We present theory and implementation of an advanced quantum mechanics/molecular mechanics (QM/MM) approach using a fully self-consistent polarizable embedding (PE) scheme. It is a polarizable layered model designed for effective yet accurate inclusion of an anisotropic medium in a quantum mechanical calculation. The polarizable embedding potential is described by an atomistic representation including terms up to localized octupoles and anisotropic polarizabilities. It is generally applicable to any quantum chemical description but is here implemented for the case of Kohn-Sham density functional theory which we denote the PE-DFT method. It has been implemented in combination with time-dependent quantum mechanical linear and nonlinear response techniques, thus allowing for assessment of electronic excitation processes and dynamic ground-and excited-state molecular properties using a nonequilibrium formulation of the environmental response. In our formulation of polarizable embedding we explicitly take into account the full self-consistent many-body environmental response from both ground and excited states. The PE-DFT method can be applied to any molecular system, e.g., proteins, nanoparticles and solute-solvent systems. Here, we present numerical examples of solvent shifts and excited-state properties related to a set of organic molecules in aqueous solution.

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