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This paper describes novel numerical methods for constructing reaction paths and evaluating transition state theory (TST) rate constants for multidimensional, multistate systems. The reaction path is represented as a tethered, freely jointed chain of states with configuration specified by minimization of a function that is derived from the differential description of the path. The method is general and applicable to systems of arbitrary dimension and does not require a priori knowledge of the first-order saddle point, or the topology of the states. Also presented is a novel procedure for numerical determination of the TST rate constant. The procedure is based on Monte Carlo importance sampling using a tethered chain with links modeled as harmonic springs. The beads of the chain and the points at which links pierce the dividing surface separating states serve as biased sampling points for Monte Carlo numerical integration. The methods presented here are tested using the Muller potential surface. The application to problems involving transitions between clusters of states, i.e., macrostates, is discussed.
Sevick et al. (Mon,) studied this question.