The density functional formalism, its applications and prospects
CONTENTS
I. Introduction
II. The Density as Basic Variable
A. The density functional formalism
B. The Thomas-Fermi approximation
1. The Thomas-Fermi equations
2. Modifications and improvements
III. Derivation of Single-Particle Equations
A. Exact single-particle description of a many-particle system
B. Exchange-correlation energy E„,
C. Some exact results and inequalities for E„, and V„,
D. Extensions to more general systems
IV. Local Spin-Density Approximation and its Applications
A. Atoms
1. Total energies
2. Ionization energies
3. Transfer energies
4. Multiplet structure
B. Molecules
1. First-row dimers
2. Alkaline earth dirners
3. Group-IVa molecules Cz, Si2, C3, Si3
4. Iron-series transition-metal dimers a. Cu2 b. Cr~
5. Triatomic group-VI molecules 03 SO2 S3 SOS
C. Extended systems
1. Crystalline solids a. Alkali and alkaline earth metals b. C, Si, Ge c. Transition elements
2. Polymers
3. Molecular dynamics —clusters and disordered materials
V. Local Spin-Density Calculations —Sources of Error, Modifications
A. A simple model problem
1. First-row atoms
2. Iron-series atoms
3. Small molecules
B. Modifications to local-density approximations
1. Approximations based on an exact equation for Exc
2. Self-interaction corrected approximations
3. Wave-vector analysis
4. Combination of density functional and configuration-interaction methods
VI. Excitation Energies
A. The meaning of the eigenvalues
B. Two limiting cases
C. The ASCF D. Discontinuity in the exchange-correlation potential
E. The Dyson equation approach
F. Comparison of eigenvalues and experimental excitation energies
G. General remarks on eigenvalue distributions
VII. Concluding Remarks
Acknowledgments
References
I. Introduction
II. The Density as Basic Variable
A. The density functional formalism
B. The Thomas-Fermi approximation
1. The Thomas-Fermi equations
2. Modifications and improvements
III. Derivation of Single-Particle Equations
A. Exact single-particle description of a many-particle system
B. Exchange-correlation energy E„,
C. Some exact results and inequalities for E„, and V„,
D. Extensions to more general systems
IV. Local Spin-Density Approximation and its Applications
A. Atoms
1. Total energies
2. Ionization energies
3. Transfer energies
4. Multiplet structure
B. Molecules
1. First-row dimers
2. Alkaline earth dirners
3. Group-IVa molecules Cz, Si2, C3, Si3
4. Iron-series transition-metal dimers a. Cu2 b. Cr~
5. Triatomic group-VI molecules 03 SO2 S3 SOS
C. Extended systems
1. Crystalline solids a. Alkali and alkaline earth metals b. C, Si, Ge c. Transition elements
2. Polymers
3. Molecular dynamics —clusters and disordered materials
V. Local Spin-Density Calculations —Sources of Error, Modifications
A. A simple model problem
1. First-row atoms
2. Iron-series atoms
3. Small molecules
B. Modifications to local-density approximations
1. Approximations based on an exact equation for Exc
2. Self-interaction corrected approximations
3. Wave-vector analysis
4. Combination of density functional and configuration-interaction methods
VI. Excitation Energies
A. The meaning of the eigenvalues
B. Two limiting cases
C. The ASCF D. Discontinuity in the exchange-correlation potential
E. The Dyson equation approach
F. Comparison of eigenvalues and experimental excitation energies
G. General remarks on eigenvalue distributions
VII. Concluding Remarks
Acknowledgments
References
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