Nuclear geometry transition state theory

A noteworthy qualitative aspect of variational-transition-state-theory calculations of kinetic isotope effects is that the geometry of the variational transition state may differ for each isotopic variation of a reaction. This means that the usual methods of predicting isotope effects, based on the simplifications possible when nuclear masses are changed with fixed force fields, do not apply. Instead of using such simplifications, we perform completely independent variational calculations for each isotopic case. 

In the classical Marcus-Hush theory, the initial nuclear geometry of the reactant state undergoes reorganization to the transition state prior to electron transfer [30, 31, 39]. The energy of the transition state, AGe, is gained by intermolecular collisions, in order to satisfy conservation of energy and momentum. The nuclear factor is related to the activation energy, i.e.,... 

Here E,j, is the energy of the initial state and R is the nuclear geometry. The division by 3 in (14) comes from orientational averaging. In this form, calculation of the absorption cross section requires the initial vibrational wave function, the transition dipole moment surface and the excited state potential. The reflection principle can be employed for direct or near direct photodissociation. It is again an approximation where the ground state wave function is reflected off the upper potential curve or surface. Prakash et al and Blake et al. [84-86] have used this theory to calculate isotope effects in N2O photolysis. 

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