Contributors ................................................. xiii
Preface: Choosing the Right Method for Your Problem .......... xvii
A DFT: THE BASIC WORKHORSE ..................................... 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
В HIGHER-ACCURACY METHODS .................................... 117
4 Quantum Monte Carlo, Or, Solving the Many-Particle
Schrцdinger 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
Kami 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 Strongly 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
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 Gaus
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
Ben 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 Ethy nylbenzene 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 Ching Y. 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 Conclusions ........................................... 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 Hyper Raman 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 Hyper Raman 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 К. 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
Catherine Stampfl 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 .......................... 615
Gemma C. Solomon and Mark A. Ratner
19.1 Introduction .......................................... 615
19.2 Outline of the NEGF 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
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