Computer Simulation Studies in Condensed-Matter Physics XVII (eBook)

Preface 6
Contents 7
Systems out of Equilibrium 11
1 Computer Simulation Studies in Condensed Matter Physics: An Introduction 12
Part I Systems out of Equilibrium 18
2 Shake, Rattle or Roll: Things to do with a Granular Mixture on a Computer 18
2.1 Introduction 18
2.2 Simulation Methodology 19
2.3 Chute Flow 21
2.4 Brazil-Nut E.ect 22
2.5 Granular Ratchet 23
2.6 Rotating Cylinder – Axial Segregation 25
2.7 Rotating Cylinder – Radial Segregation 27
2.8 Horizontally vibrated layer 27
2.9 Conclusion 29
References 29
3 A New Method of Investigating Equilibrium Properties from Nonequilibrium Work 30
3.1 Introduction 30
3.2 Method 30
3.3 Application for Lennard–Jones System 32
3.4 Summary and Discussion 34
References 35
4 Numerical Simulations of Critical Dynamics far from Equilibrium 36
4.1 Introduction 36
4.2 Short-Time Dynamic Scaling Form 38
4.3 Applications of Short-Time Dynamic Scaling 41
4.4 Numerical Solutions of Deterministic Dynamics 48
4.5 Conclusions 50
References 51
Part II Soft and Disordered Materials 55
5 Entropy Driven Phase Separation 56
5.1 Introduction 56
5.2 Grand Canonical Monte Carlo 58
5.3 Cluster Moves 60
5.4 Detailed Balance 61
5.5 Ergodicity 64
5.6 Early Rejection Scheme 65
5.7 Application 65
5.8 Conclusions 69
5.9 Appendix: Random Points 69
References 70
6 Supercooled Liquids under Shear: Computational Approach 72
6.1 Introduction 72
6.2 Simulation Method 73
6.3 Simulation Results 75
6.4 Conclusions 81
References 83
7 Optimizing Glasses with Extremal Dynamics 85
References 89
8 Stochastic Collision Molecular Dynamics Simulations for Ion Transfer Across Liquid – Liquid Interfaces 91
8.1 Introduction 91
8.2 Potential-energy Surface 91
8.3 Simulations of Ion Transfer 92
8.4 Conclusions 94
References 95
Part III Biological Systems 97
9 Generalized-Ensemble Simulations of Small Proteins 98
References 100
10 A Biological Coevolution Model with Correlated Individual- Based Dynamics 101
10.1 Introduction 101
10.2 Model 101
10.3 The Interaction Matrix 102
10.4 Simulation Results 103
References 105
11 An Image Recognition Algorithm for Automatic Counting of Brain Cells of Fruit Fly 106
11.1 Introduction 106
11.2 Data 107
11.3 Counting Algorithm 107
11.4 Results 109
References 110
12 Preferred Binding Sites of Gene- Regulatory Proteins Based on the Deterministic Dead-End Elimination Algorithm 111
12.1 Introduction 111
12.2 Numerical Methods 112
12.3 Results and Discussion 114
References 116
Part IV Algorithms and Methods 119
13 Geometric Cluster Algorithm for Interacting Fluids 120
13.1 Introduction and Motivation 120
13.2 Cluster Monte Carlo Algorithms 121
13.3 Generalized Geometric Cluster Algorithm 122
13.4 Performance 126
13.5 Illustration 131
13.6 Conclusion and Outlook 131
References 132
14 Polymer Simulations with a Flat Histogram Stochastic Growth Algorithm 133
14.1 Introduction 133
14.2 The Algorithm 136
14.3 Simulations 141
14.4 Conclusion and Outlook 146
References 146
15 Convergence of the Wang – Landau Algorithm and Statistical Error 147
References 152
16 Wang–Landau Sampling with Cluster Updates 153
16.1 Introduction 153
16.2 Cluster Updates 154
16.3 Performance 155
16.4 Conclusions 155
References 156
17 Multibaric-Multithermal Simulations for Lennard – Jones Fluids 157
17.1 Introduction 157
17.2 Methods 157
17.3 Computational Details 158
17.4 Results and Discussion 159
17.5 Conclusions 161
References 161
18 A Successive Umbrella Sampling Algorithm to Sample and Overcome Free Energy Barriers 162
18.1 Introduction 162
18.2 A Coarse-Grained Model for Hexadecane 162
18.3 Successive Umbrella Sampling 164
18.4 Phase Behavior and Interfacial Tension of Hexadecane 164
References 165
Part V Computer Tools 167
19 C++ and Generic Programming for Rapid Development of Monte Carlo Simulations 168
19.1 Introduction 168
19.2 Flexible Energy Calculation 170
19.3 Monte Carlo Concepts 173
19.4 Summary 178
References 179
20 Visualization of Vector Spin Con.gurations 180
20.1 Introduction 180
20.2 Models 181
20.3 AViz 181
20.4 Visualizing Vector Spins 182
20.5 Three Dimensions 184
References 184
21 The BlueGene/L Project 185
21.1 Project Background 185
21.2 BlueGene/L Architecture 185
21.3 Project Status Update 188
21.4 Conclusion 189
References 189
Part VI Molecules, Clusters and Nanoparticles 191
22 All-Electron Path Integral Monte Carlo Simulations of Small Atoms and Molecules 192
22.1 Introduction: Path Integral Theory 192
22.2 Recent Path Integral Simulations on Nanostructures 194
22.3 Motivation for Atomic and Molecular Calculations 195
22.4 Monte Carlo Simulation Technique 196
22.5 Examples and Tests for Non-Interacting Fermions 199
22.6 Calculations on Atoms 201
22.7 Calculations on Molecules 203
22.8 Conclusion and Future Work 205
References 206
23 Projective Dynamics in Realistic Models of Nanomagnets 207
23.1 Introduction 207
23.2 Model and Numerical Results 207
23.3 Summary and Conclusions 210
References 210
24 Cumulants for an Ising Model for Folded 1- d Small- World Materials 212
24.1 Introduction 212
24.2 Models and Methods 212
24.3 Results 213
24.4 Summary and Conclusions 213
References 215
25 Embryonic Forms of Nickel and Palladium: A Molecular Dynamics Computer Simulation 216
25.1 Introduction 216
25.2 The Potential Energy Function 217
25.3 Calculations and Discussion 218
25.4 Conclusion 221
References 222
Part VII Surfaces and Alloys 225
26 Usage of Pattern Recognition Scheme in Kinetic Monte Carlo Simulations: Application to Cluster Di . usion on Cu( 111) 226
26.1 Introduction 226
26.2 Theoretical Details 228
26.3 Model Systems 232
26.4 Di.usion Processes and Activation Energies 232
26.5 Results 232
26.6 Conclusions 248
References 250
27 Including Long-Range Interactions in Atomistic Modelling of Di . usional Phase Changes 252
27.1 Introduction 252
27.2 Computational Method 254
27.3 Clustering in the Al-Cu and Al-Cu-Mg Systems 260
27.4 Conclusions 264
References 267
28 Br Electrodeposition on Au(100): From DFT to Experiment 269
References 275
29 Simulation of ZnSe, ZnS Coating on CdSe Substrate: The Electronic Structure and Absorption Spectra 276
29.1 Introduction 276
29.2 Calculation Details 277
29.3 Results and Discussion 277
29.4 Conclusion 280
References 280
30 Simulation of Islands and Vacancy Structures for Si/ Ge- covered Si( 001) Using a Hybrid MC- MD Algorithm 281
30.1 Introduction 281
30.2 Simulation Method 282
30.3 Relaxation of Islands and Step Edges 283
30.4 Formation of Vacancy Structures 284
30.5 Conclusion 286
References 286
31 Spin-Polarons in the FM Kondo Model 287
References 292
List of Contributors 294

