We survey the underlying theory behind the large-scale and linear scaling DFT code, Conquest, which shows excellent parallel scaling and can be applied to thousands of atoms with diagonalisation, and millions of atoms with linear scaling. We give details of the representation of the density matrix and the approach to finding the electronic ground state, and discuss the implementation of molecular dynamics with linear scaling. We give an overview of the performance of the code, focussing in particular on the parallel scaling, and provide examples of recent developments and applications.

Given the widespread use of density functional theory (DFT), there is an increasing need for the ability to model large systems (beyond 1,000 atoms). We present a brief overview of the large-scale DFT code Conquest, which is capable of modelling such large systems, and discuss approaches to the generation of consistent, well-converged pseudo-atomic basis sets which will allow such large scale calculations. We present tests of these basis sets for a variety of materials, comparing to fully converged plane wave results using the same pseudopotentials and grids.

Core-shell nanowires made of Si and Ge can be grown experimentally with excellent control for different sizes of both core and shell. We have studied the structural properties of Si/ Ge and Ge/Si core-shell nanowires aligned along the [1 1 0] direction, with diameters up to 10.2 nm and varying core to shell ratios, using linear scaling density functional theory. We show that Vegard's law, which is often used to predict the axial lattice constant, can lead to an error of up to 1%, underlining the need for a detailed ab initio atomistic treatment of the nanowire structure. We analyse the character of the intrinsic strain distribution and show that, regardless of the composition or bond direction, the Si core or shell always expands. In contrast, the strain patterns in the Ge shell or core are highly sensitive to the location, composition and bond direction. The highest strains are found at heterojunction interfaces and the surfaces of the nanowires. This detailed understanding of the atomistic structure and strain paves the way for studies of the electronic properties of core-shell nanowires and investigations of doping and structure defects.