Kinetics of the Strongly Correlated CH3O + O2 Reaction: The

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Kinetics of the Strongly Correlated CH3O + O2 Reaction: The Importance of Quadruple Excitations in Atmospheric and Combustion Chemistry Bo Long, Junwei Lucas Bao, and Donald G. Truhlar J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b11766 • Publication Date (Web): 13 Dec 2018 Downloaded from http://pubs.acs.org on December 13, 2018

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Journal of the American Chemical Society Dec. 11, 2018

Kinetics of the Strongly Correlated CH3O + O2 Reaction: The Importance of Quadruple Excitations in Atmospheric and Combustion Chemistry Bo Long, a , b * Junwei Lucas Bao,b and Donald G. Truhlarb∗ a

College of Materials Science and Engineering, Guizhou Minzu University, Guiyang, 550025, China

b

Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, USA ABSTRACT: Kinetics measurements on radical–radical reactions are often unavailable experimentally, and obtaining quantitative rate constants for such reactions by theoretical methods is challenging because the transition states and the reactants are often strongly correlated. Treating strongly correlated systems by coupled cluster theory limited to single, double, and triple connected excitations is often inadequate. We therefore use a new method, called GMM(P), for extrapolation to the complete configuration interaction limit to go beyond triple excitations and in particular to approximate the CCSDTQ(P)/CBS limit. Here, we present this method and use it to investigate the CH3O + O2 reaction. The contribution of connected quadruple excitations to the barrier height energy is found to be –3.13 kcal/mol, and adding a quasiperturbative calculation of the effect of connected pentuple excitations brings the post-connected-triples contributions to –3.44 kcal/mol, which corresponds to Boltzmann factors that increase calculated rate constants by factors of 1.0 × 103, 3.3 × 102, and 18 at 250 K, 298 K, and 600 K, respectively. We present rate constants for temperatures from 250 K to 2000 K, and we find that the Arrhenius activation energy increases from 0.58 to 9.68 kcal/mol over this range. We also find reasonably good accuracy for the barrier height with the MN15-L exchange-correlation functional, and we calculate rate constants by a combination of GMM(P) and MN15-L electronic structure calculations and conventional and variational transition state theory, in particular canonical variational theory with small-curvature tunneling.. The present findings have broad implications for obtaining quantitative rate constants for complex reaction systems in atmospheric and combustion chemistry.

∗ To whom correspondence should be addressed. E-mail: [email protected] (Bo Long),

[email protected] (Donald G. Truhlar)

ACS Paragon Plus Environment

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I. INTRODUCTION Alkoxy radicals (RO), which are formed via the oxidation of volatile organic compounds, are key intermediates in the atmosphere and in combustion.1,2 Alkoxy radicals react with O2 and undergo unimolecular decomposition and isomerization in the atmosphere, and these reactions have a significant impact on the formation of ozone and secondary organic aerosols.3,4,5,6,7 Due to the importance of alkoxy radicals in the atmosphere, obtaining the absolute rate constants of the RO + O2 reactions is very important for fully estimate the atmospheric fates of alkoxy radicals, but obtaining these rates for the larger and functionalized alkoxy radicals from experiment is very difficult.8 Therefore we turn to computational chemistry to predict the gas-phase reaction kinetics, and our goal is to obtain experimental accuracy or better. The simplest alkoxy radical is the methoxy radical (CH3O). The dominant sink of CH3O is reaction with O2,9 which has been extensively studied both experimentally1,2,3,10,11,12,13,14,15,16 and theoretically.17,18,19,20,21 For this reaction of a small radical there are experimental kinetic data from different sources that agree with one another within a factor of 1.5–2. The CH3O + O2 reaction that dominates at low temperature occurs by abstraction of a hydrogen atom to yield HCHO + HO2; this occurs via two transition states;21 these transition states are labeled TS1 and TS2, and they are shown – as reoptimized in the present work–in Figure 1. Calculations in Table S1 with the W3X-L method22 at a geometry optimized by RCCSD(T)-F12a/jun-cc-pVTZ show a difference in classical barrier heights of 9.26 kcal/mol for the two transition states and that the enthalpy of activation at 0 K for TS1 is lower than that of TS2 by 7.49 kcal/mol. (Tables with the prefix S are in supporting information, which should also be consulted for references for basis sets (see Table S2) and explanations of coupled cluster abbreviations.) The difference in classical barrier heights given by the W3X-L calculation is even larger than an earlier estimate19 of 7.5 kcal/mol for the difference in classical barrier heights. Thus TS2 makes a negligible contribution to the CH3O + O2 reaction, and it will not be considered further. The rest of this paper concerns the hydrogen abstraction reaction proceeding through TS1. It is a difficult challenge to use theoretical methods to model the CH3O + O2 reaction because the transition state of the CH3O + O2 reaction is strongly correlated. Strongly correlated systems are systems for which a single configuration state function does not provide a good


