Direct Dynamics Simulations of the CH

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A: Kinetics, Dynamics, Photochemistry, and Excited States 2

2

Direct Dynamics Simulations of the CH + O Reaction on the Ground and Excited State Singlet Surfaces Sandhiya Lakshmanan, Subha Pratihar, and William L. Hase J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b02656 • Publication Date (Web): 29 Apr 2019 Downloaded from http://pubs.acs.org on April 30, 2019

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The Journal of Physical Chemistry

Direct Dynamics Simulations of the CH2 + O2 Reaction on the Ground and Excited State Singlet Surfaces

Sandhiya Lakshmanan, Subha Pratihar, and William L. Hase* Department of Chemistry and Biochemistry Texas Tech University Lubbock, TX 79409 *Corresponding author E-mail: [email protected]

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ABSTRACT In previous work (Lakshmanan, S.; Pratihar, S.; Machado, F. B. C.; Hase, W. L. J. Phys. Chem. A 2018, 122, 4808-4818) direct dynamics simulations at the M06/6-311++G(d,p) level of theory were reported for 3CH2 (X3B1) + 3O2 (X3∑ ― ) reaction on its ground state singlet potential energy 𝑔

surface (PES) at 300 K. However, further analyses revealed the simulations are unstable for the 3CH

2

(X3B1) + 3O2 (X3∑ ― ) reactants on the ground state singlet surface and the trajectories 𝑔

reverted to an excited state singlet surface for the 1CH2 (𝑎1A1) + 1O2 (b1∑ + ) reactants. Thus, the 𝑔

dynamics reported previously are for this excited state singlet PES. The PESs for the 3CH2 (X3B1) ―

+

+ 3O2 (X3∑𝑔 ) and 1CH2 (𝑎1A1) + 1O2 (b1∑𝑔 ) reactants are quite similar and this provided a means ―

to perform simulations for the 3CH2 (X3B1) + 3O2 (X3∑𝑔 ) reactants on the ground state singlet PES at 300 K, which are reported here. The reaction dynamics are quite complex with seven different reaction pathways and nine different products. A consistent set of product yields have not been determined experimentally, but the simulation yields for the H-atom, CO, and CO2 are somewhat lower, higher and lower respectively, than recommended values. The yields for the remaining six products agree with experimental values. Product decomposition was included in determining the product yields. The simulation 3CH2 + 3O2 rate constant at 300 K is only 3.4 times smaller than the recommended value, which may be accommodated if the 3CH2 + 3O2 → 1CH2O2 potential energy curve is only 0.75 kcal/mol more attractive at the variational transition state for 3CH

2

+ 3O2 → 1CH2O2 association. The simulation kinetics and dynamics for the 3CH2 + 3O2 and

1CH

2

+ 1O2 reactions are quite similar. Their rate constants are statistically the same, an expected

result, since their transition states leading to products have energies lower than that of the reactants and the attractive potential energy curves for 3CH2 + 3O2 → 1CH2O2 and 1CH2 + 1O2 → 1CH2O2 are nearly identical. The product yields for the 3CH2 + 3O2 and 1CH2 + 1O2 reactions are also nearly identical, only differing for the CO2 yield. The reaction dynamics on both surfaces are predominantly direct, with negligible trapping in potential energy minima, which may be an important contributor to their nearly identical product yields.


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I. INTRODUCTION Methylene (CH2) is formed as a primary product from the reaction between acetylene and oxygen atoms in the gas phase.1 Methylene is formed in both triplet, CH2 (X3B1) and singlet electronic states, CH2 (𝑎1A1), with 3CH2(X3B1) being 9 kcal/mol lower in energy than 1CH2 (𝑎 1A

2

1).

The reaction between methylene and molecular oxygen contribute significantly to the

combustion of hydrocarbons.3 This reaction opens up pathways for formation of stable species such as CO, CO2, H2CO, H2, H2O and open-shell species such as OH and CHO radicals. Both ground and excited state singlet potential energy surfaces (PESs) were considered for the CH2 + O2 reaction dynamics. The former connects to the 3CH2 (X3B1) + 3O2 (X3∑ ― ) reactants 𝑔

and the latter to the 1CH2 (𝑎1A1) + 1O2 (b1∑ + ) reactants. As shown in Figure 1, the potential energy 𝑔

curves are similar for these two singlet surfaces. They have the same potential energy minima and transition states (TSs), but the energies for these stationary points are different for the two PESs. Both surfaces form the same singlet products, with a larger potential energy release for the 1CH2 + 1O2 reactants; i.e. the experimental energy difference between the 1CH2 (𝑎1A1) + 1O2 (b1∑ + ) and 𝑔

3CH

2

(X3B1)+

3O (X3 ― ∑𝑔 ) 2

reactants is 49.7 kcal/mol and the value for the M06/6-311++G(d,p)

theory4-6 used to calculate the potential energy curves in Figure 1 with the NWChem program package7 is 60.3 kcal/mol, including a harmonic zero-point energy (ZPE) correction. In a recent study,8 UM06/6-311++G(d,p) direct dynamics simulations were reported for the 3CH2 (X3B1) + 3O2 (X3∑ ― ) reaction on the ground state singlet surface. However, analyses of 𝑔

the product energies have shown that the simulations were for the excited state singlet surface, originating from 1CH2 (𝑎1A1) and 1O2 (b1∑ + ), and not the ground state. In analyzing the origin of 𝑔

this result, it was found that the UM06/6-311++G(d,p) calculations, for the separated 3CH2 + 3O2 reactants, are not stable for the ground state surface. In initiating the trajectories with UM06/6311++G(d,p) for the 3CH2 + 3O2 reactants, the electronic structure calculations reverted to the 1CH2 (𝑎1A1) + 1O2 (b1∑ + ) excited state singlet surface. Thus, the previous simulation results are for this 𝑔

excited state singlet surface.



