Coordination Chemistry of d-Block Metals

Magnetism of transition metal complexes

Magnetic behaviour of a transition metal complex depends on whether it contains unpaired electrons. A paramagnetic species has one or more unpaired electrons and is attracted by a magnetic field. A diamagnetic species has all electrons paired and is weakly repelled. The spin-only magnetic moment is estimated by \mu = \sqrt{n(n+2)} Bohr magnetons (BM), where n is the number of unpaired electrons.

The number of unpaired electrons is set by the d-electron count and the size of the crystal field splitting \Delta_o (or \Delta_t). Strong-field ligands such as \text{CN}^- and \text{NH}_3 favour low-spin configurations in which electrons pair in the lower t_{2g} set, whereas weak-field ligands such as \text{F}^-, \text{H}_2\text{O} and \text{Cl}^- favour high-spin configurations. Tetrahedral complexes are usually high spin because \Delta_t is small.

• Low-spin d^6 — e.g. Fe^{2+} with \text{CN}^- gives a diamagnetic complex.
• High-spin d^5 — Mn^{2+} has five unpaired electrons, so its moment is about 5.92 BM.
• d^3 ions — Cr^{3+} always has three unpaired electrons, whatever the ligand.
• d^8 square planar — Ni^{2+} with four \text{CN}^- forms a diamagnetic dsp^2 complex, while the tetrahedral [\text{NiCl}_4]^{2-} is paramagnetic.
• d^9 and d^7 ions — Cu^{2+} has one unpaired electron (about 1.73 BM), and high-spin Co^{2+} has three (about 3.87 BM).

When calculating CFSE for a high-spin d^6 octahedral ion, the value is 4(-0.4\Delta_o) + 2(0.6\Delta_o) = -0.4\Delta_o, which shows why weak-field high-spin complexes are less stabilised than low-spin ones.

Metal carbonyl geometry

Metal carbonyls are zero-valent or low-valent complexes in which CO acts as a strong \pi-acceptor ligand. Each CO is a two-electron donor, so the 18-electron rule can be used to check the stability and electron count of a carbonyl. The geometry is predicted from the number of ligands and the hybridisation of the metal.

For a five-coordinate metal carbonyl with 18 valence electrons, the hybridisation is dsp^3, and the five ligands occupy a trigonal bipyramidal arrangement. The two axial and three equatorial positions are not equivalent, but the molecule belongs to the D_{3h} point group in its idealised form. Iron pentacarbonyl is the standard example of this geometry.

• Trigonal bipyramidal — five ligands, no lone pair on the metal.
• Square pyramidal — five ligands with four in a basal plane; not the geometry of \text{Fe(CO)}_5.
• Trigonal pyramidal — requires a lone pair on the central atom, which a metal carbonyl does not have.

Remember that carbonyl geometry is found by counting ligands and electrons, not by copying the geometry of the corresponding halide complex.

Geometrical isomerism of square planar complexes

Square planar complexes, typical of d^8 ions such as Pt(II), Pd(II) and low-spin Ni(II), can show geometrical (cis/trans) isomerism. The number of isomers depends on the composition of the complex, and the ligands must be counted in terms of the donor types that are identical or different.

• MA_2B_2 — two isomers, cis and trans.
• MABCD — all four ligands different. The number of geometrical isomers is given by \frac{(n-1)!}{2} with n = 4, which gives 3.
• MA_3B — only one isomer, because every arrangement is identical.

When all four monodentate ligands are different, the three isomers arise from the different placements of the four groups around the square. Check first whether the complex is square planar, since a tetrahedral d^8 complex would not show this isomerism.

For the general case, always write down the ligand positions around the square and test the arrangements for superimposability by rotation within the plane before counting.