Theory of x-ray excitons in conjugated molecules and polymers

A theory for excitons in x-ray spectra of conjugated molecules is presented. Due to the interaction with the core hole the lowest unoccupied n level splits from other empty levels. The energy position of this state is defined by the renormalized Coulomb interaction with the core hole and by the width of the unoccupied n band. The ratio of these two quantities determine whether the x-ray state is excitonic or not. It is shown that the conditions for excitcnic character are qualitatively different between occupied levels (x-ray emission) and unoccupied levels (x-ray absorption). From the specified normalization we find that only half an electron density of the unoccupied molecular orbital can be localized to the atom with the core hole, while in the x-ray emission case the electron density of the lowest occupied jr orbital can be totally localized. The degree of localization of the lowest unoccupied it level decreases when the length of the molecule increases. Contrary to lowest occupied and unoccupied molecular orbitals the electron density of higher occupied (emissi on) and higher unoccupied (absorption) it orbitals is pushed out from the core excited atom for sufficiently large Coulomb interactions between core hole and valence shell. Strong site and size dependences of the intensity and frequency of excitonic peaks in x-ray absorption spectra are predicted, the site dependency being alternant for conjugated molecules. The model predicts strong depression of the absorption intensity for the it * levels along the polyene series in good accord with ah initio data.