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.     

Rate coefficients of the CF3CHFCF3 + H → CF3CFCF3 + H2 reaction at different temperatures calculated by transition state theory with ab initio and DFT reaction paths

The minimum energy path (MEP) of the reaction, CF₃CHFCF₃ + H → transition state (TS) → CF₃CFCF₃ + H₂, has been computed at different ab initio levels and with density functional theory (DFT) using different functionals. The computed B3LYP/6‐31++G**, BH&HLYP/cc‐pVDZ, BMK/6‐31++G**, M05/6‐31+G**, M05‐2X/6‐31+G**, UMP2/6‐31++G**, PUMP2/6‐31++G**//UMP2/6‐31++G**, RCCSD(T)/aug‐cc‐pVDZ//UMP2/6‐31++G**, RCCSD(T)/aug‐cc‐pVTZ(spd,sp)//UMP2//6‐31++G**, RCCSD(T)/CBS//M05/6‐31+G**, and RCCSD(T)/CBS//UMP2/6‐31++G** MEPs, and associated gradients and Hessians, were used in reaction rate coefficient calculations based on the transition state theory (TST). Reaction rate coefficients were computed between 300 and 1500 K at various levels of TST, which include conventional TST, canonical variational TST (CVT) and improved CVT (ICVT), and with different tunneling corrections, namely, Wigner, zero‐curvature, and small‐curvature (SCT). The computed rate coefficients obtained at different ab initio, DFT and TST levels are compared with experimental values available in the 1000–1200 K temperature range. Based on the rate coefficients computed at the ICVT/SCT level, the highest TST level used in this study, the BH&HLYP functional performs best among all the functionals used, while the RCCSD(T)/CBS//MP2/6‐31++G** level is the best among all the ab initio levels used. Comparing computed reaction rate coefficients obtained at different levels of theory shows that, the computed barrier height has the strongest effect on the computed reaction rate coefficients as expected. Variational effects on the computed rate coefficients are found to be negligibly small. Although tunneling effects are relatively small at high temperatures (～1500 K), SCT corrections are significant at low temperatures (～300 K), and both barrier heights and the magnitudes of the imaginary frequencies affect SCT corrections. © 2012 Wiley Periodicals, Inc.     

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.     

Absolute rate calculations: atom and proton transfers in hydrogen-bonded systems.

We calculate energy barriers of atom- and proton-transfer reactions in hydrogen-bonded complexes in the gas phase. Our calculations do not involve adjustable parameters and are based on bond-dissociation energies, ionization potentials, electron affinities, bond lengths, and vibration frequencies of the reactive bonds. The calculated barriers are in agreement with experimental data and high-level ab initio calculations. We relate the height of the barrier with the molecular properties of the reactants and complexes. The structure of complexes with strong hydrogen bonds approaches that of the transition state, and substantially reduces the barrier height. We calculate the hydrogen-abstraction rates in H-bonded systems using the transition-state theory with the semiclassical correction for tunneling, and show that they are in excellent agreement with the experimental data. H-bonding leads to an increase in tunneling corrections at room temperature.     

The importance of tunneling in the first hydrogenation step in ammonia synthesis over a Ru(0001) surface

The hydrogenation of nitrogen (N(ads)+H(ads)-->NH(ads)) on metal surfaces is an important step in ammonia catalysis. We investigate the reaction dynamics of this hydrogenation step by time independent scattering theory and variational transition state theory (VTST) including tunneling corrections. The potential energy surface is derived by hybrid density functional theory on a model cluster composed of 12 ruthenium atoms resembling a Ru(0001) surface. The scattering calculations are performed on a reduced dimensionality potential energy hypersurface, where two dimensions are treated explicitly and all others are included implicitly by the zero-point correction. The VTST calculations include quantum effects along the reaction coordinate by applying the small curvature tunneling scheme. Even at room temperature (where ruthenium already shows catalytic activity) we find rate enhancement by tunneling by a factor of approximately 70. Inspection of the reaction probabilities shows that the major contribution to reactivity comes from the vibrational ground state of the reactants into vibrationally excited product states. The reaction rates are higher than determined in previous studies, and are compatible with experimental overall rates for ammonia synthesis.     

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.     

Theoretical study of the thermodynamics and kinetics of hydrogen abstractions from hydrocarbons

