Core-electron shake-up spectra of polyenes: A theoretical study on size and site dependences and excitonic character.

Abstract

We present calculations on x-ray photoelectron shake-up spectra of transpolyenes using the static exchange method. The trends of different shake-up features with respect to the atomic site of the core electron and with respect to the number of ethylene subunits in the oligomer chain are studied. Some salient characteristics related with the conjugated nature of the polyenes have been predicted, in particular a strongly site-dependent alternation of the shake-up intensity. The size dependences of end-atom and midatom shake-up spectra have been demonstrated for H(${\mathrm{C}}_{2}$${\mathrm{H}}_{2}$${)}_{\mathit{n}}$H chains up to n=10. The calculational results indicate that the midatom spectra, which converge to the polymer spectrum, are excitonic. Most spectral intensity derives from shake transitions from the few highest occupied molecular orbitals to the lowest, well-localized, unoccupied molecular orbital. The difference in exciton character with respect to x-ray-absorption spectra of polyenes is discussed. Spectral analyses for the first three smallest molecules---ethylene, butadiene, and hexatriene---have been made in detail, renewing previous assignments. \textcopyright{} 1996 The American Physical Society.