Springer Theses

An Interatomic Potential Derived from First Principles Quantum Mechanics

By: Albert Bartok-Partay

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Hardcover | 6 August 2010

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104 Pages

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Simulation of materials at the atomistic level is an important tool in studying microscopic structures and processes. The atomic interactions necessary for the simulations are correctly described by Quantum Mechanics, but the size of systems and the length of processes that can be modelled are still limited. The framework of Gaussian Approximation Potentials that is developed in this thesis allows us to generate interatomic potentials automatically, based on quantum mechanical data. The resulting potentials offer several orders of magnitude faster computations, while maintaining quantum mechanical accuracy. The method has already been successfully applied for semiconductors and metals.

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"This book is actually an account of the Ph.D. work of the author, and is aimed at practitioners of molecular simulation (physicists and materials scientists, mostly) who want to construct reliable empirical force fields parameterized by data obtained from equilibrium quantum mechanical computations." (Gabriel Stoltz, Mathematical Reviews, Issue 2011 j)

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Introduction	p. 1
Outline of the Thesis	p. 3
References	p. 3
Representation of Atomic Environments	p. 5
Introduction	p. 5
Translational Invariants	p. 6
Spectra of Signals	p. 6
Bispectrum	p. 7
Bispectrum of Crystals	p. 8
Rotationally Invariant Features	p. 9
Bond-Order Parameters	p. 10
Power Spectrum	p. 12
Bispectrum	p. 13
4-Dimensional Bispectrum	p. 17
Results	p. 19
References	p. 21
Gaussian Process	p. 23
Introduction	p. 23
Function Inference	p. 23
Covariance Functions	p. 25
Hyperparameters	p. 27
Predicting Derivatives and Using Derivative Observations	p. 28
Linear Combination of Function Values	p. 29
Sparsification	p. 30
References	p. 31
Interatomic Potentials	p. 33
Introduction	p. 33
Quantum Mechanics	p. 34
Density Functional Theory	p. 35
Empirical Potentials	p. 39
Hard-sphere Potential	p. 39
Lennard-Jones Potential	p. 39
The Embedded-Atom Model	p. 40
The Modified Embedded-Atom Model	p. 41
Tersoff Potential	p. 43
Long-Range Interactions	p. 44
Neural Network Potentials	p. 44
Gaussian Approximation Potentials	p. 45
Technical Details	p. 47
Multispecies Potentials	p. 48
References	p. 49
Computational Methods	p. 51
Lattice Dynamics	p. 51
Phonon Dispersion	p. 51
Molecular Dynamics	p. 53
Thermodynamics	p. 53
References	p. 56
Results	p. 57
Atomic Energies	p. 57
Atomic Expectation Value of a General Operator	p. 57
Atomic Energies	p. 59
Atomic Multipoles	p. 60
Atomic Energies from ONETEP	p. 60
Locality Investigations	p. 62
Gaussian Approximation Potentials	p. 64
Gaussian Approximation Potentials for Simple Semiconductors: Diamond, Silicon and Germanium	p. 65
Parameters of GAP	p. 66
Phonon Spectra	p. 67
Anharmonic Effects	p. 69
Thermal Expansion of Diamond	p. 71
Towards a General Carbon Potential	p. 73
Gaussian Approximation Potential for Iron	p. 75
Gaussian Approximation Potential for Gallium Nitride	p. 77
Atomic Energies from GAP	p. 79
Performance of Gaussian Approximation Potentials	p. 81
References	p. 81
Conclusion and Further Work	p. 83
Further Work	p. 84
Appendices	p. 85
A: Woodbury Matrix Identity	p. 85
B: Spherical Harmonics	p. 86
Four-Dimensional Spherical Harmonics	p. 86
Clebsch-Gordan Coefficients	p. 88
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Springer Theses

An Interatomic Potential Derived from First Principles Quantum Mechanics

At a Glance

Hardcover

Industry Reviews

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Defective items

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