In the work presented here a procedure is described for performing the simulations on the ground state PES. The 3CH2 + 3O2 reaction dynamics are then studied on this surface and the results compared with experiment and the previous simulation for the excited state singlet PES. The reaction dynamics are quite complex with multiple product channels. From the reaction energetics and results from the previous study,8 the following eleven product channels are possible for the ground and excited state PESs.

The ∆E0, is the 0 K UM06/6-311++G(d,p) reaction energy with harmonic ZPE correction, for 3CH2 + 3O2 reaction on the ground state PES. The reaction energies for the excited state singlet surface are 60.3 kcal/mol higher with the NWChem computer program. It is found that the ground and excited state singlet PESs give very similar reaction cross sections and product branching ratios. II. COMPUTATIONAL METHODS II. A. Electronic Structure Calculations and Initiating Trajectories for the Ground State Singlet Surface The calculations reported here were performed with the UM06/6-311++G(d,p) electronic structure theory.4-6 Previous work9 indicated that M06 may provide an appropriate description of the multireference nature of the wavefunction. All minima on the PES were confirmed with all positive frequencies and each transition state had only one imaginary frequency, confirming its 4 ACS Paragon Plus Environment

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maximum. The NWChem computer program7 was used for the electronic structure calculations. As discussed recently,10 NWChem gives incorrect DFT values for the energy separation between 3O

2

and 1O2 electronic states and this is discussed below. For some orientations of separated 3CH2 (X3B1) + 3O2 (X3∑ ― ), the UM06 electronic 𝑔

structure calculations were not stable for the ground state singlet surface. It was not possible to converge the SCF component of the calculations. Multiple approaches were undertaken to resolve this problem, but none were successful. Thus, it was not possible to initiate the trajectories on the ground state singlet surface with randomly orientated 3CH2 and 3O2. However, the calculations for the ground state singlet become stable when 3CH2 and 3O2 strongly interact in approaching the 1CH

2O2

potential energy minimum in Figure 1.

In contrast to the above instability in the electronic structure calculations for the ground state singlet, the calculations are stable for the excited state 1CH2 (𝑎1A1) and 1O2 (b1∑ + ) singlet. 𝑔

This provided a strategy for performing the simulations for the ground state singlet. As shown in Figure 1, the UM06/6-311++G(d,p) potential energy curves for the ground and excited state singlets, in forming their 1CH2O2 Criegee intermediates are very similar. In fact, they are nearly identical for a C-O separation as short as 1.95 Å. Thus, the trajectories were initiated on the excited singlet PES and then moved to the ground singlet PES when the C-O distance reached 1.95 Å. In this manner, it was possible to perform the direct dynamics simulation for the ground state singlet PES. It should be noted that a somewhat similar strategy was used for previous direct dynamics simulations by the Hase research group.11,12 For the F + CH3CN → HF + CH2CN reaction, the M06-2X/6-311++G(d,p) direct dynamics simulations became unstable in the product exit-channel and the trajectories were switched to a MP2/6-311++G(d,p) PES.11 In B97-1/ECP/d13 direct dynamics simulation, trajectories for [CH3--I--OH]− dissociation to CH3I + OH− were not numerically stable and continued on a CAM-B3LYP/ECP/d PES.12 TDDFT14 calculations were performed with M06-2X/6-311++G(d,p) to ensure proper characterization of the CH2 + O2 singlet electronic states. Both NWChem and Gaussian15 gave the same TDDFT energies for these electronic states. The ground state is a singlet originating from 2

(X3B1) and3O2 (X3∑ ― ). The first excited singlet state originates from 1CH2 (𝑎1A1) and 1O2

𝑔).

The second excited state, and the excited singlet state considered here, originates from 1CH2

3CH

(1∆

𝑔

(𝑎1A1) and 1O2 (b1∑ + ). The respective TDDFT energies for these states are 0.0, 26.4 and 51.9 𝑔



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kcal/mol. The DFT/M06/6-311++G(d,p) used for the dynamics presented here, gives classical energies of 0.0, 48.9 and 62.7 kcal/mol using NWChem, and 0.0, 29.7, and 48.6 kcal/mol using Gaussian. Each of these states forms the same ground state products as illustrated in Figure 2. Using NWChem for the 1CH2 (𝑎1A1) + 1O2 (b1∑ + ) excited state DFT dynamics, as done 𝑔

here, results in an energy for the reactants that is ~ 10 kcal/mol too high as compared to experiment and found with Gaussian. The result is that the energies available to the products is too high by this amount. Stationary point structures and energies for the ground state singlet PES, found with NWChem and Gaussian are in good agreement. This comparison was not made for the 1CH2 (𝑎1A1) + 1O2 (b1∑ + ) excited state PES, used for the direct dynamics. 𝑔

II. B. Direct Dynamics Simulations Direct dynamics simulations for the 3CH2 + 3O2 reaction were performed using UM06/6311++G(d,p) theory. As described above, the trajectories were initiated on the excited singlet PES for 1CH2 + 1O2 and then switched to the ground state PES for 3CH2 + 3O2 when a C-O distance for CH2 + O2 became ~ 1.95 Å. The VENUS chemical dynamics computer program16,17 interfaced with the NWChem electronic structure program18 was used for the simulations, which were performed for a temperature of 300 K. The 1CH2 + 1O2 relative translational energy is 0.9 kcal/mol, equivalent to 3RT/2 at 300 K temperature. The vibrational and rotational energies for 1CH2 and 1O

2

were sampled from their 300 K Boltzmann distributions. These energies were transformed into

the Cartesian coordinates and momenta required for trajectory calculations using quasiclassical sampling.19 Both 1O2 and 1CH2 were randomly rotated with an initial center-of-mass separation of 8 Å. The velocity-Verlet algorithm20 was used to integrate the trajectories with an integration time step of 2 fs. The total integration time for each trajectory was 2 ps. Selection of initial conditions for the trajectories are standard options in VENUS.19 II. C. Analyses of Simulation Results From the trajectory calculations various dynamical properties were analyzed. The reactive cross section is calculated from the reaction probability using the expression

 rxn 

bmax

 P (b)2bdb r

(1)

