Partial-channel Cross Sections Research Articles

Theoretical studies of photoionization in diatomic and polyatomic molecules

A review is given of recent theoretical studies of partial-channel photoionization cross sections in diatomic and polyatomic molecules. Results obtained from separated-channel static-exchange calculations and Stieltjes-Tchebycheff moment-theory techniques are compared with recent photoabsorption, electron-impact excitation, fluorescence production, photoelectron spectroscopy, and dipole (e, 2e) measurements. Various structures in the calculated and measured cross sections as functions of incident photon energy are attributed to final-state wavefunctions of either atomiclike or molecularlike composition. Specifically, σ-orbital cross sections in light diatomic and polyatomic molecules are found to be generally dominated by strong σ → σ^* photoionization resonances of molecularlike origin, whereas π-orbital cross sections in such molecules exhibit strong distinctly 2p → kd atomiclike features. These aspects of molecular photoionization are illustrated with the results of detailed theoretical and experimental studies of partial-channel cross sections in CO, CO_2, and H_2CO.

The outer valence photoionization of acetylene

We report fixed-nuclei photoionization cross-sections and asymmetry parameters for photoionization leading to the X 2Πu, A 2Σg+, B 2Σu+, and C 2Σg+ states of acetylene with emphasis on the first four states. The magnitude of the photoionization cross-sections calculated here is in excellent agreement with recent experiment at both low and high photon energy. Further, as a result of the multichannel scattering methodology used to perform the calculation, the partial channel cross-sections and asymmetry parameters reported here resolve significant structure arising from indirect photoionization processes such as autoionization. Although vibrational degrees of freedom are not included within the fixed nuclei framework employed here, we find that, even without vibrational degrees of freedom, the present theoretical results generally exhibit the same detailed features as the experimental results, both for conventional photoionization spectra and, as a result of vibrational autoionization, for threshold photoionization spectra. This general agreement suggests that a large part of the structure in the low energy or outer valence photoionization spectrum of acetylene is explicable solely in terms of Rydberg transitions. This study also predicts that dark states may cause some appreciable distortion of the profile of the photoionization asymmetry parameter in the photon region of ∼20–21.5 eV as a result of final state correlations with more intense states.

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

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.

Absolute Cross Sections for Molecular Photoabsorption, Partial Photoionization, and Ionic Photofragmentation Processes

A compilation is provided of absolute total photoabsorption and partial-channel photoionization cross sections for the valence shells of selected molecules, including diatomics (H2, N2, O2, CO, NO) and triatomics (CO2, N2O), simple hydrides (H2O, NH3, CH4), hydrogen halides (HF, HCl, HBr, HI), sulfur compounds (H2S, CS2, OCS, SO2, SF6), and chlorine compounds (Cl2, CCl4). The partial-channel cross sections presented refer to production of the individual electronic states of molecular ions and also to production of parent and specific fragment ions, as functions of incident photon energy, typically from ∼20 to 100 eV. Total photoabsorption cross sections above the first ionization threshold are reported from conventional optical measurements obtained using line and continuum sources and from ‘‘equivalent-photon’’ dipole (e,e) electron scattering experiments. Partial photoionization cross sections for production of electronic states of molecular ions are obtained from photoelectron spectroscopy and from dipole (e,2e) coincidence measurements. Photoionization mass spectrometry and dipole (e, e+ion) coincidence studies provide measurements of partial cross sections for ionic photofragmentation (i.e., dissociative photoionization). Photoelectron anisotropy factors, which together with electronic partial cross sections provide cross sections differential in photon energy and in ejection angle, are also reported. There is generally good agreement between cross sections measured by the physically distinct optical and dipole electron-impact methods. The cross sections and anisotropy factors also compare favorably with selected ab initio and model potential (X-alpha) calculations which provide a basis for interpretation of the measurements.

