  In this study we investigate the nuclear quantum effects (NQEs) on the
acidity constant (pKA) of liquid water isotopologues at the ambient condition
by path integral molecular dynamics (PIMD) simulations. We compared simulations
using a fully explicit solvent model with a classical polarizable force field,
density functional tight binding, and ab initio density functional theory,
which correspond to empirical, semiempirical, and ab initio PIMD simulations,
respectively. The centroid variable with respect to the proton coordination
number of a water molecule was restrained to compute the gradient of the free
energy, which measures the reversible work of the proton abstraction for the
quantum mechanical system. The free energy curve obtained by thermodynamic
integration was used to compute the pKA value based on probabilistic
determination. This technique not only reproduces the pKA value of liquid D2O
experimentally measured (14.86) but also allows for a theoretical prediction of
the pKA values of liquid T2O, aqueous HDO and HTO which are unknown due to its
scarcity. It is also shown that the NQEs on the free energy curve can result in
a downshift of 4.5 +/- 0.9 pKA units in the case of liquid water, which
indicates that the NQEs plays an indispensable role in the absolute
determination of pKA. The results of this study can help to inform further
extensions into the calculation of the acidity constants of isotope substituted
species with high accuracy.
