Energy densities: a systematic approach to correlation in density functional theory

Abstract

Density functional theory (DFT) has grown to become by far the most widely applied method in the modelling of electronic systems yet, in contrast to wavefunction-based ab initio methods, the reliability of a DFT calculation can be uncertain. This is because the essential ingredient required for a DFT calculation to be meaningful - the exchange & correlation energy functionals, are approximations for a type of electronic interaction with an unknown functional form. Whilst there exist types of system for which DFT does not provide a useful model - those with significant dispersion interactions and those with near-degenerate states, seeking improvements to DFT in these areas can be far from straightforward since the exchange & correlation functionals cannot be systematically improved. In this work, a mathematically rigorous description of DFT is combined with some of the most reliable & accurate ab initio electronic structure methods in a bespoke development code to obtain a detailed picture of how the exact correlation energy functional in DFT behaves. Using these insights, new approaches are investigated for modelling the correlation energy functional in local form, allowing a systematic study of how best to approximate the correlation energy functional in different types of system to be pursued. As an adjunct to this, the present work looks ahead at how to extend & generalise this investigation by considering the behaviour of systems in the presence of a magnetic field. Efficient algorithms are developed and implemented to facilitate this, enabling the advancement of this strand of investigation in subsequent work