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.     

SurfKin: An ab initio kinetic code for modeling surface reactions

In this article, we describe a C/C++ program called SurfKin (Surface Kinetics) to construct microkinetic mechanisms for modeling gas–surface reactions. Thermodynamic properties of reaction species are estimated based on density functional theory calculations and statistical mechanics. Rate constants for elementary steps (including adsorption, desorption, and chemical reactions on surfaces) are calculated using the classical collision theory and transition state theory. Methane decomposition and water–gas shift reaction on Ni(111) surface were chosen as test cases to validate the code implementations. The good agreement with literature data suggests this is a powerful tool to facilitate the analysis of complex reactions on surfaces, and thus it helps to effectively construct detailed microkinetic mechanisms for such surface reactions. SurfKin also opens a possibility for designing nanoscale model catalysts. © 2014 Wiley Periodicals, Inc.     

Separable unimolecular reaction rate theory

A new unimolecular reaction rate theory is derived on the basis of a classical model of the reaction. The fundamental assumptions are (i) instantaneous activation-deactivation events represented by a statistical transition probability, (ii) irreversible dissociation, and (iii) separability of internal and external dynamics. The third assumption is found to be satisfied when the statistical transition probability satisfies a generalized strong collision assumption and it leads to a rate theory which depends on internal molecular dynamics only through lifetime information for the isolated molecule. The new theory shows that the rate coefficient is non-Markoffian although the memory effects will not be apparent on the macroscopic time scales of traditional experiments. Thus Slater's “new approach to rate theory” is a special case of the separable rate theory when applied to slow reactions. New experimental techniques are predicted to have the capacity to resolve the memory effects in the rate coefficient and provide lifetime information which would then allow greatly improved accuracy in the prediction of rates for a wide range of unimolecular reactions.     

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.     

The stochastic theory and its relations to the general reaction rate theory

A short review of the recent development of the stochastic approach to chemical reactions in condensed media is made. The relations of this approach to a general formulation of chemical kinetics are discussed on the basis of a many-frequency oscillator model. It is shown that the classical transition-state theory is not a particular case of the stochastic theory neither in the case of small viscosity nor in the case of large viscosity. The recent quantum generalizations of the stochastic theory are identical to earlier results of a quantum transition-state theory that correspond to the case of large viscosity. Such generalizations based on previous results of a collision theory are made for the case of small viscosity. It is shown that these quantum generalizations of the stochastic theory are possible only in the temperature range of moderate tunneling defined in terms of a characteristic temperature.     

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.     

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.     

Seven dimensional quantum dynamics study of the H2+NH2-->H+NH3 reaction

Initial state-selected time-dependent wave packet dynamics calculations have been performed for the H2+NH2-->H+NH3 reaction using a seven dimensional model on an analytical potential energy surface based on the one developed by Corchado and Espinosa-Garcia [J. Chem. Phys. 106, 4013 (1997)]. The model assumes that the two spectator NH bonds are fixed at their equilibrium values and nonreactive NH2 group keeps C2v symmetry and the rotation-vibration coupling in NH2 is neglected. The total reaction probabilities are calculated when the two reactants are initially at their ground states, when the NH2 bending mode is excited, and when H2 is on its first vibrational excited state, with total angular momentum J=0. The converged cross sections for the reaction are also reported for these initial states. Thermal rate constants and equilibrium constants are calculated for the temperature range of 200-2000 K and compared with transition state theory results and the available experimental data. The study shows that (a) the reaction is dominated by ground-state reactivity and the main contribution to the thermal rate constants is thought to come from this state, (b) the excitation energy of H2 was used to enhance reactivity while the excitation of the NH2 bending mode hampers the reaction, (c) the calculated thermal rate constants are very close to the experimental data and transition state theory results at high and middle temperature, while they are ten times higher than that of transition state theory at low temperature (T=200 K), and (d) the equilibrium constants results indicate that the approximations applied may have different roles in the forward and reverse reactions.     