Thermochemical and kinetic data were calculated at four cost-effective levels of theory for a set consisting of five hydrogen abstraction reactions between hydrocarbons for which experimental data are available. The selection of a reliable, yet cost-effective method to study this type of reactions for a broad range of applications was done on the basis of comparison with experimental data or with results obtained from computationally demanding high level of theory calculations. For this benchmark study two composite methods (CBS-QB3 and G3B3) and two density functional theory (DFT) methods, MPW1PW91/6-311G(2d,d,p) and BMK/6-311G(2d,d,p), were selected. All four methods succeeded well in describing the thermochemical properties of the five studied hydrogen abstraction reactions. High-level Weizmann-1 (W1) calculations indicated that CBS-QB3 succeeds in predicting the most accurate reaction barrier for the hydrogen abstraction of methane by methyl but tends to underestimate the reaction barriers for reactions where spin contamination is observed in the transition state. Experimental rate coefficients were most accurately predicted with CBS-QB3. Therefore, CBS-QB3 was selected to investigate the influence of both the 1D hindered internal rotor treatment about the forming bond (1D-HR) and tunneling on the rate coefficients for a set of 21 hydrogen abstraction reactions. Three zero curvature tunneling (ZCT) methods were evaluated (Wigner, Skodje & Truhlar, Eckart). As the computationally more demanding centrifugal dominant small curvature semiclassical (CD-SCS) tunneling method did not yield significantly better agreement with experiment compared to the ZCT methods, CD-SCS tunneling contributions were only assessed for the hydrogen abstractions by methyl from methane and ethane. The best agreement with experimental rate coefficients was found when Eckart tunneling and 1D-HR corrections were applied. A mean deviation of a factor 6 on the rate coefficients is found for the complete set of 21 reactions at temperatures ranging from 298 to 1000 K. Tunneling corrections play a critical role in obtaining accurate rate coefficients, especially at lower temperatures, whereas the hindered rotor treatment only improves the agreement with experiment in the high-temperature range.     

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.     

Density functional theory study of beta-hydride elimination of ethyl on flat and stepped Cu surfaces

Plane wave density functional theory calculations have been used to characterize the transition states for beta-hydride elimination of ethyl on Cu(100), Cu(110), Cu(111), and Cu(221). The reaction rates predicted by these calculations have been compared to experiments by including tunneling corrections within harmonic transition state theory. Tunneling corrections are found to be important in describing the peak temperatures observed using temperature programmed desorption experiments on Cu(110), Cu(111), and Cu(221). Once these corrections are included, the effective activation energies obtained from our calculations are in good agreement with previous experimental studies of this reaction on these four Cu surfaces. The transition states determined in our calculations are used to examine two general hypotheses that have been suggested to describe structure sensitivity in metal-catalyzed surface reactions.     

CH(^4∑^-)+H2O→CH2(^3B1)+OH的直接动态学研究

用从头算方法计算了反应CH(^4∑^-)+H2O→CH2(^3B1)+OH的反应途径。在此基础上, 计算沿反应途径的动态学性质和正则变分过渡态理论的速率常数, 并进行隧道效应校正。结果表明, 电子相关能对反应活化位垒影响较大; 反应存在返回效应和隧道效应, 用正则变分过渡态方法和小曲率近似的隧道校正是有效的。     

Double hydrogen tunneling revisited: the breakdown of experimental tunneling criteria

Formic acid dimer was chosen as a model system to investigate synchronous double proton transfer by means of variational transition state theory (VTST) for various isotopically modified hydrogen species. The electronic barrier for the double proton transfer was evaluated to be 7.9 kcal/mol, thus being significantly lower than it was determined in previous studies. The tunneling probabilities were evaluated at temperatures from 100 up to 400 K and typical Arrhenius behavior with enhancement by tunneling is observed. When comparing the transmission factors kappa in dependence of the mass of the tunneling hydrogen, it was found that there are two maxima, one at very low masses (e.g., 0.114 amu, corresponding to the muonium entity) and one maximum at around 2 amu (corresponding to deuterium). With the knowledge of the VTST-hydrogen transfer rates and the corresponding tunneling corrections, various tunneling criteria were tested (e.g., Swain-Schaad exponents) and were shown to fail in this reaction in predicting the extent of tunneling. This finding adds another aspect in the ongoing "Tunneling-Enhancement by Enzymes" discussion, as the used tunneling criteria based on experimental reaction rates may fail to predict tunneling behavior correctly.     

Tunneling and classical paths for proton transfer in an enzyme reaction dominated by tunneling: oxidation of tryptamine by aromatic amine dehydrogenase

Proton tunneling dominates the oxidative deamination of tryptamine catalyzed by the enzyme aromatic amine dehydrogenase. For reaction with the fast substrate tryptamine, a H/D kinetic isotope effect (KIE) of 55 +/- 6 has been reported-one of the largest observed in an enzyme reaction. We present here a computational analysis of this proton-transfer reaction, applying combined quantum mechanics/molecular mechanics (QM/MM) methods (PM3-SRP//PM3/CHARMM22). In particular, we extend our previous computational study (Masgrau et al. Science 2006, 312, 237) by using improved energy corrections, high-level QM/MM methods, and an ensemble of paths to estimate the tunneling contributions. We have carried out QM/MM molecular dynamics simulations and variational transition state theory calculations with small-curvature tunneling corrections. The results provide detailed insight into the processes involved in the reaction. Transfer to the O2 oxygen of the catalytic base, Asp128beta, is found to be the favored reaction both thermodynamically and kinetically, even though O1 is closer in the reactant complex. Comparison of quantum and classical models of proton transfer allows estimation of the contribution of hydrogen tunneling in lowering the barrier to reaction in the enzyme. A reduction of the activation free energy due to tunneling of 3.1 kcal mol-1 is found, which represents a rate enhancement due to tunneling by 2 orders of magnitude. The calculated KIE of 30 is significantly elevated over the semiclassical limit, in agreement with the experimental observations; a semiclassical value of 6 is obtained when tunneling is omitted. A polarization of the C-H bond to be broken is observed due to the close proximity of the catalytic aspartate and the (formally) positively charged imine nitrogen. A comparison is also made with the related quinoprotein methylamine dehydrogenase (MADH)-the much lower KIE of 11 that we obtain for the MADH/methylamine system is found to arise from a more endothermic potential energy surface for the MADH reaction.     

