Breakdown of the Born-Oppenheimer approximation

The Born-Oppenheimer approximation is the starting point for all quantum chemistry and crystal band structure calculations. It allows one to factorise the electron-nuclear quantum state. It can be justified because nuclei are much heavy than electrons. However, it breaks down near electronic degeneracies. A case that has attracted a lot of attention are conical intersections between two potential energy surfaces for different electronic states of molecules. Such intersections provide a rapid means for non-radiative decay of excited states.

Going beyond Born-Oppenheimer represents a major challenge. A nice recent review for molecules is by Worth and Cederbaum.

A few years ago in a Phys. Rev. A paper, Andrew Hines, Chris Dawson, Gerard Milburn and I considered two different Jahn-Teller model Hamiltonians and quantified the entanglement of the electronic and nuclear degrees of freedom. One of these models has a conical intersection.