  X-ray photoelectron spectroscopy (XPS) measures core-electron binding
energies (CEBEs) to reveal element-specific insights into chemical environment
and bonding. Accurate theoretical CEBE prediction aids XPS interpretation but
requires proper modeling of orbital relaxation and electron correlation upon
core-ionization. This work systematically investigates basis set selection for
extrapolation to the complete basis set (CBS) limit of CEBEs from $\Delta$MP2
and $\Delta$CC energies across 94 K-edges in diverse organic molecules. We
demonstrate that an alternative composite scheme using $\Delta$MP2 in a large
basis corrected by $\Delta$CC-$\Delta$MP2 difference in a small basis can
quantitatively recover optimally extrapolated $\Delta$CC CEBEs within 0.02 eV.
Unlike $\Delta$CC, MP2 calculations do not suffer from convergence issues and
are computationally cheaper, and, thus, the composite $\Delta$MP2/$\Delta$CC
scheme balances accuracy and cost, overcoming limitations of solely using
either method. We conclude by providing a comprehensive analysis of the choice
of small and large basis sets for the composite schemes and provide practical
recommendations for highly accurate (within 0.10-0.15 eV MAE) ab initio
prediction of XPS spectra.
