  Experimental studies indicate that optical cavities can affect chemical
reactions, through either vibrational or electronic strong coupling and the
quantized cavity modes. However, the current understanding of the interplay
between molecules and confined light modes is incomplete. Accurate theoretical
models, that take into account inter-molecular interactions to describe
ensembles, are therefore essential to understand the mechanisms governing
polaritonic chemistry. We present an ab-initio Hartree-Fock ansatz in the
framework of the cavity Born-Oppenheimer approximation and study molecules
strongly interacting with an optical cavity. This ansatz provides a
non-perturbative, self-consistent description of strongly coupled molecular
ensembles taking into account the cavity-mediated dipole self-energy
contributions. To demonstrate the capability of the cavity Born-Oppenheimer
Hartree-Fock ansatz, we study the collective effects in ensembles of strongly
coupled diatomic hydrogen fluoride molecules. Our results highlight the
importance of the cavity-mediated inter-molecular dipole-dipole interactions,
which lead to energetic changes of individual molecules in the coupled
ensemble.
