Multi-structural variational transition state theory: kinetics of the 1,5-hydrogen shift isomerization of the 1-butoxyl radical including all structures and torsional anharmonicity

We investigate the statistical thermodynamics and kinetics of the 1,5-hydrogen shift isomerization reaction of the 1-butoxyl radical and its reverse isomerization. The partition functions and thermodynamic functions (entropy, enthalpy, heat capacity, and Gibbs free energy) are calculated using the multi-structural torsional (MS-T) anharmonicity method including all structures for three species (reactant, product, and transition state) involved in the reaction. The calculated thermodynamic quantities have been compared to those estimated by the empirical group additivity (GA) method. The kinetics of the unimolecular isomerization reaction was investigated using multi-structural canonical variational transition state theory (MS-CVT) including both multiple-structure and torsional (MS-T) anharmonicity effects. In these calculations, multidimensional tunneling (MT) probabilities were evaluated by the small-curvature tunneling (SCT) approximation and compared to results obtained with the zero-curvature tunneling (ZCT) approximation. The high-pressure-limit rate constants for both the forward and reverse reactions are reported as calculated by MS-CVT/MT, where MT can be ZCT or SCT. Comparison with the rate constants obtained by the single-structural harmonic oscillator (SS-HO) approximation shows the importance of anharmonicity in the rate constants of these reactions, and the effect of multi-structural anharmonicity is found to be very large. Whereas the tunneling effect increases the rate constants, the MS-T anharmonicity decreases them at all temperatures. The two effects counteract each other at temperatures 385 K and 264 K for forward and reverse reactions, respectively, and tunneling dominates at lower temperatures while MS-T anharmonicity has a larger effect at higher temperatures. The multi-structural torsional anharmonicity effect reduces the final reverse reaction rate constants by a much larger factor than it does to the forward ones as a result of the existence of more low-energy structures of the product 4-hydroxy-1-butyl radical than the reactant 1-butoxyl radical. As a consequence there is also a very large effect on the equilibrium constant. The neglect of multi-structural anharmonicity will lead to large errors in the estimation of reverse reaction rate constants.     

Including anharmonicity in the calculation of rate constants. II. The OH+H2-->H2O+H reaction

A recently developed method for calculating anharmonic vibrational energy levels at nonstationary points along a reaction path that is based on second-order perturbation theory in curvilinear coordinates is combined with variational transition state theory with semiclassical multidimensional tunneling approximations to calculate thermal rate constants for the title reaction. Two different potential energy surfaces were employed for these calculations, an improved version of the author's surface 5 and the WSLFH surface of Wu et al. [J. Chem. Phys. 113, 3150 (2000)]. We present detailed comparisons of rate constants computed for the two surfaces with and without anharmonicity and with various approximations for incorporating tunneling along the reaction path. The results for this system are quite sensitive to the surface employed, the choice of coordinates (curvilinear versus rectilinear), and the inclusion of anharmonicity. A comparison with experiment provides information on the accuracy of these surfaces.     

Computational study of the reactions of methanol with the hydroperoxyl and methyl radicals. 1. Accurate thermochemistry and barrier heights

The reactions of CH(3)OH with the HO(2) and CH(3) radicals are important in the combustion of methanol and are prototypes for reactions of heavier alcohols in biofuels. The reaction energies and barrier heights for these reaction systems are computed with CCSD(T) theory extrapolated to the complete basis set limit using correlation-consistent basis sets, both augmented and unaugmented, and further refined by including a fully coupled treatment of the connected triple excitations, a second-order perturbative treatment of quadruple excitations (by CCSDT(2)(Q)), core-valence corrections, and scalar relativistic effects. It is shown that the M08-HX and M08-SO hybrid meta-GGA density functionals can achieve sub-kcal mol(-1) agreement with the high-level ab initio results, identifying these functionals as important potential candidates for direct dynamics studies on the rates of these and homologous reaction systems.     

