Correlation of molecular valence- and K-shell photoionization resonances with bond lengths

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Abstract
A theoretical study of the relationship between interatomic distances and the spectral positions of valence- and K-shell σ* photoionization resonances is reported for a selected series of molecules. Three-dimensional graphical representations of the occupied and virtual-valence σ-symmetry orbitals of these compounds reveal their striking similarity to the wave functions of a particle in a cylindrical well, substantiating qualitative notions long employed in free-electron molecular orbital (FEMO) approximations. Accordingly, the molecular potential along the symmetry axis in these compounds is modeled after a finite square well, with a depth approximately equal to the energy of the lowest σ-symmetry valence molecular orbital and a width determined from analogies to FEMO theory. Calculated minimal-basis-set molecular-orbital energies for both occupied and virtual states are seen to correlate accurately with the simple square-well energy level formula (π2 /2)(n2/l 2 ) when measured in Hartree atomic units from the bottom of the well. The calculated σ* orbital energies are furthermore in excellent agreement with experimentally and theoretically determined valence-shell photoionization resonance positions, the latter consequently also satisfying the square-well correlation formula. A similar situation obtains for experimentally and theoretically determined K-shell resonance positions, although energy shifts from minimal-basis values are evident in these cases. These circumstances are clarified quantitatively on basis of Feshbach–Fano considerations, in which minimal-basis-set virtual-valence σ* orbitals play the roles of zeroth-order states subject to modification by interactions with nonresonant background continua. Concluding remarks contrast and compare molecular-orbital and square-well approaches to photoionization resonances with those based on multiple-scattering and barrier models. The present results appear to clarify the origins of recently reported empirical correlations of bond lengths with resonance positions, and help to determine their range of applicability.