Accurate and approximate calculations of Franck–Condon intensities in the carbon 1s photoelectron spectrum of methane

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Abstract
The level of theory needed in order to accurately compute the bond contraction following core ionization in methane is examined with an emphasis on one-electron bases and treatment of electron correlation. At our highest level of theory, including core–valence electron correlation, a value of 4.82 pm is computed for the bond contraction in core-ionized methane, in good agreement with experimental findings. The associated potential energy curve in the symmetric stretching coordinate is used to form relative intensities of the peaks in the C 1s photoelectron spectrum of methane. For use in more approximate studies, it is proposed that the ionized core may be conveniently represented by effective core potentials during geometry optimization, and the prospect of this approach is explored in some depth.