Computer Simulation of Materials at Atomic Level with CD-ROM

715 Pages·2000·56.589 MB·English

by  Peter Deak, Thomas Frauenheim, Mark R. Pederson

Computer Simulation
of Materials
at Atomic Level
edited by Peter Deak,
Thomas Frauenheim, and Mark R. Pederson
®WILEY-VCH
Berlin • Weinheim • New York • Chichester • Brisbane • Singapore • Toronto
Computer Simulation of Materials at Atomic Level. Edited by P. Deak, T. Frauenheim, M. R. Pederson
Copyright © 2000 WILEY-VCH Verlag Berlin GmbH, Berlin
ISBN: 3-527-40290-X
Editors:
Professor Dr. Peter Deak, Technical University of Budapest, Department of Atomic Physics, Hungary
Professor Dr. Thomas Frauenheim, University of Paderborn, Department of Physics, Paderborn,
Germany
Professor Dr. Mark R. Pederson, Naval Research Laboratories, Complex Systems Theory Branch,
Washington, DC, USA
With 238 figures
1st edition
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ISBN 3-527- 40290-X
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Preface
The idea for this compilation of papers grew out of two workshops organized by Tho-
mas Frauenheim during the last four years. The first (Chemnitz, 1996) was entitled
"First-Principles, Tight-Binding and Empirical Methods for Materials Simulation" and
the second (Paderborn, 1998) was entitled "Massively Parallel and Superscalar Applica-
tions in Computational Materials Science". Many of the participants of these workshops
had collaborations or cooperations with one another. Lectures from 26 prominent
groups representing 9 countries were presented during these workshops. While many
workshops revolve around a group of related methodologies, the "cohesive quality"
that emerged from these two workshops was in fact due to the diversity of the meth-
odologies discussed. Because of this diversity the materials applications exhibited a
commensurately broader range than what would generally be observed in a more spe-
cialized workshop where the limitations of any given methodology tend to partially lead
to problem preselection. Actual materials-based questions, of course, arise by practical
needs and are indeed wide ranged. As such, we observed that a broad repertoire of
materials methodologies at one's finger tips might indeed be the optimal way to avoid
problem preselection and instead bridge some gaps and allow us to go beyond the con-
ventional limits of computational materials science, condensed matter physics and chem-
istry. Indeed, the sheer complexity of the materials problems in the new millenium will
require a new generation of computational scientists to be fluent in many, rather than
one or two, computational methods and duely informed about the problem areas for
which each and every computational methodology is applicable. Realization of this goal
will be nontrivial since the complexity of computational materials science and con-
densed matter physics presently requires most groups to concentrate their efforts on
one or two computational methodologies. Presently young researchers from a given
group must spend several years learning a specific methodology and thereby become
"hostage" to their own expertise. Exchanges, such as these workshops, then provide an
excellent avenue for younger developing scientists, and even senior scientists, to broad-
en their understanding of methods outside their immediate scope and hopefully expand
their computational arsenal so that higher compexity materials-related problems can be
tackled.
We believe all participants enjoyed the excitement that was generated by the wide
variety of topics covered and the very real prospect of theoretical prediction of techno-
logically useful materials properties. Further, we expect that many researchers would
benefit from the dissemination of this diverse set of tools. As such, we have attempted
to compile this information in a way that would be useful to novice computational solid
state physicists arid materials scientists. The hope here is that as the field matures
young scientists will more often decide on an interesting application and then deter-
mine the methodology or methodologies that will most beneficially impact their area of
interest.
Of course, no group of theorists interested in real-life materials problems can work
without close contact to experimental and technological research and development
groups. Indeed almost all the groups represented herein have such contacts. The poten-
tial of microscopic modeling on a physical basis for helping to understand and solve
problems could be more widely recognized and enhanced by the experimental materials
science and technology community. Such interactions could be extended if the latter had
2 Preface
a better overview of the possibilities of the former and intensified if the Edisonian com-
munity could fully appreciate the limits and capabilities of the various theoretical meth-
ods. The other purpose of this compilation is to demonstrate to the other fields of mate-
rials science and technology the wide range of problems for which atomistic modeling
will provide insight and to enable this community to independently determine which
methodology is most appropriate for reliably answering their particular questions.
