Gaussian Approximation Potential: an interatomic potential derived from first principles Quantum Mechanics

Simulation of materials at the atomistic level is an important tool in studying microscopic structure and processes. The atomic interactions necessary for the simulation are correctly described by Quantum Mechanics. However, the computational resources required to solve the quantum mechanical equations limits the use of Quantum Mechanics at most to a few hundreds of atoms and only to a small fraction of the available configurational space. This thesis presents the results of my research on the development of a new interatomic potential generation scheme, which we refer to as Gaussian Approximation Potentials. In our framework, the quantum mechanical potential energy surface is interpolated between a set of predetermined values at different points in atomic configurational space by a non-linear, non-parametric regression method, the Gaussian Process. To perform the fitting, we represent the atomic environments by the bispectrum, which is invariant to permutations of the atoms in the neighbourhood and to global rotations. The result is a general scheme, that allows one to generate interatomic potentials based on arbitrary quantum mechanical data. We built a series of Gaussian Approximation Potentials using data obtained from Density Functional Theory and tested the capabilities of the method. We showed that our models reproduce the quantum mechanical potential energy surface remarkably well for the group IV semiconductors, iron and gallium nitride. Our potentials, while maintaining quantum mechanical accuracy, are several orders of magnitude faster than Quantum Mechanical methods.

Tests of an adaptive QM/MM calculation on free energy profiles of chemical reactions in solution.

We present reaction free energy calculations using the adaptive buffered force mixing quantum mechanics/molecular mechanics (bf-QM/MM) method. The bf-QM/MM method combines nonadaptive electrostatic embedding QM/MM calculations with extended and reduced QM regions to calculate accurate forces on all atoms, which can be used in free energy calculation methods that require only the forces and not the energy. We calculate the free energy profiles of two reactions in aqueous solution: the nucleophilic substitution reaction of methyl chloride with a chloride anion and the deprotonation reaction of the tyrosine side chain. We validate the bf-QM/MM method against a full QM simulation, and show that it correctly reproduces both geometrical properties and free energy profiles of the QM model, while the electrostatic embedding QM/MM method using a static QM region comprising only the solute is unable to do so. The bf-QM/MM method is not explicitly dependent on the details of the QM and MM methods, so long as it is possible to compute QM forces in a small region and MM forces in the rest of the system, as in a conventional QM/MM calculation. It is simple, with only a few parameters needed to control the QM calculation sizes, and allows (but does not require) a varying and adapting QM region which is necessary for simulating solutions.

The fracture energy of metal fibre reinforced ceramic composites (MFCs)

A model is presented for prediction of the fracture energy of ceramic-matrix composites containing dispersed metallic fibres. It is assumed that the work of fracture comes entirely from pull-out and/or plastic deformation of fibres bridging the crack plane. Comparisons are presented between these predictions and experimental measurements made on a commercially-available composite material of this type, containing stainless steel (304) fibres in a matrix predominantly comprising alumina and alumino-silicate phases. Good agreement is observed, and it's noted that there is scope for the fracture energy levels to be high (~20kJm-2). Higher toughness levels are both predicted and observed for coarser fibres, up to a practical limit for the fibre diameter of the order of 0.5mm. Other deductions are also made concerning strategies for optimisation of the toughness of this type of material. © 2010 Elsevier Ltd.

Evaluating boundary dependent errors in QM/MM simulations.

Hybrid quantum mechanics/molecular mechanics (QM/MM) simulations provide a powerful tool for studying chemical reactions, especially in complex biochemical systems. In most works to date, the quantum region is kept fixed throughout the simulation and is defined in an ad hoc way based on chemical intuition and available computational resources. The simulation errors associated with a given choice of the quantum region are, however, rarely assessed in a systematic manner. Here we study the dependence of two relevant quantities on the QM region size: the force error at the center of the QM region and the free energy of a proton transfer reaction. Taking lysozyme as our model system, we find that in an apolar region the average force error rapidly decreases with increasing QM region size. In contrast, the average force error at the polar active site is considerably higher, exhibits large oscillations and decreases more slowly, and may not fall below acceptable limits even for a quantum region radius of 9.0 A. Although computation of free energies could only be afforded until 6.0 A, results were found to change considerably within these limits. These errors demonstrate that the results of QM/MM calculations are heavily affected by the definition of the QM region (not only its size), and a convergence test is proposed to be a part of setting up QM/MM simulations.

Cryogenic on-chip multiplexer for the study of quantum transport in 256 split-gate devices

We present a multiplexing scheme for the measurement of large numbers of mesoscopic devices in cryogenic systems. The multiplexer is used to contact an array of 256 split gates on a GaAs/AlGaAs heterostructure, in which each split gate can be measured individually. The low-temperature conductance of split-gate devices is governed by quantum mechanics, leading to the appearance of conductance plateaux at intervals of 2e^2/h. A fabrication-limited yield of 94% is achieved for the array, and a "quantum yield" is also defined, to account for disorder affecting the quantum behaviour of the devices. The quantum yield rose from 55% to 86% after illuminating the sample, explained by the corresponding increase in carrier density and mobility of the two-dimensional electron gas. The multiplexer is a scalable architecture, and can be extended to other forms of mesoscopic devices. It overcomes previous limits on the number of devices that can be fabricated on a single chip due to the number of electrical contacts available, without the need to alter existing experimental set ups.