分子模拟--从算法到应用

UnderstandingMolecularSimulation.FromAlgorithmstoApplicationsContentsPreface to the Second editionX111PrefaceXVList of SymbolsXIX1 IntroductionParti Basics2 Statistical Mechanics2.1 Entropy and Temperature2.2 Classical Statistical Mechanics132.2. 1 Ergodicity152.3 Questions and Exercises173 Monte Carlo simulations233. 1 The monte Carlo method233.1.1 Importance Sampling243.1.2 The Metropolis method273. 2 A Basic Monte Carlo algorithm313.2.1 The algorithm313.2.2 Technical Details323.2.3 Detailed Balance versus Balance423.3 Trial moves3. 3. 1 Translational Moves3.3.2 Orientational moves3.4 Applications513.5 Questions and exercisesContents4 Molecular dynamics Simulations4.1 Molecular dynamics: The Idea634.2 Molecular Dynamics: A Program644.2.1 Initialization.654.2.2 The Force Calculation4.2.3 Integrating the equations of Motion4.3 Equations of Motion714.3.1 Other Algorithms744.3.2 Higher-Order Schemes4.3.3 Liouville Formulation of Time-Reversible algorithms. 774.3.4 Lyapunov Instability814.3.5 One More Way to Look at the verlet Algorithm824.4 Computer Experiments844.4.1 Diffusion874.4.2 Order-n algorithm to Measure Correlations904.5 Some Applications4.6 Questions and Exercises105Part Ii Ensembles1095 Monte Carlo Simulations in Various Ensembles1115.1 General approach,1125.2 Canonical Ensemble1125.2.1 Monte Carlo Simulations1135.2.2 Justification of the Algorithm1145.3 Microcanonical Monte Carlo1145.4 Isobaric-Isothermal Ensemble1155.4.1 Statistical Mechanical Basis1165.4.2 Monte Carlo simulations1195.4.3 Applications1225.5 Isotension-Isothermal Ensemble1255.6 Grand-Canonical Ensemble1265.6.1 Statistical Mechanical Basis1275.6.2 Monte Carlo simulations1305.6. 3 Justification of the Algorithm1305.6.4 Applicatio5.7 Questions and Exercises1356 Molecular Dynamics in Various Ensembles1396.1 Molecular dynamics at Constant Temperature1406.1.1 The Andersen Thermostat1416.1.2 Nose-Hoover Thermostat147Contents016.1.3 Nose-Hoover Chains1556.2 Molecular dynamics at Constant pressure1586.3 Questions and exercises160art Ill Free Energies and Phase Equilibria1657 Free Energy calculations1677.1 Thermodynamic Integration1687.2 Chemical potentials1727. 2. 1 The Particle Insertion Method.1737.2.2 Other Ensembles1767. 2.3 Overlapping Distribution Method1797.3 Other Free Energy Methods7.3.1 Multiple histograms1837.3.2 Acceptance Ratio Method1897.4 Umbrella Sampling1927.4.1 Nonequilibrium Free Energy Methods1967.5 Questions and Exercises8 The Gibbs Ensemble2018.1 The Gibbs Ensemble Technique2038.2 The partition Function,,,.2048.3 Monte Carlo Simulations2058.3.1 Particle Displacement2058.3.2 Volume Change2068. 3. 3 Particle Exchange088.3.4 Implementation2088.3.5 Analyzing the results2148.4 Applications.2208.5 Questions and exercises223g Other methods to Study coexistence2259.1 Semigrand ensemble2259.2 Tracing Coexistence Curves23310 Free Energies of Solids24110. 1 Thermodynamic Integration24210.2 Free Energies of Solids24310.2.1 Atomic Solids with Continuous potentials24410.3.1 Atomic Solids with Discontinuous Potentials.....24510.3 Free Energies of Molecular Solids24810.3.2 General Implementation Issues24910.4 Vacancies and interstitials26301lContents10.4.1 Free energies26310.4.2 Numerical Calculations26611 Free Energy of Chain Molecules26911.1 Chemical Potential as Reversible Work...,..26911.2 Rosenbluth Sampling27111.2.1 Macromolecules with Discrete Conformations27111.2.2 Extension to Continuously Deformable Molecules... 27611.2.3 Overlapping Distribution Rosenbluth Method28211.2. 