Absolute rate calculations. Proton transfers in solution

The reaction path of the intersecting-state model is used in transition-state theory with the semiclassical correction for tunneling (ISM/scTST) to calculate the rates of proton-transfer reactions from hydrogen-bond energies, reaction energies, electrophilicity indices, bond lengths, and vibration frequencies of the reactive bonds. ISM/scTST calculations do not involve adjustable parameters. The calculated proton-transfer rates are within 1 order of magnitude of the experimental ones at room temperature, and cover very diverse systems, such as deprotonations of nitroalkanes, ketones, HCN, carboxylic acids, and excited naphthols. The calculated temperature dependencies and kinetic isotope effects are also in good agreement with the experimental data. These calculations elucidate the roles of the reaction energy, electrophilicity, structural parameters, hydrogen bonds, tunneling, and solvent in the reactivity of acids and bases. The efficiency of the method makes it possible to run absolute rate calculations through the Internet.     

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.     

Ab initio rate constants from hyperspherical quantum scattering: application to H+C2H6 and H+CH3OH

The dynamics and kinetics of the abstraction reactions of H atoms with ethane and methanol have been studied using a quantum mechanical procedure. Bonds being broken and formed are treated with explicit hyperspherical quantum dynamics. The ab initio potential energy surfaces for these reactions have been developed from a minimal number of grid points (average of 48 points) and are given by analytical functionals. All the degrees of freedom except the breaking and forming bonds are optimized using the second order perturbation theory method with a correlation consistent polarized valence triple zeta basis set. Single point energies are calculated on the optimized geometries with the coupled cluster theory and the same basis set. The reaction of H with C2H6 is endothermic by 1.5 kcal/mol and has a vibrationally adiabatic barrier of 12 kcal/mol. The reaction of H with CH3OH presents two reactive channels: the methoxy and the hydroxymethyl channels. The former is endothermic by 0.24 kcal/mol and has a vibrationally adiabatic barrier of 13.29 kcal/mol, the latter reaction is exothermic by 7.87 kcal/mol and has a vibrationally adiabatic barrier of 8.56 kcal/mol. We report state-to-state and state-selected cross sections together with state-to-state rate constants for the title reactions. Thermal rate constants for these reactions exhibit large quantum tunneling effects when compared to conventional transition state theory results. For H+CH3OH, it is found that the CH2OH product is the dominant channel, and that the CH3O channel contributes just 2% at 500 K. For both reactions, rate constants are in good agreement with some measurements.     

Reaction rates for O + HD → OH + D and O + HD → OD + H

We have calculated reaction rates for the reactions O + HD → OH + D and O + DH → OD + H using improved canonical variational transition state theory and least-action ground-state transmission coefficients with an ab initio potential energy surface. The kinetic isotope effects are in good agreement with experiment. The optimized tunneling paths and properties of the variational transition states and the rate enhancement for vibrationally excited reactants are also presented and compared with those for the isotopically unsubstituted reaction O + H₂ → OH + H. The thermal reactions at low and room temperature are predicted to occur by tunneling at extended configurations, i.e., to initiate early on the reaction path and to avoid the saddle point regions. Tunneling also dominates the low and room temperature reactions for excited vibrational states, but in these cases the results are not as sensitive to the nature of the tunneling path. Overbarrier mechanisms dominate for both thermal and excited-vibrational state reactions for T > 600 K. For the excited-state reaction (with initial vibrational quantum number n > 0) a transition state switch occurs for T > 1000 K for the O + HD(n = 1) → OD + H case and for T > 1500 K for the O + DH(n = 1) → OD + H reaction, and this may be a general phenomenon for excited-state reactions at higher temperature. In the present case the switch occurs from an early variational transition state where the vibrationally adiabatic approximation is expected to be valid to a tighter variational transition state where nonadiabatic effects are probably important and should be included.     

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.     

Insights Gained by Modeling the Kinetics of Archetypal Hydrogen Atom Transfer Reactions: NH3 + ·H ⇆ H2N· + H2 and CH4 + ·H ⇆ H3C· + H2

Experimental measurements of the kinetics of the title reactions extend to temperature ranges of 1360 K for the ammonia‐hydrogen reaction and of 1602 K for the methane‐hydrogen reaction. Curved plots of ln(k) versus 1/T are obtained. Many theoretical calculations modeling these reactions routinely use tunneling corrections to match experiment. The steepness and curvatures of the plots are modeled successfully in this work and are shown to be caused solely by changes in the bond dissociation energies of the bonds involved in the reactions without invoking tunneling or any other adjustable parameters. The conclusion that tunneling does not contribute significantly to the rates in the temperature range of the measurements is in stark contrast with those theoretical calculations invoking large tunneling factors in the experimental temperature range. Support for the conclusion is provided by theoretical calculations of harmonic quantum transition state theory implementing instanton theory. There is direct experimental evidence that significant tunneling occurs in some H atom transfers, as with isotopomers of H₂ + ·H and other H transfers at very low temperatures. However, there is no direct experimental evidence of significant tunneling contributions to the rates of the title reactions in the temperature range of the measurements. Insights are gained into what specific forces must be overcome by the enthalpy of activation for reaction to occur.     

