Chemical and photochemical reactivity, as well as supramolecular organization
and several other molecular properties, can be modified by strong interactions
between light and matter. Theoretical studies of these phenomena require the
separation of the Schr\"odinger equation into different degrees of freedom as
in the Born-Oppenheimer approximation. In this paper, we analyze the
electron-photon Hamiltonian within the cavity Born-Oppenheimer approximation
(CBOA), where the electronic problem is solved for fixed nuclear positions and
photonic parameters. Specifically, we focus on intermolecular interactions in
representative dimer complexes. The CBOA potential energy surfaces are compared
with those obtained using a polaritonic approach, where the photonic and
electronic degrees of freedom are treated at the same level. This allows us to
assess the role of electron-photon correlation and the accuracy of CBOA.Comment: 9 pages, 8 figure