  Within the framework of density functional theory, the inclusion of exact
exchange and non-local van der Waals/dispersion (vdW) interactions is crucial
for predicting a microscopic structure of ambient liquid water that
quantitatively agrees with experiment. In this work, we have used the local
structure index (LSI) order parameter to analyze the local structure in such
highly accurate $ab$ $initio$ liquid water. At ambient conditions, the LSI
probability distribution, P($I$), was unimodal with most water molecules
characterized by more disordered high-density-like local environments. With
thermal excitations removed, the resultant bimodal P($I$) in the inherent
potential energy surface (IPES) exhibited a 3:1 ratio between high- and
low-density-like molecules, with the latter forming small connected clusters
amid the predominant population. By considering the spatial correlations and
hydrogen bond network topologies $among$ water molecules with the same LSI
identities, we demonstrate that the signatures of the experimentally observed
low- (LDA) and high-density (HDA) amorphous phases of ice are present in the
IPES of ambient liquid water. Analysis of the LSI autocorrelation function
uncovered a persistence time of $\sim$ 4 ps---a finding consistent with the
fact that natural thermal fluctuations are responsible for transitions between
these distinct yet transient local aqueous environments in ambient liquid
water.
