ITALIAN PHYSICAL SOCIETY
CONFERENCEPROCEEDINGS
VOLUME 49
Euroconference on Computer Simulationin Condensed Matter Physics and Chemistry
Monte Carlo and Molecular Dynamicsof Condensed Matter Systems
edited by K. Binder and G. CiccottiCorao, 3-28 July 1995
UNtVERSITATSBIBUOTHEKHANNOVER
TECHNISCHEINFORMATIONSBIBLIOTHEK
Italian Physical SocietyBologna - Italy
CONTENTS
PREFACE v
ACKNOWLEDGEMENTS ix
ORGANIZERS xiii
LECTURERS xiv
STUDENTS xix
VISITORS xxv
CONTENTS xxix
PARTI
STATISTICAL MECHANICS AND SIMULATION METHODS
Chapter 1Statistical mechanics for computer simulators 3by Daan Frenkel
1 Introduction 71.1 Who needs statistical mechanics? 7
2 Entropy and temperature 82.1 System at constant temperature 92.2 Other ensembles . ' 11
3 Fluctuations 123.1 Histograms and Landau Free energies 13
4 Classical Statistical Mechanics 144.1 Ergodicity 16
5 Free energy and phase behavior 185.1 Thermodynamic Integration 185.2 Tracing coexistence curves 20
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X X X
6 Perturbation Theory 216.1 Perturbation theory for hard-core systems? 23
7 Mean-field theory 258 Onsager's regression hypothesis 269 Linear Response Theory 29
9.1 Static response 309.2 Dynamic response 319.3 Dissipation 339.4 Rare Events 38References 41
Chapter 2Introduction to molecular dynamics methods 43by M. Sprik
1 Introduction 472 Basic Molecular Dynamics 48
2.1 Newton's equations of motion 482.2 Criteria for time iteration in MD 492.3 Verlet algorithm 50
3 Dynamics in Phase Space 513.1 Hamiltonian dynamics 513.2 Liouville operators 533.3 Factorization of phase space propagators 55
4 MD under Constant Pressure and Temperature 564.1 Equilibrium statistical mechanics 574.2 Instantaneous temperature and pressure 584.3 Constant pressure MD 614.4 Constant temperature MD 64
5 Multiple Time Scales 665.1 Constraint dynamics 675.2 Multiple time steps 69
6 Long-Range Interactions 706.1 Dielectrics 706.2 The reaction field method 736.3 Ewald summation 756.4 Polarization fluctuations and dielectrics 79
7 Free Energy and Rare Events 827.1 Potential of mean force and reversible work 827.2 Constraints and free energy 84References ' 87
Chapter 3Molecular dynamics for hard particles 89by Michael P. Allen
1 Introduction 932 Motivation 93
2.1 Hard particle models 93
2.2 Hard particle reference systems 942.3 Molecular timescales 94
3 Simulation method 953.1 Free flight dynamics 953.2 Locating collisions 953.3 Collision dynamics 963.4 Housekeeping 97
4 Calculation of results 985 Case study • 100
References 105
Chapter 4Molecular dynamics simulation of rare events: calculation of rateconstants 107by Giovanni Ciccotti and Mauro Ferrario
1 Introduction 1112 Reactive Flux Correlation Formulas and Blue Moon ensemble 112
2.1 Theory 1122.2 Blue Moon Ensemble 113
3 Quantum Extensions 1173.1 Adiabatic dynamics 1183.2 Path integral molecular dynamics 120References 122
Chapter 5Introduction to Monte Carlo methods I 123by K. Binder
1 Preliminaries and Overview 1272 Calculation of thermodynamic averages by importance sampling Monte
Carlo methods 1293 Application of the Monte Carlo method to study the phase transition
of the Ising model 1334 Solid-liquid transition of hard disks 1365 Application of Monte Carlo simulation to study interdiffusion in binary
mixtures 140References 144
Chapter 6Introduction to Monte Carlo methods II • 147by Dietrich Stauffer
1 Down with Vienna Imperialism 1512 Detailed balance and other fundamentals 1513 Dynamics 1544 Error estimates 1575 Summary 162
References 162
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Chapter 7Configurational-bias Monte Carlo 163by Daan Frenkel and Germonda Mooij
