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. Theoretical chemistry is the use of non-experimental reasoning to explain or predict chemical phenomena. ... The Born-Oppenheimer approximation, also known as the adiabatic approximation, is a technique used in quantum chemistry and condensed matter physics in order to de-couple the motion of nuclei and electrons. ...

Vibronic coupling is large in the case two adiabatic potential energy surfaces come close to each other, i.e. 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. 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 due to the fact that 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. A potential energy surface is generally used within the adiabatic or Born-Oppenheimer approximation in quantum mechanics and statistical mechanics to model reactions and interactions in simple chemical and physical systems. ... The eigenvalues of a Hermitian matrix depending on N continuous real parameters cannot cross except at a manifold of N-1 dimensions. ... A potential energy surface is generally used within the adiabatic or Born-Oppenheimer approximation in quantum mechanics and statistical mechanics to model reactions and interactions in simple chemical and physical systems. ... In quantum mechanics, an adiabatic process is an infinitely slow change in the Hamiltonian of a system. ... The Born-Oppenheimer approximation, also known as the adiabatic approximation, is a technique used in quantum chemistry and condensed matter physics in order to de-couple the motion of nuclei and electrons. ... Geometry of the water molecule Molecules have fixed equilibrium geometries--bond lengths and angles--that are dictated by the laws of quantum mechanics. ... In quantum mechanics, an adiabatic process is an infinitely slow change in the Hamiltonian of a system. ... In quantum chemistry, the potential energy surfaces are obtained within the adiabatic or Born-Oppenheimer approximation. ... A potential energy surface is generally used within the adiabatic or Born-Oppenheimer approximation in quantum mechanics and statistical mechanics to model reactions and interactions in simple chemical and physical systems. ... In quantum mechanics, the Berry phase is a phase acquired by quantum states when subjected to adiabatic processes, resulting from the geometrical properties of the parameter space of the Hamiltonian. ... In quantum mechanics, the Berry phase is a phase acquired by quantum states when subjected to adiabatic processes, resulting from the geometrical properties of the parameter space of the Hamiltonian. ... In quantum chemistry, a conical intersection of two potential energy surfaces of the same spatial and spin symmetries is the set of molecular geometry points where the two potential energy surfaces are degenerate (intersect). ... In quantum mechanics, the Berry phase is a phase acquired by quantum states when subjected to adiabatic processes, resulting from the geometrical properties of the parameter space of the Hamiltonian. ...

Perhaps the earliest demonstration of the importance of vibronic coupling was during the 1930's. 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. [1] In quantum mechanics, an excited state of a system (such as an atom, molecule or nucleus) is any configuration of the system that has a higher energy than the ground state (that is, more energy than the absolute minimum). ... Benzene, C6H6, PhH, or benzol is a colorless and flammable liquid with a pleasant, sweet smell. ... In quantum chemistry, molecular orbitals are the statistical states electrons can have within molecules. ... Spectroscopy is the study of spectra, that is, the dependence of physical quantities on frequency. ...

References

1) Fischer, Gad. "Vibronic Coupling - The Interaction between the Electronic and Nuclear Motions", Academic Press, New York, 1984. ISBN 0-12-257240-8