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. (C) 2011 American Institute of Physics. [doi:10.1063/1.3656686]