8 Stochastic Collision Molecular Dynamics Simulations for Ion Transfer Across Liquid–Liquid Interfaces (p. 80)

S. Frank, and W. Schmickler

1 Abteilung Elektrochemie, Universität Ulm, 89069 Ulm, Germany

2 Current address: Center for Materials Research and Technology and School of Computational Science and Information Technology, Florida State University, Tallahassee, FL 32306-4350, USA

wolfgang.schmickler@chemie.uni-ulm.de, sfrank@csit.fsu.edu

Abstract.

We compute the potential-energy surface for ion transfer across liquid– liquid interfaces from a lattice gas model and simulate the transfer as a random walk of the ion coupled to a heat bath. The kinetics obey Tafel behavior. The reaction rate is slowed down due to friction, and the friction effect is stronger than for a free particle.

8.1 Introduction

Ion transfer across liquid–liquid interfaces, though of considerable experimental interest, still lacks an established theoretical description. It is not clear whether this process should be viewed as a chemical reaction requiring an activation energy, or simply as a mass transport across a viscous boundary. Molecular dynamics simulations have shown a continuous increase of the chemical part of the free energy of ion transfer and no barrier (see, e.g., [1]).

However, the simulations were performed in the presence of a high field driving the ion across the interface, and in the absence of space charge regions. Thus, an essential part of the interaction energy of the transferring ion has been missing. In a model proposed by Schmickler [2], it is the combination of several interactions that constitutes a barrier at the interface. Here, we follow Schmickler’s ideas and treat ion transfer as a chemical reaction. The reaction coordinate – simply the distance from the average interface position – is singled out, and all the other degrees of freedom are represented as a heat bath, the same approach as in Kramers’ theory [3]. With this simplification, we can observe the reaction directly in a simulation.

8.2 Potential-energy Surface

We calculate the potential-energy surface of a transferring ion as the con.gurational energy of a positively charged test particle with fixed position in a simple cubic lattice gas, as a function of the distance z from the average interface position. Our model contains two solvents S1 and S2 and a different base electrolyte in each phase, and each lattice site is occupied by one particle.

The configurational energy is given by the sum over all nearestneighbor interactions, plus for ions the energy in the instantaneous electrostatic potential caused by all ions in the system. We calculate the equilibrium properties of this model using the Metropolis Monte Carlo algorithm. Details are given elsewhere [4]. The system is polarizable in a certain potential window, and the absolute value of the free energy of ion transfer, which is governed by a single interaction parameter ±r for the interaction with the two solvents, must be low enough for the ion to be transferable within this window.