Classical flux integrals in transition state theory: Generalized reaction coordinates

Transition state theory (TST) approximates the reactive flux in an elementa ry chemical reaction by the instantaneous flux passing through a hypersurfa ce (the "transition state") which completely divides the reactant and produ ct regions of phase space. The rigorous classical evaluation of this instan taneous flux is carried out as a trace in phase space: effectively a multid imensional integral. We present an analysis of the momentum-space component of this flux integral for the case of a generalized reaction coordinate. T he classic analysis of the canonical flux by Marcus [J. Chem. Phys. 41, 262 4 (1964)] is refined by reducing the determinant which appears in the trans ition state partition function to a very simple form, facilitating the ensu ing integration over coordinate space. We then extend the analysis to provi de analytic expressions for the momentum flux integrals in both the energy- resolved, and the energy+angular-momentum-resolved microcanonical ensembles . These latter expressions allow substantial gains in the efficiency of mic rocanonical variational implementations of Transition State Theory with gen eralized reaction coordinates. (C) 1999 American Institute of Physics. [S00 21-9606(99)00528-0].