Cavity-modified local and non-local electronic interactions in molecular ensembles under vibrational strong coupling

Resonant vibrational strong coupling (VSC) between molecular vibrations and quantized field modes of low-frequency optical cavities constitutes the conceptual cornerstone of vibro-polaritonic chemistry. In this work, we theoretically investigate the role of complementary nonresonant electron-photon interactions in the cavity Born-Oppenheimer (CBO) approximation. In particular, we study cavity-induced modifications of local and non-local electronic interactions in dipole-coupled molecular ensembles under VSC. Methodologically, we combine CBO perturbation theory (CBO-PT) [E. W. Fischer and P. Saalfrank, J. Chem. Theory Comput. 19, 7215 (2023)] with non-perturbative CBO Hartree-Fock (HF) and coupled cluster (CC) theories. In a first step, we derive up to second-order CBO-PT cavity potential energy surfaces, which reveal non-trivial intra- and inter-molecular corrections induced by the cavity. We then introduce the concept of a cavity reaction potential (CRP), minimizing the electronic energy in the cavity subspace to discuss vibro-polaritonic reaction mechanisms. We present reformulations of CBO-HF and CBO-CC approaches for CRPs and derive second-order approximate CRPs from CBO-PT for unimolecular and bimolecular scenarios. In the unimolecular case, we find small local modifications of molecular potential energy surfaces for selected isomerization reactions dominantly captured by the first-order dipole fluctuation correction. Excellent agreement between CBO-PT and non-perturbative wave function results indicates minor VSC-induced state relaxation effects in the single-molecule limit. In the bimolecular scenario, CBO-PT reveals an explicit coupling of interacting dimers to cavity modes besides cavity-polarization dependent dipole-induced dipole and van der Waals interactions with enhanced long-range character. An illustrative CBO-coupled cluster theory with singles and doubles-based numerical analysis of selected molecular dimer models provides a complementary non-perturbative perspective on cavity-modified intermolecular interactions under VSC.