Natural resonance theory description

Quantum mechanical effects—tunneling and interference, resonances, and electronic nonadiabaticity— play important roles in many chemical reactions. Rigorous quantum dynamics studies, that is, numerically accurate solutions of either the time-independent or time-dependent Schrodinger equations, provide the most correct and detailed description of a chemical reaction. While hmited to relatively small numbers of atoms by the standards of ordinary chemistry, numerically accurate quantum dynamics provides not only detailed insight into the nature of specific reactions, but benchmark results on which to base more approximate approaches, such as transition state theory and quasiclassical trajectories, which can be applied to larger systems. 

IV. Entropy of Activation and Structure From the inception of transition state theory, entropies of activation have been discussed from the twin aspects of molecular structure and reaction mechanism. Even though there is considerable overlap between these two aspects we shall utilize a formal separation, reserving much of the discussion of mechanism for the next section. In this section our primary concern shall be the effect that structural change in a non-reacting part of a molecule has upon the entropy and enthalpy of activation for that molecule. The nature of interactions (polar, steric, and resonance) between the substituent group and the reaction center clearly relates to the problem of reaction mechanism, the solution of which involves, in the final analysis, a detailed description of the disposition of the atoms in the transition state and the interactions among them. 

In the discussion of the experimental approaches to study molecular resonances, the quantum theory of photon wave packet scattering forms the natural framework. It is thus necessary to recall some of the main features of wave packet scattering (Messiah, 1965 Newton, 1966 Goldberger and Watson, 1965a) with special reference to photophysical phenomena (Shore, 1967). We begin with a brief review of the basic concepts in the formal description of time evolution. Then we consider more in detail the process of scattering of a coherent photon wave packet by a molecule. The expressions for the basic experimental observables are derived, with special emphasis on time-resolved studies. Detection is assumed to take place under short time conditions, in a lateral, nonforward direction so that no coherence of the photon states scattered by different molecules must be considered. 

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