Evaluation of thermal rate constants in the eigenbasis of a Hamiltonian with an optical potential

Miller and co-workers [J. Chem. Phys. 61, 1823 (1974); ibid., 79, 4889 (1983)] have derived an exact quantum mechanical expression for reactive thermal rate constants in terms of the time integral of a flux autocorrelation function. The evaluation of this integral in a finite basis poses the problem that spurious oscillations in the correlation function due to recurrences can occur at long times, corrupting the result. To obviate this difficulty, we add to the Hamiltonian an optical potential in the asymptotic region, and evaluate eigenvalues and eigenvectors using the technique of successive truncation. These operations allow a diagonal (although nonorthogonal) representation of the propagator in which the eigenvalues are exponentially decaying functions of time, which damp the components of the propagated vectors before the spurious reflection back into the interaction region. In this manner, the infinite time limit of the integral may be evaluated properly. Furthermore, the results of a single diagonalization may be used to compute the thermal rate constant over a range of temperatures.