Neil Drummond's Home Page

Neil Drummond

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... to my website. My email address is "n.drummond", followed by "@", followed by "lancaster.ac.uk".

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My Research: First-Principles Calculations of Material Properties

Electronic-structure calculation and quantum Monte Carlo simulation

Most 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.

Here are some of the projects I am working on / have worked on:

Binding energies and other properties of two-dimensional materials

I am currently using QMC methods to calculate the binding energy of two or more layers of boron nitride. Similar calculations will be performed for graphene (a two-dimensional carbon crystal that was the subject of the 2010 Nobel Prize in Physics). These materials are of great potential technological importance and are the subject of much experimental and theoretical research. However, producing monodisperse samples of graphene and graphene-related materials with a particular number of layers in a reliable fashion is a challenging problem that must be overcome if these materials are to achieve their full potential in nanoelectronic applications. It would clearly be desirable to model the distribution of layer thickness produced under different experimental conditions. For this to be possible, however, accurate values for the binding energies of different numbers of layers are required: hence the need for QMC calculations. This work is being carried out in collaboration with Elaheh Mostaani, Viktor Zólyomi and Vladimir Fal'ko. Layer binding
Silicene
Silicene, the silicon analogue of graphene (image created by John Wallbank). 		Other topics for study include calculating the electronic band structures of two-dimensional materials such as boron nitride and transition-metal dichalcogenides using QMC.

Behaviour of positrons immersed in electron gases

I 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 layers

I 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

C29H36 HOMO C29H36 LUMO
Highest occupied (left) and lowest unoccupied (right) molecular orbitals of the diamondoid C29H36.

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 neon

Van 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

I 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 many-body 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. 2D Wigner crystal
Charge density of a 2D Wigner crystal with a defect, generated by John Trail.
Reciprocal lattice points in a finite 2D homogeneous electron gas
Shells of plane-wave orbitals in a 2D homogeneous electron gas. Filled circles indicate orbitals that are occupied in the ground state; unfilled circles indicate orbitals that are unoccupied in the ground state.		I have also used QMC methods to calculate the quasiparticle effective mass of the 2D homogeneous electron gas, which is a model for the charge carriers in a layered semiconductor. The effective mass is the most important parameter in a phenomenological theory of the properties of interacting electron gases called Fermi liquid theory, but its behaviour at low density was poorly understood. I am currently extending my calculations to evaluate Fermi liquid parameters describing the interaction between quasiparticles.

Theoretical and technical developments to the QMC algorithms

  • I have worked on the development of methods for obtaining the energy per particle in an infinite crystal from QMC calculations of the energy per particle in a small simulation cell subject to periodic boundary conditions.
  • I have worked on the development of new forms of trial many-electron wave function.
  • I have developed a rapid and reliable method for optimising the most important class of parameters in QMC trial wave functions by minimising the unreweighted variance of the local energy.
  • I am one of the authors of the QMC code CASINO.

Studies of minerals in the Earth's lower mantle

In the absence of experimental data, computer simulation can be used to establish the properties of materials. I have studied the mineral magnesium oxide, which is found in the Earth's lower mantle, using density-functional theory. I used the quasiharmonic method to determine the equation of state (the relationship between pressure, density and temperature) of magnesium oxide. I have also calculated phonon dispersion curves (relationships between the frequencies of lattice vibrations, their wavelengths and direction). These data are of interest to geophysicists trying to understand the structure and composition of the Earth's interior. This project was carried out at Edinburgh University, where my supervisor was Graeme Ackland. Further work using my data has been carried out by Damian Swift and colleagues at Los Alamos National Laboratory. MgO dispersion curve
Phonon dispersion curve of MgO. Solid lines: theoretical results; black dots: results of neutron-scattering experiments.

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Postgraduate Research Opportunities

Applications for postgraduate study in my group are welcome from applicants with their own source of funding (although this may not be necessary, especially for UK or EU applicants). From time to time, fully funded studentships may become available. 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 application procedure can be found on Lancaster University's postgraduate study webpages. For informal enquiries, please email me.

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Teaching

I teach the following courses at Lancaster University:
  • Phys135: Optics and Optical Instruments (lecture component)
  • Phys371: Short-Project (Theoretical)
  • Phys482: Quantum Transport in Low-Dimensional Nanostructures
I teach the following course at the NoWNano doctoral training centre (Universities of Lancaster and Manchester):
  • Solid State Physics
At Cambridge University I gave a course of graduate lectures in solid state physics at the Cavendish Laboratory and I used to be a supervisor for the NST1A Maths for Natural Sciences course.

