Knowledge Bank

In zeroth approximation the vibrational wavefunction of a polyatomic molecule is a simple product of harmonic oscillator functions. In higher approximation the oscillator functions become mixed and the wavefunction, for the case of a triatomic structure, can be written in which the $\Psi \circ$ are harmonic oscillator functions and the a's are coefficients which may be unity but in general are determined by the harmonic energy eigenvalues and the higher-than-quadratic force constants. In an electronic band system this mixing to some extent modifies the usual Franck-Condon considerations, and may cause transitions forbidden in the harmonic oscillator approximation---for example, the 2-0 transition in a non-totally symmetrical vibration---to appear with considerable intensity.