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My Research: FirstPrinciples Calculations of Material PropertiesElectronicstructure calculation and quantum Monte Carlo simulationMost properties of solids and molecules are determined by the behaviour of the electrons that bind their atoms together. The ability to make quantitative predictions about this behaviour is therefore of great importance in a wide range of sciences, from solidstate physics to biochemistry. However, calculating the distribution and energies of electrons in materials—the electronic structure—is a nontrivial problem because of the need to simulate large numbers of strongly interacting particles.Quantum Monte Carlo (QMC) methods enable the calculation of the electronic structures of solids and molecules with unrivalled accuracy. The methods are stochastic, generating random sets of electron coordinates with the appropriate distribution. Useful quantities, such as energies, are recovered from these data using statistical methods. All my QMC calculations are carried out using the CASINO code, of which I am one of the authors.
Binding and optoelectronic properties of twodimensional materialsTwodimensional (2D) materials such as graphene, silicene, hexagonal boron nitride and transitionmetal dichalcogenides (MoS_{2}, MoSe_{2}, MoTe_{2}, NbSe_{2}, TaS_{2}, WS_{2}, WSe_{2}, WTe_{2}, …) are currently of enormous interest in physics, chemistry and materials science. 2D materials are potentially of great technological importance due to their extreme and unusual electronic, optical and mechanical properties. In collaboration with Marcin Szyniszewski, Ryan Hunt, Elaheh Mostaani, Viktor Zólyomi and Vladimir Fal'ko, I am using QMC and density functional theory methods to calculate and explore many different aspects of these materials. In particular I am investigating the nature and strength of the van der Waals attraction between 2D materials, to understand how they interact with each other, and how they stack to form layered heterostructures. I am also studying excitons, trions and biexcitons (complexes of charge carriers, resembling 2D hydrogen atoms, H^{−} ions and H_{2} molecules), which play a key role in the optical properties of semiconducting transitionmetal dichalcogenides. Lastly I am interested in the mechanical properties and electronic structure of novel 2D materials such as indium and gallium chalcogenides (InS, InSe, InTe, GaS, GaSe and GaTe).Molecular hydrogen at high pressureHydrogen makes up about three quarters of the observed mass in the universe. Hydrogen has been studied extensively, yet there are many unanswered basic questions about its phase diagram. Establishing the atomic structure of highpressure phases of hydrogen is challenging because hydrogen only scatters Xrays weakly, and the energy differences between competing structures are tiny. In collaboration with Jonathan LloydWilliams, Bartomeu Monserrat, Pablo López Ríos, Chris Pickard and Richard Needs of Cambridge University I am using QMC methods to determine the atomic structures of Phases II, III and IV of solid hydrogen at pressures of up to 400 GPa. This work involves use of Oak Ridge Leadership Computing Facility's computer Titan.Behaviour of positrons immersed in electron gasesI have used both density functional theory (DFT) and QMC methods to calculate the behaviour of positrons immersed in electron gases. In particular, I have calculated the immersion energy, annihilation rate and momentum density of the annihilation radiation as a function of the density of the electron gas. These data will facilitate the interpretation of the results of positron annihilation experiments, in which positrons are injected into metals or semiconductors in order to learn about the type and concentration of defects that are present in the sample.van der Waals interactions between thin metallic wires and layersI have used QMC to calculate the van der Waals interaction between pairs of thin, metallic wires and layers, modelled by 1D and 2D homogeneous electron gases. Surprisingly, the form of interaction between 1D conductors assumed in many current models of carbon nanotubes (for example, those that use LennardJones potentials between pairs of atoms) can be shown to be qualitatively wrong.Optical and chemical properties of hydrogenterminated carbon nanoparticles
Hydrogenterminated carbon nanoparticles—diamondoids—are expected to have several technologically useful optoelectronic properties. The optical gap of diamond is in the UV range, and quantum confinement effects are expected to raise diamondoid optical gaps to even higher energies, enabling a unique set of sensing applications. Furthermore, it has been demonstrated that some hydrogenterminated diamond surfaces exhibit negative electron affinities, suggesting that diamondoids could also have this property. This would open up the possibility of coating surfaces with diamondoids to produce new lowvoltage electronemission devices. Measuring the optical gaps of diamondoids has proved to be challenging, due to the difficulty in isolating and characterising particular molecules. I have carried out QMC calculations designed to resolve experimental and theoretical controversies over the optoelectronic properties of diamondoids. My QMC results show that quantum confinement effects disappear in diamondoids larger than one nanometre in diameter, which actually turn out to have gaps below that of bulk diamond. This differs from the behaviour found in silicon or germanium nanoparticles, and is caused by the diffuse nature of the lowest unoccupied molecular orbital in diamondoids. In addition, the QMC calculations predict a negative electron affinity for diamondoids of up to one nanometre in diameter, again resulting from the delocalised nature of the lowest unoccupied molecular orbital. Equation of state of solid neonvan der Waals forces are of fundamental importance in a wide range of chemical and biological processes, including many that are now being investigated using firstprinciples electronicstructure methods. I have compared the accuracy with which different electronicstructure methods describe van der Waals bonding by studying solid neon, which is bound together by van der Waals forces, and is therefore an ideal test system for carrying out such a comparison.I have used the DFT and QMC methods to calculate the zerotemperature equation of state (the relationship between pressure and density) for solid neon. The DFT equation of state depends strongly on the choice of exchange–correlation functional, whereas the QMC equation of state is very close to the experimental results. This implies that, unlike DFT, QMC is able to give an accurate treatment of van der Waals bonding in real materials. Wigner crystallisation of the homogeneous electron gasI have used QMC to study the low density behaviour of the homogeneous electron gas. This system consists of a set of electrons moving in a uniform, neutralising, positively charged background. It serves as a model for the behaviour of the free electrons in a metal or semiconductor, and is also of fundamental interest as the simplest fully interacting quantum manybody system. The electron gas exists in a fluid phase at high density, but crystallises at low density, as was first pointed out by Wigner in the 1930s. I have calculated the density at which the homogeneous electron gas crystallises.
Theoretical and technical developments to the QMC algorithms
Studies of minerals in the Earth's lower mantle

Postgraduate Research OpportunitiesFunded PhD positions in condensed matter theory at Lancaster University are available for UK and EU nationals via the Graphene NOWNANO centre for doctoral training. Good computer programming skills are very desirable.Research projects range from making technical developments to the QMC algorithms to performing firstprinciples studies of twodimensional materials using both QMC and density functional theory methods. Information about the formal procedure for applying for postgraduate study can be found on Lancaster University's postgraduate study webpages. For informal enquiries, please email me. 
TeachingI teach the following course at the Graphene NOWNANO centre for doctoral training (Universities of Lancaster and Manchester):

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