The Singlet-Triplet Gap of Cyclobutadiene: The CIPSI-Driven CC($P$;$Q$) Study

TL;DR

This study combines CIPSI-selected configuration interaction with CC($P$;$Q$) methods to accurately compute the singlet-triplet gap in cyclobutadiene, reducing computational costs while maintaining high accuracy.

Contribution

It introduces a practical approach merging CIPSI with CC($P$;$Q$) to efficiently approximate CCSDT-level energetics for biradicals.

Findings

Accurately reproduces CCSDT potential surfaces for cyclobutadiene

Achieves reliable singlet-triplet gap predictions with minimal computational effort

Demonstrates effectiveness of CIPSI-driven CC($P$;$Q$) in complex electron correlation scenarios

Abstract

An accurate determination of singlet-triplet gaps in biradicals, including cyclobutadiene in the automerization barrier region where one has to balance the substantial nondynamical many-electron correlation effects characterizing the singlet ground state with the predominantly dynamical correlations of the lowest-energy triplet, remains a challenge for many quantum chemistry methods. High-level coupled-cluster (CC) approaches, such as the CC method with a full treatment of singly, doubly, and triply excited clusters (CCSDT), are often capable of providing reliable results, but the routine application of such methods is hindered by their high computational costs. We have recently proposed a practical alternative to converging the CCSDT energetics at small fractions of the computational effort, even when electron correlations become stronger and connected triply excited clusters are larger and nonperturbative, by merging the CC($P$;$Q$) moment expansions with the selected configuration interaction methodology abbreviated as CIPSI. We demonstrate that one can accurately approximate the highly accurate CCSDT potential surfaces characterizing the lowest singlet and triplet states of cyclobutadiene along the automerization coordinate and the gap between them using tiny fractions of triply excited cluster amplitudes identified with the help of relatively inexpensive CIPSI Hamiltonian diagonalizations.