TCM
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Nick Woods

 Nick Woods

Nick Woods

Member of Clare College
PhD student in Dr Hasnip's group

Office: 543 Mott Bld
Phone: +44(0)1223 3 37466
Email: nw361 @ cam.ac.uk

TCM Group, Cavendish Laboratory
19 JJ Thomson Avenue,
Cambridge, CB3 0HE UK.

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Research

My research concerns the development of methodology utilised in computational implementations of density functional theory (DFT). However, this methodology is not strictly limited to DFT, and my interests lie in all levels of electronic structure theory and their computational implementation. My current research, and the focus of my most recent thesis, concerns improving the efficiency and robustness in which self-consistency can be achieved in Kohn-Sham (KS) DFT.

DFT in the KS framework presents a non-linear eigenvalue problem whereby, in order to solve the system, the particle density one calculates from the KS equations must be equal to the particle density one uses to construct the KS equations. Such a solution defines what it means to attain self-consistency. In KS DFT, one often starts by computing an initial guess of the particle density for a given input system (set of atomic coordinates, etc.). This initial guess is then iteratively converged toward self-consistency. Perhaps the most intuitive iterative scheme one could envisage is to define a variational method which guarantees each iterate moves through phase-space toward the self-consistent solution. This defines ensemble density functional theory, a robust but extremely inefficient method. An alternative would be to treat KS DFT as a nondescript non-linear system whereby one seeks a fixed-point of the non-linear KS map, i.e. the density input into the KS equations equals the output density calculated from the single-particle wavefunctions. By combining the input and output density pairs at each iteration, one can predict a subsequent iterative input density which drives the density toward convergence. This defines a density mixing scheme. My research concerns the exploration and augmentation of potential density mixing schemes. The current paradigm is to use Pulay's discrete inversion in the iterative subspace (DIIS) technique alongside Kerker preconditioning. Pulay's DIIS is a 'black-box' non-linear solver, and preconditioning provides this solver with information about the expected dielectric response of KS electrons to assist convergence. Kerker preconditioning assumes all input systems have the dielectric response of the homogeneous electron gas. Improvements to Pulay's DIIS and Kerker preconditioning are considered.

Heres my Part III Maths essay on inflationary cosmology and non-Gaussian statistics in the CMB and another thesis on graphene band-gap engineering.

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In Plain English

Quantum mechanics is a theory that has been exceptionally successful in describing and predicting natural phenomena. Hence, knowing the precise 'quantum mechanical' description of electrons within a material provides a wealth of information about the material. For example, mechanical strength, opacity, electrical conductivity, etc. Solving the equations of quantum mechanics to obtain the 'electronic structure', however, is a difficult task. The computation required to obtain such a solution becomes prohibitively large for even just four electrons (far less electrons than in a typical material). Hence, I work with a reformulation (and approximation) of quantum mechanics that allows the calculation of the 'electronic structure' in a feasible time-frame on a computer. In turn, the aforementioned material properties can be calculated. Specifically, I work on refining the computational implementation of this theory for best performance.