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Homoatomic d10Цd10 Interactions Their Effects on Structure and Chemical and Physical Properties.

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Homoatomic d”-d’’ Interactions:
Their Effects on Structure and Chemical and Physical Properties
By Martin Jansen*
Dedicated to Professor Rudolf Hoppe on the occasion of his 65th birthday
The distinction between valence electrons and essentially inactive core electrons is the basis
of many classifying concepts in chemistry. However, it has recently been recognized that
this is an oversimplification and should, at least in some areas of chemistry, be modified.
Many cases are known where cations with closed d ” configurations are subject to homoatomic interactions that influence structure and properties. A characteristic and surprisingly
uniform structural feature (e.g., of a number of compounds containing monovalent coinage
metals) is a clusterlike assembly of d’’ cations that corresponds in geometry and bond
lengths to fragments of the metal structures themselves. Further evidence for a special type
of bonding in such compounds is provided by their physical properties; for example, the
absorption in the UV/VIS region shows a drastic redshift and the compounds are often
conductors o r semiconductors. The d electrons in such cases have obviously lost their pure
“core” nature. All bonding models so far proposed for such systems involve mixing of
higher orbitals.
1. Introduction
The nature of chemical bonding was unclear until, after
the proposal of Bohr’s atomic theory and before the development of wave mechanics, W. Kossel and G . N . Lewis
published descriptions of the limiting cases of ionic[’]and
covalent[21bonding that were plausible and consistent with
concepts of atomic structure. Some of the underlying assumptions of these bonding theories are still valid today.
This is true in particular for the subdivision of the electron
cloud into valence electrons, which largely determine the
type, strength, and number of bonds formed by an atom,
and core electrons, which do not contribute to the bonding. This simple concept has proved extraordinarily useful
for teaching purposes and in descriptive chemistry for the
classification and qualitative explanation of new experimental results. All the empirical rules that are based on the
number of electrons in a bonding system should also be
mentioned here; e.g., the noble gas rule in transition metal
chemistry, the concepts derived from the (8 - N ) rule by
Zintl-Klemm[31and Grimrn-S~mmerfeld,[~~
the introduction
of the “paraelement” concept[51 as a generalization of
Grimm’s “hydride shift rules” (a special case of a “diagonal relationship”), and the role of “valence electron concentration” in the metallic state.
Core and valence electrons are also handled differently
in quantum-chemical bonding calculations. The contributions of the core electrons are regarded as angle-independent in the form of a pseudopotential.[‘] Similar considerations lie behind the experimental determination of
bonding electron distribution (“deformation density”)
Prof. Dr. M. Jansen
lnstitut fur Anorganische Chernie der Universitat
Callinstrasse 9, D-3000 Hannover (FRG)
New address:
Anorganisch-Chernisches lnstitut
Gerhard-Dornagk-Str. 1
D-5300,Bonn (FRG)
0 VCH Verlagsgesell.whaf( mbH. 0-6940 Weinheim, 1987
using diffraction methods: a spherically symmetrical
contribution (“core”) is subtracted at each atom from the
total density.”]
Although the precise treatment of a bonding system
should involve the consideration of all states whose interaction integrals could, by symmetry, be nonzero under the
given conditions, the more approximate treatment involving only the valence electrons in the ground state proves to
be astonishingly good in practice. There are few experimental results (temperature-independent paramagnetism,
for instance) that can only be interpreted when higher energy states are considered. It is also a commonly held view
that an increase of the coordination number above four in
covalent compounds requires an expansion of the valence
Until recently there were no experimental results that
needed a consideration of the core electrons for their interpretation. This situation changed, however, on the discovery of several curious features in compounds with d ” or
d”s2 cations. In addition to the known bonding patterns,
these species seem to involve homoatomic interactions that
influence their structure and properties (cf. Ref. [8]), despite the fact that their electron configurations are generally regarded as closed-shell.
It often happens in chemistry, when modern developments generate principles of general validity, that a closer
examination of the literature shows related evidence published long before. A. Bystrom and L. Euers, in a 1950 report on Ag2Pb02 and Ag5Pb206, drew attention to the
short Ag -Ag’ contacts and discussed a form of “covalent” bonding.[’] I n 1963, G . A . Barclay and B. F. Hoskins
noted marked differences in the crystallochemical behavior of potassium and silver in KAgC03 and did not exclude the possibility of bonding between the d ” Ag’
ions.“’] In 1973, H . - L . Keller and Hk. Miilier-Buschbaum
described assemblies of silver atoms in the novel compounds SrAg6o4 and BaAg604 as “metallic regions.’”’ ‘ 1
0570-0833/87/1111-1098 $ 02 50/0
Angew Chem. Int. Ed. Engl. 26 (1987) 1098-1110
Parallel to this development in solid-state chemistry,
corresponding results from coordination chemistry became
available. The most remarkable was certainly the synthesis
and structure of [Pt(PPh3)2]2.1121
The crystal structure of this
compound shows a short platinum(0)-platinum(o) contact
that, in the absence of bridging ligands, can only be interpreted as a metal-metal bond.