1 Introduction 1671.1 Detailed balance 1681.2 Rosenbluth sampling 1681.3 CBMC as 'Dynamic' Rosenbluth sampling 1691.4 Continuously deformable chain 170
2 Efficiency of Configurational-Bias Monte Carlo 1722.1 Remark 174
3 Results 175References 177
PART II
PHASE TRANSITIONS
Chapter 8Theory of phase transitions beyond mean field theory 181by D. P. Landau
12
3
4
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IntroductionCritical Phenomena2.1 Critical Exponent Relations2.2 Scaling functions2.3 Scaling Laws2.4 Universality2.5 Multicritical Phenomena2.6 Surface Critical PhenomenaLandau Theory3.1 Expansion and Power Laws3.2 . Ginzburg criterionRenormalization Group Theory4.1 Fundamental Ideas4.2 Real space methods4.3 Momentum-space formulationDynamical Critical PhenomenaDynamics at first-order transitionsLong Flexible Polymers and the Analogy to Critical PhenomenaSummaryReferences
185185186188189190191193195195197198198201204205208210212212
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Chapter 9Simulation of phase transitions: critical phenomena 215by B. Dunweg
1 Introduction I: A Brief Repetition of Scaling Ideas 2192 Introduction II: The Computational Challenge 2223 Finite-Size Scaling 224
3.1 The order parameter distribution function 2243.2 Finite-size scaling for usual second-order transitions 2263.3 Finite-size scaling for mean-field-like second-order transitions 2293.4 Finite-size "scaling" for first-order transitions 230
4 Reweighting Techniques 2324.1 Reweighting used for data analysis 2324.2 A side remark: Determination of free energies via thermody-
namic integration, multiple histograms or multistage sampling 2344.3 Reweighting built into the simulation procedure: "umbrella
sampling", "multicanonical ensemble", "entropic sampling" 2354.4 "Expanded ensemble", "simulated tempering" 237
5 Estimates for Critical Parameters 2386 Simulation of Dynamic Critical Phenomena 240
6.1 Correlation functions at Tc 2416.2 "Quenches" to Tc 242
7 More Complicated Hamiltonians 2448 The Interfacial Free Energy 249
References 253
Chapter 10Simulation and phase diagrams 255by Michael P. Allen
1 Introduction 2591.1 Thermodynamic Background 2591.2 Simulations near a first-order phase transition 2601.3 Methods 262
2 Traversing phase transitions 2623 Free energies 263
3.1 Studies of melting 2653.2 Studies of the isotropic-nematic transition 2663.3 Free energy differences 266
4 Chemical potentials 2694.1 Introduction 2694.2 Excluded volume map sampling 2704.3 Biased sampling 2714.4 Mixtures 2724.5 Gradual insertion 2724.6 Practicalities 274
5 Bulk phase coexistence 2756 Gibbs ensemble 277
6.1 Introduction 277
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IntroductionSimple ModelsAveragingRandom FerromagnetRandom Field Ising ModelSpin GlassesConclusionsReferences
6.2 Excluded volume map sampling 2796.3 Biased sampling 2796.4 Mixtures 2796.5 Gradual transfer 279
7 Order parameter distributions 2808 Conclusions 281
References 282
Chapter 11Phase transitions in random systems 285by A. P. Young
289289291293297301305306
Chapter 12Monte Carlo simulations of interfacial phenomena 309by D. P. Landau
1 Introduction 3132 Model and simulation technique 3143 Wetting in Thick Films 315
3.1 Critical Wetting 3153.2 First Order Wetting and Layering transitions 316
4 Thin Films with Equal Walls: Capillary Condensation 3175 Thin Films with Competing Walls: Interface Delocalization 3196 Conclusions 322
References 323
Chapter 13Molecular dynamics simulation of lipid bilayers 325by Douglas J. Tobias, Kechuan Tu and Michael L. Klein
