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Electronic-structure 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 solid-state physics to biochemistry. However, calculating the distribution 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 and energies 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 extracted 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 two-dimensional materials
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 high-pressure phases of hydrogen is challenging because hydrogen only scatters X-rays weakly, and the energy differences between competing structures are tiny. In collaboration with Jonathan Lloyd-Williams, Bartomeu Monserrat, Pablo López Ríos, Chris Pickard and Richard Needs of Cambridge University I am using QMC methods to determine the atomic structure 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 Lennard-Jones potentials between pairs of atoms) can be shown to be qualitatively wrong.
Optical and chemical properties of hydrogen-terminated carbon nanoparticles
Hydrogen-terminated 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 hydrogen-terminated 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 low-voltage electron-emission 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 first-principles electronic-structure methods. I have compared the accuracy with which different electronic-structure 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 zero-temperature 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 gas
Theoretical and technical developments to the QMC algorithms
Studies of minerals in the Earth's lower mantle
NOWNANO centre for doctoral training. Good computer programming skills
are very desirable.
Possible research projects range from making technical developments to the QMC algorithms to performing first-principles studies of two-dimensional 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.
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