The Gaussian Approximation Potential

An Interatomic Potential Derived from First Principles Quantum Mechanics

By: Albert Bartok-Partay

Write A Review

Hardcover | 6 August 2010

At a Glance

Hardcover
104 Pages

Dimensions(cm)
22.86 x 15.24 x 1.27

Hardcover

$199.00

or 4 interest-free payments of $49.75 with

or

Ships in 5 to 7 business days

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.

Industry Reviews

From the reviews:

"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)

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Materials & States of Matter

Handbook of Semiconductors : Fundamentals to Emerging Applications - Ram K. Gupta

$96.75

12%
OFF

Microwave Processing of Metallic Materials : Revolutionizing Surface Engineering for Green Manufacturing - Amit Bansal

$167.75

11%
OFF

Electromagnetic Interference Shielding Technologies

Theory and Applications

Hardcover

RRP $315.00

$271.99

14%
OFF

Extended Equations for Particles

Spin, General Theory and Exact Solution

Hardcover

RRP $273.00

$236.99

13%
OFF

Beyond the Standard Model of Particle Physics : Advanced Theories in Particle Physics - Shaaban Khalil

$350.99

14%
OFF

Unravelling the Power of 2D Materials

Revolutionizing Flexible Devices

Hardcover

RRP $431.00

$368.75

14%
OFF

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
Table of Contents provided by Ingram. All Rights Reserved.

The Gaussian Approximation Potential

An Interatomic Potential Derived from First Principles Quantum Mechanics

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Materials & States of Matter

Handbook of Semiconductors

Fundamentals to Emerging Applications

Polymer Chemistry

An Introduction

Solved Problems in Applied Mechanics of Solids

Microwave Processing of Metallic Materials

Revolutionizing Surface Engineering for Green Manufacturing

Stochastic Navier-Stokes Equations on Spheres and Spherical Shells

Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series

Semiconductors and Nanostructures

An Introduction

Electromagnetic Interference Shielding Technologies

Theory and Applications

Extended Equations for Particles

Spin, General Theory and Exact Solution

Beyond the Standard Model of Particle Physics

Advanced Theories in Particle Physics

Flow Batteries

Fundamentals, Technological Advancement and Challenges

Unravelling the Power of 2D Materials

Revolutionizing Flexible Devices

Biopolymers for Impaired Wound Healing

Particle Astrophysics with Gamma-Ray Telescopes

Series in Astronomy and Astrophysics

Advanced Photonic Devices for Energy and Sensing Applications

Theory Of Itinerant Electron Magnetism, 2nd Edition ISMP Paperback

Second Edition

Carbon Superstructures

From Quantum Transport to Quantum Computation

High Entropy Materials

Fundamentals to Emerging Applications

Introduction to Photocatalysis

Fundamentals and Applications

The Compressible Fluid Physics of the Human Respiratory System

Foundations of Biochemistry and Biophysics

The Compressible Fluid Physics of the Human Respiratory System

Foundations of Biochemistry and Biophysics

Mechanical Properties of Solid Polymers

Magnetism and Magnetic Materials

Atmospheric Pressure Plasmas at Interfaces

IOP ebooks

Basic Course in Plasma Physics

Iop Expanding Physics

This product is categorised by