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

The molecular first hyperpolarizability β contributes to second-order optical non-linear signals collected from molecular liquids. For the Second Harmonic Generation (SHG) response, the first hyperpolarizability β (2 ω , ω , ω ) often depends on the molecular electrostatic environment. This is especially true for water, due to its large second hyperpolarizability γ (2 ω , ω , ω ,0). In this study we compute the electronic γ (2 ω , ω , ω ,0) and β (2 ω , ω , ω ) for water molecules in liquid water using QM/MM calculations. The average value of γ (2 ω , ω , ω ,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 〈 γ (2 ω , ω , ω ,0)〉 can be used to describe the electrostatic effects of the distant neighborhood on the first hyperpolarizability β (2 ω , ω , ω ). 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 γ 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 γ .