Large-Scale Hybrid Density Functional Theory Calculations in the Condensed-Phase: \textit{Ab Initio} Molecular Dynamics in the Isobaric-Isothermal Ensemble*

Hybrid functionals are known to alleviate the self-interaction error in density functional theory (DFT) and provide a more accurate description of the electronic structure of molecules and materials. However, hybrid DFT in the condensed-phase has a prohibitively high associated computational cost which limits their applicability to large systems of interest. In this work, we present a general-purpose order(N) implementation of hybrid DFT in the condensed-phase using Maximally localized Wannier function; this implementation is optimized for massively parallel computing architectures. This algorithm is used to perform large-scale \emph{ab initio} molecular dynamics simulations of liquid water, ice, and aqueous ionic solutions. We have performed simulations in the isothermal-isobaric ensemble to quantify the effects of exact exchange on the equilibrium density properties of water at different thermodynamic conditions. We find that the anomalous density difference between ice I$h$ and liquid water at ambient conditions as well as the enthalpy differences between ice I$h$, II, and III phases at the experimental triple point (238 K and 20 Kbar) are significantly improved using hybrid DFT over previous estimates using the lower rungs of DFT. [1] X Wu, A Selloni, and R Car, PRB 79, 08510