  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 complementary nonresonant electron-cavity
mode-interactions in the cavity Born-Oppenheimer (CBO) approximation. We focus
on 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) [Fischer, Saalfrank, JCTC 19, 7215 (2023)]
with non-perturbative CBO Hartree-Fock and coupled cluster theories. Wave
function approaches are reformulated to self-consistently address a cavity
reaction potential (CRP), which minimizes the electronic energy in the cavity
subspace. We derive up to second-order CBO-PT corrections of intra- and
intermolecular energies revealing non-trivial corrections to dipole-dipole,
dipole-induced-dipole and van-der-Waals interactions, and provide analytical
second-order CRP for unimolecular and interacting bimolecular scenarios. In the
unimolecular case, we find small local modifications of molecular PES for
selected isomerization reactions dominantly captured by the first-order dipole
fluctuation. Excellent agreement between CBO-PT and non-perturbative wave
function results is obtained indicating 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-CCSD-based
numerical analysis of selected molecular dimer models provides a complementary
non-perturbative perspective on cavity-modified intermolecular interactions
under VSC.
