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Molecular Simulations: Fundamentals and Practice [Minkštas viršelis]

  • Formatas: Paperback / softback, 344 pages, aukštis x plotis x storis: 249x175x28 mm, weight: 1134 g
  • Išleidimo metai: 17-Jun-2020
  • Leidėjas: Blackwell Verlag GmbH
  • ISBN-10: 3527341056
  • ISBN-13: 9783527341054
Kitos knygos pagal šią temą:
Molecular Simulations: Fundamentals and PracticeDidesnis paveikslėlis
  • Formatas: Paperback / softback, 344 pages, aukštis x plotis x storis: 249x175x28 mm, weight: 1134 g
  • Išleidimo metai: 17-Jun-2020
  • Leidėjas: Blackwell Verlag GmbH
  • ISBN-10: 3527341056
  • ISBN-13: 9783527341054
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783527341054.html
Raktažodžiai:
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.
Preface xiii
1 Introduction -- Studying Systems from Two Viewpoints
1(4)
2 Classical Mechanics and Numerical Methods
5(34)
2.1 Mechanics -- The Study of Motion
5(1)
2.2 Classical Newtonian Mechanics
6(2)
2.3 Analytical Solutions of Newton's Equations and Phase Space
8(7)
2.3.1 Motion of an Object Under Constant Gravitational Force
8(2)
2.3.2 One-Dimensional Harmonic Oscillator
10(2)
2.3.3 Radial Force Functions in Three Dimensions
12(3)
2.3 A Motion Under the Influence of a Drag Force
15(2)
2.4 Numerical Solution of Newton's Equations: The Euler Method
17(3)
2.5 More Efficient Numerical Algorithms for Solving Newton's Equations
20(3)
2.5.1 The Verlet Algorithm
20(1)
2.5.2 The Leapfrog Algorithm
21(1)
2.5.3 The Velocity Verlet Algorithm
22(1)
2.5 A Considerations for Numerical Solution of the Equations of Motion
23(2)
2.6 Examples of Using Numerical Methods for Solving Newton's Equations of Motion
25(3)
2.6.1 Motion Near the Earth's Surface Under Constant Gravitational Force
25(1)
2.6.2 One-Dimensional Harmonic Oscillator
26(2)
2.7 Numerical Solution of the Equations of Motion for Many-Atom Systems
28(1)
2.8 The Lagrangian and Hamiltonian Formulations of Classical Mechanics
29(10)
Chapter 2 Appendices
32(1)
2.A.1 Separation of Motion in Two-Particle Systems with Radial Forces
32(1)
2.A.2 Motion Under Spherically Symmetric Forces
33(6)
3 Intra- and Intermolecular Potentials in Simulations
39(34)
3.1 Introduction -- Electrostatic Forces Between Atoms
39(1)
3.2 Quantum Mechanics and Molecular Interactions
40(4)
3.2.1 The Schrodinger Equation
40(2)
3.2.2 The Born--Oppenheimer Approximation
42(2)
3.3 Classical Intramolecular Potential Energy Functions from Quantum Mechanics
44(10)
3.3.1 Intramolecular Potentials
45(3)
3.3.2 Bond Stretch Potentials
48(3)
3.3.3 Angle Bending Potentials
51(1)
3.3.4 Torsional Potentials
51(2)
3.3.5 The 1--4, 1--5, and Farther Intramolecular Interactions
53(1)
3.4 Intermolecular Potential Energies
54(10)
3.4.1 Electrostatic Interactions
54(1)
3.4.1.1 The Point Charge Approximation
55(4)
3.4.1.2 The Multipole Description of Charge Distribution
59(2)
3.4.1.3 Polarizability
61(2)
3.4.2 Van der Waals Interactions
63(1)
3.5 Force Fields
64(7)
3.5.1 Water Force Fields
64(2)
3.5.2 The AMBER Force Field
66(2)
3.5.3 The OPLS Force Field
68(1)
3.5.4 The CHARMM Force Field
69(1)
3.5.5 Other Force Fields
69(2)
Chapter 3 Appendices
71(2)
3.A.1 The Born--Oppenheimer Approximation to Determine the Nuclear Schrodinger Equation
71(2)
4 The Mechanics of Molecular Dynamics
73(28)
4.1 Introduction
73(1)
4.2 Simulation Cell Vectors
73(2)
4.3 Simulation Cell Boundary Conditions
75(4)
4.4 Short-Range Intermolecular Potentials
79(5)
4.4.1 Cutoff Radius and the Minimum Image Convention
79(3)
4.4.2 Neighbor Lists
82(2)
4.5 Long-Range Intermolecular Potentials: Ewald Sums
84(4)
4.6 Simulating Rigid Molecules
88(4)
Chapter 4 Appendices
92(9)
4.A.1 Fourier Transform of Gaussian and Error Functions
