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第一原理分子动力学新书 - Ab Initio Molecular Dynamics: Basic Theory and Adv....pdf

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    Cover
    Half-title
    Title
    Copyright
    Contents
    Preface
    1 Setting the stage: why ab initio molecular dynamics?
    Part I Basic techniques
    2 Getting started: unifying molecular dynamics and electronic structure
    2.1 Deriving classical molecular dynamics
    2.2 Ehrenfest molecular dynamics
    2.3 Born–Oppenheimer molecular dynamics
    2.4 Car–Parrinello molecular dynamics
    2.4.1 Motivation
    2.4.2 Car–Parrinello Lagrangian and equations of motion
    2.4.3 Why does the Car–Parrinello method work?
    2.4.4 How to control adiabaticity?
    2.4.5 A mathematical investigation
    2.4.6 The quantum chemistry viewpoint
    2.4.7 The simulated annealing and optimization viewpoints
    2.4.8 The extended Lagrangian viewpoint
    2.4.9 Analytic and numerical error estimates
    2.5 What about Hellmann–Feynman forces?
    2.6 Which method to choose?
    2.7 Electronic structure methods
    2.7.1 Introduction
    2.7.2 Density functional theory
    2.7.3 Hartree–Fock theory
    2.7.4 Post Hartree–Fock theories
    2.8 Basis sets
    2.8.1 Gaussians and Slater functions
    2.8.2 Plane waves
    2.8.3 Generalized plane waves
    2.8.4 Wavelets
    2.8.5 Discrete variable representations
    2.8.6 Augmented and mixed basis sets
    2.8.7 Wannier functions
    2.8.8 Real space grids
    3 Implementation: using the plane wave basis set
    3.1 Introduction and basic de.nitions
    3.1.1 Supercells and plane wave basis
    3.1.2 Plane wave expansions
    3.1.3 Cuto.s and k-points
    3.1.4 Real space grid and fast Fourier transforms
    3.1.5 Pseudopotentials
    3.2 Electrostatic energy
    3.2.1 General concepts
    3.2.2 Periodic systems
    3.2.3 Cluster boundary conditions
    3.3 Exchange and correlation energy
    3.4 Total energy, gradients, and stress tensor
    3.4.1 Total energy
    3.4.2 Wave function gradient
    3.4.3 Gradient for nuclear positions
    3.4.4 Internal stress tensor
    3.5 Energy and force calculations in practice
    3.6 Optimizing the Kohn–Sham orbitals
    3.6.1 Initial guess
    3.6.2 Preconditioning
    3.6.3 Direct methods
    3.6.4 Fix-point methods
    3.7 Molecular dynamics
    3.7.1 Car–Parrinello equations of motion
    3.7.2 Advanced integration
    3.7.3 Imposing geometrical constraints
    3.7.4 Using Car–Parrinello dynamics for optimizations
    3.8 Program organization and layout
    3.8.1 Data structures
    3.8.2 Computational kernels
    4 Atoms with plane waves: accurate pseudopotentials
    4.1 Why pseudopotentials?
    4.2 Norm-conserving pseudopotentials
    4.2.1 Pseudization of valence wave functions
    4.2.2 Hamann-Schluter-Chiang conditions
    4.2.3 Bachelet–Hamann–Schluter pseudopotentials
    4.2.4 Kerker pseudopotentials
    4.2.5 Troullier–Martins pseudopotentials
    4.2.6 Kinetic energy optimized pseudopotentials
    4.3 Pseudopotentials in the plane wave basis
    4.3.1 Gauss–Hermite integration
    4.3.2 Kleinman-Bylander projection
    4.4 Dual-space Gaussian pseudopotentials
    4.5 Nonlinear core correction
    4.6 Pseudopotential transferability
    4.7 Example: pseudopotentials for carbon
    Part II Advanced techniques
    5 Beyond standard ab initio molecular dynamics
    5.1 Introduction
    5.2 Beyond microcanonics: thermostats, barostats, metadynamics
    5.2.1 Introduction
    5.2.2 Imposing temperature: thermostats
    5.2.3 Imposing pressure: barostats
    5.2.4 Sampling rare events and free energies: metadynamics
    5.3 Beyond ground states: ROKS, surface hopping, FEMD, TDDFT
    5.3.1 Introduction
    5.3.2 A single excited state: ROKS dynamics
    5.3.3 A few excited states: explicit nonadiabatic dynamics
    5.3.4 Many excited states: free energy functionals
    5.3.5 RT-TDDFT: explicit real-time propagation
    5.3.6 LR-TDDFT: linear response and gradients
    5.3.6.1 Time-dependent linear response method
    5.3.6.2 Tamm–Danco. approximation
    5.3.6.3 Dynamical polarizability and oscillator strengths in extended systems
    5.3.6.4 Derivatives and LR-TDDFT molecular dynamics
    5.3.6.5 Analysis of electronic excitations
    5.4 Beyond classical nuclei: path integrals and quantum corrections
    5.4.1 Introduction
    5.4.2 Ab initio path integrals: statics
    5.4.3 Ab initio path centroids: dynamics
    5.4.4 Ab initio path integrals: spectroscopy
    5.4.5 Quantum corrections of classical susceptibilities: infrared spectra
