  We introduce an electron-photon exchange-correlation functional for quantum
electrodynamical density-functional theory (QEDFT). The approach, photon MBD
(pMBD), is inspired by the many-body dispersion (MBD) method for weak
intermolecular interactions, which is generalized to include both electronic
and photonic (electromagnetic) degrees of freedom on the same footing. We
demonstrate that pMBD accurately captures effects that arise in the context of
strong light-matter interactions, such as anisotropic electron-photon
interactions, beyond single-photon effects, and cavity modulated van der Waals
interactions. Moreover, we show that pMBD is computationally efficient and
allows simulations of large complex systems coupled to optical cavities.
