The Rydberg spectra of atoms and small molecules offers an experimentally convenient probe for exploring the exchange of energy between Rydberg electrons and other forms of electronic, vibrational, and rotational excitation. This thesis investigates a series of special topics in the field of molecular Rydberg spectra, using a diverse set of theoretical techniques all designed to take advantage of the computational efficiency of the sorts of scattering parameterizations commonly associated with the field of quantum defect theory. In particular, I consider various mechanisms by which Rydberg electrons participate in the formation (bonding) and destruction (dissociation) of molecular states.
First, I review the methodology of multichannel quantum defect theory in molecular systems, demonstrating its versatility in reducing a complicated set of channel-coupled solutions into a physically observable photoionization spectrum with exceptionally high resolution, even in regions characterized by complex resonant structures with strong energy dependence. The utility of the Fano frame transformation is discussed, two approaches to the problem of extracting resonant effects via the delay of asymptotic boundary conditions are presented, and a case study featuring the molecular hydrogen isotopomer HD is examined in detail.
Second, I turn to the question of Rydberg electrons in the presence of both an ionic core and a neutral perturbing particle, extending certain basic features of the above philosophy to a two-center geometry. This system is predicted to give rise to a potential well that supports bound states, with a potential curve minimum existing at many hundreds or thousands of Bohr radii. The problem is first handled at the level of a zero-range potential approximation, where the solution can be written by means of degenerate perturbation theory. This approach is compared to a more robust, but computationally expensive, description of the interaction in terms of a finite range model potential, requiring diagonalization of the Hamiltonian with respect to an L2 basis. Some properties of these states are also noted. Next, a more powerful but difficult formulation using the Coulomb Green\textquoterights function, subject to limiting boundary conditions at the position of the core and perturber, is derived. Finally, a semiclassical interpretation, corresponding to the trajectories of a point particle electron moving classically in a Coulombic field, is examined in detail.
Third, I return to the case of the diatomic Rydberg spectrum, this time extending the solution to accommodate dissociation pathways through the use of a Siegert pseudostate basis. Previously developed methods of treating the competition between ionization and dissociation are reviewed and evaluated. The Siegert basis is defined, together with an efficient procedure for its calcuation, and some of its unconventional properties are explicitly noted. The Siegert-MQDT method is applied to several reactive scattering or half-scattering processes, including photodissociation, dissociative ionization, and dissociative recombination.