Multiple Bonds Between Metal Atoms / 01-Introduction and Survey

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this is in good agreement with the ratio of the molecular weight of Cr2O3 to the molecular weight of Cr2(O2CCH3)4(H2O)2.

Over many decades following Peligot’s report of the acetate of CrII, virtually nothing new was learned about this or other CrII carboxylates. It was not until 1916 that an advance occurred. It was shown50 that from blue aqueous solutions of CrII, conveniently made by electrolytic reduction of acidic CrIII solutions and protected from air by a layer of ligroin, the following red compounds could be isolated by addition of the sodium or other requisite carboxylate salt:

Cr(HCO2)2υ2H2O

NH4Cr(HCO2)3

Cr(CH2OHCO2)2υH2O

Cr[CH2(CO2)2]υ2H2O

Aside from elemental analysis and the observation that dilute aqueous solutions of these red solids were blue, their properties were not elucidated. In 1925 the formate and malonate were again described, but not further studied.51

The first articulated realization that chromium(II) acetate might be of unusual interest is to be found (more than a century after the discovery of the acetate) in a paper by King and Garner52 in 1950, who noted that “the orange-tan and red colors [of the anhydrous and hydrated acetate, respectively] and their moderately low solubility in water suggest a different type of bonding of the chromium from that in the typical blue and very soluble salts of dipositive chromium. . . .” They were prompted by this consideration to make the first magnetic susceptibility measurements on any chromous carboxylate, and they discovered that neither anhydrous nor hydrated chromium(II) acetate possesses any unpaired electrons. This is in sharp contrast to all of the blue chromium(II) compounds and the aquo

ion, which have four unpaired electrons. To explain this result, they postulated a tetrahedral structure which, according to the valence bond ideas prevalent at the time, would utilize a set of d 3s hybrid orbitals on the chromium atom, thus relegating the four d-electrons to the remaining two d-orbitals with their spins paired. This explanation is, of course, wrong, but the important observation that there are no unpaired electrons is one of the two points of departure for our present day understanding of the chromium(II) carboxylates.

The other key development was the observation, in 1953, that hydrated chromium(II) acetate is isomorphous with hydrated copper(II) acetate and therefore binuclear, with bridging carboxyl groups.53 Unfortunately, the structure was not quantitatively determined, and the Cr–Cr distance was estimated to be the same as the Cu–Cu distance, namely 2.64 Å. The suggestion was also made that the diamagnetism could be attributed to “a direct bond . . . between the two chromium atoms.” The fact that at this distance two Cu atoms could not form a strong enough bond to pair even two electrons, whereas a pairing of eight electrons was required in the chromium case, was not, apparently, considered inconsistent with this proposal.

12Multiple Bonds Between Metal Atoms Chapter 1

In 1956 Figgis and Martin,54 as part of a very lengthy and detailed analysis of the electronic structure of the binuclear acetate of copper(II), devoted a few lines to the chromium(II) compound. They suggested that a set of weak d–d interactions, one μ, two /, and one β, could occur and that “the resulting exchange is apparently sufficient effectively to pair the spins of the eight electrons occupying 3d levels in each chromous acetate molecule and to account for the observed diamagnetism.” This hesitant but perceptive analysis of the chromous acetate molecule might well, under more auspicious circumstances, have led directly to a purposeful examination of the broader potentialities for the existence of M–M multiple bonds. Instead, however, chromium(II) acetate seems to have been thought of as a singular oddity and prompted no further work.

The dichromium carboxylates did not become integrated into the main stream of research on M–M multiple bonds until much later (1970), when an accurate measurement of the crystal structure of Cr2(O2CCH3)4(H2O)2 was carried out.55 This showed that the Cr–Cr distance is actually 2.362(1) Å, which made it reasonable to speak of “the quadruple M–M interaction as a strong one.” In the meantime beginning in 1964, S. Herzog and W. Kalies published a series of papers56 showing that many essentially diamagnetic, red to brown compounds, Cr2(O2CR)4L2, could be made, where R might be virtually any CnH2n+1 group and the ligand L (which might or might not be present) could be virtually any simple donor, such as H2O, ROH, or an amine. Although these essentially preparative studies did nothing to clarify the nature of the compounds, they did show the important point that a large class of compounds was at hand.