0

where b is the impact parameter at which the reactions are sampled and bmax is the maximum impact parameter at which reaction was observed. Pr(b) is the reaction probability corresponding 6 ACS Paragon Plus Environment

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to each value of b. A total of 100 trajectories were calculated for each b. Using the reactive cross section and the relative velocity (vrel) of the reactants, the rate constant of the reaction (k) was calculated using the expression

k   rxn v rel

(2)

which is sufficiently accurate since the reaction cross section is not strongly energy dependent.21,22 Reactive trajectories were categorized by visualizing and determining their atomic level mechanisms. The rate constant and the product branching ratios were compared with available experimental results. The reported uncertainties in the calculated cross sections, reaction probabilities, and product yields are standard deviations. Each trajectory was analyzed, at the time its integration was terminated, to determine its product energy partitioning from the total available energy. Rotational (Erot) and vibrational (Evib) energy was calculated for each product molecule. For product channels with two products, their relative translational energy (Erel) was calculated with respect to the center-of-mass of the system. This analysis was made for channels R1, R2, R5 and R10 identified in the introduction. For the channels R4, R8, R9, and R11, where three products are formed, the translational (Etrans) of each species with respect to its center-of-mass was calculated. The rotational energy of a product molecule was given by 𝐸𝑟𝑜𝑡 =

1

2𝛚.𝐣

(3)

where ω is the angular velocity and j the angular momentum. The molecule’s vibrational energy was then determined by subtracting Erot from the molecule’s total vibrational-rotational internal energy. Vibrational, n, and rotational, J, quantum numbers were determined for the H2, CO, and OH diatomic products, which was facilitated by fitting the M06/6-311++G(d,p) potential energy curves by the Morse function, i.e. 𝑉(𝑟) = 𝐷[1 ― exp{ -𝛽(𝑟 ― 𝑟𝑒𝑞)}]2. The fitted Morse parameters are: H2, D = 116.0 kcal/mol, β = 1.90 Å-1, req = 0.75 Å; CO, D = 272.5 kcal/mol, β = 2.34 Å-1, req = 1.13 Å; and OH, D = 113.7 kcal/mol, β = 2.29 Å-1, req = 0.97 Å. The fundamental harmonic frequencies calculated from the Morse parameters are 4419, 2262, and 3853 cm-1 for H2, CO, and OH, respectively. The internal energy for a diatomic product is given by



𝐸𝑖𝑛𝑡 =

𝑝2𝑟

𝑗2

2𝜇 + 𝑉(𝑟) + 2𝜇𝑟2

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(4)

where pr is the momentum along the internuclear axis and V(r) is the fitted Morse potential. The rotational quantum number is found from the angular momentum by 𝑗 = 𝐽(𝐽 + 1)ħ

(5)

Einstein-Brillouin-Keller (EBK) semiclassical quantization19 was used to determine the vibrational quantum number

(𝑛 + )ℎ = ∮𝑝𝑟𝑑𝑟 1 2

(6)

Vibrational energies for the product diatoms are corrected by their Morse anharmonic zero-point energies (ZPE), whereas the polyatomic products vibrational energies are corrected by harmonic zero-point energies (ZPE). The above procedures for determining product energies and quantum numbers follow that described previously for F---HCH2CN post-transition state product energy partitioning.23 When the trajectories were terminated, some of the product molecules contained sufficient internal energy to undergo secondary dissociations. Dissociation was assumed to occur if the total energy of the product molecule was in excess of its classical dissociation energy plus the product ZPE. The 0 K quantum dissociation energies for CO2 → CO + O(1D), H2O → H + OH, and HCO → H + CO were taken from the literature24 and are 171.12, 117.64 and 14.53 kcal/mol, respectively. These energies are from the reactant zero point energy level to the product zero point energy level. The harmonic M06/6-311++G(d,p) ZPEs of the reactant molecules, which are 7.5, 14.4, and 8.4 for CO2, H2O, and HCO, respectively, were then added to these energies to determine the energy criteria for dissociation, which are 178.6, 132.0, and 22.9 kcal/mol for CO2, H2O and HCO, respectively. The classical barrier for H2CO → H2 + CO molecular dissociation is 87.4 kcal/mol25 and with the transition state ZPE25 added the energy criterion for dissociation is 98.8 kcal/mol. For comparison with the above energetic criteria for dissociation, M06/6-311++G(d,p) values for the CO2, H2O, and HCO energies were determined by adding the product ZPE to the classical dissociation energy. The respective values are 171.7, 137.3, and 30.2 kcal/mol. III. RESULTS OF DIRECT DYNAMICS SIMULATIONS III. A. Reaction Pathways and Reaction Probabilities versus Impact Parameter


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Reaction dynamics on the ground state singlet PES were studied versus collision impact parameter b at a temperature of 300 K, for which the collision energy Erel is 0.9 kcal/mol. The simulations were performed for b values of 0 to 6 Å at intervals of 1 Å. At the largest b of 6 Å no reactions were observed, identifying bmax. Eight pathways R1, R2, R4, R5, R8, R9, R10 and R11 defined in the Introduction, were identified in the simulations. The total reaction probability Pr(b) and those for the above pathways, versus b, are shown in Figure 3. For the ground state singlet surface, the total reaction probability is 0.72, 0.60 and 0.64, respectively for b = 1, 2 and 3 Å and then rapidly drops with increasing b. The probability for formation of CO + H2O (R2) is high for b = 1 - 3 Å, followed almost equally by CO2 + H2 (R1) and CO + OH + H (R8). The least probable channel is CO + H2 + O (R9). At b = 5 Å, only reactions R5 and R10 are observed. On examining the trajectories, it was seen that all of the trajectories pass through the minimum of the 1CH2OO complex, with most of the trajectories not forming the complex with a lifetime. A total of 25 trajectories formed the 1CH2OO complex; i.e. with proper weighting of the impact parameter, 1.7% of the collisions formed a 1CH2OO complex. Only 2 trajectories formed dioxirane with a lifetime. For the previous direct dynamics simulations of 1CH2 + 1O2 reaction on the excited state singlet surface,8 Pr(b) for each reaction pathway and for total reaction are presented in Figure 3, where they are compared with the current results for the 3CH2 + 3O2 ground state singlet surface. The total Pr(b) for the two surfaces are very similar. The major differences in the individual Pr(b) is for HCO + OH product channel, R5. For the HCO + O + H product channel, R11, there were no reactive trajectories for the ground state PES and only one reactive trajectory for the excited state PES. III. B. Reaction Cross Sections III. B. 1. Results without Considering Product Decomposition From the reaction probabilities in Figure 3 and using eq. 1, the total cross section and cross sections for the individual product channels were calculated and summarized in Table 1, where they are compared with the previous results for 1CH2 + 1O2. The cross sections for the two surfaces are very similar, with the major differences for the HCO + OH and CO2 + H + H pathways. Some of the trajectories do not react and remain as either 1CH2OO or dioxirane when they are terminated at 2 ps. For the ground state PES, the cross section for these trapped trajectories is 4.3 Å2, for which 93% is for 1CH2OO and 7% for dioxirane. For the excited state PES, these respective 9 ACS Paragon Plus Environment