1 Introduction 3291.1 Experimental observations on lipid bilayer structure and dynamics3301.2 Membrane simulations 331
2 Constant pressure and temperature MD 3322.1 Statistical mechanics of extended systems 3332.2 Constant NPT MD in fully flexible simulation cells 3332.3 Practical aspects 335
3 Potential function for lipids 3363.1 Headgroup and glycerol ester regions 3363.2 Hydrocarbon chains 337
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4 Results for gel and liquid crystal phospholipid bilayers 337References 342
Chapter 14Interplay of melting, wetting, overheating and faceting on metalsurfaces: theory and simulation. 345by Francesco D. Di Tolla, Erio Tosatti and Furio Ercolessi
1 Overview of the high temperature behavior of crystal surfaces 3492 Surface melting, non-melting, faceting, and layering 351
2.1 Phenomenological theory for surface melting: review 3512.2 Surface free energy anisotropy and crystal shape 3542.3 Introduction to faceting 3562.4 Surface non-melting and overheating 3602.5 Incomplete Melting 3602.6 Layering at liquid metal surfaces 3602.7 Existing simulations of surface melting/non-melting and
overheating - 3613 Surface simulations with MD: technical issues 363
3.1 The glue potential 3643.2 Determination of Tm 3663.3 Processing of the simulation results 366
4 Simulation of melting/nonmelting at surfaces: results 3684.1 A case of surface melting: Al( 110) . 3684.2 Nonmelting and overheating: Al(ll l) and Al(100) 3724.3 A case of incomplete surface melting: Pb(100) 3784.4 Simulation of liquid surfaces 379
5 Layering and the microscopic origin of non-melting 3815.1 The changeable role of the layering forces on surface melting 3815.2 Dependence of the interaction on the orientation 3835.3 Simulated recrystallizations 387
6 Interplay between non-melting, wetting, and faceting 3906.1 Wetting a solid surface with a drop of melt: theory 3906.2 Non-melting induced faceting 3936.3 Quantitative results, and MD simulations 3936.4 Comparison with experiments 394
7 Summary, and outlook 396References 396
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PART III
QUANTUM THEORY AND SIMULATIONS
Chapter 15Quantum theory 401by Hans De Raedt
1 Introduction 4052 Exact Diagonalization 407
2.1 Methods to compute the full spectrum 4072.2 Methods to compute the part of spectrum 407
3 Variational Methods 4103.1 Fundamental Theorems 4103.2 Trial State Approach 4113.3 Recursive Variational Techniques 4123.4 Stochastic Diagonalization 4133.5 Computation of physical properties 414
4 Trotter-Suzuki Formulae 4155 Path Integrals 4196 Quantum Dynamics 421
6.1 Application: Quantum interference of two identical particles 4277 Quantum Monte Carlo: Application 430
7.1 Theory 4317.2 Hubbard-Stratonovitch Transformation 4337.3 Application 435References 440
Chapter 16Path integral Monte Carlo methods for fermions 443by D. M. Ceperley
1 Introduction 4472 Imaginary Time Path Integrals 4493 The Direct Fermion Path Integral Method 4514 The Restricted Path Integral Method • 4545 The Reference Point 4576 An Example of Restricted Paths 4587 Nodes of the Density Matrix 4608 Some Technical Details of RPIMC 466
8.1 The action 4668.2 Sampling restricted paths 471
9 Permutations, the Momentum Distribution and Fermi Liquids 47310 Other Fermion Methods 475
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10.1 Hall's method 47510.2 Slice-wise antisymmetrization 47610.3 Ignoring the sign 47710.4 Cancellation 477
11 Current Applications of Fermion Path Integrals 47812 Future Prospects 479
References 481