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Journal of the American Chemical Society 3

zero-order description; they are often called multireference systems because their treatment with a low level of excitations (up to only double or triple excitations) often requires a multi-configuration reference function, but they may also be treated with single-configuration reference functions if one includes higher excitations. In the present work we use both single-reference coupled cluster theory and multireference complete active space second-order perturbation theory (CASPT2). Hu and Dibble21 found that calculations by the single-reference CCSD(T) method predict a barrier that is several kcal/mol too high. Setokuchi et al20 investigated the reaction using the G2M(RCC1) composite electronic structure method and obtained a rate constant in reasonable agreement with experiment based on a theoretical method containing no component at a higher level than triple excitations with a modest basis set plus a non-size-consistent empirical high-level correction, but the reliability of these methods in general is not validated. Thus, further investigations are needed to develop and validate theoretical methods that can reliably produce rate constants with experimental accuracy. In this report, we demonstrate the level of theory required to calculate the barrier height for the CH3O + O2 reaction, and we calculate the rate constant by canonical variational transition state theory with small-curvature tunneling (CVT/SCT). The present results not only address a specific gas-phase reaction, but also have broad implications for the treatment of radical–radical reactions with strongly correlated transition states such as the reactions is the classes RO2 + HO223,24,25 and RO2 + OH.26,27

II. METHODS One can often use lower-lower methods for optimizing geometries than for calculating reliable energetics, but nevertheless we calculated geometries at a high level.28 For open-shell doublet (CH3O, HO2, and transition states) and triplet (O2) states, we optimized structures and calculated frequencies with unrestricted explicitly correlated coupled cluster theory with single and double excitations and noniterative triple excitations based on restricted open-shell Hartree– Fock (ROHF) orbitals (RCCSD(T)-F12a)29,30 with the basis sets jun-cc-pVTZ and cc-pVDZ-F12. We used restricted RCCSD(T)-F12a based on based on closed-shell Hartree– Fock orbitals for singlet formaldehyde. To calculate energetics, we designed a new composite scheme to do single-point energy



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calculations at an accuracy close to frozen-core CCSDTQ(P)/CBS, where frozen-core means that core orbitals are calculated by Hartree-Fock theory and are doubly occupied in all configurations. The frozen-core approximation is expected to be good for relative energies (barrier heights and energies of reaction), and thus the relative energies should be close to FCI/CBS, where FCI denotes full configuration interaction; FCI/CBS is also called complete configuration interaction, and it is equivalent to solving the many-electron Schrödinger equation. The highest-level of the new composite scheme, formulated to approximate the unrestricted coupled cluster theory with single, double, triple, and quadruple excitations and noniterative quintuple excitations at the complete basis set limit (CCSDTQ(P)/CBS), is called GMM(P). The energy is given by 𝐸 GMM(5) = 𝐸!"#!!"# + ∆𝐸!! ! + ∆𝐸(!)!! + ∆𝐸!!(!) + ∆𝐸(!)!! + ESO

(1)

where MW2-F12 is a method originally developed for a single-point CCSD(T)/CBS energy of benzene in the recently proposed W4-F12 approach31 and was subsequently used for studying the unimolecular reaction of (CH3)2COO;32 the other terms are defined as follows: ∆𝐸!! ! = E(RCCSDT/CBS) – E[RCCSD(T)/CBS]

