We present the extension of the quantum/classical polarizable fluctuating charge model to the calculation of single residues of quadratic response functions, as required for the computational modeling of two-photon absorption cross-sections. By virtue of a variational formulation of the quantum/classical polarizable coupling, we are able to exploit an atomic orbital-based quasienergy formalism to derive the additional coupling terms in the response equations. Our formalism can be extended to the calculation of arbitrary order response functions and their residues. The approach has been applied to the challenging problem of one- and two-photon spectra of rhodamine 6G (R6G) in aqueous solution. Solvent effects on one- and two-photon spectra of R6G in aqueous solution have been analyzed by considering three different approaches, from a continuum (QM/PCM) to two QM/MM models (non-polarizable QM/TIP3P and polarizable QM/FQ). Both QM/TIP3P and QM/FQ simulated OPA and TPA spectra show that the inclusion of discrete water solvent molecules is essential to increase the agreement between theory and experiment. QM/FQ has been shown to give the best agreement with experiments.
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