High-resolution carbon1sphotoelectron spectrum of ethene: Ab initiocalculation of vibrational structure with dynamic localization of the core hole

The vibrational structure in the carbon $1s$ photoelectron spectrum of ethene has been measured with a total experimental resolution of about 55 meV, significantly better than has been previously reported. The spectrum has been calculated using ab initio electronic structure theory with a localized core hole and the equivalent-cores approximation. Agreement between the calculated spectrum and measurements (taken 29 eV above the carbon $1s$ threshold) is excellent. This agreement indicates that there is dynamic localization of the core hole, even though the $1{\sigma }_g-1\mathrm{}{\sigma }_u$ splitting is not small. The theoretical method provides an approach that is useful for analyzing such spectra and also shows some of the pitfalls of attempting to fit complex vibrational spectra without guidance from theory.