These observations, originally regarded as exceptions,
have now attained significance both in number and in consistency[”] and are worthy of detailed classification. This
article will review those results that provide evidence for
the d I”-d ’‘I interactions, present correlations between
structure and properties, and discuss proposed bonding
models. Most examples will be drawn from inorganic
solid-state chemistry; it will not be possible to discuss
more than isolated examples from the no less extensive
and interesting field of related molecular systems.
guished by a separation of the anionic and cationic components of the structure-an “aggregation” of the silver
cations to form extended silver a ~ s e m b l i e s . ~The
” ~ peculiar
resulting microheterogeneous structure and the special nature of monovalent silver become all the more apparent on
comparison with alkali metal ions in formally similar environments; the crystal structure of KAgCO,[“’I fulfills this
requirement ideally. The complete separation of potassium
and silver “substructures” by layers of C0zQ ions (Fig. 1)
is striking. The potassium ions achieve substantial interionic separations, but the silver ions aggregate to form
two-dimensional, close-packed assemblies. The shortest
K + - K + distance is 404 pm, much longer than the shortest
Ag+-Ag+ contact (297 pm).
2. Structural Chemistry
The structure of a solid is determined by the sum of the
forces present in it and thus represents an observable property important for the characterization of chemical bonding. Unfortunately, it is in principle impossible to associate
particular structural features (e.g., coordination polyhedra,
bond lengths and angles) unambiguously o r exclusively
with a particular set of bonds. However, this is still possible to a good approximation in molecular crystals; the molecular structure is determined by the predominantly covalent bonding between the constituent atoms, whereas the
molecular packing is determined by molecular shape and
van der Waals f o r ~ e s . ’ ’Such
~ ] distinctions, the limitations
of which already become apparent on comparing crystal
structures of small molecules such as CI2, Br,, and I*, become invalid for “collective” solids such as ionic crystals
or intermetallic phases. This in turn places limitations on
the significance of the following discussion of d ” systems
in crystalline solids. To minimize these limitations, we
shall present structural comparisons of compounds that
differ only in one component.
2.1. Ternary Silver(1) Oxides
Monovalent silver is in many respects (e.g., transport
properties in dilute aqueous solution, crystal chemistry in
compounds such as e l p a ~ o l i t e s “ ~intermediate
in properties between sodium and potassium. It thus seems worthwhile to compare ternary silver(]) oxides with their sodium
and potassium analogues in order to discover any structural peculiarities of the silver compounds. Such comparisons reveal almost without exception drastic differences in
the tertiary structure (the packing of the anionic and cationic components to form a three-dimensional framework), and sometimes even in the secondary and primary
structure of the complex anions present in some of these
oxides. Whereas crystal structures with cations of noblegas configuration display (in addition to the usual tendency to form characteristic cation-anion contacts) a tendency to maximize the cation-cation distances and thus
the lattice energy, the structures with Ag+ are distinAngew. Chem In!. Ed. Engl. 26 (1987) 1098-1110
Fig. 1. Crystal structure of KAgCO,; left, silver aggregate, right, KCOi
Further illustrations of this structural tendency are
shown in Figures 2-4, where the silver and anion structures are presented separately. These examples
Ag2C03,1’71and LiAg302[’s1)show that the aggregation of silver ions is essentially independent of the
particular coordination at silver and also of the “cationic”
o r “anionic” (oxoargentate) role of silver.
Although the general tendency of silver ions to form aggregates is noteworthy, the silver-silver distances within
the aggregates are even more impressive; they are approximately constant, the shortest being ca. 280 pm (shorter
than the 289 pm in metallic silver) and the longest not
longer than 330 pm (i.e., less than the van der Waals diameter of 340pm1’91).A more detailed examination of the
crystal structures shows in addition that the silver aggregates are based on a uniform motif, namely, an approximately equilateral triangle of silver atoms. The triangles
are then “condensed” to form ribbons, layers, and threedimensional frameworks (cf. Figs. 5-8). The crystal structures of the ternary silver oxides known so far show a preference for two-dimensional aggregates (ribbon or layer
structures). The silver substructures thus correspond to
fragments of the structure of metallic silver, both in geomI099
Fig. 2. Anionic (right) and silver components of Ag6Si20, (I).
Fig. 3. Anionic (right) and silver components of Ag2C03.
Fig. 4. LiOl (right) and silver components of LiAg3O2
Fig. 6. Silver aggregate in Ag,BO, (projection on (001)).
big. 5 Pdrt of the silver aggregate in AgBO,
Fig. 7. Pan of the silver aggregate in SrA&O,.
Angew. Chem. Int. Ed. Engl. 26 (1987) 1098-1110
2.2. Ternary Copper(1) and Gold(1) Oxides
Flg. 8. Silver aggregate in [Ag,SiO&.AgNO,.
etry and in interatomic distances. Table 1 presents a summary of silver compounds in which the shortest Ag-Ag
distance lies below 300 pm.
The formation of silver aggregates influences not only
the packing of anions and cations but can also govern the
secondary structure of condensed oxoanions. The first
known example of the tetrasilicate ion in a crystalline solid
was the silver salt Ag10Si4013;1Z01
AgBOz contains a polyanion with tetrahedral and trigonal-planar boron in the ratio
1 : I,["' previously known only in the high-pressure form of
Ca(B02)2; and AgzGe205 involves a three-dimensional
framework of a kind previously unknown for oxoanions of
the composition Ge20:-.1ZZ1
I n contrast to the considerable amount of information
(mostly stemming from the last few years) on ternary silver
oxides, few corresponding examples with similar structural
features are known for monovalent copper and none for
gold. This difference may simply be attributable to the
more intensive preparative studies of ternary silver([) oxides; even the more silver-rich species"' are now accessible, thanks to developments in high-pressure oxygen technique that permit solid-state reactions involving Ag2O.IX"'
Ternary oxides in which univalent gold would be cationic in nature have, to the best of our knowledge, not yet
been systematically investigated. Our group has made extensive efforts to synthesize copper-rich species such as
Cu6Siz07 o r Cu3B03-as yet without success, but our attempts are continuing. This lack of success is difficult to
explain, particularly since a series of less metal-rich ternary oxides have been described (e.g., C L I ~ M O ~ Oand
C U ~ M O ~ O , ~and
[ ~ ~new
~ ) , representatives of the type
CuMOz (with the delafossite structure) have been obtained
without great difficulty.'*'' Furthermore, R . Hoppe and coworkers have synthesized numerous alkali metal oxocuprates(i), including the only known copper-rich
(Cu :0 > I ) species, Rb3C~,04.f671
This compound, with a
shortest Cu-Cu distance of 257 pm (cf. copper, 254 pm), is
clearly related to the silver compounds described above.
