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

Abstract

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.

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• Variational coupled cluster for ground and excited states
• Relativistic EOM-CCSD for core-excited and core-ionized state energies based on the 4-component Dirac-Coulomb(-Gaunt) Hamiltonian
• Perturbation Theory in the Complex Plane: Exceptional Points and Where to Find Them
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• Seniority and Hierarchy Configuration Interaction for Radicals and Excited States
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• Specific chemical bond relaxation unravelled by analysis of shake-up satellites in the oxygen single site double core hole spectrum of CO${}_2$
• Aufbau Suppressed Coupled Cluster Theory for Electronically Excited States
• Simulating core electron binding energies of halogenated species adsorbed on ice surfaces and in solution with relativistic quantum embedding calculations
• Nuclear-electronic orbital second-order coupled cluster for excited states
• Equation-of-motion internally contracted multireference unitary coupled-cluster theory
• Two Determinant Distinguishable Cluster
• One-Body Properties and Their Perturbative Accuracy with Aufbau Suppressed Coupled Cluster Theory
• A Mountaineering Strategy to Excited States: Highly-Accurate Energies and Benchmarks for Bicyclic Systems