Studies of molecular Rydberg states by Schwinger variational-quantum defect methods: Application to molecular hydrogen

An ab initio electronic structure technique has been developed to study highly excited states of molecules by combining Schwinger variational methods of collision theory with generalized quantum defect theory. The technique exploits methods of scattering theory to study the region of highly excited Rydberg levels below and across ionization thresholds for molecules. The reaction matrix K, which describes the interaction of the Rydberg electron with the ionic core, is found at arbitrary negative electron energies by employing an unbounded Coulomb Green's function in the Lippmann--Schwinger equation for the electronic wave function. Quantal conditions are imposed to obtain discrete molecular energy levels, associated Rydberg wave functions, and quantum defect functions, all as a function of the internuclear distance. Results within the static-exchange approximation for the 1,3Σ+u(1σgnσu) and 1,3Πu(1σgnπu) Rydberg states of H2, for n=2--20 and R=1.2--5.0 a0, are presented and discussed