Extension of the CIPSI-Driven CC($P$;$Q$) Approach to Excited Electronic States

TL;DR

This work extends the CIPSI-driven CC($P$;$Q$) framework to excited electronic states by integrating it with EOM-CC theory, enabling CCSDT/EOMCCSDT-quality energies to be obtained from compact CIPSI-guided subspaces. The two-step method uses a $P$ space (singles, doubles, and CIPSI-selected triples) to solve CC/EOMCC, followed by noniterative corrections from a $Q$ space containing the remaining triples, yielding $E_{ u}^{(P+Q)} = E_{ u}^{(P)} + oldsymbol{ riangle}_{ u}(P;Q)$. Across CH$^+$, CH, and H$_2$O PES scans, the CIPSI-driven CC($P$;$Q$) approach converges toward the full CCSDT/EOMCCSDT energetics with relatively small CIPSI determinant spaces (often well below the total triples count), and the noniterative corrections effectively capture higher-order correlation, including MR effects along dissociation paths. The results show substantial improvements over CR-EOMCC(2,3) and standard EOMCCSDT in challenging multireference regimes, with the potential for state-specific P-spaces and truncated CIPSI variants to further reduce computational cost and extend applicability.

Abstract

We extend the CIPSI-driven CC($P$;$Q$) methodology [K. Gururangan et al., J. Chem. Phys. 155 (2021) 174114], in which the leading higher-than-doubly excited determinants are identified using the selected configuration interaction (CI) approach abbreviated as CIPSI, to excited electronic states via the equation-of-motion (EOM) coupled-cluster (CC) formalism. By examining vertical excitations in CH+ at equilibrium and stretched geometries, adiabatic excitations in CH, and ground- and excited-state potential cuts of water, we demonstrate that the CIPSI-driven CC($P$;$Q$) method converges parent CC/EOMCC singles, doubles, and triples energetics from relatively inexpensive Hamiltonian diagonalizations in CI spaces smaller than the corresponding triples manifolds.

Figures (1)

• Figure 1: A comparison of the PES cuts of water along the O--H bond breaking coordinate $R_{\rm OH}$ for the $\ce{H2O}\rightarrow{\rm H} + {\rm OH}$ dissociation channels correlating with the ${\rm X}\,^{2}\Pi$ ground state and the lowest-energy $^{2}\Sigma^{+}$ and $^{2}\Sigma^{-}$ states of the OH product resulting from the CIPSI-driven CC($P$)/EOMCC($P$) [panels (a), (c), and (e)] and CC($P$;$Q$) [panels (b), (d), and (f)] calculations at selected values of the CIPSI wave function termination parameter $N_{\rm det(in)}$ with their full CCSDT/EOMCCSDT counterparts. The solid and dashed lines represent the splined CC($P$)/EOMCC($P$) and CC($P$;$Q$) data, whereas the open circles, squares, triangles, and inverted triangles denote the parent CCSDT/EOMCCSDT energetics. The CC($P$)/EOMCC($P$) and CC($P$;$Q$) results shown in panels (a) and (b), obtained with $N_{\rm det(in)} = 1$, are equivalent to the CCSD/EOMCCSD and CR-CC(2,3)/CR-EOMCC(2,3) calculations, respectively.