Time-dependent self-consistent-field dynamics based on a reaction path Hamiltonian. II. Numerical tests

Numerical tests are presented for a method that combines the time-dependent self-consistent-field (TDSCF) method with the reaction path Hamiltonian (RPH) derived by Miller, Handy, and Adams [J. Chem. Phys. 72, 99 (1980)]. The theoretical basis for this TDSCF-RPH method was presented in a previous paper. The equations of motion were derived for three different cases: (1) zero coupling matrix (i.e., zero reaction path curvature and zero coupling between the normal modes); (2) zero reaction path curvature and nonzero coupling between the normal modes; and (3) zero coupling between the normal modes and nonzero but small reaction path curvature. For these three cases the dynamics can always be reduced to a one-dimensional numerical time propagation of the reaction coordinate. In this paper the TDSCF-RPH methodology for all three cases is tested by comparing the TDSCF-RPH dynamics to exact quantum dynamics based on the exact Hamiltonian for simple model systems. The remarkable agreement indicates that the TDSCF-RPH method could be useful for the calculation of the real-time quantum dynamics of a wide range of chemical reactions involving polyatomic molecules.