The assumption that copper(1) oxides could also form clusterlike metal aggregates is therefore not so unreasonable;
however, it remains essential to confirm the assumption
Table I.Shortest distances between d"' cations in compounds of monovalent copper,
silver, and gold [pm].
240 7
275. I
28 1 .o
A n y r n . Chew. In!. Ed. Engl. 26 (1987) 1095-1l10
Distance Ref.
2.3. Halides and Further Chalcogenides
of the Monovalent Coinage Metals
The current knowledge of ternary coinage-metal compounds involving other nonmetal components, such as the
halogens or the higher homologues of oxygen, is limited
and thus only isolated cases can be discussed here. Bronger
and co-workers have described silver- and copper-rich sulfides and selenides such as KzAg,Se3)8Z1C S ~ C U ~ S and
in which the singly charged coinage-metal ions
are again segregated from the rest of the structure. Figure 9
shows that the copper and silver substructures represent
fragments of the cubic face-centered metal lattices. The
structural relationship becomes even clearer through the
transition to three-dimensional aggregates. The metalmetal distances in the cited compounds are approximately
equal to those in the metals themselves, although generally
somewhat longer. A comparison with smaller metal fragments (e.g., pairs or isolated groups of atoms) can give the
impression that-as with ions of opposite charge-the
M +-M distances increase with coordination number.
An examination of halide structures yields fewer examples of similar phenomena; however, they present some re+
[*] 1 he silver compounds prepared at high oxygen pressure (6 kbar) are not
quenched high-pressure phases; they were tested by tempering below
their decomposition temperatures at normal pressure and did not revert
to "normal-pressure" phases.
markable features. SrAg,I,. 8 H20[”I displays chains of
silver atoms with an unusually short Ag-Ag distance of
278 pm. The metal atoms are tetrahedrally coordinated by
iodine, as is the case in some i o d o c u p r a t e s ( ~ ) , where
[ ~ ~ ~ the
short Cu+-Cu+ distances (241 pm) arise from the linking
of coordination polyhedra via common edges or faces. The
AuIz “dumbbells” in Rb2AgA~31xL451
are not linear; the
narrowing of the bond angle at Au’ to 173” is associated
with a short AuC-Au+ distance of 304pm. Except for
Au -Au interactions, no other reasons for the distortion
are detectable.
Fig 9 Coinage-metal aggregates in K2Ag,Se3 (above) and Cs2Cu5Ser(below)
2.4. The Structures of Zinc, Cadmium, and Silver
Subvalent Compounds
A classical problem (still unsolved) from the structural
chemistry of metals is that of the anomalous C/Q ratios in
the hexagonal close-packed crystal structures of zinc and
cadmium. There are about 20 metals that crystallize, at
least in one allotropic form, in close-packed hexagonal
structures; all except zinc and cadmium display c / a ratios
in the narrow range 1.57-1.64 (the ideal value is 1.63). The
deviations for zinc (1.856) and cadmium (1.886) are extreme (over 15%).fx41The distances to the 12 nearest neighbors distort into six shorter ones within the layers and
three longer ones both above and below the layers. Proposed explanations of this anomaly, such as the assumption of ellipsoidal Zn2+ and Cd” cores,L851
have not met
with general
Since the conduction band of
these two metals can be shown to contain two electrons per
atom, the cores must have d ” configurations; furthermore, the bonding interactions discussed in this article act
preferentially in two dimensions. The zinc and cadmium
anomalies therefore correspond perfectly to the structural
results described in the preceding section. This is the first
time that they have been classified in terms of a more general context.
Silver subfluoride, Ag,F,[”’ was also viewed very much
as an exception. It was the only known subvalent com1102
pound of silver for a long time and is still the only known
subfluoride. The compound is formed by electrochemical
reduction of silver(1) fluoride and possesses the anti-Cdl,
structure. The distances between silver atoms in the layers
are 290 pm, and those between silver atoms of different
layers 285 pm. Ag,F is no longer quite so unusual because
Ag,O, the first silver suboxide, has also been de~cribed.”~’
The structure is to a first approximation an anti-BiI, type.
The influence of the remaining valence electrons (1/3 per
silver atom) causes a deformation of the silver substructure
to form Ag;+ octahedra. The bond lengths within the cluster are significantly shorter than those between clusters
(275 and 285, compared with 297 pm). There is an interesting parallel here to the silver germanium phosphide
which also contains “isolated” Ag6 groups;
if the nonmetals germanium and phosphorus are allocated
oxidation states corresponding to their chemical and structural roles, the Ag, cluster is also formally 4 + , with a valence electron concentration of two per structural unit. The
newest member of the small family of silver subvalent
compounds, Bi4Agls012,[891
also contains silver in the oxidation state 2/3 (a coincidence?). It possesses a three-dimensional silver framework in which, remarkably, no
shortening of the silver-silver distances is observed, as
compared to the ternary silver(1) oxides discussed in Section 2.1. The published crystal structure of Ag5Pb,0, describes it as a subvalent compound,[91but the inadequate
accuracy of the structure determination precludes an
unambiguous assessment.
