Non-adiabatic quantum molecular dynamics by the basis expansion leaping multi-configuration Gaussian (BEL MCG) method: Multi-set and single-set formalisms.

Non-adiabatic transitions are quite often of critical importance in chemical reactions. We have recently developed the basis expansion leaping multi-configuration Gaussian (BEL MCG) method to obtain time-propagated wave packets describing multidimensional reactive molecular systems such as quantum tunneling [T. Murakami and T. J. Frankcombe, J. Chem. Phys. 149, 134113 (2018)]. In this work, we develop BEL MCG for multiple electronic state problems. We present two formalisms for the BEL MCG description of multi-state wave packets, namely, "multi-set" and "single-set." We pay particular attention to investigate what is required to yield accurate dynamics. When there is low population on an electronic state, it is important in the "multi-set" case that the reexpression on that electronic state is applied rigorously. The sharing of basis functions in the single-set approach leads to needing a lower number of basis functions than in the multi-set approach, making it preferable for direct dynamics.