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UPSC Combined Geo-Scientist

Chemist

  • 3 descriptive papers
  • 200 marks each
  • 3 h per paper

Mains Paper I covers inorganic chemistry.

UPSC Combined Geo-Scientist, Mains · 2026 · Mains Paper I

Q1(b). Spin-forbidden bands in 4d and 5d complexes

  • 5 marks
  • Topic: Coordination compounds
  • Answered
Question

Intensities of spin-forbidden transitions are greater for 4d- or 5d-series metal complexes than for 3d-series metal complexes. Explain it.

Answer in brief

The spin–orbit coupling constant ζ rises steeply with nuclear charge (∝ Z⁴). Large ζ mixes states of different spin, so the Δ S=0 rule is relaxed and spin-forbidden bands borrow intensity.

Key points

  • Δ S=0. A transition such as ⁴A_(2g)→²E_g in d³ changes spin and is forbidden in the absence of coupling.
  • H_(SO)=ζ L· S makes the true states mixtures: ψ=ψ(quartet)+λ ψ(doublet). The intensity is ∝λ²∝(ζ/Δ E)².
  • ζ≈400–800 cm⁻¹ for 3d ions, 1000–2000 cm⁻¹ for 4d and 3000–5000 cm⁻¹ for 5d ions, so λ² is 10 to 100 times larger.
  • larger Δₒ and greater covalency in 4d/5d complexes bring the doublet and quartet states closer in energy and enhance the mixing; the bands become comparable with spin-allowed ones, so the spin label is a poor quantum number.

The full model answer

Worked out step by step, as it should go in the answer booklet. The solution sheