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

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(2ω, ω, ω) often depends on the molecular electrostatic environment. This is especially true for water, due to its large second hyperpolarizability γ(2ω, ω, ω,0). In this study we compute the electronic γ(2ω, ω, ω,0) and β(2ω, ω, ω) for water molecules in liquid water using QM/MM calculations. The average value of γ(2ω, 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(2ω, ω, ω,0)〉 can be used to describe the electrostatic effects of the distant neighborhood on the first hyperpolarizability β(2ω, 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.