All question types · Spectroscopy & other
Crystal field splitting from a d–d absorption
UKChO Round 2 · IChO · unreviewed
d¹ octahedral complex with one absorption band; find Δo, then the CFSE.
Worked example
The violet colour of [Ti(H₂O)₆]³⁺ comes from one absorption band with λmax = 507.6 nm. Find Δo in kJ mol⁻¹ and hence the CFSE of this d¹ complex.
1. Energy per mole of photons: solve for Δo per mole
= 235.7 kJ mol⁻¹
2. Multiply by a coefficient: -0.4 × Δo per mole → CFSE = −0.4 Δo (one t₂g electron)
= −94.27 kJ mol⁻¹
Answer: CFSE = −94.3 kJ mol⁻¹
Method
For d¹ the absorption is the t₂g → e_g transition, so Δo = N_A hc/λ. The electron sits in t₂g, 0.4Δo below the average d-orbital energy: CFSE = −0.4Δo.
Common mistakes
- That is Δo itself. One electron in a t₂g orbital is 0.4Δo below the barycentre: CFSE = −0.4Δo.
- In an octahedral field the t₂g set is lowered by 0.4Δo and the e_g set raised by 0.6Δo. The single electron is in t₂g.
Formulas used
Energy per mole of photons