Chapter 17Monte Carlo variational theory of condensed phases of 4He 483by D.E. Galli and L. Reatio
1 Introduction 4872 Shadow wave function 489
2.1 Liquid and solid bulk 4He 4892.2 Local density shadow wave function 490
3 Self-binding of a quantum system 4913.1 Shadow wave function for a self-bound state 4923.2 Film 4933.3 Clusters 495
4 Excited states 4964.1 Feynman shadow wave function (F-swf) 4964.2 Feynman-Cohen shadow wave function (FC-swf) 497
5 Conclusion 498References 499
Chapter 18Path integral simulations of adsorbed molecular layers: phase transitions501by Martina Kreer and Peter Nielaba
1 Introduction 5052 Orientational Phase Transitions in Adsorbed Monolayers 505
2.1 The Order of the Herringbone Transition of N2 on Graphite 5052.2 Quantum Effects on the Orientational Phase Transition 506
3 Phase Transitions in Classical and Quantum 2D Fluids 5083.1 Phase Transitions in Nonadditive Symmetric Hard Disc Fluids 5083.2 Path Integral Monte Carlo Simulations in the Gibbs Ensemble 5093.3 Density functional theory 5103.4 i?2 and D2 adsorbed on graphite 511
4 Random-field induced rounding of the Ising-type transition inphysisorbed {CO)\-X(N2)X mixtures • 513
5 Summary 516References 517
Chapter 19Cluster algorithms with emphasis on quantum spin systems 519by J. E. Gubernatis and N. Kawashima
1 Introduction 523
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2 Background 5242.1 Monte Carlo Refresher 5242.2 Swendsen-Wang Algorithm 5252.3 The Fortuin-Kasteleyn Transformation 5262.4 Cluster Algorithm Characteristics . 528
3 Cluster Algorithm Construction 5293.1 Dual Monte Carlo 5293.2 Free Cluster Algorithms 5303.3 The Linear System of Equations 5303.4 Labeling and Joint Probabilities 5303.5 Cluster Algorithms with Local Labeling Rules 5313.6 Interim Summary 532
4 Quantum Spin Systems 5324.1 Cluster Algorithm: S — | Ferromagnetic Heisenberg Model 5324.2 Cluster Algorithm: S = 1 Ferromagnetic Heisenberg Model 5364.3 Cluster Algorithm: General XYZ Model 539
5 Summary 540References 542
Chapter 20Feynman path centroid methods for condensed phase quantum dynamics545by Gregory A. Voth
1 Introduction 5492 Activated Dynamics and Quantum Transition State Theory 550
2.1 Formalism 5502.2 Selected Applications 550
3 The Centroid Molecular Dynamics Method 5523.1 Formalism 5523.2 Numerical Applications of CMD 554
4 Concluding Remarks 556References 556
PART IV
DENSITY FUNCTIONAL APPROACH
Chapter 21Density functional theory 561by Walter Kohn
1 Introduction 5652 Basic Density Functional Theory 5663 Generalizations [2,3,4] 569
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4 Some Representative Quantitative Results 5695 A DFT/Density Matrix Method Scaling Linearly with the Number of
Atoms [12] 570References 572
Chapter 22Density functional methods at finite temperature 573by Jean-Pierre Hansen and Enrico Smargiassi
1 Inhomogeneous systems and effective interactions 5772 Density functional theory: basic principles and standard approximations 579
2.1 Linear response 5822.2 Gradient expansion 5822.3 Mean-field approximation 5832.4 Functional Taylor expansion 584
3 A gentle application of DFT: sedimentation equilibrium and osmoticequation-of-state 584
4 A density functional approach to polyelectrolytes 5865 "Ab-initio" Monte Carlo sampling 5906 The quantum regime: orbital-free density functionals 594
6.1 Thomas-Fermi Molecular Dynamics 5966.2 Gradient correction to TF 5976.3 The Hohenberg-Kohn functional 5976.4 Hybrid functionals 5986.5 Kohn-Sham vs. orbital-free functionals 598References 599
Chapter 23Molecular dynamics from first principles 601by R. Car
