The Effects of Relativity in Atoms, Molecules, and the Solid State

340 Pages·1991·10.205 MB·English

by  Pekka Pyykkö (auth.), S. Wilson, I. P. Grant, B. L. Gyorffy (eds.)

THE EFFECTS OF RELATIVITY IN
ATOMS, MOLECULES, AND THE SOLID STATE
THE EFFECTS OF RELATIVITY IN
ATOMS, MOLECULES, AND THE SOLID STATE
Edited by
S. Wilson
Rutherford Appleton Laboratory
Oxfordshire, United Kingdum
1. P. Grant
Uniuersity of Oxford
Oxford, Uniled Kingdom
aud
B. L. Gyorffy
Universily of Brislol
Brislo/, United Kingdom
SPRINGER SCIENCE+BUSINESS MEDIA, llC
Llbrarv of Congress Catalog lng-ln-Publ leat Ion Data
The Effects of relatlvity 1n atoms, oolecules, and the solid state I
edlted by S. WIIson, I.P. Grant, and B.L. Gyorffy.
p. c •.
"Proceedlngs of a .eetlng on the effects of relatlvity In atoms,
molecules, and the solid state, held March 30-Aprll 1, 1990, In
Ab lngdon, Oxfordsh 1r e, Un I ted K 1n gdom "--T. p. verso.
Inc I udes b I b li ograph 1cal references and Index.
ISBN 978-1-4613-6646-1 ISBN 978-1-4615-3702-1 (eBook)
DOI 10.1007/978-1-4615-3702-1
1. Atomic structure--Congresses, 2. Molecular structure
-Congresses. 3. Solid state physlcs--Congresses. 4. Solid state
chemlstry--Congresses. 5. Reiativity (PhYSics)--Congresses.
1. WIIson, S, (Stephen), 1950- II. Grant, 1. P. III. GyiirffY,
B. L.
QC172.E34 1991
539'.1--dc20 91-11449
CIP
Proceedings of a meeting on the Effects of Relativity in Atoms,
Molecules, and the Solid State, held March 30-ApriI 1, 1990,
in Abingdon, Oxfordshire, United Kingdom
ISBN 978-1-4613-6646-1
© 1991 Springer Science+Business Media New York
Originally published by Plenum Press, New York in 1991
Softcover reprint of the hardcover 1st edition 1991
AII rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted
in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording, or otherwise, without written permission from the Publisher
Preface
Recent years have seen a growing interest in the effects of relativity in atoms, molecules
and solids. On the one hand, this can be seen as result of the growing awareness of the
importance of relativity in describing the properties of heavy atoms and systems
containing them. This has been fueled by the inadequacy of physical models which either
neglect relativity or which treat it as a small perturbation. On the other hand, it is
dependent upon the technological developments which have resulted in computers
powerful enough to make calculations on heavy atoms and on systems containing heavy
atoms meaningful. Vector processing and, more recently, parallel processing techniques
are playing an increasingly vital role in rendering the algorithms which arise in
relativistic studies tractable.
This has been exemplified in atomic structure theory, where the dominant role of the
central nuclear charge simplifies the problem enough to permit some prediction to be
made with high precision, especially for the highly ionized atoms of importance in
plasma physics and in laser confinement studies. Today's sophisticated physical models
of the atom derived from quantum electrodynamics would be intractable without
recourse to modern computational machinery. Relativistic atomic structure calculations
have a history dating from the early attempts of Swirles in the mid 1930's but continue to
provide one of the primary test beds of modern theoretical physics.
In. non-relativistic molecular structure calculations the use of basis set expansion
techniques is almost mandatory. Although it has been known since the work of Kim in
the late 1960's that there are problems associated with the use of basis set expansion
techniques in relativistic electronic structure calculations, these difficulties have only
recently been resolved. By affording a firm foundation for the ab initio treatment of
molecules containing heavy atoms and the interactions between them these developments
open up new horizons for modern theoretical chemistry. Relativistic quantum chemistry
has a vast range of potential applications in both the academic and the commercial
sectors in fields as diverse as catalysis and pharmacology, molecular electronics and
molecular biology. However, relativistic electronic structure calculations for molecules
will remain demanding for some time to come both in the requirement for more efficient
and reliable numerical methods and algorithms, and for the computer resources which
these methods require.
Relativistic solid-state calculations will be just as demanding. In. solid-state theory the
emphasis has until now been more on deriving physically intuitive approximation
schemes which seem tractable. The consensus which has enabled atomic and molecular
physicists and theoretical chemists to build general purpose models has, so far, not
existed amongst solid-state theorists.