A perturbation molecular orbital theory of gas-phase dissociative electron-transfer rates

Gasphase dissociative electron-transfer (ET) reactions are examined in the light of modern electron-transfer theory and a perturbation molecular orbital (PMO) model for ion-molecule collision rates. Two dissociative ET reactions reported by Knighton and Grimsrud—the reaction of azulene anion with dibromodifluoromethane and with carbon tetrachloride—happened in the inverted region of the relationship between reaction rate and free energy. Carbon-halogen vibration participation in dissociative ET reactions is demonstrated in two reaction series. Carbon-hydrogen stretch (3050 cm^?1) activation of electron transfer happened in the most exothermic reaction series: dissociative capture to form bromide from bromotrichloromethane The reasons for the failure of classical ion-molecule collision theory to give a quantitative account of reactive ion-molecule collision rates are presented in some detail. The fundamental failure is a result of a previously unappreciated change in the polarizability of a molecule when the orbitals on the molecule overlap with those on an adjacent ion. The molecular orbital-based collision model used here avoids the need to evaluate the changes in the polarizability tensor with overlap.     

Factors controlling the barriers to degenerate hydrogen atom transfers

High-level electronic structure calculations have been used to study the factors contributing to the barriers to degenerate hydrogen-atom transfer (HAT) reactions. Understanding of these reactions is a prerequisite to the development of any more general theory of HAT reactions, and yet, the existing models for such reactions perform quite poorly when applied to even simple self-exchanges. The reasons behind these failures are elucidated in the present work. They include a near cancellation of bond-strength effects between reactant and transition state, as well as a strong dependence of the geometry of the transition state on the nature of the heavy atoms.     

Extended diffusion in a double well potential: Transition from classical to quantum regime

The transition between the classical and quantum regimes in the diffusion of a particle in a 2-4 double-well potential is treated via the strong collision model in the high-temperature limit. Both the classical and semiclassical position correlation functions, their spectra, and correlation times are evaluated using the memory function formalism. It is shown that even in the high temperature limit, marked classical-quantum transition effects appear in the observables when collisions are rare.     

Restoring detailed balance in the Landau-Teller probabilities for collision-induced vibrational transitions

The general quasi-classical treatment for collision-induced vibrational transitions in diatomic molecules, under near-adiabatic conditions, is used to derive quantum corrections for probabilities, calculated in the external field approximation originally used by Landau and Teller. The quantum corrections are expressed through the Landau-Teller classical collision time. The first-order correction to the classical exponent restores detailed balance for up- and down-transitions and does not depend on the properties of the bath except for its temperature. The limits of applicability of the first-order correction are discussed.     

Computational study on the mechanism of N-phenylimine derivatives’ pyrolysis reaction in the gas phase

In this work, quantum chemistry and kinetics calculations have been performed on the retro-cheletropic ene reactions of N-phenyl-1-methyl-6-methylenecyclohexa-2,4-dienylmethanimine (R1) and N-phenyl-2,2-dimethylbut-3-en (R2). Two major possible mechanisms have been considered and rate constants have been calculated using the transition state theory. The simple Wigner, Eckart zero-curvature tunneling and small-curvature tunneling (SCT) methods were evaluated. The best agreement with experimental rate coefficients was found when SCT correction was applied. A mean deviation of a factor 3 on the rate coefficients is found for the studied reactions at the temperatures of 417 and 773 K. Calculated rate coefficients showed that the tunneling corrections played a critical role in obtaining accurate rate coefficients, especially at lower temperature (417 K). Calculated rate coefficients are in good agreement with the reported experimental data and similar compounds in the case of R1 and R2, respectively. These results support the concerted and stepwise paths for the gas phase reactions of R1 and R2, respectively. Computed kinetic parameters confirmed that R1 had greater reactivity than R2. This trend explains the effects of an extra phenyl-like system on the stability of the transition state and hence increases the R1 rate constant. Calculated rate constants especially at the M06 level are in better agreement with the experimental values than the B3LYP ones. Natural bond orbital (NBO) studies of the reactants and their transition states reveal that their electron delocalization change is an important factor in the determination of the reactivity order for these compounds. Finally, the nature of bond making and breaking during the reactions has been investigated using the concepts of electron charge density and Laplacian in atom in the molecule method.     