DFT and ab initio direct dynamics studies on the hydrogen abstraction reactions of chlorine atoms with CH(4-n)F(n) (n = 1-3)

A direct dynamics study is carried out for the hydrogen abstraction reactions Cl + CH(4-n)F(n) (n = 1-3) in the temperature range of 200-1,000 K. The minimum energy paths (MEPs) of these reactions are calculated at the BH&H-LYP/6-311G(d,p) level, and the energies along the MEPs are further refined at the QCISD(T)/6-311+G(2df,2p) and QCISD(T)/6-311+G(d,p) (single-point) level. The rate constants obtained by using the improved canonical variational transition state theory incorporating small-curvature tunneling correction (ICVT/SCT) are in good agreement with the available experimental results. It is shown that the vibrational adiabatic potential energy curves for these reactions have two barriers, a situation similar to the analogous reactions CH(3)X+Cl (X=Cl, Br). The theoretical results show that for the title reactions the variational effect should not be neglected over the whole considered temperature range, while the small-curvature tunneling effect is only important in the lower temperature range. The effects of fluorine substitution on the rate of this kind of reactions are also examined.     

A direct test of the vibrationally adiabatic theory of chemical reactions

The adiabaticity assumption of the vibrationally adiabatic theory of chemical reactions in the zero-curvature approximation is directly tested for the collinear H + H₂ reaction against calculations using exact wavefunctions. It is found that the symmetric stretch motion of the transition state is adiabatic to within 10% for total energies E ranging from 0.51 eV to 0.72 eV. For E below the zero-point energy of this symmetric stretch motion non-adiabaticity is substantial and is probably due to tunneling. For E above the first excited vibrational state energy of this symmetric stretch motion the adiabaticity assumption breaks down completely.     

New analytical potential energy surface for the F(2P)+CH4 hydrogen abstraction reaction: kinetics and dynamics

A new potential energy surface for the gas-phase F(2P)+CH4 reaction and its deuterated analogues is reported, and its kinetics and dynamics are studied exhaustively. This semiempirical surface is completely symmetric with respect to the permutation of the four methane hydrogen atoms, and it is calibrated to reproduce the topology of the reaction and the experimental thermal rate constants. For the kinetics, the thermal rate constants were calculated using variational transition-state theory with semiclassical transmission coefficients over a wide temperature range, 180-500 K. The theoretical results reproduce the experimental variation with temperature. The influence of the tunneling factor is negligible, due to the flattening of the surface in the entrance valley, and we found a direct dependence on temperature, and therefore positive and small activation energies, in agreement with experiment. Two sets of kinetic isotope effects were calculated, and they show good agreement with the sparse experimental data. The coupling between the reaction coordinate and the vibrational modes shows qualitatively that the FH stretching and the CH3 umbrella bending modes in the products appear vibrationally excited. The dynamics study was performed using quasi-classical trajectory calculations, including corrections to avoid zero-point energy leakage along the trajectories. First, we found that the FH(nu',j') rovibrational distributions agree with experiment. Second, the excitation function presents an oscillatory pattern, reminiscent of a reactive resonance. Third, the state specific scattering distributions present reasonable agreement with experiment, and as the FH(nu') vibrational state increases the scattering angle becomes more forward. These kinetics and dynamics results seem to indicate that a single, adiabatic potential energy surface is adequate to describe this reaction, and the reasonable agreement with experiment (always qualitative and sometimes quantitative) lends confidence to the new surface.     

Dual-level direct dynamics studies for the reactions of OH radical with bromine-substituted ethanes

The dynamic properties of the multichannel hydrogen abstraction reactions of CH(3)CH(2)Br + OH --> products and CH(3)CHBr(2) + OH --> products are studied by dual-level direct dynamics method. For each reaction, three reaction channels, one for alpha-hydrogen abstraction and two for beta-hydrogen abstractions, have been identified. The minimum energy paths (MEPs) of both the reactions are calculated at the Becke's half-and-half (BH&H)-Lee-Yang-Parr (LYP)/6-311G(d, p) level and the energy profiles along the MEPs are further refined with interpolated single-point energies (ISPE) method at the G2M(RCC5)//BH&H-LYP level. There are complexes with energies less than those of the reactants or products located at the entrance or exit channels, which indicates that the reactions may proceed via an indirect mechanism. By canonical variational transition-state theory (CVT) the rate constants are calculated incorporating the small-curvature tunneling (SCT) correction in the temperature range of 220-2000 K. The agreement of the rate constants with available experimental values for two reactions is good in the measured temperature range. The calculated results show that alpha-hydrogen abstraction channel is the major reaction pathway in the lower temperature for two reactions, while the contribution of beta-hydrogen abstraction will increase with the increase in temperature.     

