  In this work, we revisited the idea of using the coupled-cluster ground state
formalism to target excited states. Our main focus was targeting doubly excited
states and double core hole states. Typical equation-of-motion (EOM) approaches
for obtaining these states struggle without higher-order excitations than
doubles. We showed that by using a non-aufbau determinant optimized via the
maximum overlap method the CC ground state solver can target higher energy
states. Furthermore, just with singles and doubles (i.e., CCSD), we
demonstrated that the accuracy of $\Delta$CCSD and $\Delta$CCSD(T) far
surpasses that of EOM-CCSD for doubly excited states. The accuracy of
$\Delta$CCSD(T) is nearly exact for doubly excited states considered in this
work. For double core hole states, we used an improved ansatz for greater
numerical stability by freezing core hole orbitals. The improved methods, core
valence separation (CVS)-$\Delta$CCSD and CVS-$\Delta$CCSD(T), were applied to
the calculation of the double ionization potential of small molecules. Even
without relativistic corrections, we observed qualitatively accurate results
with CVS-$\Delta$CCSD and CVS-$\Delta$CCSD(T). Remaining challenges in
$\Delta$CC include the description of open-shell singlet excited states with
the single-reference CC ground state formalism as well as excited states with
genuine multi-reference character. The tools and intuition developed in this
work may serve as a stepping stone towards directly targeting arbitrary excited
states using ground state CC methods.
