Structural and Electronic Paradigms in Cluster Chemistry

217 Pages·1997·3.086 MB·English

by  Roy L. Johnston (auth.), Prof. D. M. P. Mingos (eds.)

87
Structure and Bonding
Editorial Board:
M. J. Clarke J. B. Goodenough
l
C. K. Jsrgensen D. M. P. Mingos - G. A. Palmer
l
P. J. Sadler R. Weiss R. J. P. Williams
l l
Structural and Electronic
Paradigms in Cluster Chemistry
Volume Editor: D. M. I? Mingos
With contributions by
J. D. Corbett, M.-F. Fan, T. P. Fehlner, J.-Halet,
C.E. Housecroft, R. L. Johnston, Z. Lin, J.-Y. Saillard
Springer
ISSN 0081 - 5993
ISBN 3-540-62791-X
Springer-Verlag Berlin Heidelberg New York
Die Deutsche Bibliothek - CIP-Eiiheitsaufimhme
Structural and electronic paradigms in cluster chemistry I
vol. ed.: D. M. P. Mingos. With contributions by J. D. Corbett . . .
Berlin ; Heidelberg ; New York ; Barcelona ; Budapest, Hong Kong ;
London ; Milan ; Paris ; Santa Clara ; Singapore ; Tokyo : Springer 1997
(Structure and bonding ; 87)
ISBN 3-540-62791-X (Berlin ,.. )
ISBN O-387-62791-X (New York . ..)
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Volume Editor
Prof. D. M. P. Mingos
Chemistry Department
Imperial College of Science Technology and Medicine
South Kensington
London SW7 2AY, Great Britain
E-mail: [email protected]
Editorial Board
Prof. Michael J. Clarke Prof. John B. Goodenough
Merkert Chemistry Center Center of Materials Science and Engineering
Boston College University of Texas at Austin
2609 Beacon St. Chestnut Hill Austin, Texas 78712, USA
Massachusetts 02167-3860, USA E-mail: jgoodenough@mail,utexas.edu
E-mail: [email protected]
Prof. Christian K. Jerrgensen Prof. David M. P. Mingos
Department de Chimie Minerale Chemistry Department
de l’Universit6 Imperial College of Science
Section de Chimie - Sciences II Technology and Medicine
30 quai Ernest Ansermet South Kensington
CH-1211 Gen&e 4, Switzerland London SW7 2AY, Great Britain
E-mail: [email protected]
Prof. Graham A. Palmer Prof. Peter J. Sadler
Department of Biochemistry Department of Chemistry
and Cell Biology The University of Edinburgh
Wiess School of Natural Sciences Joseph Black Chemistry Building
Rice University King’s Building, West Mains Road
Houston, Texas 77005 - 1892, USA Edinburgh EH9 3JJ, Great Britain
E-mail: [email protected] E-mail: [email protected]
Prof. Raymond Weiss Prof. Robert J. P. Williams
Inorganic Chemistry Laboratory
Institut Le Be1 University of Oxford
Laboratoire de Cristallochimie Oxford OX1 3QR, Great Britain
et de Chimie Structurale E-maik [email protected]
4, rue Blake Pascal
F-67070 Strasbourg Cedex, France
E-mail: [email protected]
ecaferP
The last five decades have witnessed a spectacular growth in the chemistry of
polyhedral molecules of the elements. )1 In the main group area research which
started in the Cold War era with the synthesis of new boranes and carboranes
revealed a whole class of symmetrical molecules which had deltahedral poly-
hedral structures, i.e. nH~B -2 and H2_nB2C .n These compounds have been joined
subsequently by many examples of isoelectronmiocl ecules containing other main
group metals and nonmetals, e.g. 9nS -4 9iB ,+s which also have polyhedral cage
structures but do not have any extra-cage bonds to hydrogen atoms. Some indica-
tions of the possibilities for cage molecules of this type were evident in the earlier
German literature which suggested that salts such as NaPb actually were better
formulated as NaaPb4, with tetrahedral polyhedral because of their isoelectronic
relationships with As4, P4, etc. This and subsequent research firmly establishtehde
possibility of making "bare" clusters of the main group elements either as allo-
tropes of the element or as cationic and anionic derivatives. Recent developments
in this field are summarised in Professor Corbett's chapter. The isolation of such
cationic and anionic polyhedral ions on a reasonable scale required chemistst o do
their synthesis in solvent media either of low nucleophilicity or electrophilicity.
More recently it has been recognised that such species could also be generated and
studied in a mass spectrometry chamber on a molecular scale using molecular
beam techniques. It was such experiments which lead to the spectacular develop-
ment of 06C chemistry which was recognised in 1996 by the award of the Nobel
Prize jointly to Smalley, Curl and Kroto.
