Understanding Molecular Simulation

From Algorithms to Applications

3rd Edition - July 13, 2023
Authors: Daan Frenkel, Berend Smit
Language: English
Paperback ISBN:
9 7 8 - 0 - 3 2 3 - 9 0 2 9 2 - 2
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 9 1 3 1 8 - 8

Understanding Molecular Simulation explains molecular simulation from a chemical-physics and statistical-mechanics perspective. It highlights how physical concepts are use… Read more

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Understanding Molecular Simulation explains molecular simulation from a chemical-physics and statistical-mechanics perspective. It highlights how physical concepts are used to develop better algorithms and expand the range of applicability of simulations. Understanding Molecular Simulation is equally relevant for those who develop new code and those who use existing packages. Both groups are continuously confronted with the question of which computational technique best suits a given application. Understanding Molecular Simulation provides readers with the foundational knowledge they need to learn about, select and apply the most appropriate of these tools to their own work. The implementation of simulation methods is illustrated in pseudocodes, and their practical use is shown via case studies presented throughout the text.

Since the second edition’s publication, the simulation world has expanded significantly: existing techniques have continued to develop, and new ones have emerged, opening up novel application areas. This new edition aims to describe these new developments without becoming exhaustive; examples are included that highlight current uses, and several new examples have been added to illustrate recent applications. Examples, case studies, questions, and downloadable algorithms are also included to support learning. No prior knowledge of computer simulation is assumed.

