Dynamic Coupling Phenomena in Molecular Excited States. I. General Formulation and Vibronic Coupling<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

Abstract

A general formalism is described for treating diabatic coupling processes in highly excited molecular states. The method treats electronic and nuclear motion quantum mechanically, and uses the adiabatic Born-Oppenheimer states as basis function. The present paper concentrates on diagnoses of vibronic coupling matrix elements, with Rydberg and continuum states of ${\mathrm{H}}_{2}$ as the test cases. The principal contributions come from the excited electron's interactions with the oscillating finite monopole of the ion-molecule core. The electronic factors in the transition amplitudes are definitely dependent on internuclear distance, particularly in the cases of $p$ and $d$ states. The transition amplitudes accumulate their magnitudes over the full classically allowed range of internuclear distance, especially in the cases of $s$ and $p$ states. Specific application is made to vibronic coupling perturbations in $p\ensuremath{\sigma}$ and $p\ensuremath{\pi}$ Rydberg states of ${\mathrm{H}}_{2}$.