We believe that there is a connection between the existence of subvalent silver compounds and the tendency of
univalent silver to engage in homoatomic interactions. The
substructures thereby formed have empty s and p conduction bands, which can easily accommodate further electrons on reduction. The subvalent compounds thus represent a structural link with classical metal cluster compounds, which, however, lie outside the scope of this review.
2.5. Coordination Compounds
Numerous coordination compounds of copper(I), silver(]), and gold(r) have been prepared and structurally investigated.[”’ Their crystal structures generally consist of
“isolated” molecules, but they nevertheless show remarkable similarity to the compounds discussed above in terms
of their cation substructures; the M + - M + contacts are of
similar length to the interatomic distances in the elements
themselves, sometimes even shorter. Table 2 presents a
summary of the shortest contacts so far observed. There
are however significant differences between the coordination compounds and the more highly “polymeric” ternary
oxides and sulfides. The d ” atoms are often held together
in pairs by 1,3-bifunctional bidentate ligands; aggregates
of more than two d “ centers are observed only in isolated
cases, and extended two- or three-dimensional cation
structures not at all.
The reservations mentioned in Section 2 with respect to
structure-bonding relationships are therefore particularly
serious. Possible metal-metal interactions cannot be distinAngew. Chem. Int. Ed. Engl. 26 (1987) 1098-1110
Table 2. Shortest Cu-Cu, Ag-Ag, and Au-Au distances in coordination compounds [pml.
guished from the effects of the ligands. Even the deviations
from 180" at the metal atom allow no unambiguous conclusions to be drawn; they are associated with both longer
and shorter metal-metal contacts (compared with an ideal
linear geometry), and no systematic relationship can be recognized at present. It is possible that crystal packing effects are important in view of the generally small deformation energy of linear systems, but such effects are generally
ill-defined. The dimeric Ro complex [R(PPh,),], is a key
compound in this respect, since the two d'' metal atoms
are only 276.5 pm apart despite the absence of bridging
ligands.i'21The existence of this complex thus lends weight
to the assumption that bonding interactions are present between d ") centers in complexes with bridging ligands, too.
For the silver silicates and germanates, the following
compounds have been shown to be isotypic: Ag10X4013,
and IAg4X04], . AgN03, where X = Si or
Ge.1122.441 However, quantitative structural data are available only for the ortho salts. Figure 10 shows the corresponding contacts in the silicate and germanate. Whereas
the X - 0 bond lengths vary markedly and uniformly, the
Ag-0 bond lengths are not significantly different. Surprisingly, the latter is also true for the silver-silver contacts
below 330 pm (within a margin of i 3 0 ) ; the average contacts are 308 (Ge) and 309 (Si) pm. The increase in volume
in going from the silicate to the germanate is clearly not
uniform over the whole crystal structure. Since the Ag-Ag
contacts, like the Ag-0 distances, are more or less constant, it is possible to speak of a silver-silver "bond
length." Moreover, the average deviation (1.4 pm) from the
mean value of the shortest Ag-Ag contact ( < 3 3 0 p m ) is
much lower than that of those contacts between 330 and
400 pm (8.2 pm). We regard these observations as evidence
that the metal-metal interactions are indeed bonding.
The silver([) salts of sulfamide, O,S(NH,),, and their
structures are known for all possible stoichiometries
(mono- to tetrasilver salts). Apart from the differing degree
of protonation, the anions show no marked changes in this
series, and a comparison of the silver substructures should
therefore provide, to a first approximation, information
about the silver-silver interactions. The comparison shows
characteristic trends as regards both the extent of the silver
aggregates (see Fig. 11) and the interatomic distances
within them; for the m o n 0 - , [ ' ~ ~di-,11241
tri-,lh4] and tetra-
1 2 2 3 L 4 L
2 3 3 3 5 5 4
2.6. Systematic Structural Comparisons
A structural comparison of related compounds, with systematic variation of anionic o r cationic moieties, is more
profitable than an amorphous presentation of isolated results. A sufficient number of structures have now been investigated to allow such comparisons for the following
compounds :
I . isotypic compounds differing only in the nature of
the complex anion (e.g., analogous silver([) silicates
and germanates)
2. salts of the same anion with differing coinage-metal
content (e.g., silver(1) sulfamides)
3. compounds that retain the same structural type while
allowing the metal-metal distance to vary over a wide
range (e.g., copper delafossites)
Angew. Chem. Int. Ed. Engl. 26 (1987) 1098-1110
Agl 1 1 2 2 2 3 3 3 4 L 5 5
0 3 1 4 1 2 L 2 3 L l 2 3 3
Ge /SI
0 1 2 3 L
Fig. 10. Comparison of bond lengths in [Ag,XO&AgNO,
bars) and G e .
with X = S i (dark
silver s ~ l f a m i d e s , the
[ ~ ~silver
atoms occur singly, in pairs,
and in two- and three-dimensional infinite arrangements,
respectively (taking 330 pm as the upper limit for an AgAg contact). The variations in, and averages of, the Ag-Ag
distances (Fig. 12) also indicate increasing Ag-Ag interactions in going from the mono- to the tetrasilver salt.