1 Introduction 6052 The potential energy function 6073 The first-principles molecular dynamics equations 6134 Applications to phase transitions. 6205 Excited state molecular dynamics 626
References 632
Chapter 24Car-Parrinello method and adiabatic invariants 635by G. Pastore
1 Introduction 6392 From parametric optimization to adiabatic dynamics 6403 Adiabatic invariants and departure from the minimum 6434 The evolution of the slow variables 6465 Conclusions 647
References 647
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Chapter 25Path integrals and ab initio molecular dynamics 649by AH Alavi
1 Introduction 6532 Statistical Mechanical preliminaries 653
2.1 One-electron systems 6533 Path integration 6544 Path integration: an application 6565 Real-space propagators 6576 Higher-order propagators 6587 Molecular Dynamics 6588 Many-Electron systems - Non-interacting 6599 Interacting electrons - Finite temperature DFT 661
References 666
PART V
POLYMERS, PROTEINS ETC...
Chapter 26Computer simulation methods for polymer physics 669by Kurt Kremer
1 Introduction 6732 Polymer simulations: general considerations 6753 Algorithms for static properties 677
3.1 Static methods for isolated chains 6773.2 "Dynamic" methods for static properties 6873.3 More complex single polymer problems: Two examples 692
4 Simulations of polymer dynamics 6944.1 Bond fluctuation algorithm 6974.2 Molecular dynamics 7004.3 Monte Carlo versus molecular dynamics for melts 701
5 Dynamics of Melts: Reptation 7025.1 Monomer motion and relaxation functions * 7025.2 Comparison to experiment 7075.3 The crossover from semi-dilute and deviations from Rouse 708
6 Extensions: glasses and networks 7117 Further Reading 7148 Conclusions - Other Problems 719
References 720
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Chapter 27Simulation of polymers using realistic potentials 725by J.-P. Ryckaert
1 Introduction 7292 Polyethylene (PE) and polypropylene (PP) 7303 Modelling hydrocarbons 732
3.1 Fully atomic models 7333.2 United atoms models 7343.3 Flory potential 7353.4 Single chain models with excluded volume forces 736
4 Recent results on the single chain route to study PE and PP melts 7374.1 PE and PP results at 6 point according to single chain models
neglecting non local interactions 7384.2 PE results according to single chain model with non local
interactions 7384.3 PP results according to single chain model with non local
interactions 7405 Recent results on the many chains route to study PE 742
5.1 MD simulation of C44H90 melts 7425.2 Rotator phases of paraffins C19H40 743
6 Perspectives 7447 Acknowledgments 745
References 745
Chapter 28Molecular dynamics simulation of proteins 747by Massimo Marchi
1 Introduction 7512 What is a Protein 7523 Interaction Potentials 754
3.1 Bonded Interactions 7553.2 Non-bonded Interactions 757
4 Covalent Topology and Potential Parameters 7595 What to Simulate and How 7596 Handling Long Range Forces 7627 Simulations in Other Ensembles 7658 Molecular Dynamics Simulation of the Type I Crystal of BPTI 767
References 774
Chapter 29Molecular simulation methods for generating ensembles or trajectoriesconsistent with experimental data 777by W.F. van Gunsteren, A.P. Nanzer and A.E. Torda
1 Introduction 7812 Relations between observables Q and atomic degrees of freedom or force
field parameters q 782
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3 Techniques to couple < Q > to Qo in a molecular simulation 7843.1 Constraint methods 7853.2 Penalty function methods 7853.3 Extended system methods 7863.4 Weak-coupling methods 7863.5 Stochastic methods 787
