Contributors xiii
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 Schrodinger 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 Huckel 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
