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

TL;DR

This work develops cavity Born-Oppenheimer coupled cluster theory within the cavity reaction potential framework to address electron correlation under vibrational strong coupling. It derives a nonlinear CRP-CCSD formalism and introduces Lambda-linearised variants (lCRP-CCSD) to enable tractable energy optimization in cavity coordinate space, solving a self-consistent set of amplitude and multiplier equations. Applied to a Menshutkin reaction and to MeOH@$n$H2O microsolvation, the results reveal substantial correlation effects and pronounced orientation- and polarization-dependent cavity modifications that differ from mean-field predictions. The findings establish electron correlation as a nontrivial factor in vibro-polaritonic chemistry and provide a robust route toward ab initio vibro-polaritonic methods beyond mean-field theory, with future prospects for excited states and implicit-solvent integration.

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 linearisation 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$+$CH$_3$Br, 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 non-trivial 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.

Figures (2)

• Figure 1: Cavity-modified electronic energies of the Menshutkin reaction pyridine+CH$_3$Br (hyrodgen in white, carbon in grey, nitrogen in blue, bromine in dark red) at CRP-HF/aug-cc-pVDZ ($\mathcal{V}^{(ec)}_\mathrm{rhf}(\lambda)$, dashed lines) and CRP-CCSD/aug-cc-pVDZ ($\mathcal{V}^{(ec)}_\mathrm{ccsd}(\lambda)$, bold lines) levels of theory with cavity-reoriented reactant (left), transition state (top) and product (right) structures lying in the $y$,$z$-plane ($x$-axis points to the reader). We consider a single cavity mode with polarization $\lambda=x$ (red), $\lambda=y$ (orange) or $\lambda=z$ (blue) and light-matter coupling strength, $g_0=0.03\sqrt{E_h}/ea_0$. The bare electronic reference energies are given by $E^{(e)}_\mathrm{rhf}$ and $E^{(e)}_\mathrm{ccsd}$, whereas activation energy and product energy (illustratively for CCSD energies) are indicated by $\Delta_a$ and $\Delta_p$ (cf. Tab.\ref{['tab.activation_menshutkin']}).
• Figure 2: Cavity-induced modifications of microsolvation energies for cavity-reoriented MeOH@$n$H$_2$O clusters with $n=1$ (left) and $n=5$ (right) (hyrodgen in white, carbon in grey, oxygen in red) at CRP-HF/aug-cc-pVDZ ($\tilde{\Delta}_\mathrm{rhf}(\lambda)$, dashed lines) and CRP-CCSD/aug-cc-pVDZ ($\tilde{\Delta}_\mathrm{ccsd}(\lambda)$, bold lines) levels of theory. We consider a single cavity mode with polarization $\lambda=x$ (red), $\lambda=y$ (orange) or $\lambda=z$ (blue) and light-matter coupling strength, $g_0=0.03\sqrt{E_h}/ea_0$.