First hyperpolarizability of water in bulk liquid phase: long-range electrostatic effects included <i>via</i> the second hyperpolarizability

Abstract

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