Computational Methods in Band Theory: 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

581 Pages·1971·28.97 MB·English

by  John W. D. Connolly (auth.), P. M. Marcus, J. F. Janak, A. R. Williams (eds.)

COMPUTATIONAL
METHODS IN
BANDTHEORV
THE IBM RESEARCH SYMPOSIA SERIES
1971 : Computational Methods in Band Theory
Other volumes in preparation
COMPUTATIONAL
METHODS IN
BANDTHEORV
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
Edited by
P. M. Marcus, J. F. Janak, and A. R. Williams
IBM Thomas J. Watson Research Center
Yorktown Heights, New York
9:>
PLENUM PRESS • NEW YORK-LONDON • 1971
Library of Congress Catalog Card Number 77-142039
ISBN-13: 978-1-4684-1892-7 e-ISBN-13: 978-1-4684-1890-3
DOl: 10.1007/978-1-4684-1890-3
© 1971 Plenum Press, New York
Softcover reprint of the hardcover 15t edition 1971
A Division of Plenum Publishing Corporation
227 West 17th Street, New York, N. Y. 10011
United Kingdom edition published by Plenum Press, London
A Division of Plenum Publishing Company, Ltd.
Donington House, 30 Norfolk Street, London W.C.2, England
All rights reserved
No part of this publication may be reproduced in any form
without written permission from the publisher
PREFACE
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.
P. M. Marcus
J. F. Janak
A. R. Williams
v
CONTENTS
Welcoming Address xiii
A. G. Anderson
Comments on the Conference xv
P. M. 1f.arcus
1. APW-OPW METHODS IN THE BAND PROBLEM
A Comparison of Different Computer-Oriented Methods
for the Energy Bands of Solids • • • • • • 3
John W. D. Connolly
Diagona1ization of Hermitian Matrices; Maximization
of Speed and Accuracy • • • • • • • 16
R. A. Faulkner
An Alternative APW Technique: Theory and Application
to Copper 25
Dale Dean Koelling
An RAPW Expanded Basis Set 33
G. Arbman and D. Koelling
New Version of the Modified Augmented-P1ane-Wave
Method • • • • • • • • • • . • • • • • 44
H. Bross, G. Bohn, G. Meister, W. Schubtl, and
H. Stohr
Gradients of E(k) from the APW Determinant. • • • • • • • 59
J. H. Wood
APW Pseudopotentia1 Form Factors for the Alkali
Metals . . . • . 63
0 • • • • • •
Martin J. G. Lee
vii
viii CONTENTS
Self-Consistent Orthogonalized-Plane-Wave
Calculations • • • • • • • • • 82
R. N. Euwema, D. J. Stukel, and T. C. Collins
Symmetrization Techniques in Relativistic OPW
Energy Band Calculations • • • • • • • 124·
G. G. Wepfer, T. C. Collins, R. N. Euwema,
and D. J. Stukel
Some Notes on a Modified OPW Method 144
D. M. Gray and R. J. Karpien
2 • KKR METHODS IN THE BAND PROBLEM
Recent Developments in KKR Theory • • • • 157
A. R. Williams, S. M. Hu, and D. W. Jepsen
*Comments on the KKR Wavefunctions; Extension of
the Spherical Wave Expansion Beyond the
Muf fin Tins .••..••.••.... 178
O. Krogh Anderson
Efficient Numerical Techniques for the Calculation
of KKR Structure Constants • • • • • • • 183
Harold L. Davis
Calculations with "Non-Muffin-Tin" Potentials
by the Green's Function Method ••• 200
Benjamin Segall
Phase Shift Parametrization: Band Structure of
Silver • . • • . • . 207
B. R. Cooper, E. L. Kreiger, and B. Segall
Band Structure Calculations for Semiconductors
and Insulators Using the KKR Method 218
H. Overhof
