An Introduction to Complex Mechanisms
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The term complex mechanism refers to the reactions which take place with metal ions. Complexes are formed with these metal ions in solution, and these undergo a range of reactions.

The complexes are formed between a metal ion and a set of ligands. Ligands are ions or molecules which exist independently of the metal complex, and these are electron donors, and form bonds with the electron deficient metal center. The widest range of complexes are formed with the d-block, transition metals, although some complexes are formed with the s-block metals, notably the solvated ions of these metals themselves. The chemistry of the compounds made up of a metal ion center and ligands is often referred to as coordination chemistry.

Most ligands act as 1- or 2-electron donors, eg. a halide ion or water molecule, but others may provide more, eg. NO which can act as a 1- or 3- electron donor, and others still may act by donating more than one set of electrons.

The denticity (from the latin for teeth) of a ligand is the number of places in which it binds with the metal center. Ammonia has one lone pair of electrons on the nitrogen atom, and it binds as a unidentate ligand. Ethylenediamine, H2NCH2CH2NH2, has a lone pair on each of the nitrogen atoms, and it may bind with either or both of these, and so is known as a bidentate ligand. Some ligands may have large numbers of donor sites, such as EDTA4-, which has six donor sites, and these are known as polydentate ligands.

Ammonia (NH3) Ethylenediamine (H2NCH2CH2NH2) Ethylenediaminetetraacetate (EDTA4-)
unidentate bidentate polydentate

Thermodynamics of ligand addition

One can consider the formation of a metal-ligand complex, MLn, in different ways, stepwise and overall. One can write a reaction for these processes, and hence define equilibrium constants, or stability constants.

etc ... etc ...
etc ... etc ...

The values of these stability constants reflect the strength of complexation: the higher the stability constant then the more favourable the formation of the complex is, or the stronger the complex is.

These are thermodynamic quantities, and say nothing about the rates of formation or decomposition of these complexes.

It should be noted that the overall stability constant, βn, is the product of the individual stepwise stability constants, the Ki's, ie. βn= K1K2K3...Kn.

Usually, successive stepwise stability constants decrease. This is a statistical phenomenon reflecting the the decreasing numbers of available coordination sites on the metal center as the degree of complexation increases.

The Chelate Effect

One can examine the stability constants for the formation of complexes with unidentate and polydentate ligands, as seen in the reaction of the aqueous Cu2+ ion with ethylenediamine and ammonia.

log K1 = 10.6 ΔH = -54 kJmol-1 ΔS = +23 JK-1mol-1
log β2 = 7.7 ΔH = -46 kJmol-1 ΔS = -8.4 JK-1mol-1

The observation that the stability constant for the complexation of the bidentate en ligand is greater than for the complexation of two ammonia molecules is known as the chelate effect. In each case, two Cu-O bonds are broken and two Cu-N bonds are formed, so the enthalpic contributions are approximately equal. The chelate effect is largely an entropic one: in the reaction with the bidentate en, two initial molecules generate three product molecules, whereas with ammonia the number of molecules is conserved during the reaction. The first situation if more favoured entropically, and accounts for the extra stability of the complex with the bidentate ligand.

The Irving-Williams series

The magnitude of the stability constants depend upon the identity of the metal center. If we consider the stability constants of complexes of the first row divalent metal ions, we find that they fall in the order below, and this is largely independent of the nature of the ligand.

The Irving-Williams series

The order of the stability constants is largely determined by electrostatic effects: the effective nuclear charge increases across the period and so the ligands are bound more strongly, but there is also the effect of the ligand field stabilization energy, LFSE. The FeII(d6), CoII(d7), NiII(d8) and CuII(d9) complexes have extra stabilization which is proportional to the LFSE.

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