Computational Methods in Band Theory, Softcover reprint of the original 1st ed. 1971 Proceedings of a Conference held at the IBM Thomas J. Watson Research Center, Yorktown Heights, New York, May 14-15, 1970, under the joint sponsorship of IBM and the American Physical Society The IBM Research Symposia Series

This volume contains the papers presented at the Conference on Computational Methods in Band Theory sponsored jointly by IBM and the American Physical Society and held at the IBM Thomas J. Watson Research Center, Yorktown Heights, New York, on May 14-15, 1970. The purpose of the conference was a sharing of information on the computational problems involved in relating models for the electron-electron and electron-ion interactions to experimentally measurable quantities. The papers comprising this volume therefore present up-to-date methodology for the calculation of single-particle energies and wave functions for periodic and near-periodic systems, the integration over these states required to describe experiment, and computationally practicable procedures for the introduction of exchange and correlation and the achievement of self-consistency. The proceedings is actually an expansion of the conference in that, unlike the oral presentations, the papers were not limited as to length. Furthermore, time was allowed after the conference to permit the papers to be written with the conference in retrospect, and five "prepared discussion" papers written by attendees of the conference but not on the original program are included. The latter are indicated in the table of contents by asterisks. The explicit emphasis of the conference on comparison of technique generated much lively argument, which is surely an indi­ cation of the current interest in the subject and the vigor of those working in it. It is our hope that the proceedings will make these comparisons available to the widest possible audience.

1. APW-OPW Methods in the Band Problem.- A Comparison of Different Computer-Oriented Methods for the Energy Bands of Solids.- Diagonalization of Hermitian Matrices; Maximization of Speed and Accuracy.- An Alternative APW Technique: Theory and Application to Copper.- An RAPW Expanded Basis Set.- New Version of the Modified Augmented-Plane-Wave Method.- Gradients of E($$\overrightarrow k$$) from the APW Determinant.- APW Pseudopotential Form Factors for the Alkali Metals.- Self-Consistent Orthogonalized-Plane-Wave Calculations.- Symmetrization Techniques in Relativistic OPW Energy Band Calculations.- Some Notes on a Modified OPW Method.- 2. KKR Methods in the Band Problem.- Recent Developments in KKR Theory.- Comments on the KKR Wavefunctions; Extension of the Spherical Wave Expansion Beyond the Muffin Tins.- Efficient Numerical Techniques for the Calculation of KKR Structure Constants.- Calculations with “Non-Muffin-Tin” Potentials by the Green’s Function Method.- Phase Shift Parametrization: Band Structure of Silver.- Band Structure Calculations for Semiconductors and Insulators Using the KKR Method.- Approximate KKR Band-Structure Schemes for Transition Metals.- Optical Properties of the Alkalis Using the KKR-Z Method.- 3. LCAO Methods in the Band Problem.- Discrete Variational Method for the Energy Band Problem.- Discrete Variational Method for the Energy Band Problem with LCAO Basis and Non-spherical Local Potential.- Recent Developments in Applying and Extending the Method of Tight Binding (LCAO) to Energy-Band Calculations.- Energy Bands by the LCAO Cellular Method.- 4. Interpolation and Integration in k-Space.- Interpolation and k-Space Integration: A Review.- Gilat-Raubenheimer Methods for k-Space Integration.- The Calculation of Brillouin Zone Integrals by Interpolation Techniques.- Computational Method for Generalized Susceptibility.- LCAO Interpolation Method for Nonorthogonal Orbitals.- Interpolation in k-Space with Functions of Arbitrary Smoothness.- Exact Solution of the Two-Band Density of States Problem.- Thermoelectric Transport Coefficients of Cubic Crystals Via k-Space Integration.- 5. The Band Problem with Boundary Conditions.- Bands, Bonds, and Boundaries.- $$\overrightarrow K \cdot \overrightarrow \pi$$ Interpolation and the Calculation of Vacancy States in PbTe.- A KKR Method for Two-Dimensional Lattices and Its Application to Band Calculation.- The Propagation Matrix Method for the Band Problem with a Plane Boundary.- 6. Self-Consistency, Exchange, and Correlation.- The Self-Consistent Field Method for Crystals.- Approximations of the Exchange and Correlation Potentials.- Some Remarks on Exchange Inhomogeneity Corrections in Many-Electron Systems.- Dielectric Function of Uniform Electron Gas.- Kohn-Sham Self-Consistent Scheme Applied to the Calculation of Atomic Systems and Metallic Sodium.- A Potential Function for Band Structure Calculations.- Crystal Potentials Used in Energy Band Theory.- Single-Particle States in Many-Body Systems.- Towards Self-Consistency with the Tight Binding Approximation.- Toward Hartree-Fock Calculations for Simple Crystals.- The Use of the GI Method in Band Calculations on Solids.- List of Contributors.