With these goals in mind this compilation has been divided into two parts. The first
part, Methods, contains indepth descriptions of many methods used in condensed mat-
ter and molecular physics. We attempted to include every major approach which is
based on individual interatomic interactions. These approaches include classical empiri-
cal potentials, semi-empirical and non-empirical tight binding methods, and ab initio
methods which include Hartree-Fock and Density-Functional based theories. We asked
that the contributors be concise about the theoretical foundations, explaining only the
basic concepts, but to elaborate on questions associated with implementation. We also
asked them to explain the limits of the method and the critical parameters of the actual
calculations which ultimately determine the quality of the output. Such requirements
lead authors to primarily address implementations in their own area of expertise and to
briefly mention other variants. The second part, Applications, presents a diversity of
problems related to materials properties and phenomena where these methods can be
fruitfully applied. We asked the authors of this part to emphasize issues related to accu-
racy of the calculated data but also to show how the raw data can be used to interpret
and/or foretell experimental results.
For both parts of this volume, we strived to assemble a collection of individual non-
overlapping papers that as a whole represented a broad range of topics of current inter-
est in materials science. This necessitated going beyond the topics represented in the
aforementioned workshops, and the result is a mix of contributions representing those
topics as well as many other materials properties. In all cases we asked for new or
updated work, and the end result was ultimately determined by the willingness of the
invited authors to devote considerable time and effort in their contribution and to ad-
here to the restrictions arising from the broader aims of this volume. As with any vol-
ume of this nature size restrictions and author availability call for some qualifications.
This compilation is in fact a snapshot of the present field of atomistic computational
materials science. It does not and can not manage to cover every important method
and all their possible aspects. Notably absent is a methodological discussion of plane-
wave-based algorithms (which, however, is easily accessible in several recent reviews).
However, several contributions in the applications section are based on such methods.
The individual papers do not attempt to review their respective fields completely. While
useful to a young scientist it can not be a full substitute since knowledge of advanced
physics and chemistry is assumed rather than taught. Computational materials science is
the most appropriate umbrella for this collection, but this field also contains a huge
variety of problems and those which may be addressed atomistically are merely a sub-
set. Within this subset our compilation represents problems related to semiconductors,
dielectrics, molecular assembled materials and special transition metal systems.
While a photographic snapshot can record a portion of a large event, it generally
neither features nor includes all participants but often captures the overall enthusiasm
and excitement of the event. We think the snapshot of Computational Materials
Science enclosed within this special volume of physica status solidi, together with the
Preface 3
resulting book, achieve our specific aims and further illustrate the way in which the
interactions between the fields of experimental and computational materials science are
being expanded at this and other levels. In addition to the book we distribute a CD
with a collection of demonstration versions of many of the computer codes used by the
researchers. We encourage both experimentalists and theorists to play around with
these codes to develop a greater idea of what is possible with each of these codes. We
intend to continue the workshops on computational materials science as well.
We thank all authors who participated in this project. Finally we would like to thank
the publishing house Wiley-VCH for endorsing this project and express our gratitude to
the editorial office, Karin Mliller (editor of the journal version), Gesine Reiher (editor
of the book version), Dr. Michael Bar (publisher) and Professor Martin Stutzmann
(editor-in-chief).
Budapest 1999 Peter Dedk
Thomas Frauenheim
Mark R. Pederson
Contents
Methods
P. DEAK Choosing Models for Solids 9
D.W. BRENNER The Art and Science of an Analytic Potential 23
TH. FRAUENHEIM, G. SEIFERT, M. ELSTNER, Z. HAJNAL, G. JUNGNICKEL, D. POREZAG, S. SUHAI,
