  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.