(2)

∆𝐸(!)!! = E[CCSDT(Q)/CBS] – E(CCSDT/CBS)

(3)

∆𝐸!!(!) = E(CCSDTQ/VDZ(d)] – E[CCSDT(Q)/VDZ(d)]

(4)

∆𝐸(!)!! = E[CCSDTQ(P)/cc-VDZ] – E[CCSDTQ/cc-VDZ]

(5)

and ESO is the lowering of the energy by spin-orbit coupling. In eqs 2 and 3, CBS denotes extrapolation to the complete basis set limit, and this was accomplished by31,33 ∆𝐸! = ∆𝐸!"# +

! !!

(6)

where L is the highest angular momentum in the basis set. In GMM(P), we extrapolate using jun-cc-pVDZ and jun-cc-pVTZ for which L equals 2 and 3, respectively. Coupled cluster calculations based on ROHF orbitals are denoted RCC…, and coupled cluster calculations based on UHF orbitals are denoted CC…. The W3X-L procedure provides a cost-efficient approximation to the RCCSDT(Q)/CBS energy, where CBS denotes extrapolation to a complete basis set. Classical barrier height is the difference in potential energy of the saddle point and the reactants; enthalpy at 0 K is the potential energy plus the zero point vibrational energy; potential energy is the potential energy for nuclear motion, and it is the electronic energy


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including nuclear repulsion. All calculations include spin-orbit coupling for CH3O (spin-orbit coupling is zero to first order for other species). The spin-orbit coupling ESO of CH3O is estimated to be –0.09 kcal/mol, based on previous experimental34 work (see also refs. 35,36,37). This raised the barrier heights and energies of all reactions by 0.09 kcal/mol. We also define GMMQ in which we do not include ∆𝐸(!)!! and GMM(Q) in which we do not include ∆𝐸!!(!) and ∆𝐸(!)!! .

We found that special care must be exercised to be sure that the reference functions used for the coupled cluster calculations are converged to the physically correct solution. To facilitate this, we used the method of Vaucher and Reiher38 to find the best SCF orbitals by mixing pairs of randomly selected occupied−unoccupied molecular orbitals to search the multiple solutions of the unrestricted Hartree-Fock calculations. Vibrational frequencies for a given calculation (which are needed to calculate finite-temperature enthalpies and free energies) were calculated by the same method as used to optimize the geometry and were then scaled by our standard procedure39 to obtain more accurate zero point energies. The electronic structure and frequency calculations were carried out using the Gaussian 1640 and MN-GFM41 programs for density functional theory and using Molpro 201542 and MRCC43,44 for wave function theory. Rate constants were calculated using the Polyrate 2017-C45 and Gaussrate 2017-B46 dynamics codes. Structures. Tables S3 and S4 show that the transition state structures of TS1 optimized at various levels agree with one another. We conclude that using RCCSD(T)-F12a/jun-cc-pVTZ geometries should contribute negligible error; for brevity we will call this the jun method in the text and tables.

III. CONVERGENCE OF GMM(P) Details of the component calculations of GMM(P) are provided in Tables S5 and S6. We used multiple basis sets to validate that the components of the GMM(P) calculation are converged to the complete basis set limit. Table S5 shows only slight differences (0.13, 0.10 kcal/mol) for the RCCSDT – RCCSD(T) and CCSDT(Q) – CCSDT components between using cc-pV(D, T)Z basis sets to extrapolate to the CBS limit and using jun-cc-pV(D,T)Z basis sets to



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extrapolate to the CBS limit; this shows that these two components are well converged to the CBS limit. Table S5 also tells us that the CCSDT(Q) – CCSDT component makes the main contribution to the beyond-CCSD(T) calculations for the CH3O + O2 reaction, and it shows that beyond-CCSD(T) calculations at least up to CCSDTQ(P) are required to obtain quantitative results for the CH3O + O2 reaction. Based on our previous paper,32 the convergence check in Table S5, and experience in the literature with higher-order excitations,47 it is reasonable to expect that relative energies computed by our GMM(P) best estimate are in most cases within a few tenths of a kcal/mol of the frozen-core complete configuration interaction limit.

