Computational Methods for Large Systems

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 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