Strong coupling of molecules to the vacuum field of micro cavities can modify
the potential energy surfaces opening new photophysical and photochemical
reaction pathways. While the influence of laser fields is usually described in
terms of classical field, coupling to the vacuum state of a cavity has to be
described in terms of dressed photon-matter states (polaritons) which require
quantized fields. We present a derivation of the non-adiabatic couplings for
single molecules in the strong coupling regime suitable for the calculation of
the dressed state dynamics. The formalism allows to use quantities readily
accessible from quantum chemistry codes like the adiabatic potential energy
surfaces and dipole moments to carry out wave packet simulations in the dressed
basis. The implications for photochemistry are demonstrated for a set of model
systems representing typical situations found in molecules
