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Description
Provides hands-on knowledge enabling students of and researchers in chemistry, biology, and engineering to perform molecular simulations
This book introduces the fundamentals of molecular simulations for a broad, practice-oriented audience and presents a thorough overview of the underlying concepts. It covers classical mechanics for many-molecule systems as well as force-field models in classical molecular dynamics; introduces probability concepts and statistical mechanics; and analyzes numerous simulation methods, techniques, and applications.
Molecular Simulations: Fundamentals and Practice starts by covering Newton's equations, which form the basis of classical mechanics, then continues on to force-field methods for modelling potential energy surfaces. It gives an account of probability concepts before subsequently introducing readers to statistical and quantum mechanics. In addition to Monte-Carlo methods, which are based on random sampling, the core of the book covers molecular dynamics simulations in detail and shows how to derive critical physical parameters. It finishes by presenting advanced techniques, and gives invaluable advice on how to set up simulations for a diverse range of applications.
- Addresses the current need of students of and researchers in chemistry, biology, and engineering to understand and perform their own molecular simulations
- Covers the nitty-gritty — from Newton's equations and classical mechanics over force-field methods, potential energy surfaces, and probability concepts to statistical and quantum mechanics
- Introduces physical, chemical, and mathematical background knowledge in direct relation with simulation practice
- Highlights deterministic approaches and random sampling (eg: molecular dynamics versus Monte-Carlo methods)
- Contains advanced techniques and practical advice for setting up different simulations to prepare readers entering this exciting field
Molecular Simulations: Fundamentals and Practice is an excellent book benefitting chemist, biologists, engineers as well as materials scientists and those involved in biotechnology.
Table of Contents
Preface xiii
1 Introduction – Studying Systems from Two Viewpoints 1
2 Classical Mechanics and Numerical Methods 5
2.1 Mechanics –The Study of Motion 5
2.2 Classical Newtonian Mechanics 6
2.3 Analytical Solutions of Newton's Equations and Phase Space 8
2.4 Numerical Solution of Newton's Equations: The Euler Method 17
2.5 More Efficient Numerical Algorithms for Solving Newton's Equations 20
2.6 Examples of Using Numerical Methods for Solving Newton's Equations of Motion 25
2.7 Numerical Solution of the Equations of Motion for Many-Atom Systems 28
2.8 The Lagrangian and Hamiltonian Formulations of Classical Mechanics 29
3 Intra- and Intermolecular Potentials in Simulations 39
3.1 Introduction – Electrostatic Forces Between Atoms 39
3.2 Quantum Mechanics and Molecular Interactions 40
3.3 Classical Intramolecular Potential Energy Functions from Quantum Mechanics 44
3.4 Intermolecular Potential Energies 54
3.5 Force Fields 64
4 The Mechanics of Molecular Dynamics 73
4.1 Introduction 73
4.2 Simulation Cell Vectors 73
4.3 Simulation Cell Boundary Conditions 75
4.4 Short-Range Intermolecular Potentials 79
4.5 Long-Range Intermolecular Potentials: Ewald Sums 84
4.6 Simulating Rigid Molecules 88
5 Probability Theory and Molecular Simulations 101
5.1 Introduction: Deterministic and Stochastic Processes 101
5.2 Single Variable Probability Distributions 103
5.3 Multivariable Distributions: Independent Variables and Convolution 106
5.4 The Maxwell–Boltzmann Velocity Distribution 111
5.5 Phase Space Description of an Ideal Gas 125
6 Statistical Mechanics in Molecular Simulations 139
6.1 Introduction 139
6.2 Discrete States in Quantum Mechanical Systems 140
6.3 Distributions of a System Among Discrete Energy States 142
6.4 Systems with Non-interacting Molecules: The μ-Space Approach 145
6.5 Interacting Systems and Ensembles: The γ-Space Approach and the Canonical Ensemble 148
6.6 Other Constraints Coupling the System to the Environment 158
6.7 Classical Statistical Mechanics 167
6.8 Statistical Mechanics and Molecular Simulations 171
7 Thermostats and Barostats 177
7.1 Introduction 177
7.2 Constant Pressure Molecular Dynamics (the Isobaric Ensembles) 178
7.3 Constant Temperature Molecular Dynamics 185
7.4 Combined Constant Temperature–Constant Pressure Molecular Dynamics 192
7.5 Scope of Molecular Simulations with Thermostats and Barostats 195
8 Simulations of Structural and Thermodynamic Properties 199
8.1 Introduction 199
8.2 Simulations of Solids, Liquids, and Gases 200
8.3 The Radial Distribution Function 205
8.4 Simulations of Solutions 211
8.5 Simulations of Biological Molecules 214
8.6 Simulation of Surface Tension 219
8.7 Structural Order Parameters 224
8.8 Statistical Mechanics and the Radial Distribution Function 227
8.9 Long-Range (Tail) Corrections to the Potential 232
9 Simulations of Dynamic Properties 237
9.1 Introduction 237
9.2 Molecular Motions and the Mean Square Displacement 237
9.3 Molecular Velocities and Time Correlation Functions 247
9.4 Orientation Autocorrelation Functions 251
9.5 Hydrogen Bonding Dynamics 253
9.6 Molecular Motions on Nanoparticles: The Lindemann Index 254
9.7 Microscopic Determination of Transport Coefficients 256
10 Monte Carlo Simulations 269
10.1 Introduction 269
10.2 The Canonical Monte Carlo Procedure 270
10.3 The Condition of Microscopic Reversibility and Importance Sampling 277
10.4 Monte Carlo Simulations in Other Ensembles 279
10.5 Gibbs Ensemble Monte Carlo Simulations 285
10.6 Simulations of Gas Adsorption in Porous Solids 288
References 297
Index 317
