Efficient computation of adiabatic electronic populations in multi-mode vibronic systems: theory, implementation, and application - Nikoobakht, Behnam; Köppel, Horst; Cederbaum, Lorenz S. (The journal of chemical physics, 2012)
The effective-mode formalism developed earlier is applied to efficiently compute adiabatic electronic populations of multi-mode vibronic systems. Two different versions of the formalism are utilized. In the first one, the effective modes are used as new vibrational basis, and the time-dependent wave function as well as populations are calculated numerically exactly. In the second variant, the hierarchy-of-modes formalism is applied as an approximation scheme which leads to accurate results when including typically 7-10 members of the hierarchy. While in the first version, the propagation of the wave packet becomes numerically tedious, the computation of the adiabatic populations is rendered possible at all. Through the hierarchy-of-modes formalism, both the propagation as well as computation of adiabatic populations are speeded up by 1-3 orders of magnitude in typical cases. The formalism is applied to study the dynamics of pyrazine-type models for varying vibronic coupling strength and a (very) large number of bath modes.