Kinetic study on the H + SiH4 abstraction reaction using an ab initio potential energy surface

Variational transition state theory calculations with the correction of multidimensional tunneling are performed on a 12-dimensional ab initio potential energy surface for the H + SiH(4) abstraction reaction. The surface is constructed using a dual-level strategy. For the temperature range 200-1600 K, thermal rate constants are calculated and kinetic isotope effects for various isotopic species of the title reaction are investigated. The results are in very good agreement with available experimental data.     

Including anharmonicity in the calculation of rate constants. 1. The HCN/HNC isomerization reaction

A method for calculating anharmonic vibrational energy levels in asymmetric top and linear systems that is based on second-order perturbation theory in curvilinear coordinates is extended to the bound generalized normal modes at nonstationary points along a reaction path. Explicit formulas for the anharmonicity coefficients, x(ij), and the constant term, E0, are presented, and the necessary modifications for resonance cases are considered. The method is combined with variational transition state theory with semiclassical multidimensional tunneling approximations to calculate thermal rate constants for the HCN/HNC isomerization reaction. Although the results for this system are not very sensitive to the choice of coordinates, we find that the inclusion of anharmonicity leads to a substantial improvement in the vibrational energy levels. We also present detailed comparisons of rate constants computed with and without anharmonicity, with various approximations for incorporating tunneling along the reaction path, and with a more practical approach to calculating the vibrational partition functions needed for larger systems.     

High-level direct-dynamics variational transition state theory calculations including multidimensional tunneling of the thermal rate constants, branching ratios, and kinetic isotope effects of the hydrogen abstraction reactions from methanol by atomic hydrogen

We report a detailed theoretical study of the hydrogen abstraction reaction from methanol by atomic hydrogen. The study includes the analysis of thermal rate constants, branching ratios, and kinetic isotope effects. Specifically, we have performed high-level computations at the MC3BB level together with direct dynamics calculations by canonical variational transition state theory (CVT) with the microcanonically optimized multidimensional tunneling (μOMT) transmission coefficient (CVT/μOMT) to study both the CH(3)OH+H→CH(2)OH+H(2) (R1) reaction and the CH(3)OH+H→CH(3)O+H(2) (R2) reaction. The CVT/μOMT calculations show that reaction R1 dominates in the whole range 298≤T (K)≤2500 and that anharmonic effects on the torsional mode about the C-O bond are important, mainly at high temperatures. The activation energy for the total reaction sum of R1 and R2 reactions changes substantially with temperature and, therefore, the use of straight-line Arrhenius plots is not valid. We recommend the use of new expressions for the total R1 + R2 reaction and for the R1 and R2 individual reactions.     

Rate constants from the reaction path Hamiltonian. I. Reactive flux simulations for dynamically correct rates

As ab initio electronic structure calculations become more accurate, inherent sources of error in classical transition state theory such as barrier recrossing and tunneling may become major sources of error in calculating rate constants. This paper introduces a general method for diabatically constructing the transverse eigensystem of a reaction path Hamiltonian in systems with many degenerate transverse frequencies. The diabatically constructed reaction path Hamiltonian yields smoothly varying coupling constants that, in turn, facilitate reactive flux calculations. As an example we compute the dynamically corrected rate constant for the chair to boat interconversion of cyclohexane, a system with 48 degrees of freedom and a number of degenerate frequencies. The transmission coefficients obtained from the reactive flux simulations agree with previous results that have been calculated using an empirical potential. Furthermore, the calculated rate constants agree with experimental values. Comparison to variational transition state theory shows that, despite finding the true bottleneck along the reaction pathway, variational transition state theory only accounts for half of the rate constant reduction due to recrossing trajectories.     