It is also interesting that in 1964 F. Hein and D. Tille57 reported a yellow, pyrophoric microcrystalline compound to which they assigned the formula Cr(o-MeOC6H4)2, as well as orange-yellow ‘Cr(o-MeOC6H4)2υLiBrυ3Et2O.’ Both were observed to have very low magnetic moments (c. 0.5 BM), and for the former a bridged binuclear structure was proposed by which “erklärt sich die Herabsetzung des Paramagnetismus aus einer Wechselwirkung benachbarter 3d-Orbitale der beiden Chromatome, deren Abstande nahezu dem entsprich, der in metallischen Zustand vorliegt.” Here, again, we have work that could have led on to the discovery of M–M multiple bonds, but was in fact aborted and abandoned at that time, and only many years later58 was its true significance shown. Indeed, the second of the two compounds mentioned above not only contains a Cr–Cr quadruple bond, it contains the shortest known metal–metal bond, 1.830(4) Å!

Once more, as with rhenium and molybdenum, there existed prior to 1964 a number of significant experimental observations, all capable of revealing the existence of M–M quadruple bonds if properly interpreted. However, none of them were properly interpreted until after the formal proposal of a genuine, strong quadruple bond in [Re2Cl8]2<, whereupon a coherent understanding of all the earlier scattered observations became possible, and was soon developed.

1.3An Overview of the Multiple Bonds

As noted in the Preface, the extent of the literature on M–M multiple bonds is so great that this book can deal only with those compounds that fall within three structural categories. In the first, and by far the largest, are those compounds that have each of two metal atoms forming a square or square pyramidal MX4 arrangement. For molybdenum and tungsten only, there are L3M>ML3 molecules, which will be discussed in Chapter 6. Thirdly, there is now emerging class of EMAC (extended metal atom chain) compounds which have three or more metal atoms in a linear arrangement and surrounded by ligands. These compounds are reviewed in Chapter 15. Our plan is to discuss synthetic methods, structures and properties of these compounds first, and only at the end (Chapter 16) to discuss in more detail the electronic structures and some physical and theoretical techniques used to elucidate them. However, the descriptive

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material can be effectively organized only within the framework of a qualitative picture of the M–M bonding, the relationship between the different bond orders, and the electronic properties of the metal atoms that facilitate M–M multiple bond formation. Therefore, we now give a broad qualitative overview of the electronic structures of M–M multiple bonds.

1.3.1 A qualitative picture of the quadruple bond

The components of the M–M quadruple bonds include the key elements in most other multiple bonds between pairs of metal atoms. Therefore, a discussion of quadruple bonds provides a good introduction to all of the others.

A quadruple bond can occur only with transition metals, because orbitals of angular momentum quantum number 2 (d-orbitals) or higher (f, g, etc., orbitals) are required. In fact, the quadruple bond can be formulated using only d-orbitals, and by considering only d-orbital overlaps a picture that is qualitatively and even semiquantitatively reliable can be obtained. When two metal atoms approach each other, only five nonzero overlaps between pairs of d-or- bitals on the two atoms are possible because of the symmetry properties. These five nonzero overlaps are those between corresponding pairs, that is, dz2 with dz2, dxz with dxz etc. The coordinate axes shown in Fig. 1.1 may be used to define the orbitals.

The positive overlap of the two dz2-orbitals, dz2(1) + dz2(2), gives rise to a μ-bonding orbital. There is, of course, a corresponding antibonding μ-orbital formed by negative overlap, dz2(1) − dz2(2). The dxz(1) + dxz(2) and dyz(1) + dyz(2) overlaps can each give rise to a /-bond; these two are equivalent, but orthogonal, and hence constitute a degenerate pair. Again, there are the corresponding /*-orbit- als resulting from the negative overlaps. Lastly, there are the bonding and antibonding (β and β*) combinations of the dxy-orbitals. The remaining pair of d-orbitals, dx2−y2 on each metal atom, can also overlap to form bonding and antibonding combinations, but both qualitative reasoning and calculations show that each of them interacts primarily with the set of four ligands on its own metal atom. In this way they make a strong contribution to metal–ligand bonding but have very little to do with M–M bonding.

Using the basic Hückel concept, namely, that MO energies are proportional to overlap integrals, at least for similar types of orbitals, and noting that these overlaps must increase in the order β << / < μ, we expect the orbitals to be ordered in energy as follows, beginning with the most stable:

μ < / << β < β << / < μ

These considerations are summarized in Fig. 1.4.

For the [Re2Cl8]2- ion we have eight electrons to be placed in these orbitals, since the rhenium atoms are in the formal oxidation state III, leaving 7 - 3 = 4 electrons for each one. These eight electrons just fill the bonding orbitals giving a configuration we can represent as μ2/4β2. There are four pairs of bonding electrons and no antibonding electrons. According to the conventional MO theory definition of bond order,

where nb and na designate the number of electrons occupying bonding and antibonding orbitals, respectively, the bond is of order 4. It is a quadruple bond. It is worthwhile emphasizing that bond order here is being used in an ordinal and not a metrical sense; it is simply a statement of the net number of electron pairs—or halves thereof—that are serving to bind the two atoms together. It does not explicitly or implicitly provide a measure of bond strength, except in the broadest qualitative sense. Indeed, the four components, μ, two /, β, vary considerably in their contributions to total bond strength, that of the β component being very small (<10 per cent).

