ABSTRACT
Multichannel quantum defect theory (MQDT) is applied to the treatment of electron motion in molecular Rydberg states and its coupling to the vibrational and rotational motions of the nuclei. The full rovibronic Hamiltonian is taken into account and the theory formulated in terms of parameters which relate to the standard Born-Oppenheimer (BO) theory. The development is an extension of Seaton’s quantum defect theory and relies on Fano’s frame transformation method. MQDT is not restricted to the BO approximation, but includes the so-called adiabatic corrections and nonadiabatic effects (i.e., vibronic coupling and rotational l uncoupling), however strong, without requiring the explicit evaluation of the interactions between individual levels. The general formalism can be simplified for the H2 and D2 molecules in the range below or near the ionization threshold and for vibrational excitation well below the dissociation energy. The only input data required are the potential energy curve of the ion core in its ground state and the ionization potential (both of which are accurately known), plus two BO potential functions of Σ and Π symmetry, respectively. The theory has been tested in detail using recent experimental and theoretical data on the first five Rydberg absorption transitions of H2 and D2. Theoretical rovibronic levels have been obtained for the B and C states over an extended range of vibrational and rotational quantum numbers on the basis of the best ab initio potential functions currently available. They are found to agree with the experimental levels to within a few cm−1 in all cases, and represent a considerable improvement over previous calculations carried out in the BO and adiabatic approximations with the same potential curves. Conversely, MQDT has been employed to extract BO curves of comparable accuracy for the B′, D, and B″ states directly from the observed levels, without prior evaluation of molecular constants. The higher vibrational levels of the B″ and D states are subject to numerous perturbations by levels belonging to higher Rydberg states: the MQD calculation accounts for these as well, and predicts accurately all Rydberg levels with their manifold interactions, up to the ionization limit. The detailed discussion of these results is deferred, along with the extension to other molecules and to higher energies, into ranges where rotational, vibrational, or electronic preionization, predissociation, or dissociative ionization become important.