Tunneling dynamics and spatial correlations of long chain growth in solid-state photochlorination of ethylene at low temperatures

A novel method is described for preparing reactive mixed crystals by vapor deposition in argon and subsequent evaporation of the argon. The kinetics of photochlorination chain reactions of ethylene-chlorine mixtures prepared by this method have been studied by dynamic UV and IR spectroscopy. Activationless chain growth occurs with mean length 260±70 in the temperature range 17–45 K. Chain lengths greater than 100 are observed up to 60–70% conversion to products. Comparison of the experimental data with computer simulations shows that the tunneling reaction is due to formation of a close-packed reaction complex with high amplitude zero-point vibrations which lower the vibrationally adiabatic barrier to reaction. The commensurability of reactant and product crystal lattices results in linear propagation of long chains without accumulation of deformation strain. Spatial correlations caused by nonlinear propagation are considered.     

Rate-promoting vibrations and coupled hydrogen-electron transfer reactions in the condensed phase: a model for enzymatic catalysis

A model is presented for coupled hydrogen-electron transfer reactions in condensed phase in the presence of a rate promoting vibration. Large kinetic isotope effects (KIEs) are found when the hydrogen is substituted with deuterium. While these KIEs are essentially temperature independent, reaction rates do exhibit temperature dependence. These findings agree with recent experimental data for various enzyme-catalyzed reactions, such as the amine dehydrogenases and soybean lipoxygenase. Consistent with earlier results, turning off the promoting vibration results in an increased KIE. Increasing the barrier height increases the KIE, while increasing the rate of electron transfer decreases it. These results are discussed in light of other views of vibrationally enhanced tunneling in enzymes.     

Koopmans-like approximation in the Kohn-Sham method and the impact of the frozen core approximation on the computation of the reactivity parameters of the density functional theory

A Koopmans-like approximation is introduced in the spin-polarized version of the Kohn-Sham (KS) density functional theory to obtain a relation between KS orbital energies and vertical ionization potential and electron affinity. Expressions for reactivity indexes (like electronegativity, hardness, electrophilicity, and excitation energies) include KS frontier orbital energies and additional contributions associated with the self-interaction correction. Those reactivity parameters were computed with different exchange-correlation functionals to test the approach for a set of small molecules. The results show that the present approximation provides a better way to estimate hardness, electronegativity, and electrophilicity than just the use of frontier orbital energy values. However KS HOMO and LUMO energy gap gives a better agreement with excitation energies.     

H原子和(CH3)2SiH2抽提反应的理论研究

采用UMP2/6-31G(d)理论水平优化了H原子和(CH3)2SiH2抽提反应势能面上的所有驻点,并在此水平基础上进行了内禀反应坐标(IRC)的计算,得到该反应的反应途径(MEP)。应用变分过渡态理论及最小能量途径半经典绝热基态隧道效应校正(MEPSAG)、小曲率半经典绝热基态隧道效应校正(SCSAG)等方法对上述反应进行了动力学研究,期望从理论上提供一套温度范围较宽、精度较高的动力学数据,为阐明反应机理和解释实验结果提供理论依据。     

Theory of electron transfer reactions in blue-copper proteins

The rates of electron transfer reactions in azurin and plastocyanin are calculated with the Intersecting-State Model and compared with experimental data. The calculated distance, free-energy and temperature dependencies of the intraprotein rates in Ru-modified azurins are in good agreement with the experiment. These calculations do not require the fitting of any parameters. Significant tunneling contributions to the room temperature rate are found in some systems. In some cases the symmetry or the orientation of the donor and acceptor orbitals are not favorable and the ET rates are reduced by factors exceeding 4 orders of magnitude.     

Direct ab initio dynamics studies on the hydrogen-abstraction reactions of OH radicals with HOX (X = F, Cl, and Br)

The hydrogen abstract reactions of OH radicals with HOF (R1), HOCl (R2), and HOBr (R3) have been studied systematically by a dual-level direct-dynamics method. The geometries and frequencies of all the stationary points are optimized at the MP2/6-311+G(2d, 2p) level of theory. A hydrogen-bonded complex is located at the product channel for the OH + HOBr reaction. To improve the energetics information along the minimum energy path (MEP), single-point energy calculations are carried out at the CCSD(T)/6-311++G(3df, 3pd) level of theory. Interpolated single-point energy (ISPE) method is employed to correct the energy profiles for the three reactions. It is found that neither the barrier heights (DeltaE) nor the H-O bond dissociation energies [D(H-O)] exhibit any clear-cut linear correlations with the halogen electronegative. The decrease of DeltaE and D(H-O) for the three reactions are in order of HOF > HOBr > HOCl. Rate constants for each reaction are calculated by canonical variational transition-state theory (CVT) with a small-curvature tunneling correction (SCT) within 200-2000 K. The agreement of the rate constants with available experimental values for reactions R2 and R3 at 298 K is good. Our results show that the variational effect is small while the tunneling correction has an important contribution in the calculation of rate constants in the low-temperature range. Due to the lack of the kinetic data of these reactions, the present theoretical results are expected to be useful and reasonable to estimate the dynamical properties of these reactions over a wide temperature range where no experimental value is available.     

