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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.
Feynman path-integral deep potential molecular dynamics (PI-DPMD) calculations have been employed to study both light (H$_2$O) and heavy water (D$_2$O) within the isothermal-isobaric ensemble. In particular, the deep neural network is trained based o
Molecular Dynamics studies of chemical processes in solution are of great value in a wide spectrum of applications, which range from nano-technology to pharmaceutical chemistry. However, these calculations are affected by severe finite-size effects,
We demonstrate the accuracy and efficiency of a recently introduced approach to account for nuclear quantum effects (NQE) in molecular simulations: the adaptive Quantum Thermal Bath (adQTB). In this method, zero point energy is introduced through a g
Efficient computational methods that are capable of supporting experimental measures obtained at constant values of pH and redox potential are important tools as they serve to, among other things, provide additional atomic level information that cann
Within the framework of Kohn-Sham density functional theory (DFT), the ability to provide good predictions of water properties by employing a strongly constrained and appropriately normed (SCAN) functional has been extensively demonstrated in recent