New Theoretical Perspectives on Molecular Shape Resonances: Feshbach–Fano Methods for Mulliken Orbital Analysis of Photoionization Continua

Abstract

Recent progress is reported in theoretical, computational, and semiempirical studies of shape resonances in the partial photoionization cross sections of diatomic and polyatomic molecules. A multi-channel Feshbach-Fano formalism is described which is particularly well suited for the analysis of resonance ionization channels. The development allows calculations in non-degenerate point-group-symmetry scattering waves, provides compact expressions for partial-channel cross sections, and gives generalized Fanolike absorption lineshapes of parametrizable form. An appropriately selected Q space of zeroth-order molecular configurational states, corresponding to the (σ, σ*) charge-transfer excitations of Mulliken, is seen to account for the appearance of prominent features in the cross sections of simple molecules. These zeroth-order states further provide a basis for understanding and elaborating upon semi-empirically determined correlations between bond lengths and resonance energies in the valence-and K-shell cross sections of linear and quasi-linear molecules. A universal correlation is derived theoretically in these cases which relates resonance energies to effective bond lengths, square-well quantum numbers, and effective potentials, each of which is obtained a priori from elementary considerations. Recent studies of C2H2, C2H4 and C2H6 photoionization cross sections illustrate the complexities that can arise in compounds which exhibit two σ* resonances (C-C and C-H) in some channels. Mulliken configurational states underlying resonance features in these compounds are seen to account satisfactorily for the natures of calculated and measured partial cross sections in the absence of simple square-well correlation behaviour. Connections of the development with conventional computational methods based on K-matrix, S-matrix, or eigenchannel states are indicated, and cautionary remarks are made on the use of well models in describing photoionization resonances.