Methods of Electronic-Structure Calculations From Molecules to Solids

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Edition: 1st
Format: Paperback
Pub. Date: 2000-07-26
Publisher(s): WILEY
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Summary

Methods of Electronic-Structure Calculations From Molecules to Solids Michael Springborg Department of Chemistry, University of Konstanz, Germany 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.

Author Biography

Dr. Michael Springborg heads up of the three groups in Physical Chemistry at the University of Saarland where the main activities concentrate on teaching and research.

Table of Contents

Series Preface xi
Preface xiii
I PRELIMINARIES 1(70)
Introduction
3(3)
Operators
6(5)
What is an Operator?
6(2)
Expectation Values
8(1)
An Example
9(2)
Eigenvalues and Eigenfunctions
11(7)
General Properties
11(1)
Hermitian Operators
12(2)
Commuting Operators
14(4)
Factorization; Time and Spin Dependence
18(3)
Time Dependence
18(1)
Spin Dependence
19(2)
Variational Principle, Lagrange Multipliers
21(15)
Variational Principle
21(3)
An Example
24(2)
Variation
26(1)
The Hydrogen Atom
27(4)
Linear Variation and Lagrange Multipliers
31(3)
An Example
34(2)
Perturbation Theory
36(14)
The Non-degenerate Case
36(7)
An Example
43(1)
The Degenerate Case
44(3)
An Example
47(1)
Time-dependent Perturbation Theory
47(3)
Symmetry and Group Theory
50(21)
Symmetry
50(3)
Group Theory
53(11)
An Example Revisited
64(2)
A Worked Example
66(5)
II BASIC METHODS 71(176)
The Schrodinger Equation and the Born--Oppenheimer Approximation
73(9)
The Schrodinger Equation
73(2)
The Born-Oppenheimer Approximation
75(4)
The Adiabatic Approximation
79(1)
Atomic Units
79(3)
The Hartree, Hartree--Fock, and Hartree--Fock--Roothaan Methods
82(41)
The Hartree Approximation
82(3)
The Hartree--Fock Method
85(13)
Orbitals, Total Energies, and Koopmans' Theorem
98(3)
The Hartree--Fock--Roothaan Method
101(3)
Physical Properties
104(9)
Restricted, Unrestricted, Extended, and Projected Hartree--Fock Methods
113(6)
An Example
119(4)
Basis Sets
123(9)
Slater-type Orbitals
123(2)
Gaussian-type Orbitals
125(3)
Plane Waves
128(1)
Numerical Basis Functions
128(1)
Augmented Waves
128(1)
Symmetry
129(1)
Basis Set Superposition Error
130(2)
Semiempirical Methods
132(12)
The Huckel Method
132(5)
The Extended Huckel Method
137(2)
The PPP Method
139(1)
The ZDO and INDO Methods
140(4)
Creation and Annihilation Operators
144(7)
Projection Operators
144(1)
The Huckel Method
145(3)
Electronic Excitations and Configurations
148(3)
Correlation Effects
151(18)
More Configurations
151(4)
Configuration Interaction (CI)
155(6)
Multiple-configuration Method (MC-SCF)
161(1)
Size Consistency; CAS-SCF
162(2)
The Coupled-cluster Method
164(1)
Møller--Plesset Perturbation Theory
165(4)
Where are the Electrons and Atoms?
169(17)
Reduced Density Matrices
169(2)
Natural Orbitals
171(1)
Mulliken Populations
172(4)
Lowdin Populations
176(2)
Dyson Orbitals
178(4)
Atoms in Molecules
182(1)
Electron-localization Function (ELF)
183(3)
Density Functional Theory
186(32)
Thomas--Fermi and Xα Methods
186(4)
The Hohenberg--Kohn Theorems
190(4)
Functional Derivatives
194(1)
The Kohn--Sham Method
195(4)
Extensions; Spin and Symmetry
199(1)
Local and Non-local Approximations
199(3)
Fitting
202(2)
The Quasi-particles
204(2)
Physical Properties
206(2)
Self-interaction
208(2)
Hybrid Methods
210(8)
Some simplifications and Technical Details
218(13)
Frozen-core Approximation
218(2)
Pseudopotentials
220(4)
(Linearized)-Augmented-Wave Methods: LMTO and LAPW
224(6)
How to Carry a Calculation Through
230(1)
Green's Function
231(16)
General Properties
231(4)
Two Examples
235(2)
Residue Theory
237(4)
Green's Function and Electronic Structure
241(1)
Dyson's Equation
242(2)
Basis Functions
244(3)
III SPECIAL PROPERTIES 247(132)
Acidity and Basicity; Hardness and Softness
249(6)
Hardness and Softness
249(4)
Hard and Soft Acids and Bases Principle
253(2)
Periodicity and Band Structures
255(43)
Huckel-like Model for Ring Systems
255(9)
Born--von Karman Zones
264(1)
Band Structures in One Dimension
265(15)
Brillouin Zones
280(3)
Band Structures in Three Dimensions
283(4)
Bloch's Formulation
287(1)
Crystal Momentum
288(1)
Wannier Functions
289(6)
Density of States
295(3)
Structure and Forces
298(17)
Hellmann--Feynman Theorem
298(3)
Forces
301(4)
Structure Optimization
305(2)
The Classical Lagrangian
307(2)
The Car--Parrinello Method
309(6)
Vibrations
315(14)
Molecular Vibrations and Dynamical Matrix
315(4)
Phonons
319(4)
Linear-response Theory
323(3)
What is Response Theory?
326(3)
Electronic Excitations
329(29)
Eigenvalue Spectrum and Density of States
329(6)
Single-particle Excitations
335(5)
Dielectric Matrix
340(9)
Quasi-particles
349(2)
Fermi Surfaces
351(7)
Relativistic Effects
358(7)
The Dirac Equation
358(2)
The Schrodinger Equation
360(5)
Molecules and Solids in Electromagnetic Fields
365(14)
Polarizabilities and Hyperpolarizabilities
365(8)
Magnetic Resonances
373(6)
IV SPECIAL SYSTEMS 379(110)
Impurities
381(16)
The One-dimensional Case
381(4)
Supercells
385(3)
Green's Function and Impurities
388(3)
Transfer Matrices in One Dimensions
391(6)
Surfaces and Interfaces
397(26)
General Considerations
397(4)
Supercells
401(2)
Green's Functions
403(5)
Reconstructions
408(4)
Adsorbants and Catalysis
412(1)
Films
412(4)
Interfaces and Band Offsets
416(4)
Superlattices
420(3)
Non-Periodic, Extended Systems
423(20)
Amorphous Systems
423(1)
Liquids
424(2)
Quasicrystals
426(1)
Alloys
427(12)
Order-N Methods
439(4)
Phase Diagrams
443(9)
Structural Transitions of Crystalline Materials
443(5)
Segregation and Phase Separation
448(4)
Clusters
452(11)
Large Molecules
452(3)
Jellium Models
455(4)
Embedded-atom and Effective-medium Methods
459(4)
Macromolecules
463(5)
Force Fields
463(2)
Molecular Mechanics + Quantum Mechanics
465(3)
Interactions
468(11)
Chemical Reactions
468(3)
Hydrogen Bonds
471(3)
Spin--Spin Interactions
474(5)
Solvation
479(10)
Supermolecules
479(3)
Dielectrica
482(3)
Point Charges
485(4)
References 489(6)
Index 495

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