  We present an extension of the standard polarizable quantum
mechanic/molecular mechanics (QM/MM) approach for treating environmental
effects on excited state properties of embedded systems. A quantum polarizable
atom model is derived from a full quantum description of the environment using
perturbation theory for the system-environment coupling. Our model provides a
more general description of the environment, including frequency dependent
atomic polarizabilities, without loss of computational simplicity of the QM/MM
approach. The classical polarizable atom description used in polarizable QM/MM
approach can be obtained as a limiting case of the present model. This enables
us to pinpoint approximations and assumptions about the system inherent to
classical polarizable atom description of the environment. We apply our method
to fluorographene (FG) based systems to investigate effects of the FG sheet on
excited state properties of impurities on the FG surface. Comparison to full
quantum chemistry calculations and to the standard polarizable QM/MM approach
on disordered fluorograhene clusters reveals the importance of frequency
dependence of atomic polarizabilities for the proper treatment of the effects
of the environment on both the transition energy shifts and the interaction
energies.
