Performance and accuracy of recursive subspace bisection for hybrid DFT calculations in inhomogeneous systems

The high cost of computing the Hartree-Fock exchange energy has resulted in a limited use of hybrid density functionals in solid-state and condensed phase calculations. Approximate methods based on the use of localized orbitals have been proposed as a way to reduce this computational cost. In particular, Boys orbitals (or maximally localized Wannier functions in solids) were recently used in plane wave, first-principles molecular dynamics simulations of water. Recently, the recursive subspace bisection (RSB) method was used to compute orbitals localized in regular rectangular domains of varying shape and size, leading to efficient calculations of the Hartree-Fock exchange energy in the plane-wave, pseudopotential framework. In this paper, we use the RSB decomposition to analyze orbital localization properties in inhomogeneous systems (e.g., solid/liquid interfaces) in which localized orbitals have widely varying extent. This analysis reveals that some orbitals cannot be significantly localized and thus cannot be truncated without incurring a substantial error in computed physical properties, while other orbitals can be well localized to small domains. We take advantage of the ability to systematically reduce the error in RSB calculations through a single parameter to study the effect of orbital truncation. We present the errors in PBE0 ground state energies, ionic forces, band gaps, and relative energy differences between configurations for a variety of systems, including a tungsten oxide/water interface, a silicon/water interface, liquid water, and bulk molybdenum. We show that the RSB approach can adapt to such diverse configurations by localizing orbitals in different domains while preserving a 2-norm upper bound on the truncation error. The resulting approach allows for efficient hybrid DFT simulations of inhomogeneous systems in which the localization properties of orbitals vary during the course of the simulation.