Knowledge Bank

Vibronic coupling arises in the Born-Oppenheimer approximation from the cross-term that appears when the second derivative operator for the nuclear kinetic energy acts on the product of an electronic and a nuclear wave function. This cross-term is usually handled as an effective operator which has matrix elements between vibrational levels of different electronic states. In unsymmetrical linear triatomic molecules these elements follow the selection rules $\Delta \Lambda =\pm 1,\Delta l=\mp 1,\Delta v2=\pm 1,$ where $\nu 2$ is the bending vibration. The most important effects occur in $\Pi$; electronic states, because distant $\Sigma +$ and $\Sigma -$ states affect the Born-Oppenheimer components differently. If the $\Sigma$ and $\Pi$ electronic states are well separated the vibrational structure of the $\Pi$ state can be treated as if there is an operator acting within the $\Pi$ state that causes a quadratic splitting between its two components; this is the essence of the Renner- Teller effect. In transition metal-containing molecules the density of electronic states can be high enough for this approach to break down. Every electronic transition then contains intense ``forbidden'' vibrational bands, violating the usual selection rules, and large numbers of seemingly random perturbations occur. Examples will be draw from the spectra of the metal methylidynes and hydroxides.