## Research

**Overview**

My research centres on the use of computational simulations of condensed
matter systems. I use quantum mechanical methods to understand
the properties of materials, molecules and nanostructures - in fact,
anything made of atoms.. ie everything in the world!
I use a set of techniques known as "ab initio" electronic structure.
These are methods which seek to solve the Schrodinger
equation, describing the behaviour of electrons around atoms, without
making any empirical assumptions. By understanding the quantum mechanical
behaviour of complex systems containing large numbers of electrons and
nuclei, we can gain an understanding of their structure, energetics
and dynamics and understand how their properties can be improved for
use in fields as diverse as electronics, light-harvesting, chemical
engineering, nanotechnology and medicine.

**Linear-Scaling DFT**

The main technique I use is Density Functional Theory (DFT). DFT is a
computational technique which makes a set of well-founded approximations
about the way electrons interact with each other and with the nuclei of atoms.
It boils down the complexity of many-body quantum mechanics to a form
in which real problems can be solved on a computer. In most cases the
approximations made turn out to be surprisingly accurate and very good
predictions of the properties of real or putative materials can be made.
Traditional approaches to DFT are capable of describing periodic crystals
and small molecules,
with a high accuracy. However, they involve solving for single-particle
orbitals (solutions of a single-particle Schrodinger equation), which each
span the entire system studied. The computational cost of approaches based
on single-particle orbitals must inevitably scale up as the cube of the
system size for large numbers of atoms. Therefore, they become pretty much
unfeasible with current computational hardware beyond
around 1000 atoms. The code with which I work and actively develop, known
as
ONETEP, is one of a few around the world which take a "Linear-Scaling"
approach to DFT.
Linear-Scaling DFT reformulates the
problem so as to avoid ever calculating any eigenstates, and is therefore
able to scale linearly with system size up to very large numbers of atoms.
Linear-scaling DFT has many applications: anything where reaching large,
realistic system sizes is important: biological physics, nanostructures,
strongly-correlated systems, defects, interfaces and solvation models being
just a few of these. These advances promise to bring the power of
quantum-mechanical simulations to bear on systems of an unprecedented
scale, for use in applications as diverse as the design of new drug
molecules to specifically target particular diseases to the
characterisation of nanomaterials for photovoltaic solar cells.
I collaborate on a number of projects seeking to advance the methodology
of LS-DFT, including projects on TDDFT, EELS, van der Waals, projector
augmented wave methods, and many more!

**Defects in Metal Oxides**

One of my other main interests is defects in crystals, particularly
in metal oxides. With Matthew Foulkes and Mike Finnis, I have investigated
the properties of point defects (particularly vacancies) in aluminium
oxide (Al2O3). We have developed new techniques for extrapolation
to the so-called "dilute limit", of well separated defects,
which is particularly hard to achieve in calculations in a
periodic crystal. We have also investigated the way concentrations of
defects depend on the level of aliovalent doping, and developed a new framework
for the self-consistent calculation of defect concentrations under doping.
With Crispin Barnes and Massimo Barbagallo, I have investigated the properties
of Europium Monoxide. Using DFT+U simulations of EuO with and without oxygen
vacancies, we explained the enhancement of the magnetic moment of EuO under
oxygen deficient conditions - a surprising result which may have implications
for the use of EuO in spintronic devices. With Sam Murphy I have been
investigating the strongly anisotropic defects in Lithium Metatitantate (Li2TiO3)

**Semiconductor Nanocrystals**

I am working on a number of projects in the varied field of semiconductor
nanostructures. One of these is pressure-induced phase transformations
in nanocrystals, on which I supervise Niccolo Corsini in collaboration
with Peter Haynes and Carla Molteni. I have also been involved in a long-running
project to understand the behaviour of polar semiconductor nanorods.
We have carried out large-scale simulations of GaAs nanorod structures
to try to understand the behaviour of
the dipole moment of such systems. The dipole moment is central to the unusual
electrical and optical properties of nanorods, and is influenced by a wide
array of factors, including the intrinsic polarisation of the underlying crystal,
the range of possible shapes and surfaces, the surface termination by ligand
species, and solution in a variety of solvents. Only simulation-based
techniques are able to disaggregate the many factors and provide an understanding
of how we can control and improve the properties of nanorods.

**Quantum Monte Carlo**

During my PhD (supervised by Professor Matthew Foulkes) I worked on Quantum
Monte Carlo methods. These involve direct solution of the Many-Body Schrodinger
equation using statistical methods, in which the outcomes of a large number of
computer "experiments" are averaged to give quantum mechanical expectation values.
I worked on calculations of the surface energy of the electron gas (with Ben
Wood), on the properties of defects in Al2O3, and on the behaviour of polarisation
and localisation in many-body systems.