IV. ENERGIES Zero Point Energies. CH3O is a complex molecule, with Jahn–Teller (JT) and significant spin–orbit coupling.48 CH3O has been extensively investigated by both experimental and theoretical methods.48,49,50,51 Here, we only need to consider the zero-point vibrational energy of CH3O because it is required to compute the enthalpy of activation. Table S7 shows that the scaled zero-point vibrational energy of CH3O is 22.7 kcal/mol by the jun method and is the same by RCCSD(T)-F12a/jun-cc-pVTZ. This value is in excellent agreement with the experimental value of 22.6 kcal/mol.49,50,51 Reaction Barriers. We first consider calculations at the jun geometry. The W2X22 and MW2-F1231,32 procedures provide cost-efficient approximations to the RCCSD(T)/CBS energy, with the latter having a larger basis set. Table 1 shows that these methods give barrier heights and 0 K energies of activation 2.23–2.74 kcal/mol higher than our best estimate. MW3X-L is a new method introduced here that combines MW2-F12 with beyond-CCSD(T) calculations from W3X-L. Table 1 shows that including higher-than-CCSD(T) contributions by MW3X-L lowers the deviations from our best estimate to 0.99 kcal/mol, and including beyond-CCSD(T) contributions by the more expensive W3X-L method lowers this further to 0.48 kcal/mol. The difference in Table 1 between the beyond-CCSD(T) result of GMM(Q) and the CCSD(T) result of MW2-F12 is very large, in particular 3.01 kcal/mol; this also shows that the CH3O + O2 reaction is much more strongly correlated than the OH + SO2,52 CH3O + HF,53 Criegee intermediates + H2O/NH3,32,54,55 unimolecular reactions of Criegee intermediates,32,54,56 and HCl + OH57 reactions because the beyond-CCSD(T) corrections up to CCSDT(Q) in these reactions are less than 1 kcal/mol. In addition, we note that the T1, D1, and T1/D1 diagnostics


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do not reliably indicate the character of the CH3O + O2 reaction. For example, the T1 diagnostic values are less than 0.044 for CH3O, O2, and TS1 in Table S8; these diagnostics would be interpreted using customary criteria to mean that the CH3O + O2 reaction has only minor multireference character. However, our investigations have shown that the CH3O + O2 reaction is not treated accurately by the methods that usually give good results for single-reference systems. The difference between MW2-F12//RCCSD(T)-F12a/jun-cc-pVTZ and W2X//RCCSD(T)-F12a/jun-cc-pVTZ is about 0.5 kcal/mol, which shows that W2X does not give a good approximation to the complete basis set limit for CCSD(T), although our previous investigation showed that W2X agrees well with MW2-F12 for the unimolecular reaction of (CH3)2COO.32 But some systems are harder and require higher levels than others. The contribution of connected quadruple excitations to the barrier height energy is found to be –3.13 kcal/mol, and adding a quasiperturbative calculation of the effect of connected pentuple excitations brings the post-connected-triples contributions to –3.44 kcal/mol, which corresponds to Boltzmann factors that increase calculated rate constants by factors of 1.0 × 103, 47, and 6 at 250 K, 298 K, and 1000 K, respectively. The GMM(P) benchmark calculations were used to identify a density functional method that gives a semiquantitatively correct description of the reaction. We found that Kohn-Sham density functional theory with the MN15-L exchange–correlation functional58 and the MG3S basis set has a mean unsigned error of only 0.84 kcal/mol (Table 1), which is about 2 kcal/mol lower than that of MW2-F12. This shows that density functional theory with a modern functional is capable of much higher accuracy than CCSD(T) for some strongly correlated systems, a finding that is consistent with our previous results.32,54 This result is especially encouraging because the MN15-L density functional has unique properties. Most exchange-correlation functionals that give good barrier heights have some percentage of Hartree–Fock exchange, which is known to bring in static correlation error, making the functional poorly suited for strongly correlated systems.59 MN15-L is a local functional (no Hartree-Fock exchange) and so it does not have this problem, and yet a recent survey60 found that its mean unsigned error on the 76 diverse barrier heights is only 1.66 kcal/mol, the best performance of 40 local functionals tested (the other local functionals tested have an average