Title of Book
Cover image
Title page
Table of Contents
Copyright
Preface to the third edition
Preface to the second edition
Preface to first edition
Chapter 1: Introduction
(Pre)history of computer simulation
Suggested reading
How to use this book
Part I: Basics
Chapter 2: Thermodynamics and statistical mechanics
2.1. Classical thermodynamics
2.1.1. Auxiliary functions
2.1.2. Chemical potential and equilibrium
2.1.3. Energy, pressure, and chemical potential
2.2. Statistical thermodynamics
2.2.1. Basic assumption
2.2.2. Systems at constant temperature
2.2.3. Towards classical statistical mechanics
2.3. Ensembles
2.3.1. Micro-canonical (constant-NVE) ensemble
2.3.2. Canonical (constant-NVT) ensemble
2.3.3. Isobaric-isothermal (constant-NPT) ensemble
2.3.4. Grand-canonical (constant-μVT) ensemble
2.4. Ergodicity
2.5. Linear response theory
2.5.1. Static response
2.5.2. Dynamic response
2.6. Questions and exercises
Chapter 3: Monte Carlo simulations
3.1. Preamble: molecular simulations
3.2. The Monte Carlo method
3.2.1. Metropolis method
3.2.2. Parsimonious Metropolis algorithm
3.3. A basic Monte Carlo algorithm
3.3.1. The algorithm
3.3.2. Technical details
3.3.3. Detailed balance versus balance
3.4. Trial moves
3.4.1. Translational moves
3.4.2. Orientational moves
3.5. Questions and exercises
Chapter 4: Molecular Dynamics simulations
4.1. Molecular Dynamics: the idea
4.2. Molecular Dynamics: a program
4.2.1. Initialization
4.2.2. The force calculation
4.2.3. Integrating the equations of motion
4.3. Equations of motion
4.3.1. Accuracy of trajectories and the Lyapunov instability
4.3.2. Other desirable features of an algorithm
4.3.3. Other versions of the Verlet algorithm
4.3.4. Liouville formulation of time-reversible algorithms
4.3.5. One more way to look at the Verlet algorithm…
4.4. Questions and exercises
Chapter 5: Computer experiments
5.1. Static properties
5.1.1. Temperature
5.1.2. Internal energy
5.1.3. Partial molar quantities
5.1.4. Heat capacity
5.1.5. Pressure
5.1.6. Surface tension
5.1.7. Structural properties
5.2. Dynamical properties
5.2.1. Diffusion
5.2.2. Order-n algorithm to measure correlations
5.2.3. Comments on the Green-Kubo relations
5.3. Statistical errors
5.3.1. Static properties: system size
5.3.2. Correlation functions
5.3.3. Block averages
5.4. Questions and exercises
Part II: Ensembles
Chapter 6: Monte Carlo simulations in various ensembles
6.1. General approach
6.2. Canonical ensemble
6.2.1. Monte Carlo simulations
6.2.2. Justification of the algorithm
6.3. Isobaric-isothermal ensemble
6.3.1. Statistical mechanical basis
6.3.2. Monte Carlo simulations
6.3.3. Applications
6.4. Isotension-isothermal ensemble
6.5. Grand-canonical ensemble
6.5.1. Statistical mechanical basis
6.5.2. Monte Carlo simulations
6.5.3. Molecular case
6.5.4. Semigrand ensemble
6.6. Phase coexistence without boundaries
6.6.1. The Gibbs-ensemble technique
6.6.2. The partition function
6.6.3. Monte Carlo simulations
6.6.4. Applications
6.7. Questions and exercises
Chapter 7: Molecular Dynamics in various ensembles
7.1. Molecular Dynamics at constant temperature
7.1.1. Stochastic thermostats
7.1.2. Global kinetic-energy rescaling
7.1.3. Stochastic global energy rescaling
7.1.4. Choose your thermostat carefully
7.2. Molecular Dynamics at constant pressure
7.3. Questions and exercises
Part III: Free-energy calculations
Chapter 8: Free-energy calculations
8.1. Introduction
8.1.1. Importance sampling may miss important states
8.1.2. Why is free energy special?
8.2. General note on free energies
8.3. Free energies and first-order phase transitions
8.3.1. Cases where free-energy calculations are not needed
8.4. Methods to compute free energies
8.4.1. Thermodynamic integration
8.4.2. Hamiltonian thermodynamic integration
8.5. Chemical potentials
8.5.1. The particle insertion method
8.5.2. Particle-insertion method: other ensembles
8.5.3. Chemical potential differences
8.6. Histogram methods
8.6.1. Overlapping-distribution method
8.6.2. Perturbation expression
8.6.3. Acceptance-ratio method
8.6.4. Order parameters and Landau free energies
8.6.5. Biased sampling of free-energy profiles
8.6.6. Umbrella sampling
8.6.7. Density-of-states sampling
8.6.8. Wang-Landau sampling
8.6.9. Metadynamics
8.6.10. Piecing free-energy profiles together: general aspects
8.6.11. Piecing free-energy profiles together: MBAR
8.7. Non-equilibrium free energy methods
8.8. Questions and exercises
Chapter 9: Free energies of solids
9.1. Thermodynamic integration
9.2. Computation of free energies of solids
9.2.1. Atomic solids with continuous potentials
9.2.2. Atomic solids with discontinuous potentials
9.2.3. Molecular and multi-component crystals
9.2.4. Einstein-crystal implementation issues
9.2.5. Constraints and finite-size effects
9.3. Vacancies and interstitials
9.3.1. Defect free energies
Chapter 10: Free energy of chain molecules
10.1. Chemical potential as reversible work
10.2. Rosenbluth sampling
10.2.1. Macromolecules with discrete conformations
10.2.2. Extension to continuously deformable molecules
10.2.3. Overlapping-distribution Rosenbluth method
10.2.4. Recursive sampling
10.2.5. Pruned-enriched Rosenbluth method
Part IV: Advanced techniques
Chapter 11: Long-ranged interactions
11.1. Introduction
11.2. Ewald method
11.2.1. Dipolar particles
11.2.2. Boundary conditions
11.2.3. Accuracy and computational complexity
11.3. Particle-mesh approaches
11.4. Damped truncation
11.5. Fast-multipole methods
11.6. Methods that are suited for Monte Carlo simulations
11.6.1. Maxwell equations on a lattice
11.6.2. Event-driven Monte Carlo approach
11.7. Hyper-sphere approach
Chapter 12: Configurational-bias Monte Carlo
12.1. Biased sampling techniques
12.1.1. Beyond Metropolis
12.1.2. Orientational bias
12.2. Chain molecules
12.2.1. Configurational-bias Monte Carlo
12.2.2. Lattice models