92(2)
4.A.2 Electrostatic Force Expression from the Ewald Summation Technique
94(1)
4.A.3 The Method of Lagrange Undetermined Multipliers
95(3)
4.A.4 Lagrangian Multiplier for Constrained Dynamics
98(3)
5 Probability Theory and Molecular Simulations
101(38)
5.1 Introduction: Deterministic and Stochastic Processes
101(2)
5.2 Single Variable Probability Distributions
103(3)
5.2.1 Discrete Stochastic Variables
103(1)
5.2.2 Continuous Stochastic Variables
104(2)
5.3 Multivariable Distributions: Independent Variables and Convolution
106(5)
5.4 The Maxwell--Boltzmann Velocity Distribution
111(14)
5.4.1 The Concept of Temperature from the Mechanical Analysis of an Ideal Gas
112(3)
5.4.2 The Maxwell--Boltzmann Distribution of Velocities for an Ideal Gas
115(5)
5.4.3 Energy Distributions for Collections of Molecules in an Ideal Gas
120(3)
5.4.4 Generating Initial Velocities in Molecular Simulations
123(2)
5.5 Phase Space Description of an Ideal Gas
125(2)
Chapter 5 Appendices
127(1)
5.A.1 Normalization, Mean, and Standard Deviation of the Gaussian Function
127(1)
5.A.2 Convolution of Gaussian Functions
128(3)
5.A.3 The Virial Equation and the Microscopic Mechanical View of Pressure
131(2)
5.A.4 Useful Mathematical Relations and Integral Formulas
133(1)
5.A.4.1 Stirling's Approximation for N!
133(1)
5.A.4.2 Exponential Integrals
134(1)
5.A.4.3 Gaussian Integrals
134(1)
5.A.4.4 Beta Function Integrals
134(1)
5.A.5 Energy Distribution for Three Molecules
135(1)
5.A.6 Deriving the Box--Muller Formula for Generating a Gaussian Distribution
136(3)
6 Statistical Mechanics in Molecular Simulations
139(38)
6.1 Introduction
139(1)
6.2 Discrete States in Quantum Mechanical Systems
140(2)
6.3 Distributions of a System Among Discrete Energy States
142(3)
6.4 Systems with Non-interacting Molecules: The μ-Space Approach
145(3)
6.5 Interacting Systems and Ensembles: The γ-Space Approach and the Canonical Ensemble
148(10)
6.5.1 Thermodynamics Quantities
152(2)
6.5.2 Fluctuations in Thermodynamic Quantities in the Canonical Ensemble
154(2)
6.5.3 Canonical Ensemble for Systems with Non-interacting Molecules
156(1)
6.5.4 A Physical Interpretation of the Canonical Partition Function
157(1)
6.6 Other Constraints Coupling the System to the Environment
158(9)
6.6.1 Isothermal--Isobaric Ensemble (Fixed N, P, and T)
158(5)
6.6.2 Grand Canonical Ensemble (Fixed μ, V, and T)
163(3)
6.6.3 Microcanonical Ensemble (Fixed N, V, and E)
166(1)
6.6.4 Isenthalpic--Isobaric Ensemble (Fixed N, P, and H)
167(1)
6.7 Classical Statistical Mechanics
167(4)
6.7.1 The Canonical Ensemble
167(2)
6.7.2 The Isothermal--Isobaric Ensemble
169(1)
6.7.3 The Grand Canonical Ensemble
169(1)
6.7.4 The Microcanonical Ensemble
170(1)
6.7.5 Isenthalpic--Isobaric Ensemble
170(1)
6.8 Statistical Mechanics and Molecular Simulations
171(1)
Chapter 6 Appendices
172(1)
6.A.1 Quantum Mechanical Description and Determination of the Lagrange Multiplier β and Pressure for an Ideal Gas
172(2)
6.A.2 Determination of the Lagrange Multiplier β in Systems with Interacting Molecules
174(1)
6.A.3 Summary of Statistical Mechanical Formulas
175(2)
7 Thermostats and Barostats
177(622)
7.1 Introduction
177(1)
7.2 Constant Pressure Molecular Dynamics (the Isobaric Ensembles)
178(7)
7.2.1 Non-isotropic Volume Variation: The Parrinello--Rahman Method
184(1)
7.3 Constant Temperature Molecular Dynamics
185(7)
7.3.1 Extended System Method: The Nose--Hoover Thermostat
185(5)
7.3.2 The Berendsen Thermostat
190(2)
7.4 Combined Constant Temperature-Constant Pressure Molecular Dynamics
192(3)
7.5 Scope of Molecular Simulations with Thermostats and Barostats
195(1)
Chapter 7 Appendices
196(3)
7.A.1 Andersen Barostat and the Isobaric--Isenthalpic Ensemble
196(1)
