The LMTO Method: Muffin-Tin Orbitals and Electronic Structure

1. Introduction. - 1.1 The One-Electron Approximation. - 1.2 The Energy-Band Problem. - 1.3 Energy-Band Methods. - 1.4 Brief History of Linear Methods. - 1.5 Organisation of the Book. - 2. Canonical Band Theory. - 2.1 Muffin-Tin Orbitals and Tail Cancellation. - 2.2 Structure Constants and Canonical Bands. - 2.3 Potential Function and the Wigner-Seitz Rule. - 2.4 Potential Parameters, Unhybridised, and Hybridised Bands. - 2.5 Hybridised Canonical Theory. - 2.6 State Densities and Energy Scaling. - 3. One-Electron States in a Single Sphere. - 3.1 Radial Basis Functions. - 3.2 Partial Waves and Their Energy Derivatives. - 3.3 Logarithmic Derivative and Laurent Expansion. - 3.4 Potential Function and Bandwidth. - 3.5 Matrix Elements and Variational Estimate of Energies. - 4. Physically Significant Parameters. - 4.1 The Four Potential Parameters. - 4.2 How to Choose Ev? - 4.3 Chromium 3d Bands: An Example. - 4.4 Free-Electron Potential Parameters. - 4.5 Volume Derivatives of Potential Parameters. - 4.6 Potential Parameter Relations. - 5. The Linear Method. - 5.1 Partial Waves for a Single Muffin-Tin. - 5.2 Muffin-Tin Orbitals. - 5.3 Expansion Theorem for MTO Tails. - 5.4 Energy-Independent Muffin-Tin Orbitals. - 5.5 One-Centre Expansion and Structure Constants. - 5.6 The LCMTO Secular Matrix. - 5.7 The LMTO Method. - 6. The Atomic-Sphere Approximation (ASA). - 6.1 The Kinetic Energy K2. - 6.2 An Error Estimate. - 6.3 The Atomic Sphere and the ASA. - 6.4 The Canonical Structure Constants. - 6.5 Muffin-Tin Orbitals in the ASA. - 6.6 Relation Between the LMTO and KKR Matrices. - 6.7 Wave Functions and ? Character. - 6.8 Projected State Density and Density of Electrons. - 6.9 The Combined Correction Term. - 7. Ground-State Properties. - 7.1 Cohesive Properties. - 7.2 Density-Functional Theory. - 7.2.1 Spin-Density-Functional Theory. - 7.3 Self-Consistent Band-Structure Problem. - 7.4 Electronic Pressure Relation. - 7.5 First-Order Pressure Relation. - 7.6 Chromium: An Example. - 8. Many Atoms per Cell. - 8.1 Molecules and Clusters. - 8.1.1 Tail Cancellation. - 8.1.2 The Two-Centre Approximation. - 8.2 The LMTO Formalism. - 8.2.1 Muffin-Tin Orbitals and One-Centre Expansion. - 8.2.2 Structure Constants and the LMTO Method. - 8.3 Total Energy and Self-Consistent Energy Bands. - 9. Computer Programmes. - 9.1 The Self-Consistency Loop. - 9.2 Structure Constant Programme STR. - 9.2.1 Lattice Summations in STR. - 9.2.2 Listing of STR. - 9.2.3 Execution of STR. - 9.2.4 Sample Output from STR. - 9.3 Correction Structure Constant Programme COR. - 9.3.1 Listing of COR. - 9.3.2 Execution of COR. - 9.3.3 Sample Output from COR. - 9.4 Linear Muffin-Tin Orbital Programme LMTO. - 9.4.1 LMTO and Cholesky Decomposition. - 9.4.2 Listing of LMTO. - 9.4.3 Execution of LMTO. - 9.4.4 Sample Output from LMTO. - 9.4.5 Energy-Band File BND/YY/B. - 9.5 Projected State-Density Programme DDNS. - 9.5.1 The Tetrahedron Method. - 9.5.2 Mesh and Tetrahedra. - 9.5.3 Listing of DDNS. - 9.5.4 Execution of DDNS. - 9.5.5 Sample Output from DDNS. - 9.6 The Self-Consistency Programme SCFC. - 9.6.1 The Dirac Equation Without Spin-Orbit Coupling. - 9.6.2 Listing of SCFC. - 9.6.3 Execution of SCFC. - 9.6.4 Sample Output from SCFC. - 10. Self-Consistent Potential Parameters for 61 Metals. - 11. List of Symbols. - References.