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.     

Temperature dependence of carbon-13 kinetic isotope effects of importance to global climate change

We report here a theoretical study of the 13C kinetic isotope effect (KIE) and its temperature dependence for the reaction OH + CH4 --> H2O + CH3, the major sink of atmospheric methane in the troposphere. The KIE values at various atmospherically significant temperatures were determined by direct dynamics using variational transition state theory with multidimensional tunneling contributions (VTST/MT). The potential energy surfaces (PESs) were generated by hybrid density functional theory as well as by recently developed doubly hybrid density functional theory methods. Comparisons of our calculated KIEs with experimental data and theoretical values in the literature reveal the critical contributions due to multidimensional tunneling and torsion anharmonicity as well as the critical issue of the choice of internal rotational axis.     

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     

A product branching ratio controlled by vibrational adiabaticity and variational effects: kinetics of the H + trans-N2H2 reactions

The abstraction and addition reactions of H with trans-N(2)H(2) are studied by high-level ab initio methods and density functional theory. Rate constants were calculated for these two reactions by multistructural variational transition state theory with multidimensional tunneling and including torsional anharmonicity by the multistructural torsion method. Rate constants of the abstraction reaction show large variational effects, that is, the variational transition state yields a smaller rate constant than the conventional transition state; this results from the fact that the variational transition state has a higher zero-point vibrational energy than the conventional transition state. The addition reaction has a classical barrier height that is about 1 kcal∕mol lower than that of the abstraction reaction, but the addition rates are lower than the abstraction rates due to vibrational adiabaticity. The calculated branching ratio of abstraction to addition is 3.5 at 200 K and decreases to 1.2 at 1000 K and 1.06 at 1500 K.     

A semiclassical reactive flux method for the calculation of condensed phase activated rate constants

A semi classical reactive flux algorithm for calculating thermally activated rate constants is presented which is based on a semi-classical transition state theory due to Chapman, Garrett and Miller [J. Chem. Phys. 63 (1975) 2710]. This reactive flux technique, when combined with the semiclassical TST, enables one to describe dynamical recrossings of the transition state on the same footing as tunneling effects. Most importantly, the method is readily applied to nonlinear multidimensional systems over a wide range of temperatures. It will be shown that the method works very well for a variety of existing models.     

Novel theoretical studies of the dehydrogenation of LiBH2NH3

It is believed that the dehydrogenation of LiNH₂BH₃ (LAB) proceeds through a combination of the decomposition of the LiBH₂NH₃ (LBA) and LAB isomers. The dehydrogenation of LBA, an isomer of LAB, is discussed in this article. It is demonstrated that the loss of H₂ from LBA takes place in a two‐step reaction. Studies of the dehydrogenation process were performed using Møller–Plesset second‐order perturbation theory with a 6‐311++G(3df,2pd) basis set. The intrinsic reaction coordinate was calculated to determine the minimum energy paths. Finally, the rate constants were obtained using the transition‐state theory (TST), TST/Eckart, canonical variational transition‐state theory (CVT), CVT/small‐curvature tunneling correction, and CVT/zero‐curvature tunneling correction methods from 200 to 2500 K. This is the first report on a different dehydrogenation mechanism for an alkali‐metal amidoborane, and the energy barrier of LBA is much lower than that of the traditionally studied LAB. © 2012 Wiley Periodicals, Inc.     

Theoretical investigations on thermal rearrangement reactions of (aminomethyl)silane

Thermal rearrangement reactions of (aminomethyl)silane H(3)SiCH(2)NH(2) were studied by ab initio calculations at the G3 level. The results show that two dyotropic reactions could happen when H(3)SiCH(2)NH(2) is heated. In one reaction, the silyl group migrates from the carbon to the nitrogen atom while a hydrogen atom shifts from the nitrogen to the carbon atom, forming (methylamino)silane CH(3)NHSiH(3) (reaction A). This reaction can proceed via three paths: a path involving two consecutive steps with two transition states and one intermediate metastable carbene species (A-1); and two concerted paths (A-2 and A-3). In the other reaction, the amino group migrates from the carbon to the silicon atom while a hydrogen atom shifts from the silicon to the carbon atom, via a double three-membered ring transition state, forming aminomethylsilane CH(3)SiH(2)NH(2) (reaction B). Reaction rate constants, changes (DeltaS(#), DeltaH, and DeltaG) in thermodynamic functions and equilibrium constants of the reactions were calculated with the MP2(full)/6-311G(d,p) optimized geometries, harmonic vibrational frequencies and G3 energies of reactants, transition states, intermediates and products with statistical mechanical methods and the conventional transition-state theory (TST) with Wigner tunneling approximation over a temperature range 400-1800 K.