Real-time path-integral approach for general two-state multi-mode vibronic-coupling models

In this work path-integral techniques, which are well established for the so-called spin-boson problem, are extended to treat the more general case of an electronic two-level system which is diagonally as well as off-diagonally coupled to an arbitrary number of vibrational modes. This class of models includes multi-dimensional conical intersections of molecular potential-energy surfaces as well as the multi-mode Jahn-Teller effect of a doubly degenerate electronic state as special cases. Applying the usual Trotter procedure, a complete factorization of the propagator of each individual path is achieved by mapping the two-level dynamics onto a fictitious four-level dynamics. In the special case of linear electronic-vibrational coupling and a harmonic bath, the influence functional is derived. This formulation allows powerful numerical methods for the evaluation of path integrals, e.g. partial resummation of paths or Monte Carlo sampling, to be applied to an extended range of vibronic-coupling problems.