and R. SCHOLZ
A Self-Consistent Charge Density-Functional Based Tigh-Binding Method
for Predictive Materials Simulations in Physics, Chemistry and Biology. . . 41
R. DOVESI, R. ORLANDO, C. ROETTI, C. PISANI, and V.R. SAUNDERS
The Periodic Hartree-Fock Method and Its Implementation in the CRYSTAL
Code 63
R.W. TANK and C. ARCANGELI
An Introduction to the Third-Generation LMTO Method 89
P.R. BRIDDEN and R. JONES
LDA Calculations Using a Basis of Gaussian Orbitals 131
J.R. CHELIKOWSKY, Y. SAAD, S. OGUT, I. VASILIEV, and A. STATHOPOULOS
Electronic Structure Methods for Predicting the Properties of Materials:
Grids in Space 173
M.R. PEDERSON, D.V. POREZAG, J. KORTUS, and D.C. PATTON
Strategies for Massively Parallel Local-Orbital-Based Electronic Structure
Methods 197
D. POREZAG, M.R. PEDERSON, and A.Y. Liu
The Accuracy of the Pseudopotential Approximation within Density-Func-
tional Theory 219
G. GALLI Large-Scale Electronic Structure Calculations Using Linear Scaling Methods 231
R.E. RUDD and J.Q. BROUGHTON
Concurrent Coupling of Length Scales in Solid State Systems 251
Applications
K. JACKSON Electric Fields in Electronic Structure Calculations: Electric Polarizabilities
and IR and Raman Spectra from First Principles 293
S. SRINIVAS and J. JELLINEK
Ab initio Monte Carlo Investigations of Small Lithium Clusters 311
6 Contents
C. ASHMAN, S.N. KHANNA, and M.R. PEDERSON
Structure and Isomerization in Alkali Halide Clusters 323
P. ORDEJON Linear Scaling ab initio Calculations in Nanoscale Materials with SIESTA 335
M. ELSTNER, TH. FRAUENHEIM, E. KAXIRAS, G. SEIFERT, and S. SUHAI
A Self-Consistent Charge Density-Functional Based Tight-Binding Scheme
for Large Biomolecules 357
P.D. TEPESCH and A.A. QUONG
First-Principles Calculations of a-Alumina (0001) Surfaces Energies with
and without Hydrogen 377
A. GROSS Ab initio Molecular Dynamics Simulations of Reactions at Surfaces . . . . 389
J. KOLLAR, L. VITOS, B. JOHANSSON, and H.L. SKRIVER
Metal Surfaces: Surface, Step and Kink Formation Energies 405
A.Y. Liu Linear-Response Studies of the Electron-Phonon Interaction in Metals . . 419
P. LEARY, C.P. EWELS, M.I. HEGGIE, R. JONES, and P.R. BRIDDON
Modelling Carbon for Industry: Radiolytic Oxidation 429
R. SCHOLZ, J.-M. JANCU, F. BELTRAM, and F. BASSANI
Calculation of Electronic States in Semiconductor Heterostructures with an
Empirical spds* Tight-Binding Model 449
H.M. URBASSEK and P. KLEIN
Constant-Pressure Molecular Dynamics of Amorphous Si 461
M. HAUGK, J. ELSNER, TH. FRAUENHEIM, T.E.M. STAAB, C.D. LATHAM, R. JONES, H.S. LEIPNER,
T. HEINE, G. SEIFERT, and M. STERNBERG
Structures, Energetics and Electronic Properties of Complex III-V Semi-
conductor Systems 473
S.K. ESTREICHER
Structure and Dynamics of Point Defects in Crystalline Silicon 513
J.E. LOWTHER Superhard Materials 533
U.V. WAGHMARE, E. KAXIRAS, and M.S. DUESBERY
Modeling Brittle and Ductile Behavior of Solids from First-Principles Cal-
culations 545
F. DELLA SALA, J. WIDANY, and TH. FRAUENHEIM
Comparison of Simulation Methods for Organic Molecular System: Por-
phyrin Stacks 565
Contents 7
F. CORA and C.R.A. CATLOW
Quantum Mechanical Investigations on the Insertion Compounds of Early
Transition Metal Oxides 577
W.R.L. LAMBRECHT and S.N. RASHKEEV
From Band Structures to Linear and Nonlinear Optical Spectra in Semicon-
ductors 599
M.J. CALDAS Si Nanoparticles as a Model for Porous Si 641
U. GERSTMANN, M. AMKREUTZ, and H. OVERHOF
Paramagnetic Defects 665
J. BERNHOLC, E.L. BRIGGS, C. BUNGARO, M. BUONGIORNO NARDELLI, J.-L. FATTEBERT,
K. RAPCEWICZ, C. ROLAND, W.G. SCHMIDT, and Q. ZHAO
Large-Scale Applications of Real-Space Multigrid Methods to Surfaces, Na-
notubes and Quantum Transport 685
A. Di CARLO Semiconductor Nanostructures 703
Subject Index 723
P. DEAK: Choosing Models for Solids 9
phys. stat. sol. (b) 217, 9 (2000)
Subject classification: 61.46.+w; 61.50.-f; 71.10.-w; 71.23.An
Choosing Models for Solids
P. DEAK
Surface Physics Laboratory, Department of Atomic Physics, TU Budapest,
Budafoki ut 8., H-llll Budapest, Hungary
(p. deak@eik. bme. hu)
(Received August 10, 1999)
The atomistic simulation of properties and phenomena in solid materials requires a suitable model
of the real system with a number of atoms which is still manageable at the chosen level of approx-
imation. Since typical solids consist of atoms in the order of 1023, only a very small fraction of
them can be treated explicitly. The effect of the rest on the explicitly treated part has to be taken
into account somehow. This paper attempts to categorize and explain the various tricks applied in
modeling solids, showing their strength and weakness.
