Methods of electronic-structure calculations : from molecules to solids / Michael Springborg.

Format:

Book

Author/Creator:

Springborg, Michael.

Series:

Wiley series in theoretical chemistry

Language:

English

Subjects (All):

Quantum chemistry.

Electronic structure.

Physical Description:

x, 501 pages : illustrations ; 24 cm.

Place of Publication:

Chichester ; New York : Wiley, 2000.

Summary:

Electronic-structure calculations of the properties of specific materials have become increasingly important over the last 30 years. Although several books on the subject have been published, it is rare to find one that covers in detail both the traditional quantum chemistry and the solid-state physics methods of electronic-structure calculations. This title bridges that gap, focusing equally on both types of method, including density-functional-and Hartree -- Fock-based approaches. The book is aimed at final-year undergraduate and postgraduate students of both chemistry and of physics. It describes in detail the fundamentals behind the various methods that are used in calculating electronic properties of materials, and that to some extent are commercially available. It should also be of interest to professional scientists working in related theoretical or experimental fields.

Contents:

2 Operators 6

2.1 What is an Operator? 6

2.2 Expectation Values 8

3 Eigenvalues and Eigenfunctions 11

3.1 General Properties 11

3.2 Hermitian Operators 12

3.3 Commuting Operators 14

4 Factorization; Time and Spin Dependence 18

4.1 Time Dependence 18

4.2 Spin Dependence 19

5 Variational Principle; Lagrange Multipliers 21

5.1 Variational Principle 21

5.3 Variation 26

5.4 The Hydrogen Atom 27

5.5 Linear Variation and Lagrange Multipliers 31

6 Perturbation Theory 36

6.1 The Non-degenerate Case 36

6.3 The Degenerate Case 44

6.5 Time-dependent Perturbation Theory 47

7 Symmetry and Group Theory 50

7.1 Symmetry 50

7.2 Group Theory 53

II Basic Methods 71

8 The Schrodinger Equation and the Born

Oppenheimer Approximation 73

8.1 The Schrodinger Equation 73

8.2 The Born

Oppenheimer Approximation 75

8.3 The Adiabatic Approximation 79

8.4 Atomic Units 79

9 The Hartree, Hartree

Fock, and Hartree

Fock

Roothaan Methods 82

9.1 The Hartree Approximation 82

9.2 The Hartree

Fock Method 85

9.3 Orbitals, Total Energies, and Koopmans' Theorem 98

9.4 The Hartree

Roothaan Method 101

9.5 Physical Properties 104

9.6 Restricted, Unrestricted, Extended, and Projected Hartree

Fock Methods 113

10 Basis Sets 123

10.1 Slater-type Orbitals 123

10.2 Gaussian-type Orbitals 125

10.3 Plane Waves 128

10.4 Numerical Basis Functions 128

10.5 Augmented Waves 128

10.6 Symmetry 129

10.7 Basis Set Superposition Error 130

11 Semiempirical Methods 132

11.1 The Huckel Method 132

11.2 The Extended Huckel Method 137

11.3 The PPP Method 139

11.4 The ZDO and INDO Methods 140

12 Creation and Annihilation Operators 144

12.1 Projection Operators 144

12.2 The Huckel Method 145

12.3 Electronic Excitations and Configurations 148

13 Correlation Effects 151

13.1 More Configurations 151

13.2 Configuration Interaction (CI) 155

13.3 Multiple-configuration Method (MC-SCF) 161

13.4 Size Consistency; CAS-SCF 162

13.5 The Coupled-cluster Method 164

13.6 Moller

Plesset Perturbation Theory 165

14 Where are the Electrons and Atoms? 169

14.1 Reduced Density Matrices 169

14.2 Natural Orbitals 171

14.3 Mulliken Populations 172

