Computational Methods for Large Systems: Electronic Structure Approaches for Biotechnology and Nanotechnology

Preface: Choosing the Right Method for Your Problem xvii

A. DFT: The Basic Workforce 1

1. Principles of Density Functional Theory: Equilibrium and Nonequilibrium Applications 3
Ferdinand Evers

1.1 Equilibrium Theories 3

1.2 Local Approximations 8

1.3 Kohn-Sham Formulation 11

1.4 Why DFT Is So successful 13

1.5 Exact Properties of DFTs 14

1.6 Time-Dependent DFT 19

1.7 TDDFT and Transport Calculations 28

1.8 Modeling Reservoirs In and Out of Equilibrium 34

2. SIESTA: A Linear-Scaling Method for Density Functional Calculations 45
Julian D. Gale

2.1 Introduction 45

2.2 Methodology 48

2.3 Future Perspectives 73

3. Large-Scale Plane-Wave-Based Density Functional Theory: Formalism, Parallelization, and Applications 77
Eric Bylaska, Kiril Tsemekhman, Niranjan Govind, and Marat Valiev

3.1 Introduction 78

3.2 Plane-Wave Basis Set 79

3.3 Pseudopotential Plane-Wave Method 81

3.4 Charged Systems 89

3.5 Exact Exchange 92

3.6 Wavefunction Optimization for Plane-Wave Methods 95

3.7 Car – Parrinello Molecular Dynamics 98

3.8 Parallelization 101

3.9 AIMD Simulations of Highly Charged Ions in Solution 106

3.10 Conclusions 110

B. Higher-Accuracy Methods 117

4. Quantum Monte Carlo, Or, Solving the Many-Particle Schrödinger Equation Accurately While Retaining Favorable Scaling with System Size 119
Michael D. Towler

4.1 Introduction 119

4.2 Variational Monte Carlo 124

4.3 Wavefunctions and Their Optimization 127

4.4 Diffusion Monte Carlo 137

4.5 Bits and Pieces 146

4.6 Applications 157

4.7 Conclusions 160

5. Coupled-Cluster Calculations for Large Molecular and Extended Systems 167
Karol Kowalski, Jeff R. Hammond, Wibe A. de Jong, Peng-Dong Fan, Marat Valiev Dunyou Wang, and Niranjan Govind

5.1 Introduction 168

5.2 Theory 168

5.3 General Structure of Parallel Coupled-Cluster Codes 174

5.4 Large-Scale Coupled-Cluster Calculations 179

5.5 Conclusions 194

6. Strong-Correlated Electrons: Renormalized Band Structure Theory and Quantum Chemical Methods 201
Liviu Hozoi and Peter Fulde

6.1 Introduction 201

6.2 Measure of the Strength of Electron Correlations 204

6.3 Renormalized Band Structure Theory 206

6.4 Quantum Chemical Methods 208

6.5 Conclusions 221

C. More-Economical Methods 225

7. The Energy-Based Fragmentation Approach for Ab Initio Calculations of Large Systems 227
Wei Li, Weijie Hua, Tao Fang, and Shuhua Li

7.1 Introduction 227

7.2 The Energy-Based Fragmentation Approach and Its Generalized Version 230

7.3 Results and Discussion 238

7.4 Conclusions 251

7.5 Appendix: Illustrative Example of the GEBF Procedure 252

8. MNDO-like Semiempirical Molecular Orbital Theory and Its Application to Large Systems 259
Timothy Clark and James J. P. Stewart

8.1 Basic Theory 259

8.2 Parameterization 271

8.3 Natural History or Evolution of MNDO-like Methods 278

8.4 Large Systems 281

9. Self-Consistent-Charge Density Functional Tight-Binding Method: An Efficient Approximation of Density Functional Theory 287
Marcus Elstner and Michael Cous