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mean unsigned error for these barrier heights of 6.80 kcal/mol). We conclude that MN15-L might be very useful for modeling reaction dynamics of strongly correlated systems. In an alternative strategy, strongly correlated systems are studied using multireference methods such as CASPT2,61 where the accuracy depends in part on active space and basis set.62 This method is quite expensive for large systems with the affordable limit often being 16 active electrons in 16 active orbitals with conventional solvers. However, CASPT2 is affordable for the present small reaction where we used an active space that has 11 electrons in 9 orbitals and is composed of four nominally doubly occupied orbitals [σ(C-H), σ(O-O), and two π(O-O)], the

p(CO) orbital that contains the unpaired electron, and four nominally unoccupied orbitals [σ*(C-H), σ*(O-O), and two π*(O-O)]. Therefore we can test it for the present reaction. Table 1 compares the energy of CASPT2(11,9)/aug-cc-pVTZ to our best estimate and shows high accuracy for the classical barrier height but poor accuracy when zero point energies are included. Tables S7 and S9-S10 show that latter is caused mainly by an inaccurate zero-point vibrational energy of CH3O in the CASPT2 calculation. We also studied the strategy of using CASPT2 geometries and frequencies for coupled cluster calculations. Again the results are of poor quality due to the inaccurate zero-point vibrational energy of CH3O. In particular, Table 1 shows a remarkable difference of 0.81 kcal/mol in enthalpy of activation at 0 K between W3X-L calculations with the RCCSD(T)-F12a/cc-pVTZ-F12 geometry and frequencies and those with the CASPT2 geometry and frequencies. Thus, the strategy if using multireference perturbation theory is not accurate in the present case.

V. RATE CONSTANTS A dual-level strategy, as used in our previous investigations,32,53,63 is employed to account for the difference between the benchmark barrier height and the density functional barrier height. First, the rate constant is calculated by conventional transition state theory (TST) without tunneling using GMM(P). Then MN15-L/MG3S was utilized to do direct dynamics calculations of the reaction rate using canonical variational transition state theory with small-curvature TST CVT/SCT tunneling.64,65 These rate constants are labeled respectively as kHL and kLL , where HL

and LL denote higher level and lower level, respectively. We can factor the latter rate constant


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as CVT/SCT CVT SCT TST SCT kLL = kLL κ LL = kLL ΓLLκ LL

(7)

CVT TST where kLL and kLL are the CVT and conventional TST rate constants (both without SCT is the tunneling) at level LL, ΓLL is the recrossing transmission coefficient, and κ LL

tunneling transmission coefficient. Then the final rate constant is calculated as TST SCT CVT/SCT ‡ ‡ k = kHL ΓLLκ LL = exp ⎡⎢− ΔGHL − ΔGLL / RT ⎤⎥ kLL ⎣ ⎦

(

)

(8)

The frequencies needed for zero point energies and partition coefficients are always calculated with the method used to optimize the geometry; thus they are calculated by the jun method for HL and by MN15-L/MG3S for LL. Then scale factors (Table S11) were used to scale all the calculated frequencies, by a method explained previously.38 The calculated rate constants are listed in Table 2 and Table S12 in the temperature range from 250 to 2000 K. The theoretical rate constant is fitted to a functional form proposed previously,66 and this yields 𝑘 = 1.22 ×10!!! cm3 molecule−1 s−1 (

!! !! !.!" ) exp !""