14.4 Lowdin Populations 176

14.5 Dyson Orbitals 178

14.6 Atoms in Molecules 182

14.7 Electron-localization Function (ELF) 183

15 Density Functional Theory 186

15.1 Thomas

Fermi and X[alpha] Methods 186

15.2 The Hohenberg

Kohn Theorems 190

15.3 Functional Derivatives 194

15.4 The Kohn

Sham Method 195

15.5 Extensions; Spin and Symmetry 199

15.6 Local and Non-local Approximations 199

15.7 Fitting 202

15.8 The Quasi-particles 204

15.9 Physical Properties 206

15.10 Self-interaction 208

15.11 Hybrid Methods 210

16 Some Simplifications and Technical Details 218

16.1 Frozen-core Approximation 218

16.2 Pseudopotentials 220

16.3 (Linearized)-Augmented-Wave Methods: LMTO and LAPW 224

16.4 How to Carry a Calculation Through 230

17 Green's Function 231

17.1 General Properties 231

17.3 Residue Theory 237

17.4 Green's Function and Electronic Structure 241

17.5 Dyson's Equation 242

17.6 Basis Functions 244

III Special Properties 247

18 Acidity and Basicity; Hardness and Softness 249

18.1 Hardness and Softness 249

18.2 Hard and Soft Acids and Bases Principle 253

19 Periodicity and Band Structures 255

19.1 Huckel-like Model for Ring Systems 255

19.2 Born

von Karman Zones 264

19.3 Band Structures in One Dimension 265

19.4 Brillouin Zones 280

19.5 Band Structures in Three Dimensions 283

19.6 Bloch's Formulation 287

19.7 Crystal Momentum 288

19.8 Wannier Functions 289

19.9 Density of States 295

20 Structure and Forces 298

20.1 Hellmann

Feynman Theorem 298

20.2 Forces 301

20.3 Structure Optimization 305

20.4 The Classical Lagrangian 307

20.5 The Car

Parrinello Method 309

21 Vibrations 315

21.1 Molecular Vibrations and Dynamical Matrix 315

21.2 Phonons 319

21.3 Linear-response Theory 323

21.4 What is Response Theory? 326

22 Electronic Excitations 329

22.1 Eigenvalue Spectrum and Density of States 329

22.2 Single-particle Excitations 335

22.3 Dielectric Matrix 340

22.4 Quasi-particles 349

22.5 Fermi Surfaces 351

23 Relativistic Effects 358

23.1 The Dirac Equation 358

23.2 The Schrodinger Equation 360

24 Molecules and Solids in Electromagnetic Fields 365

24.1 Polarizabilities and Hyperpolarizabilities 365

24.2 Magnetic Resonances 373

IV Special Systems 379

25 Impurities 381

25.1 The One-dimensional Case 381

25.2 Supercells 385

25.3 Green's Function and Impurities 388

25.4 Transfer Matrices in One Dimension 391

26 Surfaces and Interfaces 397

26.1 General Considerations 397

26.2 Supercells 401

26.3 Green's Functions 403

26.4 Reconstructions 408

26.5 Adsorbants and Catalysis 412

26.6 Films 412

26.7 Interfaces and Band Offsets 416

26.8 Superlattices 420

27 Non-Periodic, Extended Systems 423

27.1 Amorphous Systems 423

27.2 Liquids 424

27.3 Quasicrystals 426

27.4 Alloys 427

27.5 Order-N Methods 439

28 Phase Diagrams 443

28.1 Structural Transitions of Crystalline Materials 443

28.2 Segregation and Phase Separation 448

29 Clusters 452

29.1 Large Molecules 452

29.2 Jellium Models 455

29.3 Embedded-atom and Effective-medium Methods 459

30 Macromolecules 463

30.1 Force Fields 463

30.2 Molecular Mechanics + Quantum Mechanics 465

31 Interactions 468

31.1 Chemical Reactions 468

31.2 Hydrogen Bonds 471

31.3 Spin-Spin Interactions 474

32 Solvation 479

32.1 Supermolecules 479

32.2 Dielectrica 482

32.3 Point Charges 485.

Notes:

Includes bibliographical references and index.

ISBN:

0471979759

0471979767

OCLC:

42823836