Direct-dynamics VTST study of the [1,7] hydrogen shift in 7-methylocta-1,3(Z),5(Z)-triene. A model system for the hydrogen transfer reaction in previtamin D3

Direct-dynamics canonical variational transition-state theory calculations with microcanonically optimized multidimensional transmission coefficient (CVT/muOMT) for tunneling were carried out at the MPWB1K/6-31+G(d,p) level to study the [1,7] sigmatropic hydrogen rearrangement in 7-methylocta-1,3(Z),5(Z)-triene. This compound has seven conformers, of which only one leads to products, although all of them have to be included in the theoretical treatment. The calculated CVT/muOMT rate constants are in good agreement with the available experimental data. To try to understand the role of tunneling in the hydrogen shift reaction, we have also calculated the thermal rate constants for the monodeuterated compound in the interval T = 333.2-388.2 K. This allowed us to evaluate primary kinetic isotope effects (KIEs) and make a direct comparison with the experiment. Our calculations show that both the large measured KIE and the large measured difference in the activation energies between the deuterated and root compounds are due to the quantum tunneling. The tunneling contribution to the KIE becomes noticeable only when the coupling between the reaction coordinate and the transverse modes is taken into account. Our results confirm previous experimental and theoretical works, which guessed that the obtained kinetic parameters pointed to a reaction with an important contribution due to tunneling. The above conclusion would be essentially valid for the case of the [1,7] hydrogen shift in previtamin D3 because of the similarity to the studied model system.     

Kinetics of the hydrogen abstraction *CH3 + alkane --> CH4 + alkyl reaction class: an application of the reaction class transition state theory

Kinetics of the hydrogen abstraction reaction (*)CH(3) + CH(4) --> CH(4) + (*)CH(3) is studied by a direct dynamics method. Thermal rate constants in the temperature range of 300-2500 K are evaluated by the canonical variational transition state theory (CVT) incorporating corrections from tunneling using the multidimensional semiclassical small-curvature tunneling (SCT) method and from the hindered rotations. These results are used in conjunction with the Reaction Class Transition State Theory/Linear Energy Relationship (RC-TST/LER) to predict thermal rate constants of any reaction in the hydrogen abstraction class of (*)CH(3) + alkanes. Our analyses indicate that less than 40% systematic errors on the average exist in the predicted rate constants using the RC-TST/LER method while comparing to explicit rate calculations the differences are less than 100% or a factor of 2 on the average.     

Importance of anharmonicity, recrossing effects, and quantum mechanical tunneling in transition state theory with semiclassical tunneling. A test case: the H2 + Cl hydrogen abstraction reaction

The hydrogen abstraction reaction from H2 by the Cl atom is studied by means of the variational transition state theory with semiclassical tunneling coefficients on the BW2 potential energy surface. Vibrational anharmonicity and coupling between the bending modes are taken into account. The occurrence of trajectories that recross the transition state is estimated by means of the canonical unified statistical method and by classical trajectories calculations. Different semiclassical methods for tunneling calculations are tested. Our results show that anharmonicity has a small but nonnegligible effect on the thermal rate constants, recrossing can be neglected, and tunneling is adequately described by the least-action approximation, and less successfully by the large-curvature version 3 approximation. However, the large-curvature version 4 and small-curvature approximations lead to a severe underestimation of tunneling. Thermal rate constants calculated using transition state theory including anharmonicity and tunneling agree very well with accurate quantal thermal rate constants over a wide temperature range, although the improvement over the harmonic transition state theory with the microcanonically optimized semiclassical tunneling approximation (based on version 3 of the large-curvature tunneling method) used in a previous study of this reaction is only marginal.     

TheRate: Program for ab initio direct dynamics calculations of thermal and vibrational-state-selected rate constants

We introduce TheRate (THEoretical RATEs), a complete application program with a graphical user interface (GUI) for calculating rate constants from first principles. It is based on canonical variational transition-state theory (CVT) augmented by multidimensional semiclassical zero and small curvature tunneling approximations. Conventional transition-state theory (TST) with one-dimensional Wigner or Eckart tunneling corrections is also available. Potential energy information needed for the rate calculations are obtained from ab initio molecular orbital and/or density functional electronic structure theory. Vibrational-state-selected rate constants may be calculated using a diabetic model. TheRate also introduces several technical advancements, namely the focusing technique and energy interpolation procedure. The focusing technique minimizes the number of Hessian calculations required by distributing more Hessian grid points in regions that are critical to the CVT and tunneling calculations and fewer Hessian grid points elsewhere. The energy interpolation procedure allows the use of a computationally less demanding electronic structure theory such as DFT to calculate the Hessians and geometries, while the energetics can be improved by performing a small number of single-point energy calculations along the MEP at a more accurate level of theory. The CH₄+H↔CH₃+H₂ reaction is used as a model to demonstrate usage of the program, and the convergence of the rate constants with respect to the number of electronic structure calculations. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1039–1052, 1998     

Thermal and state-selected rate constant calculations for O(3p) + H2 → OH + H and isotopic analogs

We present a new parametrization (based on ab initio calculations) of the bending potentials for the two lowest potential energy surfaces of the reaction O(³P) + H₂, and we use it for rate constant calculations by variational transition-state theory with multidimensional semiclassical tunneling corrections. We present results for the temperature range 250–2400 K for both the rate constants and the intermolecular kinetic isotope effects for the reactions of O(³P) with D₂ and HD. In general, the calculated rate constants for the thermal reactions are in excellent agreement with available experiments. We also calculate the enhancement effect for exciting H₂ to the first excited vibrational state. The calculations also provide information on which aspects of the potential energy surfaces are important for determining the predicted rate constants.     

Effects of multidimensional tunneling in the kinetics of hydrogen abstraction reactions of O (3P) with CH3OCHO

Quantum tunneling paths are important in reactions when there is a significant component of hydrogenic motion along the potential energy surface. In this study, variational transition state with multidimensional tunneling corrections are employed in the calculations of the thermal rate constants for hydrogen abstraction from the cis‐CH₃OCHO by O (³P) giving CH₃OCO + OH (R1) and CH₂OCHO + OH (R2). The structures and electronic energies are computed with the M06‐2X method. Benchmark calculations with the CBS_D–T approach give an enthalpy of reaction at 0 K for R1 (−2.8 kcal/mol) and R2 (−2.5 kcal/mol) which are in good agreement with the experiment, i.e. −2.61 and −1.81 kcal/mol. At the low and intermediate values of temperatures, small‐ and large‐curvature tunneling dominate the kinetics of R1, which is the dominant path over the range of temperature from 250 to 1200 K. This study shows the importance of multidimensional tunneling corrections for both R1 and R2, for which the total rate constant at 298 K calculated with the CVT/μOMT method is 8.2 × 10⁻¹⁵ cm³ molecule⁻¹ s⁻¹ which agrees well with experiment value of 9.3 × 10⁻¹⁵ cm³ molecule⁻¹ s⁻¹ (Mori, Bull. Inst. Chem. Res. 1981, 59, 116). © 2018 Wiley Periodicals, Inc.     

Temperature dependence of the kinetic isotope effects in thymidylate synthase. A theoretical study

In recent years, the temperature dependence of primary kinetic isotope effects (KIE) has been used as indicator for the physical nature of enzyme-catalyzed H-transfer reactions. An interactive study where experimental data and calculations examine the same chemical transformation is a critical means to interpret more properly temperature dependence of KIEs. Here, the rate-limiting step of the thymidylate synthase-catalyzed reaction has been studied by means of hybrid quantum mechanics/molecular mechanics (QM/MM) simulations in the theoretical framework of the ensemble-averaged variational transition-state theory with multidimensional tunneling (EA-VTST/MT) combined with Grote-Hynes theory. The KIEs were calculated across the same temperature range examined experimentally, revealing a temperature independent behavior, in agreement with experimental findings. The calculations show that the H-transfer proceeds with ～91% by tunneling in the case of protium and ～80% when the transferred protium is replaced by tritium. Dynamic recrossing coefficients are almost invariant with temperature and in all cases far from unity, showing significant coupling between protein motions and the reaction coordinate. In particular, the relative movement of a conserved arginine (Arg166 in Escherichia coli ) promotes the departure of a conserved cysteine (Cys146 in E. coli ) from the dUMP by polarizing the thioether bond thus facilitating this bond breaking that takes place concomitantly with the hydride transfer. These promoting vibrations of the enzyme, which represent some of the dimensions of the real reaction coordinate, would limit the search through configurational space to efficiently find those decreasing both barrier height and width, thereby enhancing the probability of H-transfer by either tunneling (through barrier) or classical (over-the-barrier) mechanisms. In other words, the thermal fluctuations that are coupled to the reaction coordinate, together with transition-state geometries and tunneling, are the same in different bath temperatures (within the limited experimental range examined). All these terms contribute to the observed temperature independent KIEs in thymidylate synthase.     

