Real-space Hubbard-corrected density functional theory

We present an accurate and efficient framework for real-space Hubbard-corrected density functional theory. In particular, we obtain expressions for the energy, atomic forces, and stress tensor suitable for real-space finite-difference discretization and develop a large-scale parallel implementation. We verify the accuracy of the formalism through comparisons with established plane-wave results. We demonstrate that the implementation is highly efficient and scalable, outperforming established plane-wave codes by more than an order of magnitude in minimum time to solution, with increasing advantages as the system size and/or the number of processors is increased. We apply this framework to examine the impact of exchange-correlation inconsistency in local atomic orbital generation and introduce a scheme for optimizing the Hubbard parameter based on hybrid functionals, both while studying TiO2 polymorphs.