# Fully Polarizable QM/Fluctuating Charge Approach to Two-Photon Absorption of Aqueous Solutions

## TL;DR

This paper extends a polarizable fluctuating charge model to compute two-photon absorption spectra, demonstrating its effectiveness in accurately modeling aqueous rhodamine 6G solutions and highlighting the importance of explicit solvent effects.

## Contribution

The paper introduces a variational formalism for quantum/classical polarizable coupling to calculate quadratic response functions, applicable to two-photon absorption spectra in solution.

## Key findings

- QM/FQ model best matches experimental spectra
- Explicit solvent modeling improves spectral accuracy
- Inclusion of water molecules is essential for realistic results

## Abstract

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.