Thursday, August 30, 2007.

Crystal Field Theory or CFT in short, is a simple but elegant theory to describe the behaviour of coordination complexes and how it changes based on the ligands and the orbitals.

Before one starts on understanding CFT, one starts on understanding the concept of ligand bonding. A ligand (e.g. H₂O or NH₃) forms a dative (coordinate covalent) bond with the usually empty d-orbital of the transition metal, and thus binds to it. Thus there is a subtle but important difference between CuSO₄ (aq) and CuSO₄. 5H₂O.

But that isn’t enough. As we all learnt, the empirical formula of hydrated copper (II) sulphate is “CuSO₄. 5H₂O”, which is deemed correct by many people. But to be more precise, what CuSO₄. 5H₂O implies is that in the lattice of the CuSO₄ molecule, there are on average 5 H₂O molecules “trapped” in the lattice structure, which is not true, as experimentally determined. But through experiments the empirical formula of hydrated copper (II) sulphate is not CuSO₄. 5H₂O but rather [Cu (H₂O)₄]SO₄. 5H₂O. Note that in this formula, it clearly shows that the Cu²⁺ ion is bonded to 4 H₂O molecules, and in the whole crystal one H₂O molecule is trapped per every [Cu (H₂O)₄]²⁺ and SO₄^2- ion. That is why although there is a compound called CrCl₃. 6H₂O, there are actually 3 different salts of it, known as isomers, with different colours in solution and even chemical properties.

For a compound/ion to be a ligand it must most obviously have a lone pair (or else how would it ever form a coordinate covalent bond?). They are Lewis bases (remember? Lewis bases are electron-pair donors), and the most common ligand is H₂O and NH₃. There are many more of them, like CN^- and S₂O₃^2-, and I will be elaborating later about some properties of them (in the 2^nd part).

Now back to the transition metal ion. I believe you know how an s-orbital looks like? A p-orbital? To refresh your minds:

(Pictures generously taken from http://en.wikipedia.org/wiki/Atomic_orbital (since it is free to take, as stated so in the license agreement))

Let’s focus on the d-orbitals. Notice the shapes of the orbitals. All of them actually look nearly the same except 2. (Pictures from www.chemsoc.org/VISELEMENTS/orbital/orbital_d.html) In order- from dxy to dxz to dyz to d_x²_-y² to d_z²:

The 1^st thing that is obvious is that the 3d_z² orbital looks different from the other 4 orbitals-it has only 2 lobes, both on the z-axis, and an inner region of high electron density. Next, one can also realize that the 3d_xy, 3d_xz and 3d_yz orbitals look exactly the same except for the axes (all have lobes of high electron density in between the axes), while the 3d_x²_-y² orbital has its 4 lobes (regions of high electron density) all on the x and y axes. This will come in important later on.

Now lets try to figure out the significance in the shape of the orbitals with respect to the energy level. These are the orbitals binding to the electron pairs of the ligands, and as known, the lower the energy level the more stable the bond formed. Since in an isolated ion (aka no ligands) the d atomic orbitals are degenerate (have the same energy levels), thus one will expect it to be degenerate also when bonded to ligands. Not true. When the electron pair in the ligands bond, for the d_x²_-y² and the d_z² orbitals the electron is forced to go near the region of higher electron density (since the electron pair of the ligands bond at the axes), thus it will experience more electrostatic repulsion, and thus the energy of the electron increases due to like charges.

Labels: chem

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