First hyperpolarizability of water in bulk liquid phase: long-range electrostatic effects included the second hyperpolarizability.

The molecular first hyperpolarizability contributes to second-order optical non-linear signals collected from molecular liquids. For the Second Harmonic Generation (SHG) response, the first hyperpolarizability (2, , ) often depends on the molecular electrostatic environment. This is especially true for water, due to its large second hyperpolarizability (2, , ,0). In this study we compute the electronic (2, , ,0) and (2, , ) for water molecules in liquid water using QM/MM calculations. The average value of (2, , ,0) is smaller than the one for the gaz phase, and its standard deviation among the molecules is relatively small. In addition, we demonstrate that the average bulk second hyperpolarizability 〈(2, , ,0)〉 can be used to describe the electrostatic effects of the distant neighborhood on the first hyperpolarizability (2, , ). In comparison with more complex schemes to take into account long-range effects, the approximation is simple, and does not require any modifications of the QM/MM implementation. The long-range correction can be added explicitly, using an average value of for water in the condensed phase. It can also be easily added implicitly in QM/MM calculations through an additional embedding electric field, without the explicit calculation of .