Valence bond theory and magnetism

Valence bond theory (VBT) explains the shape and magnetism of a complex by saying the metal mixes some empty orbitals into hybrid orbitals, and each ligand puts an electron pair into one of them.

• Coordination number 4: sp³ gives a tetrahedron; dsp² gives a square planar shape.
• Coordination number 6: d²sp³ or sp³d² both give an octahedron.

Whether the metal's own d electrons pair up depends on the ligand. A strong ligand such as CN⁻ or CO forces them to pair, which frees inner (n–1)d orbitals. A weak ligand such as F⁻, Cl⁻ or H₂O does not, so the outer nd orbitals have to be used.

A method that works every time:

• Write the metal's configuration in boxes, then remove electrons to make the ion (4s first).
• Strong ligand? Pair the d electrons. Weak ligand? Leave them.
• Fill the empty orbitals with the ligands' electron pairs, as many as the coordination number. Read off the hybridisation.
• Count unpaired electrons: none means diamagnetic; any means paramagnetic.

Example 1, [Fe(CN)₆]³⁻. Fe³⁺ is 3d⁵. CN⁻ is strong, so the five d electrons squeeze into three orbitals, leaving one unpaired electron and two empty 3d orbitals. With 4s and 4p these give d²sp³: octahedral. It uses inner d orbitals, so it is an inner orbital (or low spin) complex, and it is paramagnetic with one unpaired electron.

Example 2, [CoF₆]³⁻. Co³⁺ is 3d⁶. F⁻ is weak, so there is no pairing, and four electrons stay unpaired. The six F⁻ must use 4s, 4p and 4d orbitals: sp³d², octahedral, an outer orbital (or high spin) complex, strongly paramagnetic.

The number of unpaired electrons n can be checked from the measured magnetic moment: µ = √(n(n + 2)) BM.

VBT has limits. It cannot explain the colour of complexes, it cannot say in advance which ligands are strong and which are weak, and it gives no numbers for the energies involved.