7.A.2 The Lagrangian for a Constant Pressure System with Non-isotropic Volume Change: The Parrinello--Rahman Method
196(1)
7.A.3 Nose Thermostat System and the Canonical Ensemble Distribution Function
197(2)
8 Simulations of Structural and Thermodynamic Properties
199(1)
8.1 Introduction
199(1)
8.2 Simulations of Solids, Liquids, and Gases
200(5)
8.2.1 Setting Up Initial Structures for Molecular Simulations of Solids, Liquids, and Gases
202(3)
8.3 The Radial Distribution Function
205(6)
8.4 Simulations of Solutions
211(3)
8.5 Simulations of Biological Molecules
214(5)
8.6 Simulation of Surface Tension
219(5)
8.7 Structural Order Parameters
224(3)
8.8 Statistical Mechanics and the Radial Distribution Function
227(5)
8.9 Long-Range (Tail) Corrections to the Potential
232(1)
Chapter 8 Appendices
233(4)
8.A.1 Force Fields for Simulations in the Figures of
Chapter 8
233(1)
8.A.1.1 Nitrogen Force Field
233(1)
8.A.1.2 NaCl Simulation Force Field
233(1)
8.A.2 The PDB File Format
234(3)
9 Simulations of Dynamic Properties
237(32)
9.1 Introduction
237(1)
9.2 Molecular Motions and the Mean Square Displacement
237(10)
9.2.1 Motion in Bulk Phases
237(7)
9.2.2 Motion in Confined Spaces and on Surfaces
244(3)
9.3 Molecular Velocities and Time Correlation Functions
247(4)
9.3.1 Collisions and the Velocity Autocorrelation Function
247(4)
9.3.2 Time Correlation Functions for Stationary Systems
251(1)
9.4 Orientation Autocorrelation Functions
251(2)
9.5 Hydrogen Bonding Dynamics
253(1)
9.6 Molecular Motions on Nanoparticles: The Lindemann Index
254(2)
9.7 Microscopic Determination of Transport Coefficients
256(7)
9.7.1 The Transport Coefficients
256(5)
9.7.2 Nonequilibrium Molecular Dynamics Simulations of Transport Coefficients
261(1)
9.7.3 The Green--Kubo Relations and Simulation of Transport Coefficients
261(2)
Chapter 9 Appendices
263(6)
9.A.1 Brownian Motion and the Langevin Equation
263(2)
9.A.2 The Discrete Random Walk Model of Diffusion
265(2)
9.A.3 The Solution of the Diffusion Equation
267(1)
9.A.4 Relation Between Mean Square Displacement and Diffusion Coefficient
268(1)
10 Monte Carlo Simulations
269(28)
10.1 Introduction
269(1)
10.2 The Canonical Monte Carlo Procedure
270(7)
10.2.1.1 Determining Which Molecule to Move
273(1)
10.2.1.2 Determining Whether a Translation or Rotation Is Performed
273(1)
10.2.1.3 Translation Moves
274(1)
10.2.1.4 Rotational Moves
274(3)
10.3 The Condition of Microscopic Reversibility and Importance Sampling
277(2)
10.4 Monte Carlo Simulations in Other Ensembles
279(6)
10.4.1 Grand Canonical Monte Carlo Simulations
279(4)
10.4.2 Isothermal--Isobaric Monte Carlo Simulations
283(1)
10.4.3 Biased Monte Carlo Sampling Methods
284(1)
10.5 Gibbs Ensemble Monte Carlo Simulations
285(3)
10.5.1 Simulations of Liquid--Gas Phase Equilibrium
285(3)
10.6 Simulations of Gas Adsorption in Porous Solids
288(7)
10.6.1 Simulations of the Gas Adsorption Isotherm and Heat of Adsorption
288(3)
10.6.2 Force Fields for Gas Adsorption Simulations
291(1)
10.6.3 Block Averaging of Data from Monte Carlo and Molecular Dynamics Simulations
291(4)
Chapter 10 Appendices
295(2)
10.A.1 Thermodynamic Relation for the Heat of Adsorption
295(2)
References 297(80)
Index 377
Saman Alavi, PhD, is Adjunct Professor at the Department of Chemical and Biological Engineering at the University of British Columbia (Vancouver, Canada) and acts as a Scientific Evaluator at Health Canada. After obtaining his PhD from the University of British Columbia, he spent research periods in the National Research Council of Canada, at Oklahoma State University (USA) and the University of Ottawa (Canada). Saman Alavi has authored over 120 scientific publications on molecular simulations of different classes of materials.