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Useful Links

University links

Journal links

Computer-related links

Search engines

Online newspapers, etc.

Miscellaneous links

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List of Publications

  1. B. Monserrat, N. D. Drummond and R. J. Needs, Anharmonic vibrational properties in periodic systems: energy, electron-phonon coupling, and stress, submitted to Phys. Rev. B (2013).
  2. V. Zólyomi, N. D. Drummond and V. I. Fal'ko, Band structure and optical transitions in atomic layers of hexagonal gallium chalcogenides, submitted to Phys. Rev. Lett. (2013). Preprint: arXiv:1302.6067. [Download]
  3. N. D. Drummond and R. J. Needs, Quantum Monte Carlo calculation of the Fermi liquid parameters of the two-dimensional homogeneous electron gas, submitted to Phys. Rev. B (2013).
  4. W. W. Tipton, N. D. Drummond and R. G. Hennig, Importance of high angular-momentum channels in pseudopotentials for quantum Monte Carlo, submitted to Phys. Rev. B (2013). Preprint: arXiv:1203.5458. [Download]
  5. N. D. Drummond and R. J. Needs, Diffusion quantum Monte Carlo calculation of the quasiparticle effective mass of the two-dimensional homogeneous electron gas, Phys. Rev. B 87, 045131 (2013). [Download]
  6. P. López Ríos, P. Seth, N. D. Drummond and R. J. Needs, Framework for constructing generic Jastrow correlation factors, Phys. Rev. E 86, 036703 (2012). [Download]
  7. N. D. Drummond, V. Zólyomi and V. I. Fal'ko, Electrically tunable band gap in silicene, Phys. Rev. B 85, 075423 (2012). [Download]
  8. F. Marsusi, J. Sabbaghzadeh and N. D. Drummond, Comparison of quantum Monte Carlo with time-dependent and static density-functional theory calculations of diamondoid excitation energies and Stokes shifts, Phys. Rev. B 84, 245315 (2011). [Download]
  9. N. D. Drummond, P. López Ríos, C. J. Pickard and R. J. Needs, Quantum Monte Carlo study of a positron in an electron gas, Phys. Rev. Lett. 107, 207402 (2011). [Download]
  10. R. M. Lee, G. J. Conduit, N. Nemec, P. López Ríos and N. D. Drummond, Strategies for improving the efficiency of quantum Monte Carlo calculations, Phys. Rev. E 83, 066706 (2011). [Download]
  11. R. M. Lee and N. D. Drummond, Ground-state properties of the one-dimensional electron liquid, Phys. Rev. B 83, 245114 (2011). [Download]
  12. N. D. Drummond, N. R. Cooper, R. J. Needs and G. V. Shlyapnikov, Quantum Monte Carlo calculation of the zero-temperature phase diagram of the two-component fermionic hard-core gas in two dimensions, Phys. Rev. B 83, 195429 (2011). [Download]
  13. R. Maezono, N. D. Drummond, A. Ma and R. J. Needs, Diamond to β-tin phase transition in Si within diffusion quantum Monte Carlo, Phys. Rev. B 82, 184108 (2010). [Download]
  14. S. J. Binnie, S. J. Nolan, N. D. Drummond, D. Alfè, N. L. Allan, F. R. Manby and M. J. Gillan, Bulk and surface energetics of crystalline lithium hydride: Benchmarks from quantum Monte Carlo and quantum chemistry, Phys. Rev. B 82, 165431 (2010). [Download]
  15. Y. Kita, M. Tachikawa, N. D. Drummond and R. J. Needs, A variational Monte Carlo study of positronic compounds using inhomogeneous backflow transformations, Chem. Lett. 39, 1136 (2010). [Download]
  16. N. D. Drummond, P. López Ríos, C. J. Pickard and R. J. Needs, First-principles method for impurities in quantum fluids: Positron in an electron gas, Phys. Rev. B 82, 035107 (2010). [Download]
  17. R. J. Needs, M. D. Towler, N. D. Drummond and P. López Ríos, Continuum variational and diffusion quantum Monte Carlo calculations, J. Phys.: Condens. Matter 22, 023201 (2010). [Download]
  18. N. D. Drummond and R. J. Needs, Quantum Monte Carlo calculation of the energy band and quasiparticle effective mass of the two-dimensional Fermi fluid, Phys. Rev. B 80, 245104 (2009). [Download]