4 Recursive Sampling28311.2.5 Pruned-Enriched Rosenbluth Method.285Part iv Advanced Techniques2892 Long-Range Interactions9112.1 Ewald sums29212.1.1 Point Charges29212.1.2 Dipolar particles12.1.3 Dielectric Constant30112. 1.4 Boundary Conditions30312. 1.5 Accuracy and computational complexity30412.2 Fast Multipole Method30612.3 Particle Mesh Approaches31012.4 Ewald Summation in a Slab Geometry3161 3 Biased Monte Carlo Schemes32113. 1 Biased Sampling techniques.32213. 1.1 Beyond metropolis32313.1.2 Orientational Bias32313.2 Chain molecules33113.2.1 Configurational-Bias Monte Carlo33113.2.2 Lattice Models33213.2.3 Off-lattice Case33613. 3 Generation of Trial Orientations,34113.3. 1 Strong intramolecular interactions34213.3.2 Generation of Branched molecules35013. 4 Fixed endpoints35313.4.1 Lattice models35313.4.2 Fully Flexible Chain35513.4.3 Strong Intramolecular Interactions35713.4.4 Rebridging Monte Carlo35713.5 Beyond polymers,,,,.36013.6 Other Ensembles365Contents13.6.1 Grand-Canonical Ensemble.36513.6.2 Gibbs Ensemble Simulations37013.7 Recoil Growth37413.7.1 Algorithm37613.7.2 Justification of the Meth37913. 8 Questions and Exercises38314 Accelerating Monte Carlo Sampling38914.1 Parallel Tempering38914.2 Hybrid Monte Carlo..,39714.3 Cluster moves39914.3.1 Clusters....39914.3.2 Early rejection Scheme40515 Tackling Time-Scale Problems40915.1 Constraints41015.1.1 Constrained and Unconstrained Averages41515.2 On-the-Fly Optimization Car-Parrinello Approach42115.3 Multiple Time Steps42416 Rare Events43116.1 Theoretical Background43216.2 Bennett-Chandler Approach43616.2.1 Computational Aspects43816.3 Diffusive Barrier Crossing44316.4 Transition Path Ensemble45016.4.1 Path Ensemble45116.4.2 Monte Carlo simulations.45416.5 Searching for the Saddle point46217 Dissipative Particle Dynamics46517.1 Description of the Technique46617.1.1 Justification of the Method46717. 1.2 Implementation of the Method46917. 1.3 DPD and Energy Conservation47317.2 Other Coarse-Grained Techniques...,476Part V Appendices479a Lagrangian and hamiltonian481A 1 Lagrangian483A2 Hamiltonian486A 3 Hamilton Dynamics and Statistical Mechanics488ContentsA.3.1 Canonical Transformation489A 3.2 Symplectic Condition490A.3.3 Statistical mechanics492B Non-Hamiltonian dynamics495B.1 Theoretical Background,,495B2 Non-Hamiltonian Simulation of the N, V,T Ensemble ..... 497B 2.1 The Nose -Hoover Algorithm498B 2.2 NoSe-Hoover Chains502B. 3 The N PT Ensemble505C Linear Response Theory509C1 Static Response509C2 Dynamic response..511C3 Dissipation513C.3.1 Electrical Conductivity516C.3.2 Viscosity518C 4 Elastic Constants519D Statistical errors525D 1 Static Properties: System Size.525D 2 Correlation Functions527D 3 Block averages529E Integration Schemes533E1 Higher-Order Schemes....533E2 Nose-Hoover Algorithms535E 2.1 Canonical Ensemble536E 2.2 The Isothermal-Isobaric Ensemble540f Saving CPU Time545F 1 Verlet List545F2 Cell Lists550F3 Combining the Verlet and Cell Lists550F4 Efficiency552G Reference States559G 1 Grand-Canonical Ensemble Simulation559h Statistical Mechanics of the Gibbs"Ensemble"563H 1 Free Energy of the Gibbs Ensemble563H 1. 1 Basic definitions5H.1.2 Free Energy density565H 2 Chemical Potential in the Gibbs Ensemble.570ContentsI Overlapping Distribution for Polymer573j Some General Purpose algorithms577K Small research Projects581K 1 Adsorption in porous media581K 2 Transport Properties in Liquids582K 3 Diffusion in a Porous media583K 4 Multiple-Time- Step Integrators584K5 Thermodynamic Integration585L Hints for Programming587Bibliography589Author Index619Index628