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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.

Polarization of CI Kfi x-ray fluorescence following selective excitation of gaseous CH3CI with synchrotron radiation is reported. The degree of polarization of the fluorescence depends sensitively on the chosen incident excitation energy in the CI A^-edge region. Theoretical considerations indicate that the fluorescence-polarization measurements can provide directly absorption and emission anisotropics, molecular-orbital symmetries, and relative fluorescence transition strengths.PACS numbers: 33.20. Rm, 33.50.Dq, 33.90.+h X-ray emission spectroscopy under conditions of unpolarized excitation and detection has a long history of elucidating core-level phenomena in a wide variety of contexts. ! Synchrotron-radiation sources in the x-ray range now provide both tunable and polarized exciting radiation throughout the spectral regions near core-level thresholds in atoms, molecules, and solids. 2 Combining the advantages offered by synchrotron radiation with polarization analysis of the x-ray fluorescence, we report here results of valence-electron x-ray fluorescencepolarization measurements following energy-selected and polarized excitation near the CI K edge of methyl chloride (CH3CI). Theoretical interpretation of the measured polarized-fluorescence spectra indicates that the anisotropy of the photoexcitation process and the orientations and relative magnitudes of fluorescent dipole transition moments may be obtained directly from experiment. The x-ray polarized-fluorescence technique reported here thus provides a new approach to molecular photoabsorption and emission, as well as molecularstructure studies.Previous work has used ultraviolet and visible fluorescence polarization to infer alignment of molecular ions and fragments following polarized excitation of valence electrons. 3 The present study reports initial observations of fluorescence polarization following core-level excitation. 4 For molecular systems, core-level studies offer two distinct advantages. First, because core levels undergo rapid Auger decay (< 10 ~1 4 s), fluorescence is observed on a time scale that is short compared with normal molecular tumbling periods (10 -11 -10 -12 s). Valenceshell hole states, in contrast, are sufficiently long lived (>10~1 0 s) that rotational motion can occur prior to radiative decay, complicating the interpretation of fluorescence-polarization measurements. 3 Second, corelevel spectroscopy is highly selective to a specific atomic absorption edge and, with sufficient resolution, to the same atomic species in different environments.Core-level fluorescence-polarization measurements require (i) a source of polarized x rays, (ii) highthroughput and high-resolution primary and secondary x-ray monochromators, and (iii) polarization sensitivity of the secondary spectrometer. The first requirement is satisfied by synchrotron radiation, which in this work was provided by beam line X-24A at the National Synchrotron Light Source (NSLS), where a large-aperture crystal-diffraction primary monochromator selects the desired incident...

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