Chemical Sciences: A Manual for CSIR-UGC National Eligibility Test for Lectureship and JRF/Vibronic coupling

In theoretical chemistry, the vibronic coupling terms, (which are neglected within the Born–Oppenheimer approximation), are proportional to the interaction between electronic and nuclear motions of molecules. The term "vibronic" originates from the concatenation of the terms "vibrational" and "electronic". The word coupling denotes the idea that in a molecule, vibrational and electronic interactions are interrelated and influence each other.

Vibronic coupling is large in the case of two adiabatic potential energy surfaces coming close to each other (that is, when the energy gap between them is of the order of magnitude of one oscillation quantum). This usually happens in the neighbourhood of an avoided crossing of potential energy surfaces corresponding to distinct electronic states of the same spatial and spin symmetry. However, vibronic coupling also exists at real crossings. In this case the adiabatic or Born–Oppenheimer approximation fails and non-adiabatic terms (the so-called vibronic coupling terms) have to be taken into account. The vibronic coupling terms are usually difficult to evaluate. This is because they are proportional to the first and second derivatives of the electronic wave function with respect to the molecular coordinates. A simpler way to solve this problem is to switch from the adiabatic to the diabatic representation of the potential energy surfaces. The vibronic terms are responsible for example for surface hopping or the Berry phase. The Berry phase has been discovered by Longuet-Higgins in this context. The vibronic coupling becomes infinite in the neighbourhood of a conical intersection. This singularity in the potential energy landscape is the origin of the Berry phase.

Perhaps the earliest examples of the importance of vibronic coupling were found during the 1930s. In 1934 Renner wrote about the vibronic coupling in an electronically excited Π-state in CO2. Calculations of the lower excited levels of benzene by Sklar in 1937 (with the valence bond method) and later in 1938 by Goeppert-Mayer and Sklar (with the molecular orbital method) demonstrated a correspondence between the theoretical predictions and experimental results of the benzene spectrum. The benzene spectrum was the first qualitative computation of the efficiencies of various vibrations at inducing intensity absorption.