    5.4.6 Related ab initio quantum approaches
    5.5 Mixed quantum/classical hybrid molecular dynamics 5.5.1 Introduction
    5.5.2 Embedding in atomistic environments
    5.5.2.1 CP-PAW/AMBER interface
    5.5.2.2 CPMD/GROMOS interface
    5.5.2.3 EGO/CPMD interface
    5.5.3 Embedding in continuum environments
    5.5.4 QM/MM molecular dynamics involving excited states
    6 Beyond norm-conserving pseudopotentials
    6.1 Introduction
    6.2 The PAW transformation
    6.3 Expectation values
    6.4 Ultrasoft pseudopotentials
    6.5 PAW energy expression
    6.6 Integrating the Car–Parrinello equations
    7 Computing properties
    7.1 Adiabatic density-functional perturbation theory: Hessian, polarizability, NMR
    7.1.1 Introduction
    7.1.2 Coupled perturbed Kohn–Sham equations
    7.1.3 Nuclear Hessian
    7.1.3.1 Selected eigenmodes of the Hessian
    7.1.4 Polarizability
    7.1.5 NMR chemical shifts
    7.1.5.1 Chemical shifts and susceptibilities
    7.1.5.2 The gauge origin problem
    7.1.5.3 The position operator problem
    7.1.5.4 Density functional perturbation theory
    7.1.5.5 Pseudopotential correction
    7.2 Wannier functions: dipole moments, IR spectra, atomic charges
    7.2.1 Introduction
    7.2.2 Position operator in periodic systems
    7.2.3 Localization functionals
    7.2.4 Localization methods
    7.2.4.1 Generalized localization procedure
    7.2.4.2 Orbital rotations
    7.2.4.3 Exponential representation
    7.2.5 Wannier functions in Car–Parrinello simulations
    7.2.6 Applications: dipole moments, infrared spectra, and atomic charges
    7.2.6.1 Molecular dipole moments
    7.2.6.2 Solute infrared absorption spectra
    7.2.6.3 Atomic charges
    8 Parallel computing
    8.1 Introduction
    8.2 Data structures
    8.3 Computational kernels
    8.4 Massively parallel processing
    Part III Applications
    9 From materials to biomolecules
    9.1 Introduction
    9.2 Solids, minerals, materials, and polymers
    9.3 Surfaces, interfaces, and heterogeneous catalysis
    9.4 Mechanochemistry and molecular electronics
    9.5 Water and aqueous solutions
    9.6 Non-aqueous liquids and solutions
    9.7 Glasses and amorphous systems
    9.8 Matter at extreme conditions
    9.9 Clusters, fullerenes, and nanotubes
    9.10 Complex and .uxional molecules
    9.11 Chemical reactions and transformations
    9.12 Homogeneous catalysis and zeolites
    9.13 Photophysics and photochemistry
    9.14 Biophysics and biochemistry
    10 Properties from ab initio simulations
    10.1 Introduction
    10.2 Boys–Wannier, population, ELF, and Fukui electronic structure analyses
    10.3 Dipole moments, infrared and Raman spectroscopy
    10.4 Magnetism, NMR and EPR spectroscopy
    10.5 Electronic spectroscopy and redox properties
    10.6 X-ray di.raction and Compton scattering
    10.7 External electric .elds, scanning probe imaging, conductivity, and currents
    11 Outlook
    Bibliography
    Index
    This page intentionally left blank
    AB INITIO MOLECULAR DYNAMICS: BASIC THEORY AND ADVANCED METHODS Ab initio molecular dynamics revolutionized the field of realistic computer simulation of complex molecular systems and processes, including chemical reactions, by unifying molecular dynamics and electronic structure theory. This book provides the first coherent presentation of this rapidly growing field, covering a vast range of methods and their applications, from basic theory to advanced methods. This fascinating text for graduate students and researchers contains systematic derivations of various ab initio molecular dynamics techniques to enable readers to understand and assess the merits and drawbacks of commonly used methods. It also discusses the special features of the widely used Car–Parrinello approach, correcting various misconceptions currently found in the research literature. The book contains pseudo-code and program layout for typical plane wave electronic structure codes, allowing newcomers to the field to understand commonly used program packages, and enabling developers to improve and add new features in their code. Dominik Marx is Chair of Theoretical Chemistry at Ruhr-Universität Bochum, Germany. His main areas of research are in studying the dynamics and reactions of complex molecular many-body systems and the development of novel ab initio simulation techniques. Jürg Hutter is a Professor at the Physical Chemistry Institute at the University of Zürich in Switzerland, where he researches problems in theoretical chemistry, in particular, methods for large-scale density functional calculations.