Potential energy surface for the F(2P(3/2),2P(1/2)) + CH4 hydrogen abstraction reaction. kinetics and dynamics study

A modified and recalibrated potential energy surface (PES) is reported for the gas-phase F(2P(3/2),2P(1/2)) + CH4 reaction and its deuterated analogue. This semiempirical surface is completely symmetric with respect to the permutation of the four methane hydrogen atoms and is calibrated with respect to the updated experimental and theoretical stationary point properties and experimental thermal rate constants. To take into account the two spin-orbit electronic states of the fluorine atom, two versions of the surface were constructed, the PES-SO and PES-NOSO surfaces, which differ in the choice of the zero reference level of the reactants. On both surfaces, the thermal rate constants were calculated using variational transition-state theory with semiclassical transmission coefficients over a wide temperature range, 180-500 K. While the PES-SO surface overestimates the experimental rate constants, the PES-NOSO surface shows a better agreement, reproducing the experimental variation with temperature. The influence of the tunneling factor is negligible, due to the flattening of the surface in the entrance valley, and we found a direct dependence on temperature, and therefore positive and small activation energies, in agreement with experiment. The kinetic isotope effects calculated showed good agreement with the sparse experimental data at 283 and 298 K. Finally, on the PES-NOSO surface, other dynamical features, such as the coupling between the reaction coordinate and the vibrational modes, were analyzed. It was found qualitatively that the FH stretching and the CH3 umbrella bending modes in the products appear vibrationally excited. These kinetics and dynamics results seem to indicate that a single, adiabatic PES is adequate to describe this reaction.     

Calculation of vibronic couplings for phenoxyl/phenol and benzyl/toluene self-exchange reactions: implications for proton-coupled electron transfer mechanisms

The vibronic couplings for the phenoxyl/phenol and the benzyl/toluene self-exchange reactions are calculated with a semiclassical approach, in which all electrons and the transferring hydrogen nucleus are treated quantum mechanically. In this formulation, the vibronic coupling is the Hamiltonian matrix element between the reactant and product mixed electronic-proton vibrational wavefunctions. The magnitude of the vibronic coupling and its dependence on the proton donor-acceptor distance can significantly impact the rates and kinetic isotope effects, as well as the temperature dependences, of proton-coupled electron transfer reactions. Both of these self-exchange reactions are vibronically nonadiabatic with respect to a solvent environment at room temperature, but the proton tunneling is electronically nonadiabatic for the phenoxyl/phenol reaction and electronically adiabatic for the benzyl/toluene reaction. For the phenoxyl/phenol system, the electrons are unable to rearrange fast enough to follow the proton motion on the electronically adiabatic ground state, and the excited electronic state is involved in the reaction. For the benzyl/toluene system, the electrons can respond virtually instantaneously to the proton motion, and the proton moves on the electronically adiabatic ground state. For both systems, the vibronic coupling decreases exponentially with the proton donor-acceptor distance for the range of distances studied. When the transferring hydrogen is replaced with deuterium, the magnitude of the vibronic coupling decreases and the exponential decay with distance becomes faster. Previous studies designated the phenoxyl/phenol reaction as proton-coupled electron transfer and the benzyl/toluene reaction as hydrogen atom transfer. In addition to providing insights into the fundamental physical differences between these two types of reactions, the present analysis provides a new diagnostic for differentiating between the conventionally defined hydrogen atom transfer and proton-coupled electron transfer reactions.     

H2O(HOD) + Cl→HCl(DCl) + OH(OD)反应动态学的理论研究

用从头算方法, 获得了H2O + Cl→HCl + OH(R1), HOD +Cl→DCl + OH(R2), HOD + Cl→HCl + OD(R3)反应的内禀反应坐标(IRC)。根据传统过渡态、变分过渡态理论及相应的隧道效应校正, 计算了反应的速率常数。对已有实验速率常数值的R1反应, 我们计算的结果和实验一致。根据Truhlar的振动选态公式, 分别讨论了激发HOD中OH, OD振动模式对反应速率的影响,得到激发HOD中的OH振动模式将有利于产物OD + HCl生成, 和实验的结论相一致。     

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.