  Mean-field Ring Polymer Molecular Dynamics (MF-RPMD) offers a computationally
efficient method for the simulation of reaction rates in multi-level systems.
Previous work has established that, to model a nonadiabatic state-to-state
reaction accurately, the dividing surface must be chosen to explicitly sample
kinked ring polymer configurations where at least one bead is in a different
electronic state than the others. Building on this, we introduce a population
difference coordinate and a kink-constrained dividing surface, and we test the
accuracy of the resulting mean-field rate theory on a series of linear vibronic
coupling model systems as well as spin-boson models. We demonstrate that this
new MF-RPMD rate approach is efficient to implement and quantitatively accurate
for models over a wide range of driving forces, coupling strengths, and
temperatures.
