A new time-dependent approach to the direct calculation of reaction rates

A wave packet dynamical approach to the direct calculation of the rate constant of a chemical reaction is presented. Based on the position-flux correlation function of Miller, Schwartz, and Tromp [J. Chem. Phys. 79, 4889 (1983)] a reaction rate operator is introduced, which can be viewed as the thermal analog of the energy-dependent reaction probability operator [J. Chem. Phys. 99, 3411 (1993)]. It is shown that this reaction rate operator has in general only a small number of eigenstates with nonvanishing eigenvalues. These eigenstates can be interpreted as the vibrational ground state and the vibrationally excited states of the activated complex. The eigenstates and eigenvalues can efficiently be computed via an iterative (Lanczos) diagonalization scheme. The number of wave packet propagations required equals approximately the number of relevant states of the activated complex, it is considerably smaller as in previous approaches to the calculation of rate constants based on wave packet dynamics. The new approach is illustrated by three examples: transmission through a one-dimensional (Eckart) potential barrier, the collinear model of the H+H2 reaction, and the H+H2 reaction in its full dimensionality for J=0. For temperatures below 1000 K, in all examples presented, the rate constant can be calculated employing only a single wave packet. This result suggests that the approach can efficiently be applied to problems with a larger number of degrees of freedom.