis of our experience in generating such PESs,21 we anticipated needing roughly 100 000 configurations for the present PES. As noted above, we did select the efficient density functional theory UB3LYP/6-311+G(d,p)22 method to generate the electronic energies for the fitting database. We supplemented this database, as described below, with the more compute-intensive CASSCF(8,8)/6-311+G(d,p) calculations. These calculations were done using both Molpro200823 and Gaussian 200924 electronic structure codes. 11666

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Table 1. Stationary Point Energies (kcal mol−1) of the Fitted Potential Energy Surface (PES), UB3LYP/6-311+G(d,p) and UCCSD(T)/CBS Calculations and Zero Point Energies (ZPE)

CH3NO2 cis-CH3ONO transCH3ONO TS1 TS2 TS3 TS4 vdW CH3+NO2 CH3O+ NO CH2O + HNO

Figure 1. Distribution of electronic energies relative to the CH3NO2 global minimum used for the PES fit.

UB3LYP/6311+G(d,p)

PES

UCCSD(T)/ CBSa

ZPEc

0.0 3.98 4.06

0.0 3.85 3.94

0.0 2.51 3.94

31.17 30.18 30.00

59.58 67.65 46.31 17.02 17.79 60.04 42.51 21.31

59.98 66.35 46.25 16.29 17.78 60.07 42.35 21.34

65.79 72.2 54.3 14.79 15.8b 66.8 48.6 21.9

24.47 28.25 25.81 29.33 26.67 24.15 24.46 25.38

a Reference 15. bCalculated at the UCCSD(T)/cc-pVTZ//UB3LYP/ 6-311+G(d,p) level. cCalculated at the UB3LYP/6-311+G(d,p) level.

E0) for a configuration at energy E, where E0 is the electronic energy of the global minimum. The weighted (using the above weight) root-mean square deviation between the fitted potential energy surface and the database of energies is 0.56 kcal mol−1. The weighted rootmean square for the energy-points below 100 kcal mol−1 is 0.24 kcal mol−1. The total energies of QCT calculations of NM decomposition in the present work are at most 94.1 kcal mol−1. More detailed comparisons between the PES and direct electronic energies are given in the next subsection, which describes properties of the PES. II.C. Properties of the PES. We located all stationary points of ref 15 and a new van der Waals complex relevant to the CH2O + HNO fragments at the UB3LYP/6-311+G(d,p) level of theory, the method used for developing the PES. (The vdW complex was confirmed using the UCCSD(T)/ccpVTZ//UB3LYP/6-311+G(d,p) calculations.) Normal-mode analysis of the stationary points was also done at the UB3LYP/ 6-311+G(d,p) level of theory. Figure 2 shows the usual schematic of the “ZPE-corrected” potential energies from the fitted PES. The energy zero is the harmonic ZPE of CH3NO2 at the global minimum. The relative energies without ZPE are given in Table 1 and will be discussed below. The stationary point structures obtained from

