Reviews in Computational Chemistry / Edition 1

Reviews in Computational Chemistry / Edition 1

by Kenny B. Lipkowitz

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ISBN-10: 047168239X

ISBN-13: 9780471682394

Pub. Date: 04/01/2005

Publisher: Wiley

This book series contains pedagogically driven reviews of computational methods for the novice molecular modeler as well as for the expert computational scientist. Topics covered in this volume include computational methods needed to computer π interactions accurately, quantum mechanical methods used for computing weakly bound clusters, computing excited state


This book series contains pedagogically driven reviews of computational methods for the novice molecular modeler as well as for the expert computational scientist. Topics covered in this volume include computational methods needed to computer π interactions accurately, quantum mechanical methods used for computing weakly bound clusters, computing excited state properties with time-dependent density functional theory, and methods for computing quantum phase transitions. Also covered are real-space and multi-grid methods, hybrid methods for atomic level simulations spanning multiple time scales and multiple length scales, techniques used for extending time scales in atomic level simulations, and strategies for simulating ionic liquids.

Product Details

Publication date:
Reviews in Computational Chemistry Series, #25
Product dimensions:
6.34(w) x 9.49(h) x 1.09(d)

Table of Contents

1 Computations of Noncovalent π Interactions C. David Sherrill 1

Introduction 1

Challenges for Computing π Interactions 3

Electron Correlation Problem 3

Basis Set Problem 5

Basis Set Superposition Errors and the Counterpoise Correction 6

Additive Basis/Correlation Approximations 9

Reducing Computational Cost 11

Truncated Basis Sets 12

Pauling Points 14

Resolution of the Identity and Local Correlation Approximations 14

Spin-Component-Scaled MP2 17

Explicitly Correlated R12 and F12 Methods 21

Density Functional Approaches 22

Semiempirical Methods and Molecular Mechanics 24

Analysis Using Symmetry-Adapted Perturbation Theory 25

Concluding Remarks 29

Appendix: Extracting Energy Components from the SAPT2006 Program 29

Acknowledgments 30

References 30

2 Reliable Electronic Structure Computations for Weak Noncovalent Interactions in Clusters Gregory S. Tschumper 39

Introduction and Scope 39

Clusters and Weak Noncovalent Interactions 40

Computational Methods 42

Weak Noncovalent Interactions 43

Historical Perspective 43

Some Notes about Terminology 45

Fundamental Concepts: A Tutorial 46

Model Systems and Theoretical Methods 46

Rigid Monomer Approximation 47

Supermolecular Dissociation and Interaction Energies 48

Counterpoise Corrections for Basis Set Superposition Error 50

Two-Body Approximation and Cooperative/Nonadditive Effects 53

Size Consistency and Extensivity of the Energy 60

Summary of Steps in Tutorial 61

High-Accuracy Computational Strategies 61

Primer on Electron Correlation 63

Primer on Atomic Orbital Basis Sets 64

Scaling Problem 68

Estimating Eint at the CCSD(T) CBS Limit: Another Tutorial69

Accurate Potential Energy Surfaces 71

Less Demanding Computational Strategies 72

Second-Order Moller-Plesset Perturbation Theory 72

Density Functional Theory 75

Guidelines 77

Other Computational Issues 77

Basis Set Superposition Error and Counterpoise Corrections 77

Beyond Interaction Energies: Geometries and Vibrational Frequencies 80

Concluding Remarks 80

Acknowledgments 81

References 81

3 Excited States from Time-Dependent Density Functional Theory Peter Elliott Filipp Furche Kieron Burke 91

Introduction 91

Overview 94

Ground-State Review 95

Formalism 95

Approximate Functionals 100

Basis Sets 102

Time-Dependent Theory 104

Runge-Gross Theorem 104

Kohn-Sham Equations 106

Linear Response 107

Approximations 111

Implementation and Basis Sets 112

Density Matrix Approach 112

Basis Sets 113

Convergence for Naphthalene 114

Double-Zeta Basis Sets 114

Polarization Functions 114

Triple-Zeta Basis Sets 116

Diffuse Functions 117

Resolution of the Identity 117

Summary 117

Performance 118

Example: Naphthalene Results 118

Influence of the Ground-State Potential 120

Analyzing the Influence of the XC Kernel 124

Errors in Potential vs. Kernel 125

Understanding Linear Response TDDFT 126

Atoms as a Test Case 127

Quantum Defect 128

Testing TDDFT 131

Saving Standard Functionals 132

Electron Scattering 135

Beyond Standard Functionals 136

Double Excitations 136

Polymers 137

Solids 137

Charge Transfer 138

Other Topics 139

Ground-State XC Energy 139

Strong Fields 141

Electron Transport 143

Summary 146

Acknowledgments 147

References 147

4 Computing Quantum Phase Transitions Thomas Vojta 167

Preamble: Motivation and History 167

Phase Transitions and Critical Behavior 169

Landau Theory 169

Scaling and the Renormalization Group 171

Finite-Size Scaling 173

Quenched Disorder 174

Quantum vs. Classical Phase Transitions 176

How Important Is Quantum Mechanics? 176