12.2.3. Off-lattice case
12.3. Generation of trial orientations
12.3.1. Strong intramolecular interactions
12.4. Fixed endpoints
12.4.1. Lattice models
12.4.2. Fully flexible chain
12.4.3. Strong intramolecular interactions
12.5. Beyond polymers
12.6. Other ensembles
12.6.1. Grand-canonical ensemble
12.7. Recoil growth
12.7.1. Algorithm
12.8. Questions and exercises
Chapter 13: Accelerating Monte Carlo sampling
13.1. Sampling intensive variables
13.1.1. Parallel tempering
13.1.2. Expanded ensembles
13.2. Noise on noise
13.3. Rejection-free Monte Carlo
13.3.1. Hybrid Monte Carlo
13.3.2. Kinetic Monte Carlo
13.3.3. Sampling rejected moves
13.4. Enhanced sampling by mapping
13.4.1. Machine learning and the rebirth of static Monte Carlo sampling
13.4.2. Cluster moves
13.4.3. Early rejection method
13.4.4. Beyond detailed-balance
Chapter 14: Time-scale-separation problems in MD
14.1. Constraints
14.1.1. Constrained and unconstrained averages
14.1.2. Beyond bond constraints
14.2. On-the-fly optimization
14.3. Multiple time-step approach
Chapter 15: Rare events
15.1. Theoretical background
15.2. Bennett-Chandler approach
15.2.1. Dealing with holonomic constraints (Blue-Moon ensemble)
15.3. Diffusive barrier crossing
15.4. Path-sampling techniques
15.4.1. Transition-path sampling
15.4.2. Path sampling Monte Carlo
15.4.3. Beyond transition-path sampling
15.4.4. Transition-interface sampling
15.5. Forward-flux sampling
15.5.1. Jumpy forward-flux sampling
15.5.2. Transition-path theory
15.5.3. Mean first-passage times
15.6. Searching for the saddle point
15.7. Epilogue
Chapter 16: Mesoscopic fluid models
16.1. Dissipative-particle dynamics
16.1.1. DPD implementation
16.1.2. Smoothed dissipative-particle dynamics
16.2. Multi-particle collision dynamics
16.3. Lattice-Boltzmann method
Part V: Appendices
Appendix A: Lagrangian and Hamiltonian equations of motion
A.1. Action
A.2. Lagrangian
A.3. Hamiltonian
A.4. Hamilton dynamics and statistical mechanics
A.4.1. Canonical transformation
A.4.2. Symplectic condition
A.4.3. Statistical mechanics
Appendix B: Non-Hamiltonian dynamics
Appendix C: Kirkwood-Buff relations
C.1. Structure factor for mixtures
C.2. Kirkwood-Buff in simulations
Appendix D: Non-equilibrium thermodynamics
D.1. Entropy production
D.1.1. Enthalpy fluxes
D.2. Fluctuations
D.3. Onsager reciprocal relations
Appendix E: Non-equilibrium work and detailed balance
Appendix F: Linear response: examples
F.1. Dissipation
F.2. Electrical conductivity
F.3. Viscosity
F.4. Elastic constants
Appendix G: Committor for 1d diffusive barrier crossing
G.1. 1d diffusive barrier crossing
G.2. Computing the committor
Appendix H: Smoothed dissipative particle dynamics
H.1. Navier-Stokes equation and Fourier's law
H.2. Discretized SDPD equations
Appendix I: Saving CPU time
I.1. Verlet list
I.2. Cell lists
I.3. Combining the Verlet and cell lists
I.4. Efficiency
Appendix J: Some general purpose algorithms
J.1. Gaussian distribution
J.2. Selection of trial orientations
J.3. Generate random vector on a sphere
J.4. Generate bond length
J.5. Generate bond angle
J.6. Generate bond and torsion angle
Part VI: Repository
Appendix K: Errata
Appendix L: Miscellaneous methods
L.1. Higher-order integration schemes
L.2. Surface tension via the pressure tensor
L.3. Micro-canonical Monte Carlo
L.4. Details of the Gibbs “ensemble”
L.4.1. Free energy of the Gibbs ensemble
L.4.2. Graphical analysis of simulation results
L.4.3. Chemical potential in the Gibbs ensemble
L.4.4. Algorithms of the Gibbs ensemble
L.5. Multi-canonical ensemble method
L.6. Nosé-Hoover dynamics
L.6.1. Nosé-Hoover dynamics equations of motion
L.6.2. Nosé-Hoover algorithms
L.7. Ewald summation in a slab geometry
L.8. Special configurational-bias Monte Carlo cases
L.8.1. Generation of branched molecules
L.8.2. Rebridging Monte Carlo
L.8.3. Gibbs-ensemble simulations
L.9. Recoil growth: justification of the method
L.10. Overlapping distribution for polymers
L.11. Hybrid Monte Carlo
L.12. General cluster moves
L.13. Boltzmann-sampling with dissipative particle dynamics
L.14. Reference states
L.14.1. Grand-canonical ensemble simulation
Appendix M: Miscellaneous examples
M.1. Gibbs ensemble for dense liquids
M.2. Free energy of a nitrogen crystal
M.3. Zeolite structure solution
Appendix N: Supporting information for case studies
N.1. Equation of state of the Lennard-Jones fluid-I
N.2. Importance of detailed balance
N.3. Why count the old configuration again?
N.4. Static properties of the Lennard-Jones fluid
N.5. Dynamic properties of the Lennard-Jones fluid
N.6. Algorithms to calculate the mean-squared displacement
N.7. Equation of state of the Lennard-Jones fluid
N.8. Phase equilibria from constant-pressure simulations
N.9. Equation of state of the Lennard-Jones fluid - II
N.10. Phase equilibria of the Lennard-Jones fluid
N.11. Use of Andersen thermostat
N.12. Use of Nosé-Hoover thermostat
N.13. Harmonic oscillator (I)
N.14. Nosé-Hoover chain for harmonic oscillator
N.15. Chemical potential: particle-insertion method
N.16. Chemical potential: overlapping distributions
N.17. Solid-liquid equilibrium of hard spheres
N.18. Equation of state of Lennard-Jones chains
N.19. Generation of trial configurations of ideal chains
N.20. Recoil growth simulation of Lennard-Jones chains
N.21. Multiple time step versus constraints
N.22. Ideal gas particle over a barrier
N.23. Single particle in a two-dimensional potential well
N.24. Dissipative particle dynamics
N.25. Comparison of schemes for the Lennard-Jones fluid
Appendix O: Small research projects
O.1. Adsorption in porous media
O.2. Transport properties of liquids
O.3. Diffusion in a porous medium
O.4. Multiple-time-step integrators
O.5. Thermodynamic integration
Appendix P: Hints for programming
Bibliography
Acronyms
Glossary
Index
Author index

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