The simplifications of band-structure calculations which are now referred to as linear methods were introduced by Ole K. Andersen almost ten years ago. Since then these ideas have been taken up by several workers in the field and translated into computer programmes that generate the band structure of almost any material. As a result, running times on computers have been cut by orders of magnitude. One of the strong motivations behind the original proposal was a desire to give the conventional methods' a physically meaningful content which could be understood even by the non-specialist. Unfortunately, this aspect of lin­ ear methods seems to have been less well appreciated, and most workers are content to use the latter as efficient computational schemes. The present book is intended to give a reasonably complete description of one particular linear method, the Linear Muffin-Tin Orbital (LMTO) method, without losing sight of the physical content of the technique. It is also meant as a guide to the non-specialist who wants to perform band-structure calculations of his own, for example, to interpret experimental results. For this purpose the book contains a set of computer programmes which allow the user to perform full-scale self-consistent band-structure calculations by means of the LMTO method. In addition, it contains a listing of self-con­ sistent potential parameters which, for instance, may be used to generate the energy bands of metallic elements.

Inhalt

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.