Theoretical studies of photoexcitation and ionization in H2O

Theoretical studies are reported of the complete dipole excitation and ionization spectrum in H2O employing Franck–Condon and static-exchange approximations. Large Cartesian Gaussian basis sets are used to represent the required discrete and continuum electronic eigenfunctions at the ground-state equilibrium geometry, and previously devised moment-theory techniques are employed in constructing the continuum oscillator-strength densities from the calculated spectra. Detailed comparisons are made of the calculated excitation and ionization profiles with recent experimental photoabsorption studies and corresponding spectral assignments, electron impact–excitation cross sections, and dipole (e, 2e)/(e, e+ion) and synchrotron-radiation studies of partial-channel photoionization cross sections. The various calculated excitation series in the outer-valence (1b−11, 3a−11, 1b−12) region are found to include contributions from valence-like 2b2 (σ*) and 4a1 (γ*) virtual orbitals, as well as appropriate nsa1, npa1, nda1, npb1, npb2, ndb1, ndb2, and nda2 Rydberg states. Transition energies and intensities in the ∼7 to 19 eV interval obtained from the present studies are seen to be in excellent agreement with the measured photoabsorption cross section, and to provide a basis for detailed spectral assignments. The calculated (1b−11) X 2B1, (3a1−1)2A1, and (1b2−1)2B2 partial-channel cross sections are found to be largely atomic-like and dominated by 2p→kd components, although the 2b2(σ*) orbital gives rise to resonance-like contributions just above threshold in the 3a1→kb2 and 1b2 →kb2 channels. It is suggested that the latter transition couples with the underlying 1b1→kb1 channel, accounting for a prominent feature in the recent high-resolution synchrotron-radiation measurements. When this feature is taken into account, the calculations of the three outer-valence channels are in excellent accord with recent synchrotron-radiation and dipole (e, 2e) photoionization cross-sectional measurements. The calculated inner-valence (2a1−1) cross section is also in excellent agreement with corresponding measured values, although proper account must be taken of the appropriate final-state configuration-mixing effects that give rise to a modest failure of the Koopmans approximation, and to the observed broad PES band, in this case. Finally, the origins of the various spectral features present in the measured 1a1 oxygen K-edge electron energy-loss profile in H2O are seen to be clarified fully by the present calculations.

Theoretical studies of partial-channel photoionization cross sections in diatomic and polyatomic molecules

An account is given of recent theoretical studies of partial-channel photoionization cross sections in diatomic and polyatomic molecules employing separated-channel static-exchange calculations and Stieltjes-Tchebycheff moment-theory techniques. The calculated cross sections, which refer to production of specific parent molecular-ionic states upon removal of electrons from individual orbitals, are compared with the results of photoabsorption, electron-impact-excitation, fluorescence-production, photoelectron spectroscopy, and dipole (e, 2e) measurements. Various structures in the calculated and measured partial-channel cross sections as functions of incident photon energy are identified as having either atomiclike or molecularlike origins. Specifically, σ-orbital cross sections in light diatomic and polyatomic molecules are found to be generally dominated by strong σ - σ^* photoionization resonances of molecularlike origin, whereas π-Orbital cross sections in such molecules exhibit distinctly 2p → kd atomiclike features. These aspects of molecular photoionization are illustrated by detailed theoretical studies of partial-channel cross sections in CO, C0_2, and H_2CO, the results of which are in generally good accord with corresponding measured values.

Photoexcitation and ionization in molecular oxygen: Theoretical studies of electronic transitions in the discrete and continuous spectral intervals

Theoretical studies of valence-electron (1πg, 1πu, 3σg) photoexcitation and ionization cross sections in molecular oxygen are reported employing separated-channel static-exchange calculations and the Stieltjes–Tchebycheff moment-theory technique. As in previously reported investigations of photoexcitation and ionization in small molecules following this approach, canonical Hartree–Fock orbitals, large Gaussian basis sets, and many-electron eigenstates of correct symmetry are used in defining appropriate noncentral static-exchange potentials and in computations of the appropriate discrete and continuum transition strengths. It is particularly important in molecular oxygen to incorporate the appropriate ionic parentages of the various photoionization multiplet states in order to obtain the correct partial-channel cross sections. The calculated discrete series associated with 1πg excitation are found to be in good agreement with available experimental assignments and previously reported theoretical studies, and the predicted states associated with 1πu and 3σg excitations are in general accord with assignments for the higher series based on spectral and quantum-defect analysis. Although the observed photoelectron spectra and photoionization cross sections are relatively complex, the calculated total vertical electronic photoabsorption cross section and the partial-channel photoionization cross sections for production of X 2πg, a 4πu, A 2πu, 2 2πu, 3 3Πu, b 4Σg−, and B 2Σg− ionic states are found to be in good accord with recent synchrotron radiation, line-source, electron-impact, and (e,2e) dipole oscillator-strength measurements when proper account is taken of the parentages of the various multiplet states. The partial-channel cross sections exhibit resonancelike structures that can be attributed to contributions from diabatic valencelike virtual states that appear in the appropriate photoionization continua, rather that in the corresponding discrete spectral intervals. These features in the dipole spectrum of molecular oxygen are discussed and are contrasted and compared with the results of previously reported related studies in molecular nitrogen and carbon monoxide.