[−

[!.!" !"#$/!"#](!! !! ) !(! ! !!!! )

]

(9)

where R is the gas constant, T is temperature, and T0 is 434 K. The fit reproduces the calculations within 5%. The experimental rate constants from several groups over the temperature range from 250 K to 610 K have been fit to16 k = 3.81×10-21 T 2.40 exp(-208/T) cm3 molecule-1 s-1

250-610 K

(11)

and we compare to this data over the range 250 K to 450 K. We do not compare to experiment above 450 K because Wantuck et al.14 concluded that the measured rate constant above 450 K might contain significant contributions from other processes (collision-induced isomerization and collision-induced decomposition) as well as abstraction. Equation 11 agrees with the recommendation of an earlier review1 at temperatures 298-450 K within 10% (results below 298 K were not available at the time of the earlier review), and the various experimental data agree with each other within a factor of about 1½–2 over this temperature range. The final calculated rate constants in Table 2 agree with experimental results fitted by eq 11 within 34% over the 250-450 K temperature. Considering that quadruple and higher



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excitations affect the rate constant in this temperature range by a factor of 47 at 450 K and a factor of 1.0×103 at 250 K, the quantitative agreement with experiment is remarkable (and perhaps even fortuitously better than it ought to be), but the main take-home message is that the predicted rate constant would be orders of magnitude off from experiment if one stopped with CCSDT.

VI. ACTIVATION ENERGIES The temperature-dependent activation energies in the CH3O + O2 reaction were computed from the fit as67 Ea = −R

d ln k d(1/ T )

(10)

that is, Ea is local slope of the Arrhenius plot and would be a constant for a linear Arrhenius plot. It has been known for a long time68,69 that deviations for constant Ea can be large when one considers a wide temperature range (that is, Arrhenius plots are far from linear), but the results in Table 2 are a particularly striking example, with Ea increasing from 0.58 to 9.86 kcal/mol. The dependence of Ea on temperature is large even above 800 K, where the variational effects and tunneling are negligible.

VII. CONCLUDING REMARKS Obtaining quantitative rate constants by theoretical methods requires obtaining quantitative energy barriers, which are determined by three factors: optimized geometries, zero-point vibrational energies, and single-point energies. Here, we show how to design computational strategies and methods to obtain quantitative energy barriers for strongly correlated systems in a practical way by electronic structure methods. We investigated the CH3O + O2 reaction acted as a prototype reaction with a strongly correlated electronic structure, and we calculated quantitative rate constants. We used coupled cluster theory, where the accuracy of the method depends on excitation level and basis set. We showed that RCCSD(T)-F12a/jun-cc-pVTZ can yield a reliable geometrical optimization and zero-point vibrational energy, whereas CASPT2(11,9)/aug-cc-pVTZ cannot provide reliable zero-point vibrational energies. We included connected excitations up to pentuple, and we used two choices of basis set to extrapolate key components to the complete basis set limit to show whether each coupled cluster component in the scheme is well converged to the complete basis


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set limit. The combination of connected excitations up to pentuple with complete basis set extrapolation is judged to give a best estimate of the barrier height within a few tenths of a kcal/mol of the frozen-core complete configuration interaction limit. We then found that Kohn-Sham density functional theory with the MN15-L exchange-correlation functional has remarkable accuracy, which is much higher than that of CCSD(T)/CBS. These findings in this work are broadly relevant to kinetics processes involves strongly correlated states, which includes many processes in atmospheric and combustion chemistry.

! ASSOCIATED CONTENT SSupporting Information The Supporting Information is available free of charge on the ACS Publications website DOI: 10.1021/

at

References for basis sets and number of contracted basis functions for transition state calculations; computational details of orbitals and coupled cluster calculations, W2X, MW2-F12, MW3X-L, and W3X-L composite methods, electronic partition functions, symmetry numbers, and spin-orbit coupling; scale factors for the vibrational frequencies; activation enthalpies at 0 K and barrier heights for TS1 and TS2; components of barrier height increments (kcal/mol) for TS1; selected internuclear distances and bond angles of TS1; frequencies and zero-point vibrational energies of CH3O, O2, and TS1; rate constants, transmission coefficients, and activation energies; and coordinates and absolute energies of optimized structures. (PDF ) ! AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected], , [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ORCID Bo Long: 0000-0002-9358-2585 Junwei Lucas Bao: 0000-0002-4967-663X



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Donald G. Truhlar: 0000-0002-7742-7294 Notes The authors declare no competing financial interest.

