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

摘要

Second-Harmonic Scatteringh (SHS) experiments provide a unique approach toprobe non-centrosymmetric environments in aqueous media, from bulk solutions tointerfaces, living cells and tissue. A central assumption made in analyzing SHSexperiments is that the each molecule scatters light according to a constantmolecular hyperpolarizability tensor $\boldsymbol{\beta}^{(2)}$. Here, weinvestigate the dependence of the molecular hyperpolarizability of water on itsenvironment and internal geometric distortions, in order to test the hypothesisof constant $\boldsymbol{\beta}^{(2)}$. We use quantum chemistry calculationsof the hyperpolarizability of a molecule embedded in point-charge environmentsobtained from simulations of bulk water. We demonstrate that both theheterogeneity of the solvent configurations and the quantum mechanicalfluctuations of the molecular geometry introduce large variations in thenon-linear optical response of water. This finding has the potential to changethe way SHS experiments are interpreted: in particular, isotopic differencesbetween H$_2$O and D$_2$O could explain recent second-harmonic scatteringobservations. Finally, we show that a simple machine-learning framework canpredict accurately the fluctuations of the molecular hyperpolarizability. Thismodel accounts for the microscopic inhomogeneity of the solvent and representsa first step towards quantitative modelling of SHS experiments.