4 Conclusions 787References 788
PART VI
MICROSCOPIC APPROACH TO DYNAMICAL AND NONEQUILIBRIUMPHENOMENA
Chapter 30The character of the nonequilibrium steady state: beautiful formalismmeets ugly reality 791by Brad Lee Holian
1 Introduction 7952 Response Theory 8053 Free Energy at the Nonequilibrium Steady State 8124 Conclusions 821
References 822
Chapter 31Simple and complex fluids under shear 823by S. Hess, M. Kroger, W. Loose, C. Pereira Borgmeyer, R. Schramek,H. Voigt, and T. Weider
1 Introduction 8272 Fluids of Spherical Particles 827
2.1 Molecular dynamics 8272.2 Plane Couette flow 8292.3 Viscosity and other rheological properties 8302.4 Structural changes in the various flow regimes ' 8302.5 Colloidal dispersions 8322.6 Mixtures 834
3 Complex fluids 8353.1 Polymer melts 8353.2 Nematic liquid crystals 8373.3 Ferro-fluids and magneto-rheological fluids 839References 840
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Chapter 32Schematic modelling of superionic conduction 843by J. Marro
1 Introduction 8472 Phase Transitions 8493 Correlations 854
References 857
Chapter 33Search for a cheap molecular dynamics 859by Berni Alder
1 Introduction 8632 Navier-Stokes 8633 Lattice Boltzmann 8644 Molecular Dynamics 8655 Lattice Gas 8656 Bird Method 8667 Hybrid Scheme or Adaptive Algorithm 8678 Consistent Boltzmann and Enskog extension 8699 Conclusions 869
References 869
Chapter 34Round-table discussions on large-scale computations by non-equilibrium molecular dynamics: how far we can go? 871by Michel Mareschal
PART VII
MISCELLANEOUS TOPICS: ASPECTS OF COMPUTATIONALIMPLEMENTATION, HISTORICAL RECOLLECTIONS, ETC...
Chapter 35Parallelization of computational physics problems • 887by Dieter W. Heermann
1 Introduction 8912 Concepts to Exploit Parallelism 8923 Poor Mans Parallelization 892
3.1 Data Parallel Algorithms 8933.2 Algorithmic Parallelism 8953.3 Domain Decomposition 897
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4 Machine Considerations5 Language Considerations 8996 A new algorithm for the simulation of large lattice systems 9007 A Case Study 902
7.1 The Hybrid Monte Carlo Method 9027.2 Parallelization of the Polymer System 904References 906
Chapter 36On some additional recollections, and the absence thereof, about theearly history of computer simulations in statistical mechanics 907by W. W. Wood
Chapter 37Biologically motivated Monte Carlo: immunology and ageing' 913by Dietrich Stauffer
1 Introduction 9172 Concepts and models for ageing 9183 Techniques for ageing 9194 Ageing results 9205 Immunology 921
References 924
PART VIII
SEMINARS
Seminar 1Wigner Approach in Quantum Statistical Mechanics and QuantumGeneralization Molecular Dynamics Method 927by V.S. Filinov
Seminar 2Complex - valued path integrals Monte Carlo simulation of quantumelectrons in disordered system of scatterers 931by V.S. Filinov
Seminar 3Symplectic algorithms for the simulation of hamiltonian dynamic 935by Lapo Casetti
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Seminar 4On the adsorption process in polymer brushes: a Monte Carlo study 939by A. Kopf, J. Baschnagel, J. Wittmer and K. Binder
Seminar 5Cluster approach and Monte Carlo efficient dynamics in frustrated anddisordered spin systems 943by Mario Nicodemi
Seminar 6Ordered and chaotic dynamics in the simulation of real systems 947by Alexander Tenenbaum
Seminar 7Do conformal crystals exist in uniform fields? 951by K.W. Wojciechowski, J. Klos and A.C. Brarika
Seminar 8Relaxation times in an anharmonic crystal with diluted impurities 955by Roberto Livi
