Breakdown of the Born-Oppenheimer Approximation

This is a non-trivial, much discussed issue and in actual fact still the topic of present research. From our discussion in the previus section we understand that adiabaticity is lost if transitions between electronic states $\vert\alpha(X)\rangle\to\vert\alpha'(X')\rangle$ occur while change $X$. One example for is the so-called Landau-Zener tunneling between nearby energy levels $E_\alpha(X)$ and $E_{\alpha'}(X)$. Also discussed in this context are the Renner-Teller and the Jahn-Teller effects, cf. the short summary by B. T. Sutcliffe in ch. 36 of Vol. 1 of the `Handbook of Molecular Physics and Quantum Chemistry', Wiley (2003).