Sudden approximation theory

Kulander, K.C. and Light, J.C. (1986). Theory of polyatomic photodissociation in the reactive infinite order sudden approximation Application to the Rydberg states of H3, J. Chem. Phys. 85, 1938-1949. 

At low temperature the classical approximation fails, but a quantum generalization of the long-range-force-law collision theories has been provided by Clary (1984,1985,1990). His capture-rate approximation (called adiabatic capture centrifugal sudden approximation or ACCSA) is closely related to the statistical adiabatic channel model of Quack and Troe (1975). Both theories calculate the capture rate from vibrationally and rotationally adiabatic potentials, but these are obtained by interpolation in the earlier work (Quack and Troe 1975) and by quantum mechanical sudden approximations in the later work (Clary 1984, 1985). 

This paper reviews this classical S-matrix theory, i.e. the semiclassical theory of inelastic and reactive scattering which combines exact classical mechanics (i.e. numerically computed trajectories) with the quantum principle of superposition. It is always possible, and in some applications may even be desirable, to apply the basic semiclassical model with approximate dynamics Cross7 has discussed the simplifications that result in classical S-matrix theory if one treats the dynamics within the sudden approximation, for example, and shown how this relates to some of his earlier work8 on inelastic scattering. For the most part, however, this review will emphasize the use of exact classical dynamics and avoid discussion of various dynamical models and approximations, the reason being to focus on the nature and validity of the basic semiclassical idea itself, i.e., classical dynamics plus quantum superposition. Actually, all quantum effects—being a direct result of the superposition of probability amplitudes—are contained (at least qualitatively) within the semiclassical model, and the primary question to be answered regards the quantitative accuracy of the description. 

This book describes the proceedings of a NATO Advanced Research Workshop held at CECAM, Orsay, France in June, 1983. The Workshop concentrated on a critical examination and discussion of the recent developments in the theory of chemical reaction dynamics, with particular emphasis on quantum theories. Several papers focus on exact theories for reactions. Exact calculations on three-dimensional reactions are very hard to perform, but the results are valuable in testing the accuracy of approximate theories which can be applied, with less expense, to a wider variety of reactions. Indeed, critical discussions of the merits and defects of approximate theories, such as sudden, distorted-wave, reduced dimensionality and transition-state methods, form a major part of the book. The theories developed for chemical reactions have found useful extensions into other areas of chemistry and physics. This is illustrated by papers describing topics such as photodissociation, electron-scattering, molecular vibrations and collision-induced dissociation. Furthermore, the important topic of how to treat potential energy surfaces in reaction dynamics calculations is also discussed. 

Abstract. We present an overview of the influence of C.F. Curtiss on the theory of molecular collisions, as exemplified by the title paper. Both authors were graduate students of Curtiss and, as such, were strongly influenced by his ideas and approaches to theoretical chemistry. This resulted in a subsequent collaboration that provided the rigorous basis for understanding the success of the so-called centrifugal sudden and energy sudden approximations (the two combined being the infinite order sudden approximation). 

According to the shake theory and the sudden approximation the probability of excitation of the j th final state l j(N-l) is given by33,34... 

Adiabatic energy transfer occurs when relative collision velocities are small. In this case the relative motion may be considered a perturbation on adiabatic states defined at each intermolecular position. Perturbed rotational states have been introduced for T-R transfer at low collision energies and for systems of interest in astrophysics.A rotational-orbital adiabatic basis expansion has also been employed in T-R transfer,as a way of decreasing the size of the bases required in close-coupling calculations. In T-V transfer, adiabatic-diabatic transformations, similar to the one in electronic structure studies, have been implemented for collinear models.Two contributions on T-(R,V) transfer have developed an adiabatical semiclassical perturbation theory and an adiabatic exponential distorted-wave approximation. Finally, an adiabati-cally corrected sudden approximation has been applied to RA-T-Rg transfer in diatom-diatom collisions. 

The theory behind body-fixed representations and the associated angular momentum function expansions of the wavefunction (or wave packet) in terms of bases parameterized by the relevant constants of the motion and approximate constants of the motion is highly technical. Some pertinent results will simply be stated. The two good constants of the motion are total angular momentum, J, and parity, p = +1 or 1. An approximate constant of the motion is K, the body-fixed projection of total angular momentum on the body-fixed axis. For simplicity, we will restrict attention to the helicity-decoupled or centrifugal sudden (CS) approximation in which K can be assumed to be a constant of the motion. In terms of aU its components, and the iteration number k, the real wave packet is taken to be [21]... 

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