A route to improving RPA excitation energies through its connection to equation-of-motion coupled cluster theory

Abstract

We revisit the connection between equation-of-motion coupled cluster (EOM-CC) and random phase approximation (RPA) explored recently by Berkelbach [J. Chem. Phys. 149, 041103 (2018)]. We bring together various methodological aspects of these diverse treatment of ground and excited states and present a unified outlook. We present numerical results showing the equivalence that was previously proved on theoretical grounds. We then introduce new approximations in EOM-CC (and RPA) family of methods, assess their numerical performance and explore a way to reap the benefits of such a connection to improve on excitation energies. Our results suggest that addition of perturbative corrections to account for double excitations and missing exchange effects could result in significantly improved estimates.

Formulation and Implementation of Frequency-Dependent Linear Response Properties with Relativistic Coupled Cluster Theory for GPU-Accelerated Computer Architectures

“…We note that HF underestimates the excitation energy of B 3 Π 0 + compared to the CC values, no matter what relativistic effects are included. This can be attributed to the triplet instability of the TDHF model. − On the other hand, such underestimation can be largely avoided by using the simpler configuration interaction singles (CIS) approach. Thus, we perform nonrelativistic CIS calculations by DALTON and find that the CIS value indeed is higher by about 0.011 au for the B 3 Π 0 + state.…”

Reference Energies for Valence Ionizations and Satellite Transitions

“…IP-EOM-CC calculations, i.e., diagonalization of the CC effective Hamiltonian in the ( N – 1)-electron sector of the Fock space, − have been performed for CCSD, ,,− CCSDT, ,− and CCSDTQ. − At the CCSD level, the EOM space includes the one-hole (1h) and the two-hole-one-particle (2h1p) configurations, while the three-hole-two-particle (3h2p) and four-hole-three-particle (4h3p) configurations are further added at the CCSDT and CCSDTQ, respectively. Note that, within the CC formalism, we assume that the IP and electron affinity (EA) sectors are decoupled. − For CC2, , CC3, ,,− and CC4, ,− diagonalization in the ( N – 1)-electron sector of the Fock space is not available yet. Hence, it has been carried out in the N -electron sector of the Fock space ,,− with an additional very diffuse (or bath) orbital with zero energy to obtain ionization and satellite energies.…”

Dark Doubly Excited States with Modified Coupled Cluster Models: A Reliable Compromise between Cost and Accuracy?

“…Another less explored, though naive route to excited states and excitation energies using coupled cluster theory is the ΔCC approacha CC treatment of both the ground and excited state and obtaining excitation energy as the difference of converged CC energies. normalΔ ω C C = E e x c i t e d C C − E g r o u n d C C This is a less explored route due to the difficulty in converging to a mean-field solution of the excited state and then subsequently converging the coupled cluster equations. Some of these convergence issues have been a research focus recently and our goal here is to revisit this route with modified coupled cluster techniques such as Distinguishable Cluster ,,,− and pair CCD. , …”

“…Our hypothesis for this work is that a superior treatment of a ground state for nondynamic correlation, could be obtained by a modified coupled cluster method such as the Distinguishable Cluster approximation and pCCD. In a previous work, we developed a general framework for EOM approximations based on the modified CCSD methods ,, including the Distinguishable Cluster approximation and for a small set of excited states, it showed encouraging results for excited states dominated by double excitation character . Our aim in this paper is to benchmark these and certain other methods for a wider set of challenging situations.…”