Non-separable State Research Articles

Ab initio calculation of anharmonic constants for a transition state, with application to semiclassical transition state tunneling probabilities

“Good” (i.e. conserved) action variables exist in the vicinity of a saddle point (i.e. transition state) of a potential energy surface in complete analogy to those related to a minimum on the surface. Transition state theory tunneling (or transmission) probabilities can be expressed semiclassically in terms of these “good” action variables, including the effects of non-separable coupling of all degrees of freedom with each other. This paper shows how ab initio quantum chemistry methods recently developed for calculating anharmonic constants about a potential minimum (i.e. for ordinary vibrational energy levels) can be readily adapted to obtain those related to a transition state, thus providing a rigorous and practical way to apply this non-separable transition state theory. Application is made to the transition state for he reaction D 2CO→D 2 + CO.

A nonseparable quantum mechanical transition state theory

A quantal transition state bound on the rate of chemical reactions in any dimension is derived. The magnitude of the bound is dependent on the location of a dividing surface and thus is variational. Analysis of the quality of the bound in one and two dimensions shows that the quality of the bound improves with increasing dimensionality of the problem. The new theory requires only the computation of diagonal density matrix elements and so should prove to be computationally useful.

On nonadiabatic transition state theory

A nonseparable semiclassical transition state approximation for reactions involving more than one electronic surface is suggested. The single surface formulation in terms of quasiprobability distributions used by Miller is discussed along with a separable semiclassical approximation for the nonadiabatic rate suggested in the Soviet literature. A thermally averaged nonadiabatic rate is defined, and a semiclassical approximation is presented, wherein the surface through which flux is calculated in the transition state approach is determined by the intersection of adiabatic electronic surfaces viewed as functions of imaginary (or complex) time.