Towards a non-local density functiona description of exchange and correlation

Abstract

Kohn-Sham density functional theory (DFT) is a popular method used to investigate the properties of matter. Although exact in principle, DFT is in practice limited by a single approximation for the exchange-correlation functional - the quantity that describes the many-body interactions between electrons. This thesis is concerned with developing improved exchange-correlation functionals for use in practical DFT calculations. The standard functional currently used in solid state physics, and also popular in quantum chemistry, is the generalised gradient approximation (GGA), which requires only the local density, n(r), and the density gradient, ∆n(r), as input. A flexible semi-empirical GGA form, containing 15 free parameters that are fitted to near-exact molecular data is implemented within the plane-wave pseudopotential (PW-PP) Kohn-Sham scheme, to assess the possibility of employing semi-empirical GGAs in solid state applications. Self-consistent calculations performed for several bulk semiconductor properties using this GGA reveal that, overall, no improvement is attained over a conventional non-empirical GGA used in solid state physics. The remainder of the thesis focuses on a fully non-local functional known as the weighted density approximation (WDA), which utilises the global density of a system, n(r'), as input. An efficient computational algorithm is devised for use within the PW-PP formalism which enables fully self-consistent WDA calculations to be performed. Physical properties are shown to be intimately related to the particular form used for the pair-correlation function, Gwda/xc(r,r'), and by comparing with recent variational Monte Carlo (VMC) data, it is shown that the forms that provide a good description of exchange-correlation holes, nxc(r,r'), also lead to the most accurate bulk properties. For strongly inhomogeneous electron gas systems, the WDA provides close agreement with the VMC method for a variety of exchange-correlation quantities. The success of the fully non-local approach given by the WDA for other model electron gas systems studied suggests that the WDA is a very promising functional.