Excited states via coupled cluster theory without equation-of-motion methods: Seeking higher roots with application to doubly excited states and double core hole states

In this work, we revisited the idea of using the coupled-cluster (CC) 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) (triples) 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 multireference character. The tools and intuition developed in this work may serve as a stepping stone toward directly targeting arbitrary excited states using ground state CC methods. Published under license by AIP Publishing.