optimization on the fitted PES are given in Figure 3; these are in very good agreement with optimized geometries at the UB3LYP/6-311+G(d,p) level. This schematic is in accord with previous ones, notably with the most recent one of Zhu and Lin,15 with some differences in the energies, as indicated below. For NM isomerization to the cis-CH3ONO (TS1), the C−N bond length changes from 1.49 to 3.33 Å. These agree well with the values of 1.5 and 3.6 Å, respectively reported by Zhu and Lin.15 There is also a tight isomerization transition state (TS2) that connects the GM to the trans-CH3ONO isomer. The C−N bond distance for TS2 is 1.98 Å at the UB3LYP/6-311+G(d,p) level and 2.09 Å with the PES. Also note that cis- and transCH3ONO both dissociate to CH3O + NO. There are two pathways to decomposition to CH2O + HNO. One is isomerization via the high energy TS2 to trans-CH3ONO and then via TS3 to the products. The other is to cis-CH3ONO via TS1 and then isomerization to trans-CH3ONO and then via TS3 to the products. Table 1 shows the energy comparison between the PES, the UB3LYP/6-311+G(d,p) and the benchmark UCCSD(T)/CBS stationary point energies in kcal mol−1 as well as zero point energies at the UB3LYP/6-311+G(d,p) level of theory. (The UCCSD(T)/CBS potential energies reported here are calculated from relative energies of Table 1 of ref 15 minus the recalculated ZPEs at the UB3LYP/6-311+G(3df,2p) level of theory that they used for geometry optimization and normalmode analysis.) As seen, and as already noted by Zhu and Lin, the largest differences in the DFT are roughly 6 kcal mol−1 from the benchmark ones (percent differences are roughly 10%) and, as is usually seen, the DFT energies, especially for the TS barriers are below the benchmark ones. Next we compare six minimum energy and intrinsic reaction coordinate (IRC) paths for the PES against direct UB3LYP/6311+G(d,p) calculations. First, we consider the dissociation of CH3NO2 and trans-CH3ONO to CH3 + NO2. This is illustrated in Figure 4, which shows two relaxed potential cuts, one is for dissociation from the GM to CH3 + NO2 and the other from trans-CH3ONO to CH3O + NO. As seen, the PES and direct electronic energies agree very well and there is no potential barrier for these dissociations. The PES harmonic D0 for the first path is 53.04 kcal mol−1, which is 6.76 kcal mol−1 below the UCCSD(T)/CBS result. The PES dissociation

Figure 2. Energy schematic for the fitted PES for CH 3NO2 isomerization-dissociation pathways. Energies include the harmonic zero-point energy and are relative the CH3NO2 minimum. 11667

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Figure 3. Structures (angstroms and degrees) of stationary points: (a) CH3NO2, (b) trans-CH3ONO, (c) cis-CH3ONO, (d) vdW, (e) TS1, (f) TS2, (g) TS3, (h) TS4. Optimized geometries parameters at UB3LYP/6-311+G(d,p) level (black) are given followed by PES values (red).

energy to CH3O + NO is 42.35 kcal mol−1 in good agreement with the UB3LYP/6-311+G(d,p) calculations and about 6 kcal mol−1 below the benchmark calculations. Intrinsic reaction coordinate (IRC) analyses26 were performed to confirm the connection between transition states and designated reactants, products or intermediates. Figure 5 shows a comparison of the direct electronic IRC from TS1 to the GM (negative s) and cisCH3ONO. As seen, there is good agreement between the PES and DFT calculations. As noted above, TS1 lies 53.28 kcal mol−1 above the ZPE of GM, 5.9 kcal mol−1 below the UCCSD(T)/CBS calculations. Figure 6 compares the TS2-IRC form the UB3LYP/6-311+G(d,p) calculations and the PES, where again very good agreement is seen between the PES and the direct electronic energies. Note that the barrier for this SP from the PES is 53.39 kcal mol−1, which is 5.96 kcal mol−1 below the benchmark value of ref 15. However, in both calculations TS2 is about 10 kcal mol−1 above TS1 (10.16 for the PES and 10.2 kcal mol−1 for the UCCSD(T)/CBS calculations.) Finally, Figure 7 compares IRCs for TS3 and the vdW well to CH2O and HNO from the PES and direct DFT calculations. The vdW complex is about 3.5 kcal mol−1 below the CH2O + HNO products asymptote at the UB3LYP/ 6-311+G(d,p) level of theory and the PES. The PES gives the CH2O + HNO electronic dissociation energy of 21.34 kcal mol−1 above the GM in a very good agreement with DFT calculations (21.31 kcal mol−1) and the UCCSD(T)/CBS