1. Introduction
Even though the term "material" is more general, when talking about "materials prop-
erties and phenomena", usually condensed matter is meant. This implicit distinction
comes from the fact that materials science and technology evolved by dealing with
structural and functional engineering materials, whereas fluids and gases were the work-
ing media only. The majority of the contributions in the present volume deals with an
even more restricted class of materials: the solids. By that those pieces of condensed
matter are meant which:
— are in the solid state under normal conditions and have characteristic relaxation times
under stress r > 1010 s (r = rflE\ where rj is the viscosity and E is the Young modulus),
— exhibit at least short-range order on the atomic scale (i.e., at least one of the atom
types has the same first neighbor coordination everywhere),
— are larger than about 10 nm in diameter (consist roughly over 50000 atoms).
This last criterion separates solids from clusters which are also treated in this volume
but — due to their size — do not need simplified models. The goal of the present paper
is to give a short guide to those models which scale down the problem of real solids to
a level tractable by present day atomistic computer simulations.
A special class of solids are crystals, i.e., solids with long-range order. The fact that
the coordination of every atom type in any neighbor shell is identical, ensures transla-
tional symmetry in the bulk of the material. Considering the critical size of solids, the
surface to volume ratio can be neglected and artificial boundary conditions can be ap-
plied to extrapolate the translational symmetry to infinity. As a consequence, (New-
tonian) equations of motion or (Schrodinger) equation of state has to be solved only
for one periodically repeated unit cell. Due to the translational symmetry, the calcula-
tions can be conveniently performed in momentum space. Indeed, between 1940 and
1970, the main task of solid state physics was to determine the properties of perfect
crystals within this construction.
Computer Simulation of Materials at Atomic Level. Edited by P. Deak, T. Frauenheim, M. R. Pederson
Copyright © 2000 WILEY-VCH Verlag Berlin GmbH, Berlin
ISBN: 3-527-40290-X
10 P. DEAK
Even local deviations from the overall periodicity (i.e. bulk defects and surfaces), let
alone the lack of long-range order, forfeit the principal basis for applying conventional
momentum space description. Since these "imperfections" cannot be neglected, or
rather they make most practical application of the material possible, the papers of this
volume have to deal with this situation. The usual way is to handle the immediate
environment of the critical part explicitly, taking into account somehow the effect of the
rest of the solid. It is the purpose of my contribution to categorize and explain the
tricks usually applied when facing the problem of having to solve equations — in princi-
ple — for a many-body system of particles well in excess of 105. The paper is intended
to be a tutorial, rather than a review. Therefore, emphasis lies on the main ideas of
modeling without any claim of completeness. In Section 2 the treatment used for per-
fect crystals is shortly given. Section 3 describes models of defective crystals, while Sec-
tion 4 deals with surfaces and solids without long-range order.
2. The Perfect Crystal
A general assumption (almost always made) is the Born-Oppenheimer approximation.
If the atomic vibrations in the crystal are strictly harmonic, a many-body Schrodinger
equation for the electrons can be solved at fixed nuclei, and the total energy of the
electrons can be added to the effective potential of the vibrating nuclei. The assump-
tion is justified as long as the solid remains essentially elastic (Hook's law) and the
temperature is sufficiently low (thermal expansion negligible). Of course, neither condi-
tion is satisfied exactly but the deviation can be taken into account by interaction be-
tween the (nominally independent) elementary excitations of both systems. This is also
usually the case even for such defects (non-radiative recombination centers) where the
two systems are definitely coupled. In Jahn-Teller unstable systems a vibronic rather
than an electronic wavefunction should be used.
As mentioned above, the perfect crystal is assumed to be invariant to translations by
the lattice vectors
where a/ are the primitive unit vectors and 1 = [l\ , /2, h] are arbitrary integers. As a
consequence, a reciprocal lattice can be defined for the crystal in momentum space
with lattice vectors
G« = £&*/, (2)
/
where the primitive unit vectors b satisfy the condition
y
a/by = 2jtdij . (3)
The symmetric unit cell of the reciprocal lattice (defined as points closer to one lattice
point than to all others) is the Brillouin zone (BZ). Due to the translational symmetry,
the elementary excitations of the many-electron system (Bloch electrons) or of the
vibrating lattice (phonons) can be expressed by Bloch waves of the form
<Pnk(*) = M k(r)exp(*r) (4)
W
with wave vector k restricted to the BZ. The microscopic periodicity of the crystal is
expressed by the fact that the Bloch waves satisfy Bloch's periodicity condition,
cp (r + R,) = <^ (r) exp (ikR,) , (5)
nk k