The transition state method
TL;DR: In this article, the authors considered the problem of estimating the reaction rate of elementary reactions in terms of the energy and velocity distribution of the molecules in the system, and showed that the results can be obtained by the application of quantum mechanics to molecular systems.
Abstract: According to our present notions, the theory of reaction rates involves three steps. First, one should know the behaviour of all molecules present in the system during the reaction, how they will move, and which products they will yield when colliding with definite velocities, etc. Practically, this amounts in most cases to the construction of the energy surface for the reacting system. Professor Eyring told us about the results which can be obtained by the application of quantum mechanics to molecular systems for this part of the theory. The second step in the theory I would call the statistical part. It endeavours to solve the problem of the rate of elementary reactions. Assuming only the material on the left side of a chemical equation to be present in a vessel, and the molecules of these to have the Maxwell-Boltzman energy and velocity distribution, one wants to know how many molecules corresponding to the right side of the equation will be formed in unit time. The elementary properties of the molecules are supposed to be known in this second step and one wants to express the reaction rate of elementary reactions in terms of these. The present paper will be devoted entirely to this second step. The third step is the consideration of the co-operation of the various elementary reactions, which may occur beside and must occur after each other in order to complete a real reaction. In especially favourable cases there is only one important chain of reactions leading to the final products and this has one link which is so much slower than all the others, that it is made responsible for the observed rate. The others are then assumed to be so much faster that one has practically equilibrium between the two sides of their chemical equations.
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TL;DR: In this article, a modification of the nudged elastic band method for finding minimum energy paths is presented, where one of the images is made to climb up along the elastic band to converge rigorously on the highest saddle point.
Abstract: A modification of the nudged elastic band method for finding minimum energy paths is presented. One of the images is made to climb up along the elastic band to converge rigorously on the highest saddle point. Also, variable spring constants are used to increase the density of images near the top of the energy barrier to get an improved estimate of the reaction coordinate near the saddle point. Applications to CH4 dissociative adsorption on Ir~111! and H2 on Si~100! using plane wave based density functional theory are presented. © 2000 American Institute of Physics. @S0021-9606~00!71246-3#
14,071 citations
TL;DR: In this paper, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry.
Abstract: The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.
5,180 citations
TL;DR: In this article, a two-part review of distribution functions in physics is presented, the first part dealing with fundamentals and the second part with applications, focusing on the so-called P distribution and generalized P distribution.
2,421 citations
TL;DR: In this article, the authors present an overview of the current status of transition-state theory and its generalizations, including recent improvements in available methodology for calculations on complex systems, including the interface with electronic structure theory, progress in the theory and application of transitionstate theory to condensed-phase reactions, and insight into the relation of transition state theory to accurate quantum dynamics.
Abstract: We present an overview of the current status of transition-state theory and its generalizations. We emphasize (i) recent improvements in available methodology for calculations on complex systems, including the interface with electronic structure theory, (ii) progress in the theory and application of transition-state theory to condensed-phase reactions, and (iii) insight into the relation of transition-state theory to accurate quantum dynamics and tests of its accuracy via comparisons with both experimental and other theoretical dynamical approximations.
1,919 citations
TL;DR: In this paper, the authors used time correlation function methods to discuss classical isomerization reactions of small nonrigid molecules in liquid solvents and derived molecular expressions for a macroscopic phenomenological rate constant.
Abstract: In this article, time correlation function methods are used to discuss classical isomerization reactions of small nonrigid molecules in liquid solvents. Molecular expressions are derived for a macroscopic phenomenological rate constant. The form of several of these equations depend upon what ensemble is used when performing averages over initial conditions. All of these formulas, however, reduce to one final physical expression whose value is manifestly independent of ensemble. The validity of the physical expression hinges on a separation of time scales and the plateau value problem. The approximations needed to obtain transition state theory are described and the errors involved are estimated. The coupling of the reaction coordinate to the liquid medium provides the dissipation necessary for the existence of a plateau value for the rate constant, but it also leads to failures of Wigner’s fundamental assumption for transition state theory. We predict that for many isomerization reactions, the transmissio...
1,247 citations