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Neil Drummond

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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, which is developed by the QMC group at Cambridge University.

Here are some of the projects that I have carried out:

Van der Waals interactions between thin metallic wires and layers

I have used QMC to calculate the van der Waals interaction between 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) has recently been shown to be qualitatively wrong. My QMC calculations have produced accurate data for the binding energies of pairs of 1D and 2D electron gases.

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 density-functional theory (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 uniform electron gas

I have used QMC to study the low density behaviour of the uniform 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 3D uniform electron gas crystallises.

I am currently studying the phase behaviour of a 2D uniform electron gas (i.e., a gas of electrons confined to a plane).

2D Wigner crystal
Charge density of a 2D Wigner crystal with a defect.

Theoretical and technical developments to the QMC algorithms

  • I am trying to improve the accuracy with which the energy per atom of an infinite crystal can be calculated by extrapolation from QMC results for a set of finite simulation cells 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 main authors of the Cambridge 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 periclase (MgO), 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 MgO. I have also calculated phonon dispersion curves (relationships between the frequencies of lattice vibrations, their wavelengths and direction) for MgO. 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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List of Publications

  1. R. J. Needs, M. D. Towler, N. D. Drummond and P. Lopez Rios, CASINO version 2.5 User Manual, University of Cambridge, Cambridge (2009).
  2. 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]
  3. 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]
  4. 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]
  5. 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]
  6. 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]
  7. N. D. Drummond and R. J. Needs, Van der Waals interactions between thin metallic wires and layers, Phys. Rev. Lett. 99, 166401 (2007). [Download]
  8. N. D. Drummond, Nanomaterials: Diamondoids display their potential, Nature Nanotechnol. 2, 462 (2007). [Download]
  9. N. D. Drummond, A. J. Williamson, R. J. Needs and G. Galli, DMC study of the optoelectronic properties of diamondoids, Mater. Res. Soc. Symp. Proc. 958, 0958-L09-04 (2007).
  10. P. Lopez Rios, 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]
  11. N. D. Drummond, P. Lopez Rios, 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]
  12. 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]
  13. 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]
  14. 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]
  15. N. D. Drummond and R. J. Needs, Variance-minimization scheme for optimizing Jastrow factors, Phys. Rev. B 72, 085124 (2005). [Download]
  16. 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]
  17. 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]
  18. 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]
  19. 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]
  20. N. D. Drummond, D. C. Swift and G. J. Ackland, Ab initio model of porous periclase, AIP Conf. Proc. 706, 1436 (2004).
  21. 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. Cond. Mat. 16, 5435 (2004). [Download]
  22. B. Wood, W. M. C. Foulkes, M. D. Towler and N. D. Drummond, Coulomb finite-size effects in quasi-two-dimensional systems, J. Phys. Cond. Mat. 16, 891 (2004). [Download]
  23. 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]
  24. 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]
  25. G. J. Ackland and N. D. Drummond, Thermodynamic properties from static-lattice calculations with soft modes, Mater. Res. Soc. Symp. Proc. 718, 131 (2002).
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