numbers are 5.4 Å2, 92% and 8%. The cross section for these trapped trajectories constitutes 13 and 17% of the total cross section for the ground and excited states PESs, respectively. Though an approximation, if these trajectories are assumed to form products in accord with the product branching ratios found here, the cross sections for forming products increase as given in Table 1. However, as discussed below, there are not any significant changes in the product yields. III. B. 2. Results Considering Product Decomposition When the trajectories were terminated, some of the product molecules contained sufficient internal energy to undergo secondary dissociations. As discussed in Section II. C, dissociation was assumed to occur if the total energy of the product molecule was in excess of its classical dissociation energy plus the product ZPE. None of the CO2 product molecules contained sufficient internal energy to dissociate to CO and O(1D), as was also the case for H2CO dissociation to H2 + CO. In contrast, H2O and HCO product molecules had sufficient internal energy to dissociate. The average H2O internal energy was 132.82 and 103.23 kcal/mol for the CO + H2O (R2) product channel for the excited and ground state dynamics, respectively. For the excited state, 57% of H2O dissociates to HO + H, while this percentage is 27% for the ground state. For the HCO + OH (R5) product channel, the average HCO internal energy is 51.39 and 28.96 kcal/mol for the excited and ground state PESs respectively. The respective HCO → H + CO dissociation for these two surfaces are 100% and 95%. Taking these dissociations into account, reaction cross sections for the reactive trajectories are given in Table 2 for both the ground and excited state singlet PESs. As discussed above, some of the trajectories remained trapped as 1CH2OO or dioxirane in Figure 2, when the trajectories were terminated. To account for these trajectories, it was assumed they form products with the same branching ratios as for the reactive trajectories. Cross sections, with this accounting of the trapped trajectories, are also included in Table 2. Comparison of the cross sections in Tables 1 and 2, shows that decomposition is more important for the excited state surface, since the products contain more energy. For each surface, the principal differences between the cross sections without and with corrections for product decomposition are for the CO + H2O, CO + OH + H, HCO + O + H and HCO + OH pathways. III. C. Product Yields Product yields were calculated from the reactive cross sections obtained from the ground and excited state singlet simulations, following the procedure used to analyze experimental product 10 ACS Paragon Plus Environment

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yields for the 3CH2 + 3O2 reaction.3 The cross sections used for this analysis are those for which product decomposition is considered and dissociation of the trapped trajectories is accounted for. The product yields for the dynamics on the excited and ground state PESs are summarized in Table 3. The product yields for the two surfaces are remarkably similar. Only for CO2 do the two yields not agree within statistical uncertainties. The product yields for the excited state are different than those reported earlier (incorrectly for the ground state),8 since the previous study did not consider product decomposition. As discussed below, the ground state singlet product yields may be compared with experiment if the ground state singlet PES dominates the 3CH2 + 3O2 reaction over the ground state triplet PES. III. D. Product Energy Partitioning Partitioning of the available product energy to translation, rotation, and vibration of the products was determined for each product channel, for the simulations on both the ground and excited state singlet surfaces. In Table 4, the product energy partitioning is presented as fractions of the available energy partitioned to the different product degrees of freedom. Overall, product energy partitioning is similar for the ground and excited state dynamics. The most significant difference in their dynamics is for reaction R4, forming CO2 + H + H, where for the excited state energy partitioning to rotation and translation is higher and to vibration is lower. For the ground state dynamics, energy partitioning to product vibration is more than 50% for each reaction, with the highest and lowest partitioning to vibration for R10 and R9, respectively. For the excited state, energy transfer to vibration is also highest for R10, with similar lowest energy transfers to vibration for R4 and R9. The average vibrational and rotational quantum numbers, and , are given in Table 5 for the diatomic products of reactions R1, R2, R5, R8, and R9. The patterns in and are similar for ground and excited states, except the and values are larger for the excited state as a result of the larger reaction exothermicities. CO is formed in high J states in reactions R2, R8, and R9. CO vibrational excitation is higher for R2 than for R8 and R9. For R8, OH receives more vibrational excitation than CO. However, for R9 CO and H2 receive similar vibrational excitations. IV. Comparison with Experiment



The 3CH2 + 3O2 rate constant and product yields determined from the simulations on the ground state singlet PES may be compared with experiment. As given in Table 1, the total reaction cross section for the ground state PES is 32.0 ± 9.6 Å2 resulting in a 300 K rate constant of 0.96 ± 0.28 x 10-12 cm3molecule-1s-1 using Eq. (2) with a correction for spin degeneracies.26,27 The 3CH2 + 3O2 collisions are on quintet and triplet PESs, in addition to the ground state singlet and 1/9 of the collisions are on the singlet surface. The reaction cross section is multiplied by this factor in obtaining the rate constant. Collisions of 3CH2 + 3O2 on the quintet surface are highly repulsive and do not contribute to the reaction rate. As shown in Figure 1, for the UM06/6-311++G(d,p) theory used here, the 3CH

