Propagators in Quantum Chemistry, 2nd Edition

Chapter 13

Propagators and Chemical Reaction Rate

Chemical reactions and their rates are central to chemical research. The quantum mechanical theory of reaction rates invokes quantum mechanical scattering theory and statistical mechanics. Thus, one considers the propagation of a system from an initial situation to a different one. Expressions for such processes are developed by means of quasi-stationary nonequilibrium theory.

Central to the development is an ensemble operator Γ akin to the one considered in the previous chapter and constructed from the appropriate system hamiltonian H of the reacting system and a bias operator B. A self-adjoint orthogonal operator B is constructed as the difference between a projector onto the product states and a projector Q_R onto the reactant states, such that

Obviously it holds that B² = 1. A suitable ensemble operator is

where β = 1/kT, F is the free energy, and λ is the energy bias parameter. A positive value of the bias favors the product subspace of states. The expectation value of B is a measure of the difference in the number of systems present in the product and that present in the reactant states. The bias operator induces a perturbed equilibrium, and to first order in the parameter λ, the change can be calculated by perturbation theory ...