The Splitting of D-Orbitals

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Complex ions consist of a metal ion surrounded by anions or molecules known as ligands. Unlike most metals, complex ions form dative bonds, rather than the usual ionic bonds. A dative bond is similar to a covalent bond, but rather than forming a bond with one electron from each atom, the bond is created by the donation of a pair of electrons by one atom or ion. Ligands that have these lone pair electrons behave like Lewis bases which are defined as an electron pair donor. The metal ion in the middle is said to behave like a Lewis acid, which accepts pairs of electrons. The ligands make complex ions non-degenerate because the ligands repel the d-orbitals near them, causing those only those orbitals to increase in energy. There are a few types of complexes, but only complexes with a transition metal ion at the centre will produce coloured solutions. According to the crystal field theory, the splitting of d-orbitals occurs in transition metal complex ions. It can be assumed that the splitting of d-orbitals is related to the coloured solutions produced.

Complex Structures

There are many complex structures, however only octahedral, trigonal bipyramidal, square pyramidal, square planar and tetrahedral have sp hybridisation. Octahedral, tetrahedral and square planar are more common.

In octahedral complex is defined as a structure containing six ligands arranged around a metal ion. When ligands bond with a transition metal ion, the repulsion between the ligands and the metal's electrons causes the energy of the d-orbitals to increase. Because of the way the d-orbitals are arranged, the energies are raised in different amounts, splitting them into two groups: t2g orbitals ( ) and eg orbitals ( ). The t2g orbitals have greater energy than the eg orbitals.

This diagram shows the energy of the d-orbitals of the metal ion before attaching to ligands, and the energy of the split d-orbitals after attaching to ligands. The Δ0 shows the difference in energy (the energy gap) between the two groups of split orbitals.

In octahedral complexes, the electrons can fill the orbitals in two ways due to two conflicting factors:

Hund's Rule states that each orbital must have one electron before an additional electron is added to any orbital. Orbitals filled this way have lower energy.

Atom's with incomplete sub-shells are said to desire stability. According to crystal field stabilization energy, the "crystal field" is more stable when the eg orbitals are filled first. This system of filling the orbitals still obey Hund's rule, so the eg orbitals are filled one by one first, and then additional electrons are added. Orbitals filled this way have higher energy.

Octahedral transition metal ions that have d1, d2 or d3 configurations have d-orbitals that are filled according to Hund's Rule. They are said to be "high spin" because they contain many unpaired electrons. However, the d-orbitals of d8, d9 and d10 configurations are filled according to crystal field stabilization energy and are said to be "low spin" as they contain few unpaired electrons. The configurations d4, d5, d6 and d7 can fill d-orbitals such that they can be either "high spin" or "low spin".

A tetrahedral complex is defined as a structure with four ligands arranged around a metal ion. In tetrahedral complexes, the four ligands are arranged differently than in octahedral complexes, however the d-orbitals split into the same groups. The difference in the splitting of d-orbitals of tetrahedral complexes is that the eg orbitals have greater energy than the t2g orbitals.

A square complex is defined as a structure in which a metal ion is found at the centre of a plane with ligands at its four corners. Square-planar complexes don't split into t2g or eg like tetrahedral complexes and octahedral complexes. They split into three groups rather than two.


A ligand is an ion, molecule, or molecular group that binds to another chemical entity to form a larger...
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