Vibronic Coupling. V. Several Theorems Concerning the Eigenfunctions and Spectra of the Vibronic Oscillator

Abstract

Three theorems concerning the nature of vibronic coupling in a simple system are proven. These are that the eigenfunction of the lowest state of the negative system (a ``forbidden'' system in many dimers) is always of one sign, that the lowest eigenvalue of the negative system is lower than the lowest eigenvalue of the positive system (usually an allowed system in a dimer), and that the lowest eigenvalue of the negative system is lower than the lowest eigenvalue in the absence of coupling between the units comprising the dimer. Some physical implications of these theorems concerning the radiative lifetimes of certain excited states are derived and discussed.