Towards large-scale accurate Kohn-Sham DFT for the cost of tight-binding

Abstract

Density functional theory (DFT) is a widely used ab initio quantum mechanical method to study the properties of materials. Over the past 20 years a huge amount of work has been done developing codes that are able to tackle calculations containing large numbers of atoms. AIMPRO, a DFT code which uses Gaussian type orbitals (GTO) as a basis set, uses a filtration methodology which makes calculations with a few thousand atoms routinely possible on desktop machines. Previous implementations of filtration have focused on the time saving aspect of the methodology and performed calculations on structures containing only atoms from a small subset of the periodic table. In this thesis a novel basis set generation routine is presented and the filtration methodology is modified and expanded to include most of the atoms in the periodic table. The focus of this work lies in demonstrating the potential gains in accuracy, in addition to efficiency, available through use of the filtration algorithm and shows that results comparable to codes using systematic basis set can be achieved for each of the elements considered across the periodic table. Two huge advantages present themselves using this scheme; firstly, the time to solution is essentially decoupled from the basis size; secondly, basis sets that would be unstable in a conventional calculation can be used allowing for more accurate calculations. The work presented here is assessed using a recently developed benchmark, the ∆-test. This, together with the increases in speed previously demonstrated, shows that a filtered basis calculation can now achieve the accuracy of a plane wave calculation at the asymptotic cost, with respect to system size, of a tight-binding calculation, enabling Kohn-Sham calculations of unprecedented size to be performed at the basis set limit