Splitting In The d-Orbital

Crystal Field Theory

The Crystal Field Theory (CFT) was developed by Bethe and Van Vleck in the mid 20^th Century. It is an electrostatic model and simply uses the ligand electrons to create an electrostatic field around the metal centre. Ligands are considered as points of charge and there are no metal-ligand covalent interactions

Octahedral Crystal Fields

An octahedral complex has six ligands surrounding the Atom each ligand has a negative charge. These ligands are repelled by the orbital electrons, but are also attracted by the [M⁺] metal ion; this can have any oxidation state, within boundaries of each individual metal. This as well as the charge on the ligand will vary the over all charge on the complex.

E.g. [Ti(OH₂)₆]³⁺ this has a charge of 3+ because H₂O in neutral (has no overall charge) and Ti has an oxidation state of +III.

But [Ti (Cl^-)₆]^3- has an overall charge of 3- because Cl- has a charge of -1 and the Ti has an oxidation state of +III

Metal ions can change oxidation state depending on the conditions. Different oxidation states have different orbital configurations
These are d⁰ d¹ d² d³ d⁴ d⁵ d⁶ d⁷ d⁸ d⁹ d¹⁰
When a metal ion forms a complex such as [Ti(OH₂)₆]³⁺ the d orbital splits:

This is an octahedral d¹ orbital, this has split with the d_z² and dx2-y2 moving up 3/5 D_oct and the dzx dxy and dzy moving down 2/5 D_oct

There are two different spins in the ligand field splitting high spin and low spin. Example, you have a d⁴ complex, you have to put the 3e^- in the t₂g split but where do you put the 4^th e^-?

Should it be low spin or high spin? This depends on how big the splitting is, if the splitting is big then it will be more favourable to pair electrons but if the splitting isn't too big then it will go for the high spin option as pairing electrons isn't as stable.

General trend for octahedral ligand field splitting

1. d⁰ - No splitting
2. d¹ - Low spin only
3. d² - Low spin only
4. d³ - Low spin only
5. d⁴ - High or Low
6. d⁵ - High or Low
7. d⁶ - High or Low
8. d⁷ - High or Low
9. d⁸ - High or Low
10. d⁹ - High only
11. d¹⁰ - No splitting

Metal complexes have colour, this is because when light passes through the complex an electron is excited from the t₂g to the Eg hence absorbing a certain wavelength of light.
Obviously d⁰ d⁵(High Spin) and d¹⁰ have no absorption, apart from Mn⁷⁺ which forms d⁰ complex and is a dark purple in colour. A good explenation for this is charge transfer, this is an electron jumping from either another orbital or from a loan pair on the ligand.