2

+ 3O2 → 1CH2O2 classical potential energy curve is purely attractive with no barrier. In

previous CASSCF/CASPT2 calculations,28 the 298 K activation enthalpy for reaction on the triplet surface is 3.5 kcal/mol higher than for the singlet surface. This result suggests reaction on the triplet surface is unimportant at 300 K, which is assumed for the analysis made here. From above, the rate constant for reaction on the singlet surface is 0.96 ± 0.28 x 10-12 cm3molecule-1s-1. In contrast, the recommended value is 3.3 x 10-12 cm3molecule-1s-1; i.e. 3.4 times larger. This factor may be accommodated if the 3CH2 + 3O2 → 1CH2O2 potential energy curve is only 0.75 kcal/mol more attractive at the variational transition state29 for 3CH2 + 3O2 → 1CH2O2 association. Experimental measurements of the 3CH2 + 3O2 product yields3,30-34 and the current results for reaction on the ground state singlet surface are compared in Table 6. There are differences between the experimental findings. The most extensive experimental studies are those by Alvarez and Moore30 and Bley et al.32 In addition, from analyses of the experimental measurements, product yields were suggested by Blitz et al.31 and Leung and Lindstedt.34 Overall, the results of Alvarez and Moore,30 Blitz et al.,31 and Leung and Lindstedt34 are consistent and in agreement. There are agreements and disagreements between the simulation and experimental product yields. The simulations are in disagreement with the above three experimental studies for the yields of H, CO, and CO2. Compared to these three experiments, the simulation yields are too low for H, too high for CO, and too low for CO2. Given statistical uncertainities, the upper bound for the simulation H yield of 0.54 ± 0.20 almost matches the suggested value of 0.78,31,34 but agrees with the value of 0.8 ± 0.2.33 The lower bound for the simulation CO yield of 0.64 ± 0.26 is consistent with the yields suggested by Alvarez and Moore,30 Blitz et al.,31 and Leung and Lindstedt.34 The CO simulation yield agrees with the value of 0.72 by Lindstedt and Skevis.3 12 ACS Paragon Plus Environment

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V. Summary The 3CH2 + 3O2 reaction dynamics are complex and the UM06/6-311++G(d,p) direct dynamics simulations reported here are quite demanding. A previous direct dynamics simulation of the 3CH2 + 3O2 reaction dynamics reported results for the singlet ground state PES, but further analyses of the simulations showed that the actual dynamics were on the 1CH2 (𝑎1A1) and 1O2 (b1∑ + ) excited 𝑔

state singlet surface. The UM06/6-311++G(d,p) electronic structure calculations are unstable for some orientations of the separated 3CH2 + 3O2 reactants and the direct dynamics reverted to the excited singlet state PES. For the work reported here, a strategy was found for performing the 3CH2 + 3O2 reaction dynamics on the ground state singlet PES. The 3CH2 + 3O2 potential energy curve leads to the 1CH

2O2

Criegee intermediate. The UM06 electronic structure calculations and direct dynamics

become stable as 3CH2 + 3O2 approach this intermediate, which provides a means for performing the 3CH2 + 3O2 direct dynamics on the ground state singlet PES. As shown in Figure 1, the 3CH2 + 3O2 → 1CH2O2 and 1CH2 + 1O2 → 1CH2O2 potential energy curves are nearly identical and the direct dynamics were initiated on the 1CH2 + 1O2 PES and then shifted to the 3CH2 + 3O2 → 1CH2O2 PES when a C-O distance reached ~ 1.95 Å. In this manner it was possible to perform the 3CH2 + 3O

2 direct

dynamics simulation on the ground state singlet PES.

A comparison of potential energy curves for 3CH2 + 3O2 reaction on the ground state singlet and triplet PESs,28 indicates that reaction occurs on the singlet PES at 300 K. From the direct dynamics simulations, the calculated rate constant is 0.96 ± 0.28 x 10-12 cm3molecule-1s-1 and 3.4 times smaller than the recommended 3CH2 + 3O2 reaction rate of 3.3 x 10-12 cm3molecule-1s-1. This difference may be accommodated if the 3CH2 + 3O2 → 1CH2O2 potential energy curve is only 0.75 kcal/mol more attractive at the variational transition state for 3CH2 + 3O2 → 1CH2O2 association. The 3CH2 + 3O2 reaction dynamics on the ground state singlet surface is quite complex with seven different reaction pathways and nine different products. A consistent set of product yields have not been determined experimentally, but the simulation yields for the H-atom, CO, and CO2 are somewhat lower, higher and lower respectively, than the recommended values by Alvarez and Moore,30 Blitz et al.,31 and Leung and Lindstedt.34 The yields for the remaining six products agree with experimental values. The 3CH2 + 3O2 reaction has an entrance channel potential energy well for the 1CH2O2 Criegee intermediate. However, trapping of trajectories in this well is negligible and a statistical model is not applicable for calculating the product branching ratio. The trajectories 13 ACS Paragon Plus Environment


