Approximating Hartree–Fock Theory via an Efficiently Local Reformulation

Abstract We explore a reorganized framework for the Hartree–Fock equations that allows varying patterns of locality to be imposed on the molecular orbitals while maintaining a highly efficient self-consistent field optimization algorithm. Rather than limiting orbitals’ spread and then variationally minimizing the energy within those limits, our reorganization neatly pairs each local degree of freedom with a specific solution condition that itself has a naturally local interpretation. These pairs can each be turned on or off, and, regardless of the sparsity pattern used to make such choices, the overall method maintains a fast self-consistent field optimization. We use this structure to test reaction-matched schemes for imposing orbital locality and, through Fock builds that exploit this locality, achieve competitive timings even in modestly sized molecules. Our initial tests also suggest that this approach to imposed orbital locality can be arranged so as to do minimal damage to both Hartree–Fock and MP2 reaction energy predictions.