Formation and relaxation of excited states in solution: a new time dependent Polarizable Continuum Model based on Time-Dependent Density Functional theory

In this paper a novel approach to study the formation and relaxation of excited states in solution is presented within the integral equation formalism version of the polarizable continuum model. Such an approach uses the excited state relaxed density matrix to correct the time dependent density functional theory excitation energies and it introduces a state-specific solvent response, which can be further generalized within a time dependent formalism. This generalization is based on the use of a complex dielectric permittivity as a function of the frequency, ˆ. The approach is here presented in its theoretical formulation and applied to the various steps involved in the formation and relaxation of electronic excited states in solvated molecules. In particular, vertical excitations and emissions, as well as time dependent Stokes shift and complete relaxation from vertical excited states back to ground state, can be obtained as different applications of the same theory. Numerical results on two molecular systems are reported to better illustrate the features of the model.