14Multiple Bonds Between Metal Atoms Chapter 1

Fig. 1.4. Diagram of the overlaps of d-orbitals and the resulting energy levels as they are involved in the formation of M–M multiple bonds in a X4M–MX4 structure. In practice, the ordering of orbitals, especially those having antibonding nature, might differ.

It is worthwhile to note, parenthetically, that a simple valence bond or hybridized orbital description of the quadruple bond is possible.59

The μ2/4β2 description of a quadruple bond unequivocally accounts for its two most conspicuous features: its extreme shortness and its tendency to impose an eclipsed configuration. Obviously the high multiplicity (i.e. the presence of four pairs of bonding electrons) will account for the shortness. The conformational preference is also unambiguously explained. The μ-bond is, of course, cylindrically symmetrical. A pair of /-bonds is also cylindrically symmetrical. For one of these the amplitude of the wave function as a function of an angle ρ, measured from the x-axis around the bond in the xy-plane, is proportional to sin2ρ. For the other /-bond, perpendicular to the first one, the angular dependence is given by cos2ρ. Thus, the combined / wave function has an angular dependence of cos2ρ + sin2ρ, which is, by a well-known trigonometric identity, a constant, viz. unity. Hence the μ2/4 part of the bond is insensitive to the angle of internal rotation.

The β component of the bond, however, is markedly angle sensitive. As shown in Fig. 1.5, the dxy(1) + dxy(2) overlap has its maximum value when the two ReCl4 moieties are precisely eclipsed and it has a value of zero when the rotational conformation is precisely staggered. Thus, any rotation away from the eclipsed conformation causes a loss of β-bond energy and, when carried to the limit of precise staggering, causes complete disappearance of the β-bond. It is this dependence of the β-bond on rotation angle that opposes the tendency of nonbonded repulsions to favor a staggered conformation.

This argument does not predict that the fully eclipsed conformation is preferred, but only that a conformation approaching the eclipsed one should be preferred. In many crystal structures the crystallographic symmetry (e.g., a center of inversion between the metal atoms) dic-

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Fig 1.5. The relationship of one dxy-orbital to the other for (a) an eclipsed structure and (b) a fully staggered one.

tates that the average of the torsional angles is, in fact, exactly zero. However, in other cases net torsional rotation does occur, to the extent of a few degrees. It should be noted that the dependence of the β overlap60 on the angle of internal rotation ρ is given by cos2ρ. Therefore, considerable deviation from perfect eclipsing can occur without serious loss of β-bonding. Indeed a rotation of 30˚, that is, two thirds of the way towards the fully staggered conformation, causes a loss of only half of the β overlap. The interplay of the inherent preference of the β bond for an eclipsed configuration and all of the other intramolecular forces (bonded and nonbonded) in determining molecular structures is very complex. Only a few efforts have been made to tackle these problems by molecular modeling (or molecular mechanics).61

1.3.2 Bond orders less than four

The energy level diagram shown in Fig. 1.4 shows that within the tetragonal structural framework of two metal atoms surrounded by eight ligand atoms with an eclipsed relationship of the two MX4 halves, many ground state electron configurations are possible.62 Bond orders may vary, in steps of 1/2, from 1/2 to 4, as shown in Fig. 1.6. It will be noted that all bond orders except 4 can result in two ways. Those to the left of 4 may be called “electron-poor” and those to the right “electron-rich.” Not shown in Fig. 1.6 are electron-poor bonds of orders 1/2 to 21/2 because, to date, no real examples within the tetragonal geometry specified are known.

It must also be noted that there is another much more limited but important structural motif for multiple metal–metal bonding. Molybdenum and tungsten form a large number of triply-bonded compounds63,64 of the trigonal type L3M>ML3, with D3d symmetry, shown by the representative example, Mo2(NMe2)6, in Fig. 1.7. These compounds, which are fully reviewed in Chapter 6, have an acetylene-like triple bond (μ2/4) and an ethane-like structure.

1.3.3 Oxidation states

The most common oxidation states for the M2n+ units in paddlewheel complexes correspond to values of n of 4, 5, and 6. A few electrochemical studies have shown values outside that range but it was not until very recently that compounds with V23+, Os27+, and Re27+ cores have been characterized structurally and by other techniques (Chapters 2, 10 and 8, respectively). The difficulties in finding compounds with values below the common range (such as n = 3) lie in that oxidation numbers of less than 2+ are not common in transition metal chemistry, except with pi-acid ligands which generally do not occur in paddlewheel complexes. For values of n greater than 6, it has generally been thought that the decrease in the size of the ion with in-

16Multiple Bonds Between Metal Atoms Chapter 1

creasing oxidation number would weaken overlap in the metal–metal bond too severely. An increase in atomic charge would also create repulsion between metal centers, further diminishing the strength of the metal-metal bonding. However, the examples of n = 3 and 7 recently found open up possibilities of finding appropriate ligands that could stabilize still more compounds with oxidation numbers outside the common range.