Fig. 12. Distribution of silver-silver distances in di- (a), iri- (b), and tetrasilver sulfamide (c).
Fig. 1 I . Silver aggregates in (from above) di-, tri-, and tetrasilver sulfamide.
The delafossites (general formula A B3 +02)
two-dimensional infinite networks of d'' cations based on
equilateral triangles. This can be readily explained in terms
of the preferred coordination geometries of the constituent
metal ions (octahedral and linear coordination by oxygen).
In the context of this article, however, the aggregation phenomenon appears in a different light. The structure can accommodate different sizes of B3+ ions, thereby allowing
systematic comparison of the ensuing variations; the A + A + distances are identical with the value of a for the hexagonal crystal system, which is in turn determined by the
radius of B 3 + . The known CU(I)delafossites have a values
of 280-380 pm and thus form a structural group in which
the C u + - C u + distances also vary over this wide range. If
Cu+-Cu interactions are present, these should vary systematically with the Cu-Cu distance, and the physical prop+
1 I04
erties dependent on the band structure should vary uniformly with the value of a.
A study of bond lengths in delafossite structures determined by single-crystal X-ray analysis reveals a previously
unknown tendency: the C u - 0 bond lengths decrease significantly with increasing radius of B3+. The obvious assumption that the shortening of the C u - 0 bonds occurs at
the expense of the B 3 * - 0 bonds can be shown to be invalid using the bond length/bond strength concept.['251The
contributions of the trivalent cations to the valence sum (s)
of oxygen remain constant.'"' Accordingly, the expected
valence sum of 2 for oxygen would constrain the contribution from copper to remain constant at 0.5. Copper would
then display the expected valence sum of 1 for all compounds of the series. This conclusion is unfortunately
not consistent with the experimental observation that
the C u - 0 bond lengths decrease with increasing radius
of B ~ + .
Table 3. Contributions of various bonds to the valence sum of copper in
some copper delafossites.
Cu-Cu [pmj
186 5
Since the valence s of the 0 - 0 bond in CuYO, has a
higher value than in CuAIOz (according to the observed
bond lengths), the question arises as to the origin of the
additional valence needed to saturate the copper atom.
Angew. Chem. int. Ed. Engl. 26 (1987) 1098-1110
The only possibility is Cu-Cu interactions, since all other
contacts outside the inner coordination sphere are too
long. An estimate based on Brown’s
is that the
Cu-Cu interactions contribute 3% to the valence sum of
copper in CuYOz but the impressive amount of more than
20% in CuAIOz (cf. Table 3).
3. Physical Properties as Indicators of d”-d”
As already stated, unambiguous conclusions regarding
chemical bonding cannot always be drawn from structural
data. This can be demonstrated clearly in the case of
Na,AgO,, which, with a shortest Ag-Ag distance of
296 pm, can reasonably be classified with the compounds
discussed in this article. However, the best description of
the structure (as published by R . H ~ p p e [ ~is~ as
I ) a structural variant of Na,O; the shortest distances between all
cations ( N a + and Ag+) are practically equal and are determined by the matrix of oxide ions. Bond lengths alone are
plainly unreliable indicators of bonding interactions between d ’” cations and it becomes necessary to back u p the
structural data with evidence from additional sources.
Suitable properties to study are clearly those that unambiguously demonstrate marked changes in the electronic
structure of the d “ cations associated with the homoatomic interactions.
3.1. Absorption in the UV/VIS Region
One change in properties associated with the structural
features discussed here is qualitatively apparent; intensely
colored compounds are formed, even with anions that (like
the “isolated” univalent coinage-metal cations) d o not
themselves absorb in the visible region. Figure 13 summarizes the known UV/VIS spectroscopic studies[’26Jand presents the reflection spectrum of Ag2S04 for comparison.
The spectra typically show absorption edges with relatively
steep gradients (explaining the brilliant coloration of the
compounds), the position of the absorption edge corresponding to the particular color. Compared with Ag2S04,
which has “isolated” Ag+ ions, the absorption edges of the
compounds described in Section 2.1 are shifted by u p to
18000 c m - ’ (!) to lower wavenumber. This represents a
striking correlation between structure and properties, rendered even more significant by the increase in redshift with
increasing silver content and with increasing metal aggregation (Table 4). A more rigorous quantitative treatment of
this correlation is impossible because we d o not yet understand the complicated mutual effects of metal-metal distances and extent of aggregation. A pressure increase also
brings about a shift to lower wavenumber, which identifies
the associated transitions as those between bands. The UV
shift o n cooling could then be attributed to a reduction of
thermally induced band broadening.
Table 4. Silver content and energy of the absorption edge in selected silver
v [cm- ‘1
Proportion o f
(per formula unit)
Ag2H2 N202S
pale yellow
33 100
25 600
24 600
23 700
23 000
17 300
(Ag,HN2O2S)NH3.H 2 0
Fig. 13. Reflection bpectra of oxoanionic silver(i) compounds: Ag2S04 (I),
Ag,PO, (21, Ag2COz (3j, AgBO, (4), Ag2Ge20S(5), Ag,BO, at room temperature and at 5 K (6 and 6‘).A&Si207 (7), Ag,,Si,013 @), Ag,,Ge,013 (9).
