Strong Coulomb Correlations in Electronic Structure Calculations

by Anisimov; Vladimir I

• ISBN13: 9789056991319
• ISBN10: 9056991310
• Edition: 1st
• Format: Hardcover
• Copyright: 2000-05-30
• Publisher: CRC Press

Summary

Materials where electrons show nearly localized rather than itinerant behaviour, such as the high-temperature superconducting copper oxides, or manganate oxides, are attracting interest due to their physical properties and potential applications. For these materials, the interaction between electrons, or electron correlation, plays an important role in describing their electronic strucuture, and the standard methods for the calculation of their electronic spectra based on the local density approximation (LDA) breakdown. This is the first attempt to describe recent approaches that go beyond the concept of the LDA, to successfully describe the electronic structure of narrow-band materials.

Table of Contents

Contributors	ix
Introduction	xi
The GW Approximation and Vertex Corrections
Ferdi Arysetiawan
Introduction	1	(3)
Theory	4	(17)
The Green function and the self-energy	4	(5)
The response and polarization function	9	(1)
The Hedin equations	10	(1)
The self-energy expansion	10	(1)
Spectral representations	11	(3)
The GW approximation	14	(7)
Computational Method	21	(13)
Basis functions	21	(3)
Special directions	24	(3)
Evaluation of the Coulomb Matrix	27	(2)
Evaluation of the polarization P	29	(3)
Evaluation of the self-energy Σ	32	(2)
Applications	34	(21)
Simple metals and semiconductors	35	(3)
Transition metals	38	(16)
f system: Gd	54	(1)
Vertex Corrections: Beyond GW	55	(25)
The cumulant expansion	59	(9)
T-matrix approximation	68	(12)
Self-consistency and Total Energies	80	(17)
Self-consistency	80	(5)
Total energies	85	(2)
References	87	(10)
LDA+U Method: Screened Coulomb Interaction in the Mean-field Approximation
Vladimir I. Anisimov
A.I. Lichtenstein
Introduction	97	(1)
LDA+U Method: Formulation and Practical Realization	98	(3)
Relationship Between LDA+U and GW Approximation	101	(8)
Localized States: 3d and 4f Orbitals	109	(7)
Rare-earth metals: Gd	109	(2)
Transition metal impurities in alkaline metals	111	(1)
Rare-earth elements compounds: CeSb	111	(3)
PrBa2Cu3O7	114	(2)
Mott-Hubbard Insulators	116	(7)
3d-transition metal oxides	116	(5)
Transition metal impurities in insulators: Fe-impurity in MgO	121	(2)
Linear chain (MX) compounds	123	(1)
Electron-lattic Interactions: Jahn-Teller Distortions and Polarons	123	(7)
Cooperative Jahn-Teller distortions in transition metal compounds: KCuF3	123	(4)
Polarons in doped Mott insulators: La2-x Srx CuO4 and La2-x Srx NiO4	127	(3)
Metal-insulator Transition	130	(4)
FeSi	130	(3)
LaCoO3	133	(1)
Charge and Orbital Ordering	134	(10)
Magnetite Fe3O4	134	(4)
Doped manganite Pr1-xCaxMnO3	138	(6)
Beyond the Mean-field Approximation: Spectral Properties and Quasiparticle Bands	144	(15)
Spectral properties from the Anderson impurity model	144	(6)
Quasiparticle bands in FLEX approximation	150	(2)
Dynamical mean-field theory	152	(7)
Conclusion	159	(8)
References	161	(6)
LSDA and Self-Interaction Correction
Takeo Fujiwara
Masao Arai
Yasushi Ishii
Introduction	167	(1)
Total Energy and Self-Interaction Correction	168	(14)
LSDA total energy	168	(2)
LSDA self-interaction correction	170	(6)
Canonical orbitals	176	(3)
Self-interaction correction in metallic systems	179	(1)
Canonical orbitals and many-electron wavefunctions	180	(2)
SIC in Solid Hydrogen and Transition Metal Monoxides	182	(12)
Solid hydrogen	183	(2)
Transition metal compounds	185	(9)
SIC in Rare Earth Metals and Rare Earth Metal Compounds	194	(5)
Rare earth metals	195	(3)
Rare earth compounds---cerium pnictides	198	(1)
Conclusion	199	(4)
References	200	(3)
Orbital Functionals in Density Functional Theory: The Optimized Effective Potential Method
T. Grabo
T. Kreibich
S. Kurth
E.K.U. Gross
Introduction	203	(6)
The OEP Method, Basic Formalism	209	(27)
Derivation of the OEP equations	209	(3)
Approximation of Krieger, Li and Iafrate	212	(5)
Rigorous properties of the OEP and KLI potentials	217	(18)
Hartree-Fock versus x-only OEP, a comparison	235	(1)
Relativistic Generalization of the OEP and KLI Methods	236	(9)
Relativistic optimized effective potential method	238	(2)
Relativistic KLI approximation	240	(4)
Relativistic OEP in the electrostatic case	244	(1)
Numerical Results	245	(52)
Exchange-only calculations for nonrelativistic systems	245	(17)
Comparison of nonrelativistic with relativistic results	262	(8)
Inclusion of correlation contributions for nonrelativistic systems	270	(23)
Solids	293	(4)
Beyond the OEP---A Connection with Many-Body Perturbation Theory	297	(9)
Acknowledgments	306	(1)
References	307	(6)
Index	313