    AB INITIO MOLECULAR DYNAMICS: BASIC THEORY AND ADVANCED METHODS DOMINIK MARX Ruhr-Universität Bochum and JÜRG HUTTER University of Zürich
    CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521898638 © D. Marx and J. Hutter 2009 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2009 ISBN-13 978-0-511-53333-4 eBook (EBL) ISBN-13 978-0-521-89863-8 hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
    Contents Preface 1 Setting the stage: why ab initio molecular dynamics? page viii 1 2 3 4 Introduction and basic definitions Part I Basic techniques Getting started: unifying MD and electronic structure 2.1 Deriving classical molecular dynamics 2.2 Ehrenfest molecular dynamics 2.3 Born–Oppenheimer molecular dynamics 2.4 Car–Parrinello molecular dynamics 2.5 What about Hellmann–Feynman forces? 2.6 Which method to choose? 2.7 Electronic structure methods 2.8 Basis sets Implementation: using the plane wave basis set 3.1 3.2 Electrostatic energy 3.3 Exchange and correlation energy 3.4 Total energy, gradients, and stress tensor 3.5 Energy and force calculations in practice 3.6 Optimizing the Kohn–Sham orbitals 3.7 Molecular dynamics 3.8 Program organization and layout Atoms with plane waves: accurate pseudopotentials 4.1 Why pseudopotentials? 4.2 Norm-conserving pseudopotentials 4.3 Pseudopotentials in the plane wave basis 4.4 Dual-space Gaussian pseudopotentials 9 11 11 22 24 27 51 56 67 75 85 85 93 99 104 109 111 119 128 136 137 138 152 157 v
    vi 5 6 7 8 9 Contents 4.5 Nonlinear core correction 4.6 Pseudopotential transferability 4.7 Example: pseudopotentials for carbon Part II Advanced techniques Beyond standard ab initio molecular dynamics 5.1 5.2 Beyond microcanonics: thermostats, barostats, meta- Introduction dynamics 5.3 Beyond ground states: ROKS, surface hopping, FEMD, TDDFT 5.4 Beyond classical nuclei: path integrals and quantum corrections Introduction 5.5 Hybrid QM/MM molecular dynamics Beyond norm-conserving pseudopotentials 6.1 6.2 The PAW transformation 6.3 Expectation values 6.4 Ultrasoft pseudopotentials 6.5 PAW energy expression 6.6 Computing properties 7.1 Perturbation theory: Hessian, polarizability, NMR 7.2 Wannier functions: dipole moments, IR spectra, atomic Integrating the Car–Parrinello equations charges Introduction Parallel computing 8.1 8.2 Data structures 8.3 Computational kernels 8.4 Massively parallel processing Part III Applications From materials to biomolecules 9.1 9.2 9.3 9.4 Mechanochemistry and molecular electronics 9.5 Water and aqueous solutions Introduction Solids, minerals, materials, and polymers Interfaces 160 162 167 175 177 177 178 194 233 267 286 286 287 290 292 296 297 309 309 327 350 350 352 354 359 369 371 371 372 376 380 382
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