Angew. Chem. Int. Ed. Engl. 26 (1987) 1098-1110
13 500
3.2. Electrical Conductivity
Electrical conductivity is a physical property dependent
on band structure. The conductivities of several compounds have been determined,”27’ allowing for the effects
of ionic conductivity, which can be appreciable f o r d ” univalent cations. In contrast to Ag2SO4, which is essentially a
complete insulator, all compounds with d ’ ” cation aggregates so far investigated have proved to be semiconductors. Figure 14 presents Arrhenius diagrams of the conduc-
-9’ ‘
lo3 T-I [ K’l]
Fig. 14. Electrical conductivity of Ag,GelO, (a), Ag,BO, (bj, AgzGe205(c),
Ag6Si207(d), and AgBO, (e).
1 I05
tivity of some representative compounds. An analysis of
the intrinsic conductivity curves gives the corresponding
activation energy, which is compared in Figure 15 with the
optical band gap. The relationship between spectroscopic
band gaps and those determined by conductivity measurements is unmistakable. As would be expected, the agreement extends only to relative changes, not to absolute values; the optical transitions with the selection rule Ak=O
and the induction of electrical conductivity are governed
by different mechanisms.
lation. Since the conductivities of the constitutive sesquioxides are three orders of magnitude smaller, and the
conductivity of the delafossites is thus almost entirely attributable to the Cu/O part of the structure, this is a further
independent confirmation of interactions between centers
with "closed" d'" configurations.
It should be possible to induce electrical conductivity
optically as well as thermally; silver sulfamides indeed
show a photoinduced rise in conductivity over several orders of magnitude when the wavelength of the irradiated
light reaches a value corresponding to the position of the
absorption edge (determined independently by reflection
spectroscopy)1t2*. (Fig. 17). The observed reduction in
the band gap with increasing silver content is consistent
with the associated changes in the silver substructures (see
2 20
a Ipml
B 1103~m-11
Fig. 17. UV/VIS absorption and p h o t o i n d u e d conducrivity of Ag,HzN20ZS
( I ) , (Ag,HNZOzS)NH,.H20 (2), and Ag,N,O?S (3).
3.3. Other Physical Properties
The bistable switching of amorphous silver(1) silicate~['~''and phosphate^"^'] may also be connected with
their microheterogeneous structure and d'"-dto interactions. Such materials can, after suitable pretreatment, be
reversibly switched between high and low resistance by the
application of short square-wave electrical pulses. This behavior is illustrated for a silver(1) silicate glass in Figure 18.
Fig. 16. A c t i \ d t i o n energy ot the electrical conductivity, E A ( o ) ,as a function
of the cell constant a in copper(!) delafossites CuAIOz (a), CuCrOz (b),
CuGaO? (c), CuFeO? (d), CuSc02 (e),and CuYOz (0.
1 I06
-3 - 5
The silver substructures of the oxides investigated so far
differ appreciably in structural detail and are thus difficult
to compare quantitatively. Conductivity measurements
were therefore carried out on a series of copper delafossites, in which the copper substructures remain qualitatively the same but the Cu-Cu distances vary. It was essential to prevent the formation of C u 2 + defects in order to
obtain reliable results; this was to a large extent achieved
by fixing the oxygen activity during the
Samples prepared in this way show a very low ionic conductivity and give purely intrinsic electrical conductivity curves.
The conductivities vary over the range 0 = 1 0 - ~ - 1 0 - ~S
c m - ' at 273 K. The plot of electrical conductivity against
Cu-Cu distance (Fig. 16) shows a practically linear corre-
70 90
Fig. 15. Optical and conducti\it~-determinedband separations in Ag,GezOs
(a), AgBOz (b), Ag,BO, (c), Ag6Si207(d), and Ag6Ge2O7(e). €,=energy of
the optical absorption edge: E,(o)=activation energy of the electrical conductivity.
0.001 0.01
U[Vl +
Fig. 18. Current/voltage characteristic 01' a silver(!) bilicdte
treatment. A-D=switching cycle.
giaba alter
Angew. Chern. Inr. Ed. Engl. 26 (1987) 1098-1110
Investigations using dielectric methods have given some
indication of the presence of silver "clusters" in such
Solid-state Io9Ag-NMR spectroscopy can also be a sensitive probe of changes in bonding; this is shown by the
drastic changes in chemical shift between Ag4Rb15 and
Ag,F compared with AgF."33JOur own preliminary studies
of AgIoSi401,with Io9Ag MAS N M R spectroscopy have
shown a shift to low field of 320 ppm compared with solid
Anomalies in the dynamic behavior of Ag +,manifested
for example in the phonon spectra"3s1 of AgCl or AgBr,
have been discussed for a long time. Although no unusual
Ag+-Ag+ contacts are involved (NaCI structure), it is generally agreed that the difference between silver and alkali
metal halides is due to attractive interactions between Ag
Finally, it should be remembered that the dominant defect type in silver halides is the Frenkel defect, the formation of which requires the accommodation of short metalmetal contacts.
4. Correlations and Models
There is now enough empirical material to permit initial
attempts to (1) establish conditions under which interactions between d l o electron systems, usually regarded as
closed, become effective, (2) demonstrate correlations between structure and properties, and (3) set u p preliminary
bonding models.
4.1. Conditions for the Existence of d*'-d''
The influence of homoatomic interactions is regarded as
decisively less than that of classical bonding between "anions" and "cations." The tendency of d" cations to undergo aggregation is only realized when their primary
coordination requirements are satisfied. An analysis of
available structural information shows that a high ratio of
electropositive to electronegative species (e.g., the cationto-oxygen ratio in the ternary silver oxides) is a necessary
condition for the development of the characteristic collective bonding that essentially determines the tertiary structure. The excess of cations forces them into mutual proximity, which is clearly necessary in order that the attractive
forces should become effective. A high proportion of d "
cations alone is not a necessary requirement, as is shown,
for example, by the case of KAgCO,. At present, the lowest known cation/oxygen ratio capable of producing d"
aggregation is 415 (in Ag2Ge20,).
