  The problem of orbital relaxation in computational core-hole spectroscopies,
including x-ray absorption and x-ray photoionization, has long plagued linear
response approaches, including equation-of-motion coupled cluster with singles
and doubles (EOM-CCSD). Instead of addressing this problem by including
additional electron correlation, we propose an explicit treatment of orbital
relaxation via the use of "transition potential" reference orbitals, leading to
a transition-potential coupled cluster (TP-CC) family of methods. One member of
this family in particular, TP-CCSD(1/2), is found to essentially eliminate the
orbital relaxation error and achieve the same level of accuracy for core-hole
spectra as is typically expected of EOM-CCSD in the valence region. These
results show that very accurate x-ray absorption spectra for molecules with
first-row atoms can be computed at a cost essentially the same as that for
EOM-CCSD.
