Beyond transition-state theory: A rigorous quantum theory of chemical reaction rates
TL;DR: In this article, the authors present a theoretical approach for calculating the rate constant of a chemical reaction that avoids the need to solve the complete state-to-state reactive scattering problem, with no explicit information about reactant and product states being required.
Abstract: Transition-state theory (TST) provides a simple and useful way to understand and estimate the rates of chemical reactions. The fundamental assumption of transition-state theory, however, is based inherently on classical mechanics, so the theory must be quantized if it is to provide a quantitative description of chemical reaction rates. Unlike classical mechanics, though, there seems to be no way to construct a rigorous quantum mechanical theory that contains as its only approximation the transition-state assumption of [open quotes]direct dynamics[close quotes]. Pechukas has discussed this quite clearly: as soon as one tries to rid a quantum mechanical version of transition-state theory of all approximations (e.g., separability of a one-dimensional reaction coordinate) beyond the basic transition-state assumption itself, one is faced with having to solve the full (multidimensional) quantum reaction dynamics problem. But a correct treatment of the full quantum dynamics must yield the exact rate constant and is no longer a transition-state [open quotes]theory[close quotes]. Though there is no rigorous quantum prescription for determining the rate constant of a chemical reaction that avoids, the necessity of solving the Schroedinger equation, there is nevertheless a rigorous theoretical approach that avoids having to solve the complete state-to-state reactive scattering problem; one does notmore » avoid solving the Schroedinger equation, but needs to solve it only locally, in the vicinity of the transition state, with no explicit information about reactant and product states being required. After reviewing some of the notions alluded to above, the purpose of the Account is to describe this [open quotes]direct[close quotes] theoretical approach for calculating chemical reaction rates, the logical conclusion in the quest for a [open quotes]rigorous[close quotes] quantum mechanical version of transition-state theory. 20 refs., 3 figs.« less
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TL;DR: This review is concerned with the theoretical and computational modeling of bimolecular reactions, especially with generally applicable methods for kinetics (i.e., overall rates as opposed to detailed dynamics), and includes a basic theoretical framework that can be used for gas-phase thermal reactions, gas- phase microcanonical and state-selected reactions, and condensed-phase chemical reactions.
Abstract: A review of the theoretical and computational modeling of bimolecular reactions is given. The review is divided into several sections which are as follows: gas-phase thermal reactions; gas-phase state-selected reactions and product state distributions; and condensed-phase bimolecular reactions. The section on gas-phase thermal reactions covers the enthalpies and free energies of reaction, kinetics, saddle points and potential energy surfaces, rate theory for simple barrier reactions and bimolecular reactions over potential wells. The section on gas-phase state-selected reactions focuses on electronically adiabatic reactions and electronically nonadiabatic reactions. Finally, the section on condensed-phase bimolecular reactions covers reactions in liquids, reactions on surfaces and in solids and tunneling at low temperature.
534 citations
TL;DR: In this paper, a quantum mechanical reactive scattering program for atom-diatom chemical reactions is described, which uses a coupled-channel hyperspherical coordinate method to solve the Schrodinger equation for the motion of the three nuclei on a single Born-Oppenheimer potential energy surface.
453 citations
TL;DR: This review discusses recent quantum scattering calculations on bimolecular chemical reactions in the gas phase and emphasises the recent development in time-dependent wave packet theories and the applications of reduced dimensionality approaches for treating polyatomic reactions.
Abstract: This review discusses recent quantum scattering calculations on bimolecular chemical reactions in the gas phase. This theory provides detailed and accurate predictions on the dynamics and kinetics of reactions containing three atoms. In addition, the method can now be applied to reactions involving polyatomic molecules. Results obtained with both time-independent and time-dependent quantum dynamical methods are described. The review emphasises the recent development in time-dependent wave packet theories and the applications of reduced dimensionality approaches for treating polyatomic reactions. Calculations on over 40 different reactions are described.
376 citations
TL;DR: The study of chemical reaction dynamics has now advanced to the stage where even comparatively weak van der Waals interactions can no longer be neglected in calculations of the potential energy surfaces of chemical reactions.
