# Solvent Fluctuations and Nuclear Quantum Effects Modulate the Molecular Hyperpolarizability of Water

## TL;DR

This study reveals that solvent heterogeneity and quantum effects cause significant variations in water's molecular hyperpolarizability, challenging the assumption of constant hyperpolarizability in SHS experiments and enabling improved modeling.

## Contribution

It demonstrates the environmental dependence of water's hyperpolarizability and introduces a machine learning model to predict its fluctuations, advancing the interpretation of SHS data.

## Key findings

- Solvent heterogeneity causes large hyperpolarizability variations.
- Quantum fluctuations significantly impact water's nonlinear optical response.
- A machine learning model accurately predicts hyperpolarizability fluctuations.

## Abstract

Second-Harmonic Scatteringh (SHS) experiments provide a unique approach to probe non-centrosymmetric environments in aqueous media, from bulk solutions to interfaces, living cells and tissue. A central assumption made in analyzing SHS experiments is that the each molecule scatters light according to a constant molecular hyperpolarizability tensor $\boldsymbol{\beta}^{(2)}$. Here, we investigate the dependence of the molecular hyperpolarizability of water on its environment and internal geometric distortions, in order to test the hypothesis of constant $\boldsymbol{\beta}^{(2)}$. We use quantum chemistry calculations of the hyperpolarizability of a molecule embedded in point-charge environments obtained from simulations of bulk water. We demonstrate that both the heterogeneity of the solvent configurations and the quantum mechanical fluctuations of the molecular geometry introduce large variations in the non-linear optical response of water. This finding has the potential to change the way SHS experiments are interpreted: in particular, isotopic differences between H$_2$O and D$_2$O could explain recent second-harmonic scattering observations. Finally, we show that a simple machine-learning framework can predict accurately the fluctuations of the molecular hyperpolarizability. This model accounts for the microscopic inhomogeneity of the solvent and represents a first step towards quantitative modelling of SHS experiments.