Evaluation of thermal rates for reactions with intermediate wells: Removal of bound state contributions to quantum flux correlation functions

We consider the calculation of rates of chemical reactions that have bound intermediate states (i.e., wells along the reaction path) using flux correlation function methods. When time-dependent wave packets are used to evaluate the propagator matrix elements, and the dividing surface is located at a point where bound states have nonzero probability density, the standard expression for the flux correlation function shows infinitely long lived oscillations due to these bound states, making the evaluation of rate constants numerically ill-behaved. However, if the bound part of the initial wave packet is projected out, the resulting continuum-only propagators produce rapidly decaying correlation functions, and numerically well-behaved rate constants. We illustrate this projection operator approach by considering a one-dimensional reaction path model in which the potential is taken to be an Eckart well, and the dividing surface is located at the minimum. In another application, we consider a two degree of freedom model of H₂ dissociative chemisorption on a rigid metal surface. This application is sufficiently complex that it is impractical to calculate the chemisorption rate using conventional flux correlation function methods, but with the projected wavepacket approach, the problem is made relatively, easy. We also consider a second approach to the treatment of bound states in which the flux correlation function is altered to remove implicitly the bound state contributions to the propagator at long times. This second expression can be used with the full propagator, eliminating the need to construct and project explicitly the bound states. This should be advantageous when many bound states are present.