Abstract: The van der Waals forces in the entrance valley of the Cl + HD reaction are shown here to play a decisive role in the reaction9s dynamics. Exact quantum mechanical calculations of reactive scattering on a potential energy surface without Cl–HD van der Waals forces predict that the HCl and DCl products will be produced almost equally, whereas the same calculations on a new ab initio potential energy surface with van der Waals forces show a strong preference for the production of DCl. This preference is also seen in crossed molecular beam experiments on the reaction. The study of chemical reaction dynamics has now advanced to the stage where even comparatively weak van der Waals interactions can no longer be neglected in calculations of the potential energy surfaces of chemical reactions.
278 citations
TL;DR: In this paper, the semiclassical (SC) initial value representation (IVR) is applied to models of unimolecular isomerization and electronic non-adiabatic transitions coupled to an infinite bath of harmonic oscillators.
Abstract: Transition state theory (TST) has provided the qualitative picture of chemical reaction rates for over sixty years Recent theoretical developments, however, have made it possible to calculate rate constants fully quantum mechanically and efficiently, at least for small molecular systems; vestiges of TST can be seen both in the resulting flux correlation functions and in the algorithmic structure of the methodology itself One approach for dealing with more complex molecular systems is the semiclassical (SC) initial value representation (IVR), which is essentially a way of generalizing classical molecular dynamics simulations to include quantum interference; electronic degrees of freedom in an electronically non-adiabatic process can also be included on a dynamically equivalent basis Application of the SC-IVR to models of unimolecular isomerization and of electronically non-adiabatic transitions, both coupled to an infinite bath of harmonic oscillators, gives excellent agreement with (essentially exact) quantum path integral calculations for these systems over the entire range of coupling strength
269 citations
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TL;DR: In this article, a more reliable transition state theory that has many of the advantages of conventional TST can also be formulated, and it can be applied to practical problems with an effort that is much closer to that required for conventional transition-state theory than to the effort required for quantal dynamics calculations.
Abstract: In recent years our research group has made a systematic effort to study the validity of transition state theory (TST). We have found that the conventional theory is sometimes remarkably accurate, but in many other cases it leads to large errors. Fortunately we have found that a much more reliable theory that has many of the advantages of conventional TST can also be formulated, and it can be applied to practical problems with an effort that is much closer to that required for conventional transition state theory than to that required for quantal dynamics calculations. The two most important features in the improved approach to transition state theory state theory are the variational determination of the transition state and the incorporation of tunneling contributions by multidimensional semiclassical approximations. 13 refs.
1,186 citations
TL;DR: Several formally exact expressions for quantum mechanical rate constants (i.e., bimolecular reactive cross sections suitably averaged and summed over initial and final states) are derived and their relation to one another analyzed in this paper.
Abstract: Several formally exact expressions for quantum mechanical rate constants (i.e., bimolecular reactive cross sections suitably averaged and summed over initial and final states) are derived and their relation to one another analyzed. It is suggested that they may provide a useful means for calculating quantum mechanical rate constants accurately without having to solve the complete state‐to‐state quantum mechanical reactive scattering problem. Several ways are discussed for evaluating the quantum mechanical traces involved in these expressions, including a path integral evaluation of the Boltzmann operator/time propagator and a discrete basis set approximation. Both these methods are applied to a one‐dimensional test problem (the Eckart barrier).
791 citations
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.
768 citations
TL;DR: Theoretical calculation of rotation-vibration energy levels of polyatomic molecules is a topic with a long history, characterized by a close symbiotic relationship with molecular spectroscopy on one side and quantum chem- istry on the other as discussed by the authors.
Abstract: Theoretical calculation of rotation-vibration energy levels of polyatomic molecules is a topic with a long history, characterized by a close, symbiotic relationship with molecular spectroscopy on one side and quantum chem istry on the other. What brings them together is the notion of the potential energy surface, which plays a central role in our understanding of the molecular structure and dynamics. In the case of polyatomic molecules, the experimental spectra cannot be inverted directly to yield potential surfaces [see Ref. (1) for some recent efforts within the semiclassical SCF approach], but they do provide a stringent test for the theoretically obtained potential surfaces and observables derived from them. These surfaces, usually from ab initio calculations, seldom meet the standards of spectroscopic accuracy, especially if more extended, high-energy regions are of interest. The only practical way available to test and improve them is by comparing the calculated and the experimental spectra, and minimizing the difference between the two. The subject of the theoretical treatment of coupled molecular vibrations has undergone a real renaissance in the past decade. Significant conceptual advances have been made, particularly concerning highly vibrationally and
761 citations