Development of more accurate computational methods within linear-scaling density functional theory

Abstract

Kohn-Sham Density Functional Theory (DFT) provides a method for electronic structure calculations applicable to a wide variety of systems. Traditional implementations of DFT are cubic-scaling which limits the size of the systems that can be studied. However recently developed linear-scaling methods, such as onetep, are available which allow much larger systems to be considered. Regardless of scaling DFT has limitations as the exact exchange-correlation functional (a key term in the Kohn-Sham equations) is not known and so approximations have to be made. These approximate functionals generally describe dispersion interactions poorly. In this thesis empirical corrections for dispersion have been developed with parameters optimised for a large set of dispersion bound complexes for the onetep code. This provides a much improved description of dispersion forces which are especially important for biological systems. There is a hierarchy of exchange-correlation functionals available the most accurate of which include a portion of Hartree-Fock exchange. Methods for calculating Hartree- Fock exchange energy in onetep have been developed and are described in this thesis. A quadratic-scaling method using Fourier transforms has been implemented as a benchmark for other implementations. Hartree-Fock exchange may be calculated in a linear-scaling manner by using a numerical pointwise or auxiliary basis set method. Spherical waves have been used as an auxiliary basis set. Linear-scaling has been demonstrated for a polythene chain for these methods. Several hybrid functionals have also been implemented in onetep. These have been validated by comparison with a Gaussian basis set approach in calculations on the reaction paths of an organometallic system

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Identifiers

ORCID for Chris-Kriton Skylaris: orcid.org/0000-0003-0258-3433

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