# 15.3: Metal-Metal Bonds


## Molecular orbital considerations in Dinuclear Metal Complexes with Multiple M-M Bonds

Let us begin a new chapter and think about dinuclear transition metal complexes with multiple metal-metal bonds. What is the maximum bond order that we could expect? The transition metals have five d-orbitals available, and in order to determine the maximum possible bond order we need to see how they overlap to form molecular orbitals (Fig. 11.1.1).

If we define the M-M bond axis as the z-axis, then two dz2-orbitals can overlap in σ-fashion to form a bonding and an anti-bonding σ-molecular orbital. A dxz, and a dyz can overlap with another dxz and another dyz in π-fashion to form two degenerated bonding π and two degenerated anti-bonding π*-orbitals. π-overlap is smaller than σ-overlap, therefore the split in energy between the bonding and the anti-bonding π-orbitals is smaller than the split between the bonding and the anti-bonding σ-orbitals. The dxy orbital can overlap with another dxy orbital in $$\delta$$-fashion, and so can the dx2-y2 with another dx2-y2. This gives two bonding $$\delta$$-orbitals and two anti-bonding $$\delta$$-orbitals. The $$\delta$$-overlap is even smaller than the π-overlap, therefore the energy split between the bonding and the anti-bonding $$\delta$$-orbitals is even smaller than those for the π and π*-orbitals. So what would be the maximum bond order that could be achieved? The maximum bond order would be achieved when all bonding MOs were full, and all anti-bonding MOs were empty. We have overall five bonding MOs that we could fill with ten electrons from two metal atoms with d5-electron configuration. The maximum bond order BO would therefore be BO=5. However, in practice only bond orders up to 4 are well known. This is because the dx2-y2 orbital is usually too involved in the bonding with the ligands thereby becoming unavailable for metal-metal interactions. The dx2-y2 orbital makes the strongest interactions with the ligands because most ligands approach on or near the x and the y-axes.

### Electron Configurations and Multiple M-M Bonds

We can easily predict now which electron configuration leads to which metal-metal bond order. The bond order increases from 1 to 4 with the electron configuration changing from d1 to d4. At d4 all bonding MOs are full with eight electrons.

An example of a complex with a bond order of 4 is the tetraacetatodiaquadichromium complex shown (Fig. 11.1.2). Cr is in the oxidation state +2, which makes the chromium a d4 species. We can quickly show this by counting the valence electrons. A neutral Cr atom has 6 VE, and an electron configuration 3d54s1. There are four acetate ligands having a 1- charge each which gives four negative charges overall. The complex is overall neutral which means that each Cr must have formally a 2+ charge, and the electron configuration is 3d4.

With even more electrons in the metal d-orbitals the bond order begins to decrease again as anti-bonding MOs need to be filled (Fig. 11.1.3). The combination of two metals with d5 electron configuration leads to a triple bond, two d6-metals give a double bond, and two d7 metals give a single bond. A metal-metal bond should not exist for two d8-metals because then the bond order is zero.

### Evidence for M-M Multiple Bonds

What experimental evidence can support the existence of a particular bond order (Fig. 11.1.4)? One argument is the bond length which can be obtained through the crystal structure determination of the complex. The shorter the bond, the higher the bond order. For instance, in the four tungsten complexes shown the bond lengths decrease from 272 pm, to 248 pm, to 230 pm to 221 pm corresponding to a single, double, triple, and quadruple bond, respectively.

Another hint can be the conformation of a molecule (Fig. 11.1.5). For instance, the two square-planar units of the Re2Me82- complex anion show eclipsed conformation. Steric repulsion arguments would favor the staggered conformation, so there must be a reason why the two ReMe4 units are eclipsed. The rhenium is in the oxidation state +3, thus it is a d4 species, and we would argue that there may be a Re-Re quadruple bond. This quadruple bond can only form when the dxy orbitals are in eclipsed conformation, and this is only possible when the two ReMe4 fragments are in eclipsed conformation. The very short bond length of 218 pm further supports the existence of the quadruple bond.

Dr. Kai Landskron (Lehigh University). If you like this textbook, please consider to make a donation to support the author's research at Lehigh University: Click Here to Donate.

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