calculations (21.9 kcal mol−1). From these comparisons we conclude that the PES describes the electronic energies very accurately in comparison with the UB3LYP/6-311+G(d,p) calculations. But the DFT calculations and thus the PES too show at most 6 kcal mol−1 differences in relative energies compared to the benchmark UCCSD(T)/CBS calculations. Finally, we present the relevant harmonic vibrational frequencies of TS1 and CH3 + NO2 fragments in Table 2. As seen, the frequencies of TS1 and CH3 + NO2 are quite similar. This adds to the evidence that TS1 is located in the near dissociation channel of the radicals CH3 and NO2. This in turn supports the characterization of TS1 as a possible “roaming saddle point” made by Zhu and Lin. Next we consider some preliminary quasiclassical trajectory calculations of NM decomposition reactions R1, R2, and R3.

III. QUASICLSSICAL TRAJECTORY CALCULATIONS The QCT calculations of the NM decomposition were performed using the global fitted PES. We focused these calculations up to 10 kcal mol−1 above TS1. Specifically, calculations were initiated from the global minimum at six total energies, 84.3, 86.1, 87.5, 88.5, 90.1, and 94.1 kcal mol−1; these include the harmonic zero-point energy of NM, 31.2 kcal mol−1. Thus, these energies correspond to values of 53.1, 54.9, 56.3, 57.3, and 62.9 kcal mol−1 relative to the harmonic ZPE of NM. Referring to Figure 2, these span the threshold for 11668

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Figure 6. IRC for TS2 (isomerization path), calculated at the UB3LYP/6-311+G(d,p) level and compared with the PES.

Figure 4. CH3NO2 dissociation pathway to CH3 + NO2 (a) and transCH3ONO dissociation pathway to CH3O + NO products (b). The red curve is from the PES, and black squares are UB3LYP/6-311+G(d,p) energies.

Figure 7. IRC for TS3 (a) and vdW dissociation to CH2O + HNO (b) at the UB3LYP/6-311+G(d,p) level compared with the PES. Red lines show the PES, and black squares are the UB3LYP/6-311+G(d,p) level calculations.

Figure 5. IRC for TS1, calculated at the UB3LYP/6-311+G(d,p) level and compared with the PES.

formation of CH3 + NO to just below the energy of TS2. Initial conditions were generated using microcanonical sampling of the initial kinetic energy and with the constraint of zero total angular momentum. Ten thousand trajectories were run with a maximum of 4 000 000 steps (with 0.097 fs step-size) per energy. The trajectories were terminated when one of the internuclear distances became larger than 20 bohr.

As usual in QCT calculations, ZPE issues for the various products need to be addressed. Here we adopt the “softconstraint” in which trajectories are discarded if products are formed with less than the sum of the (harmonic) ZPEs of each fragment. This constraint enforces the correct threshold energy 11669

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Table 2. Harmonic Vibrational Frequencies (cm−1) of TS1 and CH3 and NO2 Fragments from the PES ω1 ω2 ω3 ω4 ω5 ω6 ω7 ω8 ω9

TS1

CH3

679 747 1376 1390 1409 1662 3159 3307 3315

563

NO2 703 1382

1425 1436 1697 3142 3322 3325

Figure 10. Longest C−N distances distribution of isomerization step for reactive trajectories leading to CH3O + NO.

channels, shown in Figure 8. As seen, just at the threshold for formation of CH3 + NO2, the channel CH3O + NO dominates, with a small amount of flux in the CH2O + HNO channel. As expected, and totally consistent with the previous statistical calculations of Zhu and Lin, the contribution of channel R2 decreases and the fraction of channel R1 increases rapidly with the total energy. The fraction of channel R3 remains small and does not change more than 0.09 with increasing energy. We examined a number of trajectories that form the CH3O + NO products, and a typical one is depicted in Figure 9. As seen, the energized CH3NO2 initially enters the dissociation channel CH3---NO2, and at a CN distance of roughly 4.58 Å these incipient fragments reorient and recombine to transiently form the cis-CH3ONO isomer, which goes on to form CH3O + NO. This mechanism is consistent in words with the one proposed originally by Wodtke et al.7 and also in the calculations of Zhu