The various classes of compounds are represented by
widely varying numbers of known examples (a fact largely
determined by the amount of preparative study invested in
the individual systems); we believe that it is not yet possible to derive systematic correlations. General tendencies
are already recognizable, however, in that the necessary
cation/anion ratio is more difficult to attain with highly
charged cations or with anions of low charge (halides)-a
result of simple arithmetic. This could be the explanation
for the readily formed metal aggregates involving the uniAnyen. Chrm. Int. Ed. Engl. 26 11987) 1098-1110
valent coinage metals and the chalcogenides. For divalent
cations, the mutual electrostatic repulsion would be highly
disadvantageous ; it is therefore not surprising that indications of bonding relationships between the core electrons
of divalent atoms have only been obtained for zinc, cadmium, and mercury. Accordingly, the crystal structures of
these elements are of key interest because they are ideally
suited for studying pure d l0-df0interactions. The influence
of bonds to the anions on metal-metal distances, which
could be critical, obviously plays no part in metallic zinc,
cadmium, and mercury.
4.2. The Causes of Color and Conductivity
We have already shown that there are correlations between the structures of the compounds discussed here and
their properties. However, the correlations alone provide
no information on the nature of the electronic transitions
involved. Classical ligand field transitions can be ruled out
because of their localized nature, and, particularly, because the absorption phenomena in the visible and ultraviolet regions have proved to be independent of the ligand
and of the coordination geometry. Another e ~ p l a n a t i o n " ~ "
of the color of silver(1) compounds based on the covalent
character of the Ag-X bond (as indicated by bond length)
proved to be insupportable"381because many compounds
are now known that have equal Ag-X bond lengths but
different colors. There remain two feasible explanations:
( 1 ) band transitions between a valence band of predominantly d character and a conduction band with predominantly s and p character within the silver substructure or
(2) transitions between the highest occupied molecular orbital in the anionic part of the structure and the s or p
band in the silver substructure, or in other words, a chargetransfer phenomenon. There are two main objections to
the first explanation that are not easy to refute: first, it is
improbable that the transition fSo(4d105s0)-+
,D3(4dY5s') is
lowered from 39000 c m - ' in the free silver ion'13y1to
12000 c m - ' by band broadening induced by the Ag-Ag
interactions, and, secondly, it is becoming clear that the
position of the absorption edge also depends on the nature
of the complex anion. In the isotypic silicates and germanates previously discussed, for example, the silver aggregates are the same, but there is an IR shift of the order of
1000-3800 c m - ' on going from a silicate to a germanate.
On the other hand, there are drastic changes in groups of
related compounds with differing cation content but similar anions-e.g.,
in the series Ag2Ge20s, Ag,Ge20,,
Agl0Ge,Ol3, and [Ag4Ge0412.AgNO,. The absorption
therefore clearly depends on the type of silver aggregates
(its extent and bond lengths) and on the type of anions.
Since the bonding between Ag+ and silicate ions, for example, is mainly ionic (the irregular coordination of silver
by oxygen and the similarity of the silicate dimensions to
those in alkali metal silicates support this assumption), it
seems easiest to explain the experimental observations in
terms of charge-transfer transitions between the HOMOS
of the complex anions and the acceptor levels of the metal
aggregates, the latter being lowered in energy by the dl"d" interactions.
It should be pointed out, however, that this interpretation is in one respect in conflict with published views.
According to C. K . Jorgensen, the energy of a chargetransfer process is dependent on the differences in the
optical electronegativities of the electron donors and
as described by the following equation:
V=30000 c m - ' &opl(A)-xop,(D)). This concept was modified by J. A . Duff'411 for complex anions, xoplfor oxygen
in such anions being determined by the electronegativity of
the central nonmetal atom. A comparison of isotypic silver
silicates and germanates having the same electron acceptor
(the Ag+ aggregates) but different donors (silicate or germanate) should therefore show a lower energy absorption
edge in the silicate because of the lower electronegativity
of silicon."4z1 The opposite is observed experimentally.
This discrepancy should not be regarded too seriously,
however, because the postulated transition involves the energy level of the highest occupied state with preponderantly "anionic" character, and this cannot be determined
entirely by the electronegativity of the central nonmetal
4.3. Bonding Models
L. E. Orge/"431 suggested a valence-bond model for
bonding in compounds of d"' ions such as C u + , Ag+, and
Hgz+. He postulated hybrid orbitals 1/1/Z(dZ2-s) and
1/I/Z(dZ2+s); the former occupies a position in the xy
plane and contains two electrons, while the latter, directed
along the z axis, can accept electrons from ligands and so
stabilize the linear coordination that these ions generally
display. According to J ~ r g e n s e nlinear
coordination is rendered more favorable by a small energy separation between the ground state ('So) and the first excited state
(3D3).Rogers et a1./'441using the Orgel model as a basis,
have stressed the importance of the increased electron density in the xy plane (associated with the d,,, d , ~ - ~ 2and
l/@(d,z - s) orbitals) as regards the possibility of forming
corresponding bands with preponderantly metallic character. A deformation electron density study of CuAIOz indeed showed the expected increased electron density in the
xy plane"451 (Fig. 19); an unexpected feature of the study
was that the maxima were located not on the Cu-Cu vectors but at the centers of the equilateral triangles of copper
atoms. A detailed analysis of the results suggested the
Fig. 19. Difference electron density in CuAIOZ,section at z=O.
