# Cavity Born–Oppenheimer Coupled Cluster Theory: Toward Electron Correlation in the Vibrational Strong Light-Matter Coupling Regime

## TL;DR

This paper introduces a new method to study electron correlation in chemical reactions under vibrational strong light-matter coupling using a coupled cluster approach.

## Contribution

The novel CRP-CCSD method combines cavity reaction potential with coupled cluster theory to model cavity-modified electron correlation.

## Key findings

- lCRP-CCSD methods provide excellent results compared to CRP-CCSD in the few-molecule limit.
- Mean-field and correlated results show significant differences in both reactive and collective scenarios.
- Electron correlation under vibrational strong coupling is nontrivial and requires beyond-mean-field approaches.

## Abstract

We present a detailed derivation and discussion of cavity
Born–Oppenheimer
coupled cluster (CBO–CC) theory and address cavity-modified
electron correlation in the vibrational strong coupling regime. Methodologically,
we combine the recently proposed cavity reaction potential (CRP) approach
with the Lagrangian formulation of CC theory and derive a self-consistent
CRP-CC method at the singles and doubles excitations level (CRP-CCSD).
The CRP-CC approach is formally similar to implicit solvation CC models
and provides access to the CBO–CC electronic ground state energy
minimized in cavity coordinate space on a CC level of theory. A hierarchy
of linearization schemes (lCRP-CCSD) similar to canonical CC theory
systematically lifts the self-consistent nature of the CRP-CCSD approach
and mitigates numerical cost by approximating electron correlation
effects in energy minimization. We provide a thorough comparison of
CRP-CCSD, lCRP-CCSD, and CRP-Hartee-Fock methods for a cavity-modified
Menshutkin reaction, pyridine+CH3Br, and cavity-induced
collective electronic effects in microsolvation energies of selected
methanol–water clusters. We find lCRP-CCSD methods to provide
excellent results compared to the self-consistent CRP-CCSD approach
in the few-molecule limit. We furthermore observe significant differences
between mean-field and correlated results in both reactive and collective
scenarios. Our work emphasizes the nontrivial character of electron
correlation under vibrational strong coupling and provides a starting
point for further developments in ab initio vibro-polaritonic
chemistry beyond the mean-field approximation.