Deuterium enrichment of interstellar methanol explained by atom tunneling

We calculate, down to low temperature and for different isotopes, the reaction rate constants for the hydrogen abstraction reaction H + H(3)COH → H(2) + CH(2)OH/CH(3)O. These explain the known abundances of deuterated forms of methanol in interstellar clouds, where CH(2)DOH can be almost as abundant as CH(3)OH. For abstraction from both the C- and the O-end of methanol, the barrier-crossing motion involves the movement of light hydrogen atoms. Consequently, tunneling plays a dominant role already at relatively high temperature. Our implementation of harmonic quantum transition state theory with on the fly calculation of forces and energies accounts for these tunneling effects. The results are in good agreement with previous semiclassical and quantum dynamics calculations (down to 200 K) and experimental studies (down to 295 K). Here we extend the rate calculations down to lower temperature: 30 K for abstraction from the C-end of methanol and 80 K for abstraction from the OH-group. At all temperatures, abstraction from the C-end is preferred over abstraction from the O-end, more strongly so at lower temperature. Furthermore, the tunneling behavior strongly affects the kinetic isotope effects (KIEs). D + H(3)COH → HD + CH(2)OH has a lower vibrationally adiabatic barrier than H + H(3)COH → H(2) + CH(2)OH, giving rise to an inverse KIE (k(H)/k(D) < 1) at high temperature, in accordance with previous experiments and calculations. However, since tunneling is more facile for the light H atom, abstraction by H is favored over abstraction by D below ~135 K, with a KIE k(H)/k(D) of 11.2 at 30 K. The H + D(3)COD → HD + CD(2)OD reaction is calculated to be much slower than the D + H(3)COH → HD + CH(2)OH, in agreement with low-temperature solid-state experiments, which suggests the preference for H (as opposed to D) abstraction from the C-end of methanol to be the mechanism by which interstellar methanol is deuterium-enriched.     

Formic acid catalyzed keto-enol tautomerizations for C2 and C3 enols: Implications in atmospheric and combustion chemistry

Enols are important species in atmospheric and combustion chemistry. However, their implications in these environments are not well established due to a lack of accurate rate constants and mechanisms to determine their fate. In this work, we investigate the formic acid catalyzed keto-enol tautomerizations converting vinyl alcohol, propen-2-ol and 1-propenol into acetaldehyde, acetone and propanal, respectively. High-level ab initio and multistructural torsional variational transition state theory calculations are performed with small-curvature tunneling corrections to obtain rate constants in the temperature range 200 K-3000 K. Tunneling is shown to be pronounced as a consequence of very narrow adiabatic potential energy curves, and indicates a need to revisit previous calculations. We show the implications of the studied reactions on the fate of enols under combustion relevant conditions by detailed kinetic modeling simulations. The yield of vinyl alcohol predicted by our calculated rate constants may be useful to lessen the underestimation of organic acids concentrations in current atmospheric models.     