Approximate KKR Band-Structure Schemes for
Transition Metals • • • • • 225
N. W. Dalton
Optical Properties of the Alkalis Using the
KKR-Z Method • • • • • • 260
A. R. Wilson, G. Dresselhaus, and C-Y. Young
>'<Prepared Discussion
CONTENTS ix
3 • LCAO METHODS IN THE BAND PROBLEM
Discrete Variational Method for the Energy Band
Problem • • • • • • • • 271
D. E. Ellis and G. S. Painter
Discrete Variational Method for the Energy Band
Problem with LCAO Basis and Non-spher..ical
Local Potential ••••••••••••• 276
G. S. Painter and D. E. Ellis
Recent Developments in Applying and Extending the
Method of Tight Binding (LCAO) to
Energy-Band Calculations •••• 284
Earl E. Lafon, Roy C. Chaney, and Chun C. Lin
Energy Bands by the LCAO Cellular Method • • • 296
P. D. DeCicco
4. INTERPOLATION AND INTEGRATION IN k-SPACE
Interpolation and k-Space Integration: A Review 305
F. M. Mueller
Gilat-Raubenheimer Methods for k-Space Integration • • • • 323
J. F. Janak
The Calculation of Brillouin Zone Integrals by
Interpolation Techniques • • • • • • 340
R. L. Jacobs and D. Lipton
Computational Method for Generalized Susceptibility 347
Joshua B. Diamond
LCAO Interpolation Method for Nonorthogonal Orbitals • • • 355
L. F. Mattheiss
Interpolation in k-Space with Functions of Arbitrary
Smoothness. •••••••••.•••• 362
Donn G. Shankland
*Exact Solution of the Two-Band Density of States
Problem 368
N. W. Ashcroft
*Prepared Discussion
x CONTENTS
*Thermoelectric Transport Coefficients of Cubic
Crystals Via k-Space Integration . • • 373
J. M. Schoen
5. THE BAND PROBLEM WITH BOUNDARY CONDITIONS
Bands, Bonds, and Boundaries •.•••• 377
K. H. Johnson and F. C. Smith, Jr .
..... .....
K·rr Interpolation and the Calculation of Vacancy
States in PbTe • • 400
G. W. Pratt, Jr., E. K. Li, and F. J. Arlinghaus
A KKR Method for Two-Dimensional Lattices and Its
Application to Band Calculation • • • • 409
Kyozaburo Kambe
The Propagation Matrix Method for the Band Problem
with a Plane Boundary ••.••••. 416
D. W. Jepsen and P. M. Marcus
6. SELF-CONSISTENCY, EXCHANGE, AND CORRELATION
The Self-Consistent Field Method for Crystals 447
J. C. Slater
Approximations of the Exchange and Correlation
Potentials • • . •. •••.•• 458
L. J. Sham
>"Some Remarks on Exchange Inhomogeneity Corrections
in Many-Electron Systems • • • • . • • • . 469
Irene B. Ortenburger and Frank Herman
*Dielectric Function of Uniform Electron Gas 473
J. W. F. Woo
Kohn-Sham Self-Consistent Scheme Applied to the
Calculation of Atomic Systems and Metallic
Sodium 476
B. Y. Tong
A Potential Function for Band Structure Calculations . • • 489
David A. Liberman
>~Prepared Discussion
CONTENTS xi
Crystal Potentials Used in Energy Band Theory 495
A. M. Boring and E. C. Snow
Single-Particle States in Many-Body Systems 500
Seb Doniach
Towards Self-Consistency with the Tight Binding
Approximation •••• • • • • • • 512
Joseph Callaway and John L. Fry
Toward Hartree-Fock Calculations for Simple Crystals 517
Frank E. Harris and Hendrik J. Monkhorst
The Use of the GI Method in Band Calculations on
Solids . . . . . . . . . . 542
0 • • • • •
William A. Goddard III and Patricia M. O'Keefe
List of Contributors 571
Subject Index 575