• multiscale modeling
• density functional theory
• quasi energy

It has been amply shown experimentally that the Raman scattering intensity of a molecule can be strongly enhanced up to a factor of 10^10 − 10^15 if the
system is absorbed on a metal nanoparticle (usually silver or gold). This phenomenon gives rise to the Surface-Enhanced Raman Scattering and Surface-Enhanced Resonance Raman Scattering spectroscopies. SERS in particular has completely revolutionized the field of molecular spectroscopy, giving birth to new and powerful techniques of molecular investigation. An effective theoretical model able to treat the peculiarity of a complex system made of a molecule adsorbed on a nanoparticle, both affected by an external radiation, needs to take into account all possible interactions between the different players.
In this thesis we focus on the Corni-Tomasi (CT) model, which up to date it has been coupled with a QM treatment of an abdsorbed molecule which is treated at the Time-Dependent Hartree-Fock (TDHF). We have reformulated the CT model in the quasi-energy formalism: this allowed us to couple the CT model with a DFT Hamiltonian, and, by exploiting the properties of the response theory, the calculation of electric response functions.