Figure 8. Energy dependence of branching for the reaction products indicated.

for formation of products and is consistent with the energies shown in Figure 2. With the above constraint in mind, consider the energy dependence of the branching ratio for the three product

Figure 9. Potential energy relative to the CH3NO2 global minimum and several frames for a sample trajectory of energy 53.2 kcal mol−1 (relative to the CH3NO2 zero-point energy) leading to CH3O and NO. 11670

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(2) Lao, K. O.; Jensen, E.; Kash, P. W.; Butler, L. J. Polarized Emission Spectroscopy of Photodissociating Nitromethane at 200 and 218 nm. J. Chem. Phys. 1990, 93, 3958−3969. (3) Rockney, B. H.; Grant, E. R. Resonant Multiphoton Ionization Detection of the NO2 Fragment from Infrared Multiphoton Dissociation of CH3NO2. Chem. Phys. Lett. 1981, 79, 15−18. (4) Blais, N. C. Photofragmentaion of Nitromthane in a Molecular Beam at 193 nm. J. Chem. Phys. 1983, 79, 1723−1731. (5) Moss, D. B.; Trentelman, K. A.; Houston, P. L. 193 nm Photodissociation Dynamics of Nitromthane. J. Chem. Phys. 1992, 96, 237−247. (6) Guo, Y. G.; Bhattacharya, A.; Bernstein, E. Photodissociation Dynamics of Nitromethane at 226 and 271 nm at Both Nanosecond and Femtosecond Time Scales. J. Phys. Chem. A 2009, 113, 85−96. (7) Wodtke, A. M.; Hintsa, E. J.; Lee, Y. T. Infrared multiphoton dissociation of three nitroalkanes. J. Phys. Chem. 1986, 90, 3549−3558. (8) Dewar, M. J. S.; Ritchie, J. P.; Alster, J. Ground States of Molecules. 65. Thermolysis of Molecules Containing NO2 Groups. J. Org. Chem. 1985, 50, 1031−1036. (9) Zhang, Y. X.; Bauer, S. H. Gas-Phase Decomposition Mechanisms of C-NO2, N-NO2 Energetic Materials: Reevaluations. J. Chem. Kinet. 1999, 31, 655−673. (10) Mckee, M. L. Ab Initio Study of Rearrangements on the Nitromethane Potential Energy Surface. J. Am. Chem. Soc. 1986, 108, 5784−5792. (11) Mckee, M. L. MCSCF Study of the Rearrangement of Nitromethane to Methyl Nitrite. J. Phys. Chem. 1989, 93, 7365−7369. (12) Saxon, R. P.; Yoshimine, M. Theoretical studt of nitro-nitrite rearrengment of CH3NO2. Can. J. Chem. 1992, 70, 572−579. (13) Nguyen, M. T.; Le, H. T.; Hajgató, B.; Veszprémi, T.; Lin, M. C. Nitromethane-Methyl Nitrite Rearrangement: A Persistent Discrepancy between Theory and Experiment. J. Phys. Chem. A 2003, 107, 4286−4291. (14) Hu, W. F.; He, T. J.; Chen, D. M.; Liu, F. C. Theoretical Study of the CH3NO2 Unimolecular Decomposition Potential Energy Surface. J. Phys. Chem. A 2000, 106, 7294−7303. (15) Zhu, R. S; Lin, M. C. CH3NO2 decomposition/isomerization mechanism and product branching ratios: An ab initio chemical kinetic study. Chem. Phys. Lett. 2009, 478, 11−16. (16) Brown, H. W.; Pimentel, G. C. Photolysis of Nitromethane and of Methyl Nitrite in an Argon Matrix; Infrared Detection of Nitroxyl, HNO. J. Chem. Phys. 1958, 29, 883−888. (17) Townsend, D.; Lahankar, S.; Lee, S.; Chambreau, S.; Suits, A.; Zhang, X.; Rheinecker, J.; Harding, L.; Bowman, J. M. The Roaming Atom: Straying from the Reaction Path in Formaldehyde Decomposition. Science 2004, 306, 1158−1161. (18) Suits, A. G. Roaming Atoms and Radicals: A New Mechanism in Molecular Dissociation. Acc. Chem. Res. 2008, 41, 873−881. (19) Bowman, J. M.; Shepler, B. C. Roaming Radicals. Annu. Rev. Phys. Chem. 2011, 62, 531−553. (20) Hause, M. L.; Herath, N.; Zhu, R. S.; Lin, M. C.; Suits, A. G. Roaming-Mediated Isomerization in the Photodissociation of Nitrobenzene. Nat. Chem. 2011, 3, 932−937. (21) Bowman, J. M.; Czakó, G.; Fu, B. High-Dimensional Ab Initio Potential Energy Surfaces for Reaction Dynamics Calculations. Phys. Chem. Chem. Phys. 2011, 13, 8094−8111. (22) Becke, A. D. Densityfunctional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (23) Werner H. J.; Knizia G.; Mandy F. R.; Schütz M.; Celani P.; Korona T.; Lindh R.; Mitrushenkov A.; Rauhut G.; Shamasundar K. R.; et al. MOLPRO, version 2008. http://www.molpro.net. (24) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R .; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. GAUSSIAN 09, Revision A02; Gaussian, Inc.: Wallingford, CT, 2009. (25) Braams, B. J.; Bowman, J. M. Permutationally Invariant Potential Energy Surfaces in High Dimensionality. Int. Rev. Phys. Chem. 2009, 28, 577−606.

