# Isotope Effects in Liquid Water via Deep Potential Molecular Dynamics

## TL;DR

This study combines advanced quantum mechanical simulations, path-integral methods, and machine learning to accurately predict isotope effects on the structure of liquid water, addressing a key challenge in ab initio modeling.

## Contribution

It introduces a novel framework integrating deep potential molecular dynamics with path-integral techniques for detailed isotope effect predictions in water.

## Key findings

- Semi-quantitative agreement with experimental isotope effects
- Effective sampling of thermal and nuclear quantum fluctuations
- Accurate structural property predictions for H2O and D2O

## Abstract

A comprehensive microscopic understanding of ambient liquid water is a major challenge for $ab$ $initio$ simulations as it simultaneously requires an accurate quantum mechanical description of the underlying potential energy surface (PES) as well as extensive sampling of configuration space. Due to the presence of light atoms (e.g., H or D), nuclear quantum fluctuations lead to observable changes in the structural properties of liquid water (e.g., isotope effects), and therefore provide yet another challenge for $ab$ $initio$ approaches. In this work, we demonstrate that the combination of dispersion-inclusive hybrid density functional theory (DFT), the Feynman discretized path-integral (PI) approach, and machine learning (ML) constitutes a versatile $ab$ $initio$ based framework that enables extensive sampling of both thermal and nuclear quantum fluctuations on a quite accurate underlying PES. In particular, we employ the recently developed deep potential molecular dynamics (DPMD) model---a neural-network representation of the $ab$ $initio$ PES---in conjunction with a PI approach based on the generalized Langevin equation (PIGLET) to investigate how isotope effects influence the structural properties of ambient liquid H$_2$O and D$_2$O. Through a detailed analysis of the interference differential cross sections as well as several radial and angular distribution functions, we demonstrate that this approach can furnish a semi-quantitative prediction of these subtle isotope effects.