Efficient computation of adiabatic populations in multi-mode Jahn-Teller systems through the use of effective vibrational modes

A highly efficient scheme for computing adiabatic electronic populations in multi-mode Jahn-Teller systems is presented. It relies on the transformation to an effective-mode vibrational basis in which the relevant quantities depend on the coordinates of a single mode only. In this way, the generally tedious numerical evaluation of high-dimensional integrals is avoided and replaced by one-dimensional integrations. The effective-mode scheme is applied to a variety of two-mode and three-mode Jahn-Teller systems and gives a typical speedup of about two to three orders of magnitude as compared to the direct evaluation of the adiabatic populations. The gain grows rapidly with the numbers of modes.