This volume records the proceedings of a meeting on "The Effects of Relativity in
Atoms, Molecules and the Solid State" held under the auspices of three of the Science
and Engineering Research Council's Collaborative Computational Projects : Project 1 -
v
Electron correlation in molecules, Project 2 -Continuum states of atoms and molecules,
and Project 9 -The electronic structure of solids. The meeting was held at The Coseners
House, Abingdon, Oxfordshire, over the weekend 30th March - 1st April, 1990.
s.
July 1990 Wilson
I.P. Grant
B.L. Gyorffy
vi
Contents
Relativistic Effects on Periodic Trends
P.Pyykko
ATOMS
Relativistic Atomic Structure and Electron-Atom
Collisions 17
I.P. Grant
On the Accuracy of Oscillator Strengths 45
B.c. Fawcett
Atomic Structure Calculations in Breit-Pauli
Approximation 55
W. Eissner
Relativistic Calculations of Parity Non-Conserving
Effects in Atoms 67
A.c. Hartley and P.G.H. Sandars
High Precision Relativistic Atomic Structure
Calculations Using the Finite Basis Set
Approximation 83
H.M. Quiney
Relativistic Calculations of Electron Impact
Ionisation Cross-Sections of Highly Charged
Ions 125
D.L. Moores
MOLECULES
Nonsingular Relativistic Perturbation Theory and
Relativistic Changes of Molecular Structure 135
W.H.E. Schwarz, A. Rutkowski and G. Collignon
Basis Set Expansion Dirac-Fock SCF Calculations
and MBPT Refinement 149
Y. Ishikawa
Comments 163
Polyatomic Molecular Dirac-Hartree-Fock Calculations
with Gaussian Basis Sets 167
K.G. Dyall, K. Fregri, Jr. and P.R. Taylor
vii
Open Shell Relativistic Molecular Dirac-Hartree-Fock
SCF-Program 185
O. Visser, PJ.c. Aerts and L. Visscher
General Contraction in Four-Component Relativistic
Hartree-Fock Calculations 197
L. Visscher, P.J.c. Aerts and O. Visser
Accurate Relativistic Dirac-Fock and MBPT Calculations
on Argon with Basis Sets of Contracted
Gaussian Functions 207
Y. Ishikawa and R.C. Binning, Jr.
Comments 215
Relativistic Many-Body Perturbation Theory of
Atomic and Molecular Electronic Structure 217
S. Wilson
SOLID STATE
Relativistic Density-Functional Theory for
Electrons in Solids 255
B.L. Gyorffy, J.B. Staunton, H. Ebert, P. Strange
and B. Ginatempo
Influence of Relativistic Effects on the Magnetic
Moments and Hyperfine Fields of 5d-Impurity
Atoms Dissolved in Ferromagnetic Fe 275
H. Ebert, B. Drittler, R. Zeller and P.H. Dederichs
Relativistic Spin-Polarized Density-Functional Theory:
Simplified Method for Fully Relativistic
Calculations 285
P. Cortona
Theory of Magnetocrystalline Anisotropy 295
J. Staunton, P. Strange, B.L. Gyorffy, M. Matsumoto, J. Poulter,
H. Ebert and N.P. Archibald
The Spin Polarized Photoemission from
Non-Magnetic Metals 319
B. Ginatempo and B.L. Gyorffy
Theory of Magnetic X-Ray Dichroism 333
H. Ebert, B. Drittler, P. Strange, R. Zeller and B.L. GyorffY
Participants 349
Index 351
viii
RELATIVISTIC EFFECTS ON PERIODIC TRENDS
Pekka Pyykko
Department of Chemistry, University of Helsinki
Et. Hesperiankatu 4, 00100 Helsinki, Finland
1. INTRODUCTION
Whether we work on atoms, molecules or solids, we have in
common the Periodic System. At least seven different trends
can be found in it, see Figure 1. The last three of them are
of relativistic origin. Some of their particular consequences
on chemical and physical properties of elements are shown in
Figure 2. A few recent examples are quoted below.
2. A REVIEW OF REVIEWS
Grant (1970) reviewed the relativistic calculations on atoms
and Pyykko (1978) the ones on molecules, including a chapter
on "Relativity and the Periodic Table". These effects were
brought to the attention of many chemists by Pitzer (1979) or
Pyykko and Desclaux (1979), and have now entered the inorganic
chemistry textbooks by Cotton and Wilkinson (1988) or Mackay
and Mackay (1989).
The book by Pyykko (1986) includes 3119 references (and
seems to miss about 1% of the relevant material). Some later
reviews are mentioned in Table 1.
