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.

Current status of transition-state theory

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.

Modeling the Kinetics of Bimolecular Reactions

Unimolecular reaction systems in which multiple isomers undergo simultaneous reactions via multiple decomposition reactions and multiple isomerization reactions are of fundamental interest in chemical kinetics. The computer program suite described here can be used to treat such coupled systems, including the effects of collisional energy transfer (weak collisions). The program suite consists of MultiWell, which solves the internal energy master equation for complex unimolecular reactions systems; DenSum, which calculates sums and densities of states by an exact-count method; MomInert, which calculates external principal moments of inertia and internal rotation reduced moments of inertia; and Thermo, which calculates equilibrium constants and other thermodynamics quantities. MultiWell utilizes a hybrid master equation approach, which performs like an energy-grained master equation at low energies and a continuum master equation in the vibrational quasicontinuum. An adap- tation of Gillespie's exact stochastic method is used for the solution. The codes are designed for ease of use. Details are presented of various methods for treating weak collisions with virtually any desired collision step-size distribution and for utilizing RRKM theory for specific unimolecular rate constants. 2001 John Wiley & Sons, Inc. Int J Chem Kinet 33: 232- 245, 2001

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Multiple‐Well, multiple‐path unimolecular reaction systems. I. MultiWell computer program suite

An effective time-dependent (TD) approach to compute vibrationally resolved optical spectra from first principles is presented for the computation of one-photon electronic spectra induced by either electric or magnetic transition dipoles or by their mutual interaction, namely absorption, emission, and circular dichroism. Particular care has been devoted to generality, modularity, and numerical stability including all the contributions that play a role at the harmonic level of approximation, namely Franck-Condon, Herzberg-Teller, and Dushinsky (i.e., mode mixing) effects. The implementation shares the same general framework of our previous time-independent (TI) model, thus allowing an effective integration between both approaches with the consequent enhancement of their respective strengths (e.g., spectrum completeness and straightforward account of temperature effects for the TD route versus band resolution and assignment for the TI route) using a single set of starting data. Implementation of both models in the same general computer program allows comprehensive studies using several levels of electronic structure description together with effective account of environmental effects by atomistic and/or continuum models of different sophistication. A few medium-size molecules (furan, phenyl radical, anthracene, dimethyloxirane, coumarin 339) have been studied in order to fully validate the approach.

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General Time Dependent Approach to Vibronic Spectroscopy Including Franck-Condon, Herzberg-Teller, and Duschinsky Effects.

▪ Abstract This review discusses the reactivities and thermodynamics of small-size-specific transition metal clusters and focuses on thermodynamic information, which has not been comprehensively discussed before. Because of this focus, guided-ion-beam mass spectrometry was used to acquire much of the data. The details of this technique and the associated data analysis methods are provided. Results on the stabilities of bare transition metal clusters are provided for neutral, cationic, and anionic species. Implications for the electronic and geometrical structures are discussed, as well as the extrapolation of these values to bulk phase behavior. Detailed results for reactions of transition metal clusters with D2 and the oxygen donors O2 and CO2 are reviewed. Available bond energies between size-specific clusters and one D atom and one and two O atoms are compiled, and their implications are evaluated and favorably compared with bulk phase analogs. Several additional thermodynamic studies of various cluste...

Reactions and thermochemistry of small transition metal cluster ions

Given a positiver integer m and an ordered k-tuple c = (c1, ··· , ck) of not necessarily distinct positive integers, then any ordered k-tuple s = (s1, ··· , sk) of nonnegative integers such that m = ∑ki-1sici is said to be a partition of m restricted to c. Let Pc(m) denote the number of distinct partitions of m restricted to c. The subroutine COUNT, when given a k-tuple c and an integer n, computes an array of the values of Pc(m) for m = 1 to n. Many combinatorial enumeration problems may be expressed in terms of the numbers Pc(m). We mention two below.

Terry Beyer

Papers

Algorithm 448: number of multiply-restricted partitions