Fig. 1.6. A diagramatic representation of how M–M bond orders can change by

removal of β-electrons or addition of antibonding electrons. Ordering can change for antibonding orbitals.

Fig. 1.7. The Mo2(NMe2)6 molecule which has a μ2/4 triple bond.

1.4. Growth of the Field

Two ways in which the field has grown since 1965 are:

1.In the range of metallic elements it embraces.

2.In the number and variety of compounds.

With regard to the range of metallic elements, the expansion of the field can be seen in Fig. 1.8. There are now more than 4000 compounds, and elements in all of the groups 5 to 10 are represented. The only two elements among these eighteen for which no compound pertinent to this monograph has been reported are manganese and tantalum.

The vast majority of the tetragonal compounds have homonuclear M2n+ cores, but a few heteronuclear ones65 have been known since 1975 when MoW(O2CCMe3)4 was reported and 1976 when CrMo(O2CCMe)4 was reported. Since then several dozen compounds with MoW cores have been described, as well as two with RuOs cores. Only in 1999 were the first compounds

18Multiple Bonds Between Metal Atoms Chapter 1

Paddlewheel structures

Compounds having four bidentate, three-atom ligands that bridge the metal atoms, as in the case of the tetracarboxylate shown in Fig. 1.2, are called paddlewheel compounds. There are a great many ligands that occur in such structures. Table 1.1 displays a few of the most common ones and their abbreviations. A longer list of abbreviations is given in the Appendix. A paddlewheel molecule may have 0, 1 or 2 axial ligands.

Table 1.1. Representative ligands found in paddlewheel complexes

Several of the important ligands (or classes of ligand) that occur in paddlewheel complexes are unsymmetrical. This opens the possibility of regioisomers, as depicted in Fig. 1.10, where the notation is also shown. Compounds in which there is a mixture of paddlewheel type ligands (especially RCO2-) and monodentate ligands (anionic or neutral) are numerous.

Fig. 1.10. Designators for regioisomers of paddlewheel molecules with unsymmetrical ligands

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1.5Going Beyond Two

In approximately the past decade, compounds containing more than one pair of metal atoms or chains of more than two metal atoms have made their appearance. Such compounds are obtained in three different ways:

1.By linking dimetal units through axial linkers, Fig. 1.11(a).

2.By linking dimetal units through equatorial linkers, Fig. 1.11(b) and 1.11(c).

3.By making extended metal atom chains, EMACs, Fig. 1.11(d).

Fig. 1.11. (a) Axially linking two dimetal moieties. (b) Equatorially linking two dimetal moieties. (c) Equatorially linking four dimetal moieties. (d) Formation of EMACs.

Actually, there are some rather old examples of linking dimetal units by difunctional axial linkers although attention to this kind of synthesis has markedly increased lately. Many compounds of this kind are formed by those dimetal units that tend to bind axial ligands most strongly, particularly Cr24+, Ru25+,6+ and Rh24+, and details will be found in Chapters 3, 9 and 12, respectively. Linking dimetal units by equatorially-bridging bifunctional ligands began only in the 1990s, with the first linkers being dicarboxylic acids.66 Of the many reported products, the most numerous are dimers (with Mo2, W2 and Ru2 end units), triangles (with Mo2 and Rh2 corners) and squares (with Mo2, Rh2 and Ru2 corners). It has also been shown that diamides may serve as linkers. The main key to success in this chemistry is the use of spectator ligands (i.e., those not involved in bridging) that are not labile. Amidinates are well suited, but carboxylates present difficulties. Specific compounds will be discussed in Chapters 4, 5, 9 and 12 for Mo2-, W2-, Ru2- and Rh2- based oligomers, respectively.

Molecules with linear chains of three to eleven metal atoms, EMACs, wrapped with four polydentate ligands, are now known for the metallic elements Cr, Co, Ni, Cu, Ru and Rh. They are reviewed in Chapter 15. In some cases the metal atoms are evenly spaced, with fractional bonds between each neighboring pair of metal atoms, but in others the metal atoms pair off and form stronger bonds like those found in dinuclear molecules. For example Cr5 species can be described as CrӉCr CrӉCr Cr.

20Multiple Bonds Between Metal Atoms Chapter 1

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