Electronic structure calculations for solids and molecules : theory and computational methods

Electronic structure problems are studied in condensed matter physics and theoretical chemistry to provide important insights into the properties of matter. This 2006 graduate textbook describes the main theoretical approaches and computational techniques, from the simplest approximations to the most sophisticated methods. It starts with a detailed description of the various theoretical approaches to calculating the electronic structure of solids and molecules, including density-functional theory and chemical methods based on Hartree-Fock theory. The basic approximations are thoroughly discussed, and an in-depth overview of recent advances and alternative approaches in DFT is given. The second part discusses the different practical methods used to solve the electronic structure problem computationally, for both DFT and Hartree-Fock approaches. Adopting a unique and open approach, this textbook is aimed at graduate students in physics and chemistry, and is intended to improve communication between these communities. It also serves as a reference for researchers entering the field.

Preface	p. xi
List of symbols	p. xvi
List of acronyms	p. xx
Part I Theory	p. 1
1 The problem of the structure of matter	p. 3
1.1 Adiabatic approximation	p. 6
1.2 Classical nuclei approximation	p. 10
2 The electronic problem	p. 15
2.1 Screening: Gouy-Chapman and Debye-Huckel analysis	p. 17
2.2 The pair correlation function	p. 19
2.3 Many-body theory of electronic systems	p. 22
3 Quantum many-body theory: chemical approaches	p. 28
3.1 The Hartree-Fock approximation	p. 31
3.2 Post-Hartree-Fock methods	p. 37
4 Density functional theory	p. 51
4.1 Thomas-Fermi theory	p. 51
4.2 Modern density functional theory	p. 56
4.3 Kinetic correlation: the adiabatic connection	p. 65
4.4 Some observations about Kohn-Sham theory	p. 70
5 Exchange and correlation in DFT: approximations and their performances	p. 75
5.1 The local density approximation	p. 77
5.2 Gradient expansions	p. 85
5.3 Non-locality: the weighted density approximation	p. 94
5.4 Hybrid HF-KS approaches	p. 96
5.5 Exact exchange: the optimized effective potential method	p. 97
5.6 Orbital-dependent correlation functionals	p. 103
5.7 Van der Waals (dispersion) interactions	p. 108
5.8 Green's function approach: the GW approximation	p. 110
5.9 Strong correlations: LDA+U and LDA+DMFT	p. 112
5.10 Summary of exchange-correlation functionals	p. 113
Part II Computational methods	p. 121
6 Solving the electronic problem in practice	p. 123
6.1 Kohn-Sham and Hartree-Fock equations	p. 123
6.2 Condensed phases: Bloch's theorem and periodic boundary conditions	p. 128
7 Atomic pseudopotentials	p. 143
7.1 Pseudopotential theory	p. 144
7.2 Construction of pseudopotentials	p. 148
7.3 Separable form of atomic pseudopotentials	p. 164
7.4 Ultrasoft pseudopotentials	p. 169
7.5 Some practical aspects of pseudopotentials	p. 174
8 Basis sets	p. 178
8.1 Periodic systems	p. 181
8.2 Plane waves	p. 182
8.3 Other floating basis sets	p. 188
8.4 Atom-centered basis sets	p. 189
8.5 Mixed basis sets	p. 202
8.6 Augmented basis ets	p. 202
9 Electronic structure methods	p. 217
9.1 Multiple scattering methods: the KKR approach	p. 218
9.2 All-electron methods based on augmentation spheres	p. 220
9.3 The pseudopotential plane wave method (PPW)	p. 228
9.4 Atom-centered basis sets	p. 248
9.5 Gaussian basis sets	p. 259
10 Simplified approaches to the electronic problem	p. 270
10.1 Tight-binding methods	p. 272
10.2 Semiempirical approaches in quantum chemistry	p. 286
10.3 Relation between tight-binding and semiempirical methods	p. 294
10.4 Many-body classical potentials	p. 296
10.5 Classical force fields	p. 298
10.6 Hybrid QM-MM methods	p. 300
10.7 Orbital-free density functional approaches	p. 304
11 Diagonalization and electronic self-consistency	p. 311
11.1 Diagonalization	p. 312
11.2 Self-consistency: mixing schemes	p. 316
11.3 Direct minimization of the electronic energy functional	p. 318
12 First-principles molecular dynamics (Car-Parrinello)	p. 323
12.1 Density functional molecular dynamics	p. 324
12.2 The Car-Parrinello Lagrangian	p. 325
12.3 The Car-Parrinello equations of motion	p. 328
12.4 Orthonormalization	p. 330
12.5 Pre-conditioning	p. 332
12.6 Performance of CPMD	p. 333
Index	p. 339

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