Computational Approaches in Physics

137 Pages·2016·3.675 MB·English

by  Maria Fyta

Computational Approaches
in Physics

Computational Approaches
in Physics
Maria Fyta
Institute for Computational Physics, Universität Stuttgart
Morgan & Claypool Publishers
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ISBN 978-1-6817-4417-9(ebook)
ISBN 978-1-6817-4416-2(print)
ISBN 978-1-6817-4419-3(mobi)
DOI 10.1088/978-1-6817-4417-9
Version:20161001
IOPConcisePhysics
ISSN2053-2571(online)
ISSN2054-7307(print)
AMorgan&ClaypoolpublicationaspartofIOPConcisePhysics
PublishedbyMorgan&ClaypoolPublishers,40OakDrive,SanRafael,CA,94903USA
IOPPublishing,TempleCircus,TempleWay,BristolBS16HG,UK
To my high-school and university teachers who taught me how to learn.
To my beloved ones.

Contents
Preface xi
Acknowledgements xii
About the author xiii
Glossary xiv
1 Introduction 1-1
1.1 Computational physics 1-1
1.1.1 Length-scales and efficiency 1-2
1.1.2 Approaches and milestones 1-4
1.1.3 Setting-up the simulations 1-6
References 1-8
2 Quantum-mechanical methods 2-1
2.1 General remarks 2-1
2.1.1 Two descriptions for the electronic structure methods 2-2
2.2 The Hartree–Fock method 2-3
2.3 Post HF schemes 2-5
2.3.1 Coupled cluster 2-5
2.3.2 Møller–Plesset perturbation theory 2-6
2.3.3 Configuration interaction 2-7
2.4 Density functional theory (DFT) 2-8
2.4.1 Exchange and correlation functionals 2-10
2.4.2 Pseudopotentials 2-12
2.4.3 Basis sets 2-14
2.4.4 Quantum transport calculations (DFT + 2-15
non-equilibrium Green’s functions)
2.5 Time-dependent density functional theory (TDDFT) 2-15
2.5.1 Computational scaling 2-18
2.6 Ab initio MD and electronic structure 2-19
2.6.1 Calculation of forces in electronic structure simulations 2-19
2.6.2 Car–Parrinello MD 2-21
2.7 Semi-empirical methods 2-22
2.7.1 The tight-binding scheme 2-23
References 2-24
vii
ComputationalApproachesinPhysics
3 Atomistic methods 3-1
3.1 Classical molecular dynamics 3-1
3.1.1 Basics of MD simulations 3-1
3.1.2 Boundary conditions 3-3
3.1.3 Forces in molecular dynamics 3-4
3.2 Setting environment conditions 3-5
3.2.1 Thermostats 3-5
3.2.2 Barostats 3-8
3.3 Integration schemes 3-9
3.4 General remarks on MD 3-11
References 3-13
4 Classical potentials and force fields 4-1
4.1 Classical pair potentials 4-2
4.1.1 Simple pair potentials 4-3
4.1.2 Bond-order potentials 4-4
4.2 Multi-body reactive force fields 4-5
4.2.1 Reactive force field (ReaxFF) 4-5
4.3 Force fields for biomolecules 4-6
4.4 Embedded atom method (EAM) 4-8
4.5 Water models 4-9
4.5.1 Explicit water models 4-10
4.5.2 Implicit water models 4-11
References 4-13
5 Mesoscopic particle methods 5-1
5.1 Simulation of fluids 5-2
5.2 Continuum methods 5-3
5.2.1 Brownian dynamics 5-3
5.2.2 Langevin approach 5-3
5.3 Dissipative particle dynamics 5-5
5.3.1 Stochastic rotation dynamics 5-5
5.3.2 Smoothed particle hydrodynamics 5-6
5.4 Lattice methods 5-7
5.4.1 Lattice Boltzmann method 5-7
References 5-9
viii
ComputationalApproachesinPhysics
6 The Monte Carlo method 6-1
6.1 Random numbers 6-2
6.2 Classical Monte Carlo 6-2
6.2.1 Sampling of the phase space 6-2
6.2.2 Markov chains 6-3
6.2.3 Detailed balance 6-4
6.2.4 Umbrella sampling 6-4
6.2.5 Metropolis algorithm 6-6
6.2.6 More on acceptance probabilities 6-6
6.2.7 An example: solving the Ising model with MC 6-7
6.3 Quantum Monte Carlo (QMC) 6-8
References 6-9
7 Multiscale, hybrid, and coarse-grained methods 7-1
7.1 Coarse-graining 7-1
7.2 Multiscale or hybrid schemes 7-2
7.2.1 Examples: sequential (serial) schemes 7-4
7.2.2 Examples: concurrent (parallel) schemes 7-8
7.2.3 Quantum-mechanics molecular-mechanics (QM/MM) 7-9
7.2.4 Coupling the lattice Boltzmann method with MD 7-11
7.2.5 Other MS examples 7-12
References 7-14
8 Other common aspects 8-1
8.1 Search and sampling of the configuration space, energy 8-1
minimization
8.2 Free energy methods 8-4
8.2.1 Free energy differences 8-4
8.2.2 Free energy perturbation 8-5
8.2.3 Thermodynamic integration 8-5
8.2.4 Umbrella sampling 8-6
8.2.5 Metadynamics 8-6
8.2.6 Other free energy methods 8-7
8.3 Dealing with electrostatics/electrokinetics 8-8
8.3.1 Charges and electrostatic interactions 8-8
ix