Ab Initio Multiple Spawning Method for Intersystem Crossing Dynamics: Spin-Forbidden Transitions between 3B1 and 1A1 States of GeH2

Dynamics at intersystem crossings are fundamental to many processes in chemistry, physics, and biology. The ab initio multiple spawning (AIMS) method was originally developed to describe internal conversion dynamics at conical intersections where derivative coupling is responsible for nonadiabatic transitions between electronic states with the same spin multiplicity. Here, the applicability of the AIMS method is extended to intersystem crossing dynamics in which transitions between electronic states with different spin multiplicities are mediated by relativistic spin orbit coupling. In the direct AIMS dynamics, the nuclear wave function is expanded in the basis of frozen multidimensional Gaussians propagating on the coupled electronic potential energy surfaces calculated on the fly. The AIMS method for intersystem crossing is used to describe the nonadiabatic transitions between the B-3(1) and (1)A(1) states of GeH2. The potential energies and gradients were obtained at the CASSCF(6,6)/6-31G(d) level of theory. The spin orbit coupling matrix elements were calculated with the configuration interaction method using the two electron Breit Pauli Hamiltonian. The excited B-3(1) state lifetime and intersystem crossing rate constants were estimated by fitting the AIMS state population with the first-order kinetics equation for a reversible unimolecular reaction. The obtained rate constants are compared with the values predicted by the statistical nonadiabatic transition state theory with transition probabilities calculated using the Landau-Zener and weak coupling formulas.