Nuclear Quantum Effects in Liquid Water: A Highly Accurate \textit{ab initio} Path-Integral Molecular Dynamics Study

In this work, we report highly accurate \textit{ab initio} path-integral molecular dynamics (AI-PIMD) simulations on liquid water at ambient conditions utilizing the recently developed PBE0+vdW(SC) exchange-correlation functional, which accounts for exact exchange and a self-consistent pairwise treatment of van der Waals (vdW) or dispersion interactions, combined with nuclear quantum effects (\textit{via} the colored-noise generalized Langevin equation\footnote{M Ceriotti, DE Manolopoulus Phys. Rev. Lett., \textbf{109}, 100604 (2012).}). The importance of each of these effects in the theoretical prediction of the structure of liquid water will be demonstrated by a detailed comparative analysis of the predicted and experimental oxygen-oxygen (O-O), oxygen-hydrogen (O-H), and hydrogen-hydrogen (H-H) radial distribution functions as well as other structural properties. In addition, we will discuss the theoretically obtained proton momentum distribution, computed using the recently developed Feynman path formulation,\footnote{L Lin, JA Morrone, R Car, M Parrinello Phys. Rev. Lett., \textbf{105}, 110602 (2010).} in light of the experimental deep inelastic neutron scattering (DINS) measurements.