Nuclear quantum effects on autoionization of water isotopologs studied by ab initio path integral molecular dynamics

In this study, we investigate the nuclear quantum effects (NQEs) on the acidity constant (pK_A) of liquid water isotopologs under 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 pK_A value based on probabilistic determination. This technique not only reproduces the pK_A value of liquid D₂O experimentally measured (14.86) but also allows for a theoretical prediction of the pK_A values of liquid T₂O and aqueous HDO and HTO, which are unknown due to their scarcity. It is also shown that the NQEs on the free energy curve can result in a downshift of 4.5 ± 0.9 pK_A units in the case of liquid water, which indicates that the NQEs plays an indispensable role in the absolute determination of pK_A. The results of this study can help inform further extensions into the calculation of the acidity constants of isotope substituted species with high accuracy.