The in-depth study of transition metal cluster compounds evolved out of a
curiosity towards the valence problems posed by their novel-structural features
and a belief that small molecular clusters could prove to be effective homo-
genous catalysts for the conversion of CO and 2 H into hydrocarbons and alco-
hols. Initially cluster compounds with only 3 -6 metal atoms were isolated, but
the improvements in spectroscopic, structural and separation techniques rapid-
ly led to the characterisation of many high nuclearity cluster compounds and
there now exist examples of structurally well defined compounds with more
than 001 metal atoms. The study of cluster compounds was also stimulated by
the superconductivity properties of the Chevrel phase molybdenum-sulfido
octahedral clusters and the recognition that molybdenum-iron-sulfido clusters
may be involvedi n the active site of nitrogenase.
These experimental findings have been matched by the development of a con-
ceptual framework which have brought some intellectual order to the multitude
VIII ecaferP
of polyhedral structures revealed in main groups and transition metal chem-
istry. A detailed account of the historical development of these ideas and their
widespread applications have been given elsewhere and will not be repeated
here. )a The purpose of this Preface is to bring attention to the key papers which
led to the development of the Polyhedral Skeletal Electron Pair Theory.
In 1971 Bob Williams )3 recognised for the first time that the structures of the
boranes 4+nH~B and BnHn+ 6 were not all based on fragments of an icosahedron,
but more correctly viewed as almost complete Skeletons of the parent delta-
hedral boranes ~HnB .-2 Specifically he established triads of molecules which
were structurally related and had either the complete deltahedral cage, (the
nHnB-osolc -2 anions), one vertex missing from the complete cage )4+nHnB-odin(
or two vertices missing from the complete cage (arachno-BnHn+6). In the same
year Ken Wade recognised the validity of this structural relationship and pro-
posed a simple electronic basis for it. He developed the important principle that
the closo-, nido- and arachno-triads were structurally related because they had
the same number of electron pairs involved in skeletal bonding. Specifically the
(n+l) electron pairs characteristic of the closoboranes ~H~B -2 were retained in
the nido- and arachno-derivatives Bn_lH(n_x+4) and .)6+2_n(H2_nB )4 Wade also
recognised that the bonding pattern observed in closo-, nido- and arachno-
borane polyhedral molecules were also reproduced in metal carbonyl clusters.
Professor Fehlner's Chapter on metalloboranes illustrates how important this
relationship proved to be. These ideas were later extended to electron precise
and electron rich and capped clusters in 1972 by Wade )s and myself. )6 These
papers also recognised the importance of interstitial atoms in cluster chemistry
and the Chapter by Dr. Housecroft summarises the current methodologies used
to accommodate interstitial atoms with the electron counting generalisations.
The theoretical basis of the electron counting rules was underpinned during
the subsequent decade. The cluster compounds of the early transition metals
could be incorporated within the framework of the Polyhedral Skeletal Electron
Pair Theory, but it was recognised that the spectrum of molecular orbitals gener-
ated in such clusters differed from those in n-acceptor clusters. The Chapter by
Zhenyang Lin and Man-Fai Pan demonstrates how the great majority of n-donor
clusters may be incorporated within the general framework of the approach.
The conceptual models which were first introduced 52 years ago proved to be
important for several reasons. Firstly, they provided a structural paradigm
which could be used to rationalise the structures of polyhedral molecules in an
analagous way to that which had been achieved two decades earlier for
mononuclear compounds in the Valence Shell Electron Pair Repulsion Theory. )8
Secondly it unified for the first time the areas of main group and transition
metal cluster chemistry. The relationship between main group and transition
metal carbonyl fragments were formalised in the isolobal analogy in 1976. ~01,9
Thirdly the research established that the closed shell requirements of even
these complex molecules were governed by relatively simple electronic require-
ments. In the 1980s Stone was able to demonstrate that the closed shell require-
ments of closo-, nido- and arachno-polyhedral molecules could be rationalised
within the framework of a spherical free electron model. The Tensor Surface
Harmonic model and its group theoretical implications have provided an ele-
ecaferP IX
gant way of accounting for many features of the electron counting rules devel-
oped earlier. )11 Dr. Johnston's Chapter on the mathematical aspects of cluster
chemistry provides an excellent introduction to these fundamental aspects.
Although Polyhedral Skeletal Electron Pair theory has survived the test of
time, many new applications have developed and further theoretical work has
hightlighted the reasons for apparent exceptions to the generalisations. The
Chapter by Drs Halet and Saillard provides a good illustration of how some of
these exceptions have been rationalised using modern theoretical techniques.
I hope that collectively the Chapters provide a timely celebration of the semi-
nal contributions of Williams and Wade and a contemporary account of some of
the more important recent developments. Their perception and imagination
opened up a new area of chemistry and inspired us all.