and Lin. However, the distance of 4.58 Å is roughly an angstrom larger than the CN bond length at TS1. We examined the maximum distance in this bond length for trajectories forming the CH3O + NO products for isomerization step at 84.3 kcal mol−1. Figure 10 shows the distribution of the maximum CN bond length for trajectories that form the CH3O + NO products before dissociation. As seen, the maximum in this distribution is 4.6 Å, which as noted already is larger than the CN distance at TS1, the putative bottleneck for the products CH3O + NO. Thus, despite this TS being “loose”, the trajectories do sample considerably larger regions of configuration space. In this sense, trajectories stray considerably from this loose TS and in this sense we can use the term “roaming” to describe the dynamics to the CH3O + NO channel. However, isomerization does clearly occur prior to formation of these products and so the terminology “roaming mediated isomerization”20 is more apropos of the dynamics. It should be noted that such dynamics has also been observed in a QCT study of the HO + NO2 reaction, in which large distance isomerization of HOONO to HONO2 occurs.27 The wealth of information in the QCT calculations, including internal energy distributions of the products, will be presented in a future report, which will also include comparisons with experiments underway by Suits and coworkers.28

IV. SUMMARY AND CONCLUSIONS We reported a global potential energy surface for CH3NO2 that describes the global minimum, the cis and trans isomers, and fragment channels CH3 + NO2, CH3O + NO, and CH2O + HNO as well as numerous saddle points. The PES is a permutationally invariant, precise fit to roughly 114 000 electronic energies most at the DFT/B3LYP/level of theory supplemented with some CASSCF calculations. The PES faithfully reproduces the reaction energetics and pathways for this complex system. Preliminary quasiclassical trajectory calculations were performed on this PES, and the branching ratio to form the products CH3 + NO2, CH3O + NO, and CH3 + HNO was presented as a function of the total energy of CH3NO2. An examination of trajectories to form CH3O + NO indicates a roaming-mediated isomerization pathway to these products. Although this pathway is somewhat related to the loose transition state identified as a possible “roaming” pathway, the trajectories do stray considerably from this TS in the present calculations.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the Army Research Office (W911NF11-1-0477) is gratefully acknowledged. We thank Arthur G. Suits and Rongshun Zhu for discussions.

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REFERENCES

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