1 I08
formation of a partially hybridized valence orbital
(0.97 dZ2- 0.24s).
This model seems, at least for the delafossite structures,
to be self-consistent and to have been confirmed experimentally. However, it depends on the assumption that the
C u - 0 bonds are exactly perpendicular to the planes defined by the metal atoms, which is the case in very few
compounds in which d"-d" interactions have been postulated. For example, the silver layers in LiAg30Zare planar
and the coordination at silver is exactly linear, but the angle between the Agoz units and the silver plane is only
32 '.
Independently of such chemical considerations, and before the discovery of the numerous examples of the p a r t cular cation substructures, H . Bdz came to the conclusion
that d'' ions with low-lying excited states-especially
Ag -should be liable to attractive
considerations were prompted by differences in the
phonon spectra of AgCl and AgBr compared with alkali
metal halides."351The model involved polar interactions; it
assumed the ready excitation of d valence electrons into s
states of the conduction band associated with the formation of a quadrupole moment at the dIo centers. Although
this model was intended to explain dynamic effects, it also
seems suitable for the static phenomena observed; quadrupole-quadrupole interactions between several centers preferentially lead to two-dimensional assemblies, just as were
found to predominate in the crystal structures. The shift in
optical absorption would then be explicable in that the excited quadrupole state would be lowered in energy by the
interactions. This concept reminds one qualitatively of dispersion interactions. Incidentally, it should be noted that
Bilz's quadrupole deformation model of d'" cations relates
also to their marked mobility in ionic crystals.[14h1
R . Hoffmann et al. have concerned themselves, in a series of publications, with an explanation of the bonding in
the short metal-metal contacts frequently observed in biand polynuclear complexes of d " species.['471An EHMO
analysis showed that, even when perturbations of the d"
systems by the ligands were neglected, bonding interactions between fully occupied d shells could arise if singleelectron d functions were allowed to have partial s and p
character. R . Hoffmann et al. and J . K . Burdett showed
that such considerations of localized systems can also be
extended to "collective" structures, e.g., the silver substructures in silver-rich
Although the bonding models so far postulated differ
greatly in detail, they all lead to the same conclusion: the
presence of a low-lying excited state destroys the pure
"core" nature of the "closed" d" shell and also destroys
its spherical symmetry. This is illustrated by the determination of deformation electron density at Zn2+ in a tetrachloro complex (Fig. 20);[1491
the electron density distribution is easiest to reconcile with a configuration
(3d -e)4(3d - t$-'(4s)'.
Since the d-s separation i s
clearly of central importance, Ag' should assume a special
position with respect to the effects discussed here (Table
5). This is consistent with our current state of knowledge:
short Cu+-Cu+ and Au +-Au+ contacts have so far been
observed mainly in the presence of strongly covalently
bonded ligands and, in contrast to silver, have less ten+
Angew. Chem. Inl. Ed. Engl. 26 11987) 1098-1110
only common feature to which the postulated interactions
and their consequences can be attributed is the combination of a “closed” d ” ground state with low-lying excited
I would like to thank the co-workers and colleagues, listed
in the references, who were involved with the individual con-
tributions to this field. I am grateful to Dip1.-Chem. Konrad
Heidebrecht. Berndt Ullrich Kohler MSc, and Dr. Hartmut
Ehrhardt f o r helpful and fmitjiul discussions. The Deutsche
Forschungsgemeinschaft supported this work financially.
Fig. 20. Difference electron density in the region of the Zn2+ ion in
Table 5. Some energy separations [cm-’1 in the free ions Cu+,Ag+, and
21 928
39 163
80 172
63 052
dency to form extended, clusterlike aggregates. Isolable
subvalent compounds of copper and gold analogous to
those of silver (see Section 2.4) are unknown. The high
ionic mobility associated with the unusual bonding interactions discussed here is also most marked for silver.
5. Conclusions
The empirical results presented in this article furnish
convincing evidence that d “ cations can interact with each
other in a way that influences both structure and physical
properties. This capability is to a first approximation independent of the type of ligand and the geometry of the ligand field: it is unimportant whether the cations display
linear coordination, with strongly covalent ligands, or an
irregular geometry involving ionic bonds. The only precondition so far recognizable is that other influences (e.g.,
bridging ligands or an excess of cations) must first force
the d ” ions into mutual proximity. “Isolated” d’’ cations
d o not display the characteristic phenomena mentioned in
this article.
It is not yet clear what causal role the interactions play
in determining structure; d o they “actively” lead to a weak
bond or d o the d ” species “tolerate” the short homoatomic contacts? It seems that no general answer can be
given to this question and to others concerned with the
type of bonding. The molecular systems (coordination
compounds) will have to be treated differently from the
more “collective” (polymeric) structures, and other treatments again will be necessary to describe dynamic effects
such as the high mobility of such ions in a solid matrix in
detail. Furthermore, it can be seen from the first excitation
energies of the free ions C u + , Ag+, and Au+ (Table 5) that
no uniform picture can be expected for the group of coinage metals because of their intrinsic heterogeneity. The
Angew. Chem. I n t . Ed. Engl. 26 (1987) 1098-1110
Received: June 6, 1986 [A 642 IE]
German version: Angew. Chem. 99 (1987) 1136
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