9.1 Introduction 287

9.2 Theory 289

9.3 Performance of Standard SCC-DFTB 300

9.4 Extensions of Standard SCC-DFTB 302

9.5 Conclusions 304

10. Introduction to Effective Low-Energy Hamiltonians in Condensed Matter Physics and Chemistry 309
Sen J. Powell

10.1 Brief Introduction to Second Quantization Notation 310

10.2 Hückel or Tight-Binding Model 314

10.3 Hubbard Model 326

10.4 Heisenberg Model 339

10.5 Other Effective Low-Energy Hamiltonians for Correlated Electrons 349

10.6 Holstein Model 353

10.7 Effective Hamiltonian or Semiempirical Model? 358

D. Advanced Applications 367

11. SIESTA: Properties and Applications 369
Michael J. Ford

11.1 Ethynylbenzene Adsorption on Au(111) 370

11.2 Dimerization of Thiols on Au(111) 377

11.3 Molecular Dynamics of Nanoparticles 384

11.4 Applications to Large Numbers of Atoms 387

12. Modeling Photobiology Using Quantum Mechanics and Quantum Mechanics/Molecular Mechanics Calculations 397
Xin Li, Lung Wa Chung, and Keiji Morokuma

12.1 Introduction 397

12.2 Computational Strategies: Methods and Models 400

12.3 Applications 410

12.4 Conclusions 425

13. Computational Methods for Modeling Free-Radical Polymerization 435
Michelle L. Coote and Chung Lin

13.1 Introduction 435

13.2 Model Reactions for Free-Radical Polymerization Kinetics 441

13.3 Electronic Structure Methods 444

13.4 Calculation of Kinetics and Thermodynamics 457

13.5 Conclusion 468

14. Evaluation of Nonlinear Optical Properties of Large Conjugated Molecular Systems by Long-Range-Corrected Density Functional Theory 475
Hideo Sekino, Akihide Miyazaki, Jong-Won Song, and Kimihiko Hirao

14.1 Introduction 476

14.2 Nonlinear Optical Response Theory 478

14.3 Long-Range-Corrected Density Functional Theory 480

14.4 Evaluation of Hyperpolarizability for Long Conjugated Systems 482

14.5 Conclusions 488

15. Calculating the Raman and HyperRaman Spectra of Large Molecules and Molecules Interacting with Nanoparticles 493
Nicholas Valley, Lasse Jensen, Jochen Autschbach, and George C. Schatz

15.1 Introduction 494

15.2 Displacement of Coordinates Along Normal Modes 496

15.3 Calculation of Polarizabilities Using TDDFT 496

15.4 Derivatives of the Polarizabilities with Respect to Normal Modes 500

15.5 Orientation Averaging 501

15.6 Differential Cross Sections 502

15.7 Surface-Enhanced Raman and HyperRaman Spectra 506

15.8 Application of Tensor Rotations to Raman Spectra for Specific Surface Orientations 507

15.9 Resonance Raman 508

15.10 Determination of Resonant Wavelength 509

15.11 Summary 511

16. Metal Surfaces and Interfaces: Properties from Density Functional Theory 515
Irene Yarovsky, Michelle J. S. Spencer, and Ian K. Snook

16.1 Background, Goals, and Outline 515

16.2 Methodology 517

16.3 Structure and Properties of Iron Surfaces 521

16.4 Structure and Properties of Iron Interfaces 538

16.5 Summary, Conclusions, and Future Work 553

17. Surface Chemistry and Catalysis from Ab Initio-Based Multiscale Approaches 561
Catherin Samofl and Simone Piccinin

17.1 Introduction 561

17.2 Predicting Surface Structures and Phase Transitions 563

17.3 Surface Phase Diagrams from Ab Initio Atomistic Thermodynamics 568

17.4 Catalysis and Diffusion from Ab Initio Kinetic Monte Carlo Simulations 576

17.5 Summary 584

18. Molecular Spintronics 589
Woo Youn Kim and Kwang S. Kim

18.1 Introduction 589

18.2 Theoretical Background 591

18.3 Numerical Implementation 600

18.4 Examples 604

18.5 Conclusions 612

19. Calculating Molecular Conductance 645
Gemma C. Solomon and Mark A. Ratner

19.1 Introduction 615

19.2 Outline of the MEGF Approach 617

19.3 Electronic Structure Challenges 623

19.4 Chemical Trends 625

19.5 Features of Electronic Transport 630

19.6 Applications 634

19.7 Conclusions 639

Index 649