Preface xi List of Contributors xv Contributors to Previous Volumes xvii 1. Free-Energy Calculations with Metadynamics: Theory and Practice 1 Giovanni Bussi and Davide Branduardi Introduction 1 Molecular Dynamics and Free-Energy Estimation 3 Molecular Dynamics 3 Free-Energy Landscapes 4 A Toy Model: Alanine Dipeptide 6 Biased Sampling 8 Adaptive Biasing with Metadynamics 9 Reweighting 12 Well-Tempered Metadynamics 12 Reweighting 14 Metadynamics How-To 14 The Choice of the CV(s) 15 The Width of the Deposited Gaussian Potential 17 The Deposition Rate of the Gaussian Potential 18 A First Test Run Using Gyration Radius 19 A Better Collective Variable: Φ Dihedral Angle 23 Well-Tempered Metadynamics Using Gyration Radius 24 Well-Tempered Metadynamics Using Dihedral Angle Φ 27 Advanced Collective Variables 28 Path-Based Collective Variables 30 Collective Variables Based on Dimensional Reduction Methods 32 Template-Based Collective Variables 34 Potential Energy as a Collective Variable 35 Improved Variants 36 Multiple Walkers Metadynamics 36 Replica Exchange Metadynamics 37 Bias Exchange Metadynamics 38 Adaptive Gaussians 39 Conclusion 41 Acknowledgments 42 Appendix A: Metadynamics Input Files with PLUMED 42 References 44 2. Polarizable Force Fields for Biomolecular Modeling 51 Yue Shi, Pengyu Ren, Michael Schnieders, and Jean-Philip Piquemal Introduction 51 Modeling Polarization Effects 52 Induced Dipole Models 52 Classic Drude Oscillators 54 Fluctuating Charges 54 Recent Developments 55 AMOEBA 55 SIBFA 57 NEMO 58 CHARMM-Drude 58 CHARMM-FQ 59 X-Pol 60 PFF 60 Applications 61 Water Simulations 61 Ion Solvation 62 Small Molecules 63 Proteins 64 Lipids 66 Continuum Solvents for Polarizable Biomolecular Solutes 66 Macromolecular X-ray Crystallography Refinement 67 Prediction of Organic Crystal Structure, Thermodynamics, and Solubility 70 Summary 71 Acknowledgment 71 References 72 3. Modeling Protein Folding Pathways 87 Clare-Louise Towse and Valerie Daggett Introduction 87 Outline of this Chapter 90 Protein Simulation Methodology 90 Force Fields, Models and Solvation Approaches 90 Unfolding: The Reverse of Folding 97 Elevated Temperature Unfolding Simulations 100 Biological Relevance of Forced Unfolding 103 Biased or Restrained MD 108 Characterizing Different States 111 Protein Folding and Refolding 115 Folding in Families 118 Conclusions and Outlook 121 Acknowledgment 122 References 122 4. Assessing Structural Predictions of Protein-Protein Recognition: The CAPRI Experiment 137 Joël Janin, Shoshana J. Wodak, Marc F. Lensink, and Sameer Velankar Introduction 137 Protein-Protein Docking 138 A Short History of Protein-Protein Docking 138 Major Current Algorithms 141 The CAPRI Experiment 144 Why Do Blind Predictions? 144 Organizing CAPRI 145 The CAPRI Targets 146 Creating a Community 149 Assessing Docking Predictions 150 The CAPRI Evaluation Procedure 150 A Survey of the Results of 12 Years of Blind Predictions on 45 Targets 154 Recent Developments in Modeling Protein-Protein Interaction 160 Modeling Multicomponent Assemblies. The Multiscale Approach 160 Genome-Wide Modeling of Protein-Protein Interaction 161 Engineering Interactions and Predicting Affinity 162 Conclusion 164 Acknowledgments 165 References 165 5.

Kinetic Monte Carlo Simulation of Electrochemical Systems 175 C. Heath Turner, Zhongtao Zhang, Lev D. Gelb, and Brett I. Dunlap Background 175 Introduction to Kinetic Monte Carlo 176 Electrochemical Relationships 180 Applications 184 Transport in Li-ion Batteries 184 Solid Electrolyte Interphase (SEI) Passive Layer Formation 187 Analysis of Impedance Spectra 189 Electrochemical Dealloying 189 Electrochemical Cells 190 Solid Oxide Fuel Cells 193 Other Electrochemical Systems 197 Conclusions and Future Outlook 198 Acknowledgments 199 References 199 6. Reactivity and Dynamics at Liquid Interfaces 205 Ilan Benjamin Introduction 205 Simulation Methodology for Liquid Interfaces 207 Force Fields for Molecular Simulations of Liquid Interfaces 207 Boundary Conditions and the Treatment of Long-Range Forces 210 Statistical Ensembles for Simulating Liquid Interfaces 213 Comments About Monte Carlo Simulations 214 The Neat Interface 214 Density, Fluctuations, and Intrinsic Structure 215 Surface Tension 221 Molecular Structure 223 Dynamics 230 Solutes at Interfaces: Structure and Thermodynamics 235 Solute Density 236 Solute-Solvent Correlations 240 Solute Molecular Orientation 242 Solutes at Interfaces: Electronic Spectroscopy 243 A Brief General Background on Electronic Spectroscopy in the Condensed Phase 243 Experimental Electronic Spectroscopy at Liquid Interfaces 245 Computer Simulations of Electronic Transitions at Interfaces 249 Solutes at Interfaces: Dynamics 253 Solute Vibrational Relaxation at Liquid Interfaces 253 Solute Rotational Relaxation at Liquid Interfaces 258 Solvation Dynamics 263 Summary 269 Reactivity at Liquid Interfaces 270 Introduction 270 Electron Transfer Reactions at Liquid/Liquid Interfaces 271 Nucleophilic Substitution Reactions and Phase Transfer Catalysis (PTC) 277 Conclusions 283 Acknowledgments 284 References 284 7. Computational Techniques in the Study of the Properties of Clathrate Hydrates 315 John S. Tse Historical Perspective 315 Structures 317 The van der Waals-Platteeuw Solid Solution Theory 318 Computational Advancements 322 Thermodynamic Modelling 322 Atomistic Simulations 327 Thermodynamic Stability 344 Hydrate Nucleation and Growth 355 Guest Diffusion Through Hydrate Cages 368 Ab Initio Methods 371 Outlook 381 References 382 8. The Quantum Chemistry of Loosely-Bound Electrons 391 John M.

Herbert Introduction and Overview 391 What Is a Loosely-Bound Electron? 391 Scope of This Review 392 Chemical Significance of Loosely-Bound Electrons 394 Challenges for Theory 400 Terminology and Fundamental Concepts 402 Bound Anions 402 Metastable (Resonance) Anions 415 Quantum Chemistry for Weakly-Bound Anions 425 Gaussian Basis Sets 425 Wave Function Electronic Structure Methods 439 Density Functional Theory 456 Quantum Chemistry for Metastable Anions 471 Maximum Overlap Method 474 Complex Coordinate Rotation 477 Stabilization Methods 483 Concluding Remarks 495 Acknowledgments 495 Appendix A: List of Acronyms 496 References 497 Index 519.