3. SOME RECENT RESULTS IN CHEMISTRY
The valencies of gold. It was suggested already by Pyykko
(1978) that the relativistic destabilization of the 5d shell
would explain the well-known valency increase from Ag(I) to
Au(III). Schwerdtfeger (1989) has now compared the calculated
stabilities of the (free) halides AUX2- and AUX4-, and expli
citly demonstrated that the preference for the higher oxida
tion state, III instead of I, indeed is of relativistic ori
gin.
The "gold maximum". The relativistic contraction and stabili
zation of the ns valence shell (n = 4 to 6) suffers a local
maximum at the coinage metals, group 11. Schwarz et al. (1989)
analysed the origins of this trend.
The Effects of Relativity on Atoms, Molecules, and the Solid State
Edited by S. Wilson et al., Plenum Press, New York, 1991
"Relativistic compounds". A number of novel organometallic
compounds have recently been synthesized and characterized, in
which a weak attraction, roughly of 10 kcal/mole or half of an
00
eV, much like in a good hydrogen bond, seems exist between
formally closed-shell Au{I) atoms saving a 5d1 configuration.
MoSe generally, bonds between 5d1 , 6s2 or the configuration
5d are found. without explicit proof, these bonds are pre
sumed to have strong relativistic contributions. In any case,
this "relativistic encouragement" has been a source of inspi
ration for the syntheticians, as evidenced by some of the
titles of Balch et ale (1987), Nagle et ale (1988), Raptis et
ale (1989), Scherbaum et ale (1988), and Wang et ale (1988).
A particularly striking example is the octahedral, six
coordinate carbon complex ({Ph3PAU)6C}2+ of Scherbaum et ale
(1988). The carb~n elgctron octet could then form, in 0h
symmetry, an (a1) (t1u) "8-electron-7-centre bond". In addi
tion, the Au-Au attractions would help. The only available
calculation on it is that by Rosch et ale (1989). Both the Au
Au and the C-Au interactions are found to contribute to the
bonding.
pert~rba~ive Hartree-Fock-Slater studies on the bonding in
the 5d -6s molecule TI Pt(CN) by Ziegler et ale (1989a)
suggest that the interaction between thallium and the tetra
cyanoplatinate has both strong ionic and covalent components.
AU~+. A clean example on the 5d10_5d10 attraction would be the
gas-phase Au22+, claimed by Saunders (1989). The theoretical
situation is summarized in Table 2. The pseudopotential HF or
CI calculations and the semiempirical tight-binding calcula
tions give a repulsive ground state. The non-relativistic DVM
calculations by Li et ale (1990) are seen to considerably
overbind for AU2+ and thus lack credibility. Therefore the
observation, if true, must come from an excited electronic
state (Mukherjee et ale 1990). Both their TB calculations and
the present PP-HF ones indeed find such a m~n~mum in the
states promoting one 5da antibonding electron to the 6sa
bonding MO.
The ground-state PP-CI curve of Ermler (private communica
tion) can be divided to three domains:
a) R > 6 a.u : A large-R domain with superposed +l/R repUlsion
and an _~/R4 charge-po1arisabi1ity-type attraction. The coef
ficient of the latter gives an Au+ polarisability,~, of about
14.2 a.u.
b) About 5 < R < 6: Some extra bonding (about 0.065 eV) but no
minimum.
c) R < 5: Extra, Pauli repulsion.
Trends along triads. The bond strength trend CU > Ag < Au was
explained quite early as a relativistic effect (see Ziegler et
ale (1989b) and, for later literature, Balasubramanian
(1989a).) A similar trend is seen in various organometallic
compounds of groups 6 (Cr > Mo < W), 8 (Fe> Ru < Os), 9 (Co>
Rh < Ir), 10 (Ni > Pd < Pt), and the strengthening has also
been shown to be a relativistic effect (Ziegler et ale 1989b).
For the same trend among the group 6 dimers, see Ziegler
(1987). A recent experimental example on this D trend are the
diatomic molecules CuIn > AgIn < AuIn (Balduccieet ale 1989).
2
Trends in Periodic System(s)
l.Main vertical trend: First shell of each I ano
malously small (1s, 2p, 3d, 4f). Due to 'primo
genic repulsion', larger <r> for larger n.
2.Main horizontal trend: Smaller <r> for larger Z.
3.Main periodicity: Filled shells particularly
stable. Half-filled non-relativistic shells also.
4.Partial screening effects: d-shell contraction,
lanthanold contraction.
5.Relativistic contraction and stabilization (s, p).
6.Relativlstic expansion and destabilization (d, f)
7.Spin-orbit splitting.
No deep group-theoretical principle.
Ie) Pekka Pyykko. March 21, 1990.
Fig. 1.
3