  In this work, we report the results of a series of density functional theory
(DFT) based ab initio molecular dynamics (AIMD) simulations of ambient liquid
water using a hierarchy of exchange-correlation (XC) functionals to investigate
the individual and collective effects of exact exchange (Exx), via the PBE0
hybrid functional, non-local vdW/dispersion interactions, via a fully
self-consistent density-dependent dispersion correction, and approximate
nuclear quantum effects (aNQE), via a 30 K increase in the simulation
temperature, on the microscopic structure of liquid water. Based on these AIMD
simulations, we found that the collective inclusion of Exx, vdW, and aNQE as
resulting from a large-scale AIMD simulation of (H$_2$O)$_{128}$ at the
PBE0+vdW level of theory, significantly softens the structure of ambient liquid
water and yields an oxygen-oxygen structure factor, $S_{\rm OO}(Q)$, and
corresponding oxygen-oxygen radial distribution function, $g_{\rm OO}(r)$, that
are now in quantitative agreement with the best available experimental data.
This level of agreement between simulation and experiment as demonstrated
herein originates from an increase in the relative population of water
molecules in the interstitial region between the first and second coordination
shells, a collective reorganization in the liquid phase which is facilitated by
a weakening of the hydrogen bond strength by the use of the PBE0 hybrid XC
functional, coupled with a relative stabilization of the resultant disordered
liquid water configurations by the inclusion of non-local vdW/dispersion
interactions.