! ACKNOWLEDGMENT

This work was supported in part by the National Natural Science Foundation of China (41775125), the Science and Technology Foundation of Guizhou Province, China, ([2018]1080), the Science and Technology Foundation of Guizhou Provincial Department of Education, China ([2015]350), and the U.S. Department of Energy (DE-SC0015997). Computations were performed using resources of Minnesota Supercomputing Institute and the National Energy Research Scientific Computing Centre.


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Table 1. The enthalpy of activation (Δ𝐻!‡ , 0 Κ) and classical barrier height (𝑉 ‡ ) of the transition state TS1 (including spin-orbit coupling) and the mean unsigned error (MUE) of these quantities (in kcal/mol).a Method Geometry 𝑉‡ MUE Δ𝐻!‡ b GMM(P) (best estimate) jun 2.09 1.79 0.00 GMMQ ” 2.40 2.10 0.31 GMM(Q) ” 1.82 1.52 0.27 MW2-F12 ” 4.83 4.53 2.74 jun ” 4.21 3.91 2.12 c CASPT2 Consistent 1.41 1.77 0.35 Weizmann and modified Weizmann methods: W3X-L RCCSD(T)-F12a/cc-pVTZ-F12 ” jun ” RCCSD(T)-F12a/cc-pVDZ-F12 ” RQCISD/MG3S ” CASPT2 MW3X-L jun W2X ” ” RCCSD(T)-F12a/cc-pVDZ-F12

2.62 2.57 2.37 2.32 1.81 3.08 4.32 4.10

2.29 2.27 2.29 1.58 2.17 2.78 4.02 4.02

0.52 0.48 0.39 0.22 0.33 0.99 2.23 2.12

Density functional theory: MN15-L/maug-cc-pVTZ MN15-L/MG3S

3.31 3.19

2.45 2.36

0.94 0.84

Consistent Consistent

a

All reactant energies used to compute barrier heights and enthalpies include a spin-orbit contribution of –0.09 kcal/mol, and this raised all reported barrier heights and enthalpies of activation by 0.09 kcal/mol. b As explained in the text, jun denotes RCCSD(T)-F12a/jun-cc-pVTZ. c “Consistent” denotes that the energy and the geometry optimization were performed by the same method.



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Table 2. The calculated rate constant, factors in the rate constant, and activation energies. from !"! a T k(theory)a k(experiment)b 𝐸! (theory)c 𝑘!" к!"# !! Г !! (cm3 molecule−1 s−1) (cm3 molecule−1 s−1) (cm3 molecule−1 s−1) (K) (kcal/mol) −16 −15 −16 7.56 × 10 1.31 × 10 9.4 × 10 250 3.28 0.90 0.58 −15 −15 −15 0.85 1.42 × 10 1.65 × 10 1.6 × 10 298 2.17 0.93 −15 −15 −15 0.87 1.45 × 10 1.67 × 10 1.7 × 10 300 2.14 0.93 −15 −15 −15 1.99 × 10 1.97 × 10 2.2 × 10 330 1,84 0.95 1.06 −15 −15 −15 3.60 × 10 2.89 × 10 4.0 × 10 400 1.48 0.97 1.53 −15 −15 −15 5.07 × 10 3.71 × 10 5.6 × 10 450 1.36 0.98 1.88 −14 −15 1.12 × 10 7.10 × 10 600 1.18 1.00 2.87 −14 −14 2.44 × 10 1.41 × 10 800 1.10 1.00 4.05 −14 −14 4.45 × 10 2.46 × 10 1000 1.06 1.00 5.09 −14 −14 7.28 × 10 3.92 × 10 1200 1.04 1.00 6.08 1.34 × 10−13 7.02 × 10−14 1500 1.03 0.99 7.51 −13 −14 1.88 × 10 9.78 × 10 1700 1.02 0.99 8.45 −13 −13 2.93 × 10 1.51 × 10 2000 1.01 0.99 9.86 a from eq 8 b from eq 11 c from eq 10


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Figure 1. Optimized geometries of the transition structures for the reaction of CH3O with O2, as calculated by RCCSD(T)-F12a/jun-cc-pVTZ.

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TOC Graphic


Kinetics of the Strongly Correlated CH3O + O2 Reaction: The

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