Quantum Scaling and Quantum-to-Classical Mapping 179

Beyond the Landau-Ginzburg-Wilson Paradigm 180

Impurity Quantum Phase Transitions 181

Quantum Phase Transitions: Computational Challenges 182

Classical Monte Carlo Approaches 184

Method: Quantum-to-Classical Mapping and Classical Monte Carlo Methods 184

Transverse-Field Ising Model 184

Bilayer Heisenberg Quantum Antiferromagnet 187

Dissipative Transverse-Field Ising Chain 189

Diluted Bilayer Quantum Antiferromagnet 191

Random Transverse-Field Ising Model 194

Dirty Bosons in Two Dimensions 196

Quantum Monte Carlo Approaches 198

World-Line Monte Carlo 199

Stochastic Series Expansion 200

Spin1/2 Quantum Heisenberg Magnet 201

Bilayer Heisenberg Quantum Antiferromagnet 204

Diluted Heisenberg Magnets 205

Superfluid-Insulator Transition in an Optical Lattice 207

Fermions 210

Other Methods and Techniques 211

Summary and Conclusions 214

Acknowledgments 215

References 215

5 Real-Space and Multigrid Methods in Computational Chemistry Thomas L. Beck 223

Introduction 223

Physical Systems: Why Do We Need Multiscale Methods? 224

Why Real Space? 227

Real-Space Basics 229

Equations to Be Solved 229

Finite-Difference Representations 232

Finite-Element Representations 233

Iterative Updates of the Functions, or Relaxation 235

What Are the Limitations of Real-Space Methods on a Single Fine Grid? 236

Multigrid Methods 238

How Does Multigrid Overcome Critical Slowing Down? 238

Full Approximations Scheme (FAS) Multigrid, and Full Multigrid (FMG) 238

Eigenvalue Problems 244

Multigrid for the Eigenvalue Problem 244

Self-Consistency 245

Linear Scaling for Electronic Structure? 246

Other Nonlinear Problems: The Poisson-Boltzmann and Poisson-Nernst-Planck Equations 248

Poisson-Boltzmann Equation 248

Poisson-Nernst-Planck (PNP) Equations for Ion Transport 250

Some Advice on Writing Multigrid Solvers 253

Applications of Multigrid Methods in Chemistry, Biophysics, and Materials Nanoscience 254

Electronic Structure 255

Electrostatics 262

Transport Problems 266

Existing Real-Space and Multigrid Codes 268

Electronic Structure 269

Electrostatics 269

Transport 270

Some Speculations on the Future 270

Chemistry and Physics: When Shall the Twain Meet? 270

Elimination of Molecular Orbitals? 271

Larger Scale DFT, Electrostatics, and Transport 271

Reiteration of "Why Real Space?" 272

Acknowledgments 272

References 273

6 Hybrid Methods for Atomic-Level Simulations Spanning Multiple-Length Scales in the Solid State Francesca Tavazza Lyle E. Levine Anne M. Chaka 287

Introduction 287

General Remarks about Hybrid Methods 291

Complete-Spectrum Hybrid Methods 292

About this Review 293

Atomistic/Continuum Coupling 293

Zero-Temperature Equilibrium Methods 293

Finite-Temperature Equilibrium Methods 311

Dynamical Methods 316

Classical/Quantum Coupling 337

Static and Semistatic Methods 337

Dynamics Methodologies 344

Conclusions: The Outlook 351

Appendix: A List of Acronyms 352

References 354

7 Extending the Time Scale in Atomically Detailed Simulations Alfredo E. Cardenas Eric Barth 367

Introduction 367

The Verlet Method 367

Molecular Dynamics Potential 369

Multiple Time Steps 371

Reaction Paths 371

Multiple Time-Step Methods 372

Splitting the Force 373

Numerical Integration with Force Splitting: Extrapolation vs. Impulse 374

Fundamental Limitation on Size of MTS Methods 376

Langevin Stabilization 377

Further Challenges and Recent Advances 378

An MTS Tutorial 379

Extending the Time Scale: Path Methodologies 385

Transition Path Sampling 385

Maximization of the Diffusive Flux (MaxFlux) 387

Discrete Path Sampling and String Method 388

Optimization of Action 390

Boundary Value Formulation in Length 391

Use of SDEL to Compute Reactive Trajectories: Input Parameters, Initial Guess, and Parallelization Protocol 397

Applications of the Stochastic Difference Equation in Length 400

Recent Advances and Challenges 401

Conclusion 403

Appendix: MATLAB Scripts for the MTS Tutorial 404

Acknowledgment 413

References 413

8 Atomistic Simulation of Ionic Liquids Edward J. Maginn 421

Introduction 421

Short (Pre)History of Ionic Liquid Simulations 427

Earliest Ionic Liquid Simulations 430

More Systems and Refined Models 437

Force Fields and Properties of Ionic Liquids Having Dialkylimidazolium Cations 438

Force Fields and Properties of Other Ionic Liquids 442

Solutes in Ionic Liquids 446

Implications of Slow Dynamics when Computing Transport Properties 455

Computing Self-Diffusivities, Viscosities, Electrical Conductivities, and Thermal Conductivities for Ionic Liquids 461

Nonequilibrium Methods for Computing Transport Properties 470

Coarse-Grained Models 474

Ab Initio Molecular Dynamics 477

How to Carry Out Your Own Ionic Liquid Simulations 479

What Code? 480

Force Fields 483

Data Analysis 483

Operating Systems and Parallel Computing 484

Summary and Outlook 485

Acknowledgments 486

References 486

Author Index 495

Subject Index 523

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