London D.M.P. Mingos
March 7991
.1 Mingos DMR Wales JD (1990) Introduction to cluster chemistry, Prentice-
Hall, NewYork
.2 Johnston ,LR Mingos DMP (1987): Struct Bond, ,92 86
.3 Williams RE (1971) Inorg Chem, ,01 012
.4 Wade JK (1972) Chem Soc Chem Commun 297
.5 Wade K (1972) Inorg Nucl Chem Lett ,8 559, 563,823
.6 Mingos DMP (1972) Nature Phys Sci 99,236
.7 Mason R, Thomas ,MK Mingos DMP (1973) J Amer Chem Soc ,69 3802
.8 Gillespie ,JR Nyholm SR (1957) Quart Rev Chem Soc 11,339
.9 Elian M, Chen MML, Mingos DMP, Hoffmann R (1970) Inorg Chem ,51 8411
.01 Hoffmann R (1985) Nobel Lecture, Science, 211,995
.11 Stone JA (1980) Mol Phys ,1 1339; (1981) Inorg Chem ,02 365
stnetnoC
Mathematical Cluster Chemistry
L. R. Johnston .................................
Metal-Metal Interactions in Transition Metal Clusters
with or-Donor Ligands
Z. Lin, M.-E Fan ................................ 35
Electron Count Versus Structural Arrangement in Clusters
Based on a Cubic Transition Metal Core with Bridging
Main Group Elements
J.-E Halet, J.-Y. Saillard ............................ 18
Metallaboranes
.T .P Fehlner .................................. 111
Clusters with Interstitial Atoms from the p-Block:
How Do Wade's Rules Handle Them?
E. C. Housecroft ................................ 137
Diverse Naked Clusters of the Heavy Main-Group Elements.
Electronic Regularities and Analogies
.J D. Corbett .... ~ ............................. 157
AuthorI ndex Volumes - 1 87 ......................... 591
Contents of Volume 86
Atoms and Molecules in Intense Fields
Volume Editors: L. S. Cederbaum, K. C. Kulander, N. H. March
Molecules in Intense Laser Fields: An Experimental Viewpoint
K. Codling, L. J. Frasinski
Two Interacting Charged Particles in Strong Static Fields:
A Variety of Two-Body Phenomena
P. S. Schmelcher, L. S. Cederbaum
Semiclassical Theory of Atoms and Ions in Intense External Fields
N. H. March
Field Induced Chaos and Chaotic Scattering
H. Friedrich
Microwave Multiphoton Excitation and Ionization
T. F. Gallagher
Time-Dependent Calculations of Electron and Photon Emission
from an Atom in an Intense Laser Field
K. C. Kulander, K. J. Schafer
Mathematical retsulC yrtsimehC
Roy L. Johnston
School of Chemistry, University of Birmingham, Edgbaston, Birmingham 51B 2TT, United
Kingdom. hiam-E [email protected]
The application of mathematical methods, such as polyhedral topology, graph theory and
group theory, to the study of cluster molecules is reviewed. The development of localised
orbital and spherical harmonic methods are outlined and there is an introduction to Tensor
Surface Harmonic Theory and Group Theory on a Spherical Shell. The inter-relationships
between these approaches and their links with simple molecular orbital models, such as
Hfickel Theory, are detailed and rationalised. The review concludes with case studies which
show how some or all of these methodologies have been brought to bear on three problems
- deviations from Wade's rules in "non-spherical" borane clusters, the occurrence of approxi-
mately non-bonding skeletal molecular orhitals in hydrocarbon clusters; and the prediction
of the structures, electronic properties and stabilities of the fullerenes - truly a "mathemat-
ical chemist's delight".
:sdrowyeK Clusters; graph theory; group theory; spherical harmonics; topology
Introduction to Mathematical Cluster Chemistry ............... 2
Clusters as Polyhedra ....................................... 3
2.1 Polyhedral Topology: Euler's Relations ........................ 3
2.2 Types of Polyhedra ......................................... 4
2.3 Duality ................................................... 5
Clusters as Graphs ......................................... 6
3.1 Graph Theory and Hfickel Theory ............................ 7
3.2 Graph Theory and Moments ................................. 7
3.3 Graph Theory and Clusters .................................. 8
4 Clusters as Spheres ......................................... 10
4.1 General Methodology ....................................... 10
4.2 Tensor Surface Harmonic Model .............................. 12
5 Group Theory of Clusters ................................... 14
5.1 Group Theory on a Spherical Shell ............................ 14
5.2 Group Theory of Orbits ..................................... 15
Structure and Bonding, 87 Vol.
© Springer Verlag Berlin Heidelberg 1997