Photoexcitation and ionization in carbon dioxide: Theoretical studies in the separated-channel static-exchange approximation

Theoretical studies are reported of total and partial-channel photoexcitation and ionization cross sections in carbon dioxide. As in previously reported studies of discrete and continuum dipole spectra in diatomic (${\mathrm{N}}_{2}$, CO, ${\mathrm{O}}_{2}$, ${\mathrm{F}}_{2}$) and polyatomic (${\mathrm{H}}_{2}$O, ${\mathrm{H}}_{2}$CO, ${\mathrm{O}}_{3}$) molecules in this series, separated-channel static-exchange calculations of vertical-electronic transition energies and oscillator strengths and Stieltjes-Tchebycheff moment methods are employed in the development. Detailed comparisons are made of the static-exchange excitation and ionization spectra with photoabsorption, electron-impact excitation, and quantum-defect estimates of discrete transition energies and intensities, and with partial-channel photoionization cross sections obtained from fluorescence measurements and from tunable-source and ($e$,$2e$) photoelectron spectroscopy. The spectral characteristics of the various discrete series and continua are interpreted in terms of contributions from compact $2{\ensuremath{\pi}}_{u}({\ensuremath{\pi}}^{*})$, $5{\ensuremath{\sigma}}_{g}({\ensuremath{\sigma}}^{*})$, and $4{\ensuremath{\sigma}}_{u}({\ensuremath{\sigma}}^{*})$ virtual valence orbitals, and from more diffuse discrete and continuum Rydberg orbitals. The $2{\ensuremath{\pi}}_{u}({\ensuremath{\pi}}^{*})$ orbital is found to contribute to discrete excitation series, whereas the $5{\ensuremath{\sigma}}_{g}({\ensuremath{\sigma}}^{*})$ and $4{\ensuremath{\sigma}}_{u}({\ensuremath{\sigma}}^{*})$ orbitals generally appear in the photoionization continua as resonancelike diabatic valence features. Good agreement obtains between the calculated discrete excitation series and the results of a recent analysis of the available spectroscopic data. The calculated outer-valence-shell $(1{\ensuremath{\pi}}_{g}^{\ensuremath{-}1})X^{2}\ensuremath{\Pi}_{g}$, $(1{\ensuremath{\pi}}_{u}^{\ensuremath{-}1})A^{2}\ensuremath{\Pi}_{u}$, $(3{\ensuremath{\sigma}}_{u}^{\ensuremath{-}1})B^{2}\ensuremath{\Sigma}_{u}^{+}$, and $(4{\ensuremath{\sigma}}_{g}^{\ensuremath{-}1})C^{2}\ensuremath{\Sigma}_{g}^{+}$ partial-channel photoionization cross sections are in good accord with measured values, and clarify completely the origins of the various structures in the observed spectra. There is evidence, however, of coupling among scattering states associated with $1{\ensuremath{\pi}}_{g}^{\ensuremath{-}1}$ and $1{\ensuremath{\pi}}_{u}^{\ensuremath{-}1}$ ionic channels, giving rise to moderate disagreement with tunable-source photoelectron and fluorescence measurements over a portion of the spectrum. In the inner-valence-shell region, the calculated $2{\ensuremath{\sigma}}_{u}^{\ensuremath{-}1}$ and $3{\ensuremath{\sigma}}_{g}^{\ensuremath{-}1}$ cross sections are in qualitative accord with the observed many-electron spectral intensities, and provide a basis for quantitative interpretation when combined with appropriate intensity-borrowing calculations. The calculated carbon and oxygen $K$-edge cross sections are in good agreement with available cross sections obtained from electron-impact and photoabsorption measurements. It is of particular interest to find the oxygen $K$-edge ($1{\ensuremath{\sigma}}_{g}^{\ensuremath{-}1}$, $1{\ensuremath{\sigma}}_{u}^{\ensuremath{-}1}$) cross section exhibits both the expected $5{\ensuremath{\sigma}}_{g}({\ensuremath{\sigma}}^{*})$ and $4{\ensuremath{\sigma}}_{u}({\ensuremath{\sigma}}^{*})$ resonancelike features. Finally, comparisons are made throughout of the discrete and continuum spectra in carbon dioxide with the results of previously reported studies in CO and ${\mathrm{O}}_{2}$, and the origins of the similarities and differences in the cross sections in these cases are clarified.