We adapt the multiple-scattering method to treat unbound electronic states of molecules in the independent electron approximation. An inhomogeneous linear system is derived whose solution yields the K matrix for the electron-molecule interaction. Using the K matrix, we derive continuum electronic wavefunctions by imposing boundary conditions corresponding to electron-molecule scattering and molecular photoionization, i.e., the wavefunctions satisfy the so-called outgoing-wave and incoming-wave normalization, respectively. These wavefunctions are then used to obtain expressions for elastic scattering and photoionization differential cross sections.

Shape resonances in molecular photoionization are shown to induce strong coupling between vibrational and electronic motion over a spectral range several times broader than the resonances half-width. This coupling is manifested by large deviations from Franck-Condon intensity distributions and strong dependence of photoelectron angular distributions on the vibrational state of the residual ion. These effects are illustrated for the 3a g photoionization channel of N 2 .

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Photoionization of the CO molecule and inner-valence states of CO" between 22 and 45 eV have been studied by means of photoelectron spectroscopy using both synchrotron radiation and He ii radiation. Vibrational structure has been resolved in many bands up to 45 eV. CASSCF (complete active space self-consistent field) and MRCI (multireference configuration interaction) calculations of potential curves in the 22-30 eV range have been perfonned and these have been used to predict vibrational levels and Franck-Condon factors. In this energy range three valence states, D 'IT, 3'E' and 3% have been identified, and spectroscopic constants have been determined for the first two of these. Above 30 eV, all valence slates have been found to be repulsive. In addition to the broad bands expxted for these slates, several progressions of narrow lines are observed most probably reflecting transitions to Rydberg states.P Bultzer et a1 a1 (1994). At higher energies, above approximately 20 eV, the number of states increases quickly due to significant many-electron effects and this leads to a breakdown of the independent-particle molecular orbital approximation. The 3u-' hole state is split into a manifold of ' Z ' stales (Okuda and

We interpret the enhanced lines and frequent failure to detect Rydberg structure in the x-ray absorption spectra of molecules in terms of ``inner-well'' and ``outer-well'' states which result from an effective potential barrier located near the electronegative atoms in the molecule. The K and LII, III spectra of sulfur in SF6 are discussed in detail and all prominent features are identified. X-ray absorption spectra of molecules in which a B, S, or Si atom is combined with two or more electronegative atoms are surveyed to illustrate further the influence of effective potential barriers. It is pointed out that ``inner-well'' states have been observed in emission experiments, and that such states should also be observed in electron scattering experiments on molecules and in x-ray absorption experiments on ionic crystals. Finally, cases are described in which x-ray absorption measurements may permit the determination of the geometry of molecules.