Semiclassical extension of the Landau-Teller theory of collisional energy transfer

A semiclassical version of the quantum coupled-states approximation for the vibrational relaxation of diatomic molecules in collisions with monatomic bath gases is presented. It is based on the effective mass approximation and a recovery of the semiclassical Landau exponent from the classical Landau-Teller collision time. For an interaction with small anisotropy, the Landau exponent includes first order corrections with respect to the orientational dependence of the collision time and the effective mass. The relaxation N(2)(v=1)-->N(2)(v=0) in He is discussed as an example. Employing the available vibrationally elastic potential, the semiclassical approach describes the temperature dependence of the rate constant k(10)(T) over seven orders of magnitude across the temperature range of 70-3000 K in agreement with experimental data and quantum coupled-states calculations. For this system, the hierarchy of corrections to the Landau-Teller conventional treatment in the order of importance is the following: quantum effects in the energy release, dynamical contributions of the rotation of N(2) to the vibrational transition, and deviations of the interaction potential from a purely repulsive form. The described treatment provides significant simplifications over complete coupled-states calculations such that applications to more complex situations appear promising.     

溶液反应机理与动力学-2：影响因素与动力学方程的一般形式

对引起溶液反应与气相反应速率差异的因素进行了分析。指出大量溶剂分子的存在,并不会导致反应物分子之间的碰撞频率大幅度降低。除影响反应物活度和起催化作用之外,溶剂化和微观粘度是影响溶液反应速率的主要因素。微观粘度的影响可正可负,可能存在"负粘度"效应。基于简单碰撞理论和过渡态理论,给出了溶液反应速率公式的一般形式,可以综合活化能和微观粘度的影响。该方法可以比较合理地解释一些实验现象。     

The state-to-state-to-state model for direct chemical reactions: application to D+H2-->HD+H

A simple theoretical model is developed to predict the state-to-state dynamics of direct chemical reactions. Motivated by traditional ideas from transition state theory, expressions are derived for the reactive S matrix that may be computed using the local transition state dynamics. The key approximation involves the use of quantum bottleneck states to represent the near separable dynamics taking place near the transition state. Explicit expressions for the S matrix are obtained using a Franck-Condon treatment for the inelastic coupling between internal states of the collision complex. It is demonstrated that the energetic thresholds for various initial reagent states of the D+H(2) reaction can be understood in terms of our theory. Specifically, the helicity of the reagent states are found to correlate directly to the symmetry of the quantum bottleneck states, which thus possess very different thresholds. Furthermore, the rotational product state distributions for D+H(2) are found to be associated with interfering pathways through the quantum bottleneck states.     

Massively parallel spin–orbit configuration interaction

We describe a new approach to incorporating quantum effects into chemical reaction rate theory using quantum trajectories. Our development is based on the entangled trajectory molecular dynamics method for simulating quantum processes using trajectory integration and ensemble averaging. By making dynamical approximations similar to those underlying classical transition state theory, quantum corrections are incorporated analytically into the quantum rate expression. We focus on a simple model of quantum decay in a metastable system and consider the deep tunneling limit where the classical rate vanishes and the process is entirely quantum mechanical. We compare our approximate estimate with the well-known WKB tunneling rate and find qualitative agreement.     

Proton exchange and transesterification reactions of acetate enolates with alcohols in the gas phase

Transesterification reactions and proton exchange reactions between acetate enolates and alcohols were studied both separately and together. Kinetic analysis shows that transesterification and proton exchange happen in a single collision event. The transesterification reaction is best viewed as an endothermic proton transfer, followed by an exchange of alkoxide and an exothermic proton transfer. Reaction barriers were modeled by Rice-Ramsperger-Kassel-Marcus theory and compared to quantum calculations. CBS-QB3 achieves good agreement whereas B3LYP and MP2 give slightly higher barriers. Quantum calculations also predict that the transition state for these transesterification reactions is the same as that for direct transesterification reactions between alkoxides and esters.     

Classical theory of collisional entropy production

A classical dynamical theory of elementary collision processes is formulated in analogy to the quantum theory of the dynamical scattering matrix, which can be defined for a pure quantum stationary scattering state. The elements of this matrix are probability amplitudes for transitions between internal states defined for given values of a reaction coordinate. The squared magnitudes of these amplitudes, modeled in the proposed classical theory, define normalized internal state population distributions suitable for information theoretical analysis. Statistical entropy and surprisal are defined as dynamical functions of a reaction coordinate. This formalism differs fundamentally from concepts based on the classical Liouville equation.