The effect of polarizable environment on two-photon absorption cross sections characterized by the equation-of-motion coupled-cluster singles and doubles method combined with the effective fragment potential approach
Solvent can significantly affect nonlinear optical properties of solvated chromophores. We report an extension of a hybrid polarizable embedding method incorporating solvent effects in the electronic structure calculations of two-photon absorption (2PA) cross sections. The approach uses the equation-of-motion coupled-cluster singles and doubles method for excitation energies (EOM-EE-CCSD) for the quantum region (QM) and the effective fragment potential (EFP) method for the classical region (MM). The impact of the environment on the 2PA cross sections is investigated in microhydrated clusters of para-nitroaniline, thymine, and deprotonated anionic chromophore of photoactive yellow protein (PYPb). The performance of EOM-EE-CCSD/EFP is assessed by comparing the 2PA cross sections against full quantum calculations as well as against non-polarizable QM/MM electrostatic embedding approach. The EOM-EE-CCSD/EFP approach reproduces well the main trends in the 2PA cross sections across different clusters and its performance improves when few water molecules are included in the QM subsystem. For the studied transitions with the strong charge-transfer character, the errors in the 2PA cross sections correlate with the errors in the excitation energies, transition moments, and dipole-moment differences between the initial and final states. Analysis of the 2PA transitions in terms of natural transition orbitals is also reported. The analysis of 2PA transition densities allows us to introduce a a rigorous metric for assessing the domain of applicability of QM/MM methods for 2PA cross sections calculations. Finally, the calculations of 2PA cross section of PYPb in bulk water are used to assess the convergence of the 2PA cross sections with respect to the number of water molecules included in the QM subsystem. Relative to the small QM (chromophore only) calculations, the inclusion of water molecules from the first solvation shell leads to a large change (~22 %) in the calculated 2PA cross section. The convergence of the key properties, such as the excitation energies, transition moments, and dipole-moment differences with the size of the QM subsystem, is investigated using configuration interaction singles method.