  A number of iterative and perturbative approximations to the full
equation-of-motion coupled cluster method with single, double, and triple
excitations (EOM-CCSDT) are evaluated in the context of calculating the K-edge
core-excitation and core-ionization energies of several small molecules.
Several of these methods are found to accurately reproduce the full EOM-CCSDT
energies well, in particular the EOM-CCSD* method which, when using the
core-valence separation (CVS) ansatz, scales rigorously with the sixth power of
molecular size. The EOM-CCSDR(3) method, which has been used previously to
include triples effects in a cost-effective manner was found to perform rather
poorly, although the precise cause has not been determined. These results
highlight that very accurate NEXAFS and XPS spectra for molecules with
first-row atoms can be computed at a cost not much larger than that for
EOM-CCSD.