Tunneling in hydrogen-transfer isomerization of n-alkyl radicals

The role of quantum tunneling in hydrogen shift in linear heptyl radicals is explored using multidimensional, small-curvature tunneling method for the transmission coefficients and a potential energy surface computed at the CBS-QB3 level of theory. Several one-dimensional approximations (Wigner, Skodje and Truhlar, and Eckart methods) were compared to the multidimensional results. The Eckart method was found to be sufficiently accurate in comparison to the small-curvature tunneling results for a wide range of temperature, but this agreement is in fact fortuitous and caused by error cancellations. High-pressure limit rate constants were calculated using the transition state theory with treatment of hindered rotations and Eckart transmission coefficients for all hydrogen-transfer isomerizations in n-pentyl to n-octyl radicals. Rate constants are found in good agreement with experimental kinetic data available for n-pentyl and n-hexyl radicals. In the case of n-heptyl and n-octyl, our calculated rates agree well with limited experimentally derived data. Several conclusions made in the experimental studies of Tsang et al. (Tsang, W.; McGivern, W. S.; Manion, J. A. Proc. Combust. Inst. 2009, 32, 131-138) are confirmed theoretically: older low-temperature experimental data, characterized by small pre-exponential factors and activation energies, can be reconciled with high-temperature data by taking into account tunneling; at low temperatures, transmission coefficients are substantially larger for H-atom transfers through a five-membered ring transition state than those with six-membered rings; channels with transition ring structures involving greater than 8 atoms can be neglected because of entropic effects that inhibit such transitions. The set of computational kinetic rates were used to derive a general rate rule that explicitly accounts for tunneling. The rate rule is shown to reproduce closely the theoretical rate constants.     

Mechanistic study and kinetic properties of the CF3CHO + Cl reaction

Theoretical investigations have been carried out on the mechanism and kinetics for the reaction of CF 3 CHO + Cl using duallevel direct dynamics method. The potential energy surface information was obtained at the MCQCISD/3//MP2/cc-pVDZ level and the kinetic calculations were done using variational transition state theory with interpolated single-point energy (VTST-ISPE) approach. The calculated results show that the reaction proceeds primarily via the H-abstraction channel, while the Cl-addition channel is unfavorable due to the higher barriers. The improved canonical variational transition-state theory (ICVT) with the small-curvature tunneling correction (SCT) was used to calculate the rate constants. The theoretical rate constants at room temperature are in general agreement with the experimental values. A three-parameter rate constant expression was fitted over a wide temperature range of 200-2000 K.     

Quasi-classical trajectory and direct-dynamics CVT study on the initiation steps of methanol combustion

Direct-dynamics canonical variational transition-state theory (CVT) and quasi-classical trajectory (QCT) calculations have been performed to study the dynamics of the initiation steps in the methanol combustion at high oxygen concentration. The initiation steps in combustion of methanol is hydrogen abstraction from carbon or oxygen in methanol to produce hydroxymethyl radical (CH₂OH) or methoxy radical (CH₃O), respectively, and hydroperoxyl radical (HO₂). A new analytical potential energy function driven from our DFT calculations is constructed to study the dynamics of the title reactions. Reactive cross sections and reaction probabilities at various relative translational energies and initial vibrational and rotational reactant excitation were obtained to calculate the rate constants. The calculated rate constants from CVT and QCT calculations are compared.     

Rate constants from the reaction path Hamiltonian. II. Nonseparable semiclassical transition state theory

For proton transfer reactions, the tunneling contributions to the rates are often much larger than thermally activated rates at temperatures of interest. A number of separable tunneling corrections have been proposed that capture the dependence of tunneling rates on barrier height and imaginary frequency size. However, the effects of reaction pathway curvature and barrier anharmonicity are more difficult to quantify. The nonseparable semiclassical transition state theory (TST) of Hernandez and Miller [Chem. Phys. Lett. 214, 129 (1993)] accounts for curvature and barrier anharmonicity, but it requires prohibitively expensive cubic and quartic derivatives of the potential energy surface at the transition state. This paper shows how the reaction path Hamiltonian can be used to approximate the cubic and quartic derivatives used in nonseparable semiclassical transition state theory. This enables tunneling corrections that include curvature and barrier anharmonicity effects with just three frequency calculations as required by a conventional harmonic transition state theory calculation. The tunneling correction developed here is nonseparable, but can be expressed as a thermal average to enable efficient Monte Carlo calculations. For the proton exchange reaction NH2 + CH4 <==> NH3 + CH3, the nonseparable rates are very accurate at temperatures from 300 K up to about 1000 K where the TST rate itself begins to diverge from the experimental results.