result in a preponderance of direct reaction, without any trapping which may result in statistical dynamics. Remarkably, the reaction dynamics are quite similar on the 3CH2 + 3O2 ground state singlet PES and the 1CH2 (𝑎1A1) + 1O2 (b1∑ + ) excited state singlet PES. The reaction rate constant for 𝑔 the ground state surface is 0.96 ± 0.28 x 10-12 cm3molecule-1s-1 and nearly the same and 0.93 ± 0.22 x 10-12 cm3molecule-1s-1 for the excited state. This is expected, since the reaction rate is determined by the attractive and barrierless methylene + oxygen interaction to form 1CH2O2 and this potential energy curve is nearly identical for the two PESs (Figure 1). Within statistical uncertainties, the product yields for the ground and excited state singlet surfaces only differ for CO2. The origin of the nearly identical product yields for the ground and excited state singlet surfaces is uncertain. As shown in Figure 2, the ground and excited state PESs are similar in that they have the same stationary points leading to products, but the stationary point energies are different for the two surfaces. However, this difference may be less important than that the transition states on the PESs have energies lower than that of the reactants. This facilitates the predominant direct reaction dynamics seen in the simulations, with negligible trapping in potential energy minima on the surfaces. It is noteworthy that trapping in the pre-reaction Criegee potential minimum 1CH2O2 is unimportant. If trapping in potential energy minima on the PESs were important, it is expected that the transition state barrier heights would affect the reaction dynamics. Direct reaction dynamics on the two PESs give nearly identical product yields. In the future, a number of studies are important for the 3CH2 + 3O2 reaction. First, it would be helpful to have definitive experimental determinations of the product yields. For the simulations and calculations, it is important to determine from high level electronic structure theory, the 3CH2 + 3O2 potential energy curves for forming 1CH2O2 and 3CH2O2. It would be interesting to know the statistical product yields, for the ground state singlet reaction dynamics, and these may be determined by initiating the direct dynamics simulation in the entrance channel 1CH2O2 intermediate, with a microcanonical, statistical distribution of energy. Finally, the work reported here makes it clear that direct dynamics simulations for the 3CH2 + 3O2 reaction on the ground state singlet surface are possible. It would be of much interest to perform them with other electronic structure theories.


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Acknowledgements The research reported here is based upon work supported by the Air Force Office of Scientific Research (AFOSR) under Grant No. FA9550-17-1-0119 and the Robert A. Welch Foundation under Grant No. D-0005. The simulations were performed on the Quanah computer cluster of the High Performance Computing Center (HPCC) of Texas Tech University and the Chemdynm computer cluster of the Hase Research Group. Hai Wang and Greg Smith are thanked for important discussions concerning the 3CH2 + 3O2 kinetics, and Hendrik Zipse for discussion concerning electronic structure calculations.



References: 1. Vinckier, C.; Debruyn, W. Reactions of Methylene in the Oxidation Process of Acetylene with Oxygen Atoms at 295 K, Symposium (International) on Combustion, 1979, 17, 623631. 2. Hase, W. L.; Phillips, R. J.; Simons, J. W. Vibrational Deactivation of Singlet Methylene. Chem. Phys. Lett. 1971, 12, 161−165. 3. Lindstedt, R. P.; Skevis, G. Chemistry of Acetylene Flames. Combust. Sci. Technol. 2007, 125:1-6, 73-137. 4. Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-class Functionals and 12 other Functionals. Theor. Chem. Acc. 2008, 120, 215-241. 5. McLean, A. D.; Chandler, G. S. Contracted Gaussian-basis Sets for Molecular Calculations. 1. 2nd Row Atoms, Z=11-18. J. Chem. Phys., 1980, 72, 5639-48. 6. Clark, T.; Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. v. R. Efficient Diffuse Function-Augmented Basis-Sets for Anion Calculations. 3. The 3-21+G Basis set for 1stRow Elements, Li-F. J. Comp. Chem., 1983, 4, 294-301. 7. Valiev, M.; Bylaska, E. J.; Govind, N.; Kowalski, K.; Straatsma, T. P.; van Dam, H. J. J.; Wang, D.; Nieplocha, J.; Apra, E.; Windus, T. L.; de Jong, W. A. NWChem: A Comprehensive and Scalable Open-Source Solution for Large Scale Molecular Simulations. Comput. Phys. Commun. 2010, 181, 1477-1489. 8. Lakshmanan, S.; Pratihar, S.; Machado, F. B. C.; Hase, W. L. Direct Dynamics Simulation of the Thermal 3CH2 + 3O2 Reaction. Rate Constant and Product Branching Ratios. J. Phys. Chem. A 2018, 122, 4808-4818. 9. Alecu, I. M.; Truhlar, D. G. Computational Study of the Reactions of Methanol with the Hydroperoxyl and Methyl radicals. 1. Accurate Thermochemistry and Barrier Heights. J. Phys. Chem. A 2011, 115, 2811-2829. 10. Verma, P.; Varga, Z.; Truhlar, D. G. Hyper Open-Shell Excited Spin States of TransitionMetal Compounds: FeF2, FeF2···Ethane, and FeF2···Ethylene. J. Phys. Chem. A 2018, 122, 2563-2579.


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11. Pratihar, S.; Ma, X.; Xie, J.; Scott, R.; Eric, G.; Ruscic, B.; Aquino, A. J. A.; Setser, D. W.; Hase, W. L. Post-Transition State Dynamics and Product Energy Partitioning Following Thermal Excitation of the F∙∙∙HCH2CN Transition State: Disagreement with Experiment. J. Chem. Phys. 2017, 147, 144301. 12. Xie, J.; McClellan, M.; Sun, R.; Kohale, S. C.; Govind, N.; Hase, W. L. Direct Dynamics Simulation of Dissociation of the [CH3--I--OH]− Ion−Molecule Complex. J. Phys. Chem. A 2015, 119, 817-825. 13. Zhang, J. X.; Hase, W. L. Electronic Structure Theory Study of the F− + CH3I → FCH3 + I− Potential Energy Surface. J. Phys. Chem. A 2010, 114, 9635-9643. 14. Gross, E. K.; Dobson, J.; Petersilka, M. Density Functional Theory of Time-Dependent Phenomena. In Density Functional Theory II; Springer, 1996, 81-172. 15. 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 D.01, Gaussian, Inc., Wallingford CT, 2009. 16. Hase, W. L.; Duchovic, R. J.; Hu, X.; Komornicki, A.; Lim, K. F.; Lu, D. H.; Peslherbe, G. H.; Swamy, S. R.; Vande Linde, S. R., Varandas, A.; Wang, H.; Wolf, R. J. Quantum Chem. Program Exch. (QCPE) Bull. 1996, 16, 43. https://opus.ipfw.edu/chemistry_facpubs/81. 17. Hu, X.; Hase, W. L.; Pirraglia, T. Vectorization of the General Monte Carlo Classical Trajectory Program VENUS. J. Comp. Chem. 1991, 12, 1014-1024. 18. Lourderaj, U.; Sun, R.; Kohale, S. C.; Barnes, G. L.; de Jong, W. A.; Windus, T. L.; Hase, W. L. The VENUS/NWChem Software Package. Tight Coupling between Chemical Dynamics Simulations and Electronic Structure Theory. Comput. Phys. Commun. 2014, 185, 1074-1080. 19. Peslherbe, G. H.; Wang, H.; Hase, W. L. Monte Carlo Sampling for Classical Trajectory Simulations. Adv. Chem. Phys. 1999, 105, 171-201. 20. Schlick, T. Molecular Modelling and Simulation, Springer, New York. 2000, 400-401. 21. Swamy, K. N.; Hase, W. L. Dynamics of Ion-Molecule Recombination. III. Trends in the Recombination Efficiency. J. Am. Chem. Soc. 1984, 106, 4071-4077.



22. Paul, A. K.; Kolakkandy, S.; Hase, W. L. Dynamics of Na+(Benzene) + Benzene Association and Ensuing Na+(Benzene)2*Dissociation. J. Phys. Chem. A 2015, 119, 78947904. 23. Gutzwiller, M. C. Chaos in Classical and Quantum Mechanics; Springer: New York, 1990. 24. Ruscic, B. Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry. J. Phys. Chem. A 2015, 119, 7810-7837. 25. Shepler, B. C.; Han, Y; Bowman, J. M. Are Roaming and Conventional Saddle Points for H2CO and CH3CHO Dissociation to Molecular Products Isolated from Each Other. J. Phys. Chem. Lett. 2011, 2, 834 - 838. 26. Balucani, N.; Leonori, F.; Casavecchia, P.; Fu, B.; Bowman, J. M. Crossed Molecular Beams and Quasiclassical Trajectory Surface Hopping Studies of the Multichannel Nonadiabatic O(3P) + Ethylene Reaction at High Collision Energy. J. Phys. Chem. A 2015, 119, 12498−12511. 27. Hu, X.; Hase, W. L. Modification of the Duchovic–Hase–Schlegel Potential Energy Function for H+CH3↔CH4. Comparison of Canonical Variational Transition State Theory, Trajectory, and Experimental Association Rate Constants. J. Chem. Phys. 1991, 95, 80738081. 28. Chen, B. –Z.; Anglada, J. M.; Huang, M. –B.; Kong, F. The Reaction of CH2 (X3B1) with O2 (X3Σg- ): A Theoretical CASSCF/CASPT2 Investigation. J. Phys. Chem. A 2002, 106, 1877-1884. 29. Hase, W. L. Variational Unimolecular Rate Theory. Acc. Chem. Res. 1983, 16, 258-264. 30. Alvarez, R. A.; Moore, C. B. Absolute Yields of CO, CO2, and H2CO from the Reaction CH2(X 3B1) + O2 by IR Diode Laser Flash Kinetic Spectroscopy. J. Phys. Chem. 1994, 98, 174-183. 31. Blitz, M. A.; Kappler, C.; Pilling, M. J.; Seakins, P. W. 3CH2 + O2: Kinetics and Product Channel Branching Ratios. Z. Phys. Chem. 2011, 225, 957-967. 32. Bley, U.; Temps, F.; Wagner, H. Gg.; Wolf, M. Investigations of the Reaction Between CH2(X̃3B1) and O2 in the Temperature Range 233 K ≤ T ≤ 433 K. Ber. Bunsen-Ges. Phys. Chem. 1992, 96, 1043-1048.


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33. Blitz, M. A.; McKee, K. W.; Pilling, M. J.; Seakins, P. W. Evidence for the Dominance of Collision-induced Intersystem Crossing in Collisions of 1CH2 with O2 and a Determination of the H Atom Yields from 3CH2+O2, Using Time-resolved Detection of H Formation by vuv LIF. Chem. Phys. Lett. 2003, 372, 295-299. 34. Leung, K. M.; Lindstedt, R. P. Detailed Kinetic Modeling of C1 – C3 Alkane Diffusion Flames. Combust. Flame 1995, 102, 129-160.



Table 1. Calculated CH2 + O2 Reactive Cross Sections σr. Uncorrected for Product Decomposition Ground State Excited State Product Channel σr (Å2) σr (Å2) CO + H2O (R2) 7.5±1.3 (8.6) 8.2±2.1 (9.9)b CO2 + H2 (R1) 3.6±0.3 (4.1) 2.4±0.6 (2.9) CO + OH +H (R8) 4.7±0.6 (5.4) 5.3±1.4 (6.4) CO + H2 + O(1D) (R9) 1.9±0.1 (2.2) 2.0±0.6 (2.4) H2CO + O(1D) (R10) 4.1±0.4 (4.7) 4.6±1.1 (5.6) HCO + OH (R5) 4.3±0.3 (4.9) 2.6±0.6 (3.2) HCO + O(1D) + H (R11) 0.1±0.08 (0.12) CO2 + H + H (R4) 1.7±0.1 (1.9) 0.3±0.1 (0.4) Trapped trajs.a 4.3 (0.0) 5.4 (0.0) Total cross section with trapped trajs. 32.0±9.6 30.9±7.5 Total cross section without trapped trajs. 27.8±7.0 25.5±6.2 aTrajectories bCross

that are trapped as CH2OO or dioxirane when the trajectories are halted.

sections if the trapped trajectories are assumed to form products in accord with the

product branching ratios found here.


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Table 2. Calculated CH2 + O2 Reactive Cross Sections σr. Corrected for Product Decomposition

Ground State Excited State 2 Product Channel σr (Å ) σr (Å2) CO + H2O (R2) 4.1± 0.6 (4.6) 2.6 ± 0.07 (3.0)b CO2 + H2 (R1) 3.5± 0.3 (3.9) 1.2 ± 0.04 (1.5) CO + OH +H (R8) 11.9±1.7 (13.4) 13.4 ± 3.3 (15.6) CO + H2 + O(1D) (R9) 2.1 ± 0.1 (2.4) 3.2 ± 0.3 (3.9) H2CO + O(1D) (R10) 4.1±0.4 (4.7) 4.6 ± 1.1 (5.6) HCO + OH (R5) 0.3 ± 0.01 (1.0) 0.0 HCO + O(1D) + H (R11) 0.1 ± 0.08 (0.12) CO2 + H + H (R4) 1.7±0.1 (1.9) 0.3 ± 0.1 (0.4) Trapped trajs.a 4.3 (0.0) 5.5 (0.0) Total cross section with trapped trajs. 32.0±9.6 30.9±7.5 Total cross section without trapped trajs. 27.8±7.0 25.5±6.2 aTrajectories bCross

that are trapped as CH2OO or dioxirane when the trajectories are halted.

sections of the trapped trajectories are assumed to form products in accord with the product

branching ratios found here.



Table 3. Calculated Product Yieldsa

Product O(1D) H OH CO CO2 H2CO H2O H2 HCO

Ground State Excited State 0.22±0.07 0.32 ±0.09 0.54± 0.20 0.53 ±0.24 0.45 ±0.18 0.50 ±0.22 0.64±0.26 0.73 ±0.23 0.18±0.06 0.06±0.02 0.15±0.04 0.18±0.04 0.14 ±0.06 0.10 ±0.02 0.20±0.06 0.17±0.05 0.03 ±0.01 0.004±0.03

aThe

cross sections used for calculating the product yields are those for which product decomposition is considered and dissociation of the trapped trajectories is accounted for. Note accounting for the trapped trajectories only alters a product yield by a maximum of 2.5%.


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Table 4. Average Fractions of Product Energy Partitioning a Product

frel

ftrans

CO2 H2 CO2 + H2

fvib CO2 + H2 (R1) 0.06, 0.05 0.32, 0.42 0.10, 0.09 0.30, 0.25 0.16, 0.14 0.62, 0.67

0.22, 0.19

-

CO H2O CO + H2O

0.06, 0.07 0.10, 0.15 0.16, 0.22

CO + H2O (R2) 0.15, 0.18 0.51, 0.44 0.66, 0.62

0.18, 0.16

-

-

0.004, 0.01 0.09, 0.11 0.15, 0.19 0.24, 0.31

0.19, 0.16

-

CO + OH + H (R8) 0.08, 0.06 0.13, 0.14 0.11, 0.11 0.48, 0.53 0.19, 0.17 0.61, 0.67

-

0.04, 0.03 0.07, 0.05 0.09, 0.08 0.20, 0.16

CO H2 O(1D) CO + H2 + O(1D)

CO + H2 + O(1D) (R9) 0.08, 0.10 0.14, 0.19 0.05, 0.04 0.39, 0.29 0.13, 0.14 0.53, 0.48

-

0.04, 0.05 0.22, 0.24 0.08, 0.09 0.34, 0.38

CH2O CH2O + O(1D)

CH2O + O(1D) (R10) 0.17, 0.16 0.75, 0.73 0.17, 0.16 0.75, 0.73

0.08, 0.11 0.08, 0.11

-

CO2 H H CO2 + H + H HCO OH HCO + OH CO OH H CO + OH + H

frot

CO2 + H + H (R4) 0.11, 0.17 0.65, 0.52 0.11, 0.17 0.65, 0.52 0.12, 0.11 0.13, 0.12 0.25, 0.23

HCO + OH (R5) 0.27, 0.28 0.29, 0.33 0.56, 0.61

aThe

average fraction for the ground state singlet surface is given first followed by excited state surface.



Page 24 of 29

Table 5. Average n and J Quantum Numbers for Diatomic Productsa Product H2

CO2 + H2 (R1) 10, 11

CO

CO + H2O (R2) 42, 55

4, 7

OH

HCO + OH (R5) 11, 14

2, 4

CO OH

CO + OH + H (R8) 28, 63 8, 12

1, 3 3, 7

CO H2

CO + H2 + O(1D) (R9) 21, 41 3, 4

1, 3 1, 2

aThe

6, 6

average quantum number for the ground state singlet surface is given first followed by the excited state surface.


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Table 6. Experimental Measurements of 3CH2 + 3O2 Product Yieldsa

Product O(1D) H OH CO CO2 H2CO H2O H2 HCO

32 30 0.10 0.20 0.30 0.30±0.05 0.34±0.06 0.40±0.08 0.16±0.04

Reference 33 31 0.18±0.04 0.8±0.2 0.78 0.43 0.38 0.44 0.18 0.06 0.21 0

34 0.26 0.78

3 0.10 0.25

0.37 0.37 0.26 0.11 0.11

0.72 0.18 0.10

a. The experiments and simulations are for 300 K.


0.08

This work 0.22±0.07 0.54±0.20 0.45±0.18 0.64±0.26 0.18±0.06 0.15±0.04 0.14±0.06 0.20±0.06 0.03±0.01


Figure 1. Potential energy curve calculated at UM06/6-311++G(d,p) level of theory for the interaction of CH2 and O2 in ground and excited singlet states.


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(a)

(b) Figure 2. Energy profiles of pathways for (a) 1CH2 (𝑎1A1) + 1O2 (b1∑ + ) reaction and (b) 3CH2 𝑔 (X3B1) + 3O2 (X3∑ ― )reaction on the singlet PES, calculated at the UM06/6-311++G(d,p) level of 𝑔

theory. 27 ACS Paragon Plus Environment


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(a)

(b)

(a)

(b)

Figure 3. (a) Reaction probability of individual product channels. (b) Total reaction probability; Upper panel: Ground state singlet, Lower panel: Excited state singlet. Error bars are standard deviation. The standard deviation for the reaction probability of the individual channels range from 20% for CO + H2O to 70% for CO + H2 + O (1D).


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TOC Graphic


Direct Dynamics Simulations of the CH

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