  19. C.-R. Hsing, C.-M. Wei, N. D. Drummond and R. J. Needs, Quantum Monte Carlo studies of covalent and metallic clusters: accuracy of density functional approximations, Phys. Rev. B 79, 245401 (2009). [Download]
  20. N. D. Drummond and R. J. Needs, Phase diagram of the low-density two-dimensional homogeneous electron gas, Phys. Rev. Lett. 102, 126402 (2009). [Download]
  21. R. M. Lee, N. D. Drummond and R. J. Needs, Exciton–exciton interaction and biexciton formation in bilayer systems, Phys. Rev. B 79, 125308 (2009). [Download]
  22. N. D. Drummond and R. J. Needs, Quantum Monte Carlo study of the ground state of the two-dimensional Fermi fluid, Phys. Rev. B 79, 085414 (2009). [Download]
  23. N. D. Drummond, R. J. Needs, A. Sorouri and W. M. C. Foulkes, Finite-size errors in continuum quantum Monte Carlo calculations, Phys. Rev. B 78, 125106 (2008). [Download]
  24. N. D. Drummond and R. J. Needs, Van der Waals interactions between thin metallic wires and layers, Phys. Rev. Lett. 99, 166401 (2007). [Download]
  25. N. D. Drummond, Nanomaterials: Diamondoids display their potential, Nature Nanotechnol. 2, 462 (2007). [Download]
  26. P. López Ríos, A. Ma, N. D. Drummond, M. D. Towler and R. J. Needs, Inhomogeneous backflow transformations in quantum Monte Carlo, Phys. Rev. E 74, 066701 (2006). [Download]
  27. N. D. Drummond, P. López Ríos, A. Ma, J. R. Trail, G. G. Spink, M. D. Towler and R. J. Needs, Quantum Monte Carlo study of the Ne atom and the Ne+ ion, J. Chem. Phys. 124, 224104 (2006). [Download]
  28. N. D. Drummond and R. J. Needs, Quantum Monte Carlo, density functional theory, and pair potential studies of solid neon, Phys. Rev. B 73, 024107 (2006). [Download]
  29. I. G. Gurtubay, N. D. Drummond, M. D. Towler and R. J. Needs, Quantum Monte Carlo calculations of the dissociation energies of three-electron hemibonded radical cationic dimers, J. Chem. Phys. 124, 024318 (2006). [Download]
  30. N. D. Drummond, A. J. Williamson, R. J. Needs and G. Galli, Electron emission from diamondoids: a diffusion quantum Monte Carlo study, Phys. Rev. Lett. 95, 096801 (2005). [Download]
  31. N. D. Drummond and R. J. Needs, Variance-minimization scheme for optimizing Jastrow factors, Phys. Rev. B 72, 085124 (2005). [Download]
  32. A. Ma, M. D. Towler, N. D. Drummond and R. J. Needs, Scheme for adding electron–nucleus cusps to Gaussian orbitals, J. Chem. Phys. 122, 224322 (2005). [Download]
  33. A. Ma, M. D. Towler, N. D. Drummond and R. J. Needs, All-electron quantum Monte Carlo calculations for the noble gas atoms He to Xe, Phys. Rev. E 71, 066704 (2005). [Download]
  34. M. Y. J. Tan, N. D. Drummond and R. J. Needs, Exciton and biexciton energies in bilayer systems, Phys. Rev. B 71, 033303 (2005). [Download]
  35. N. D. Drummond, M. D. Towler and R. J. Needs, Jastrow correlation factor for atoms, molecules, and solids, Phys. Rev. B 70, 235119 (2004). [Download]
  36. S.-N. Luo, D. C. Swift, R. N. Mulford, N. D. Drummond and G. J. Ackland, Performance of an ab initio equation of state for MgO, J. Phys.: Condens. Matter 16, 5435 (2004). [Download]
  37. B. Wood, W. M. C. Foulkes, M. D. Towler and N. D. Drummond, Coulomb finite-size effects in quasi-two-dimensional systems, J. Phys.: Condens. Matter 16, 891 (2004). [Download]
  38. N. D. Drummond, Z. Radnai, J. R. Trail, M. D. Towler and R. J. Needs, Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals, Phys. Rev. B 69, 085116 (2004). [Download]
  39. N. D. Drummond and G. J. Ackland, Ab initio quasiharmonic equations of state for dynamically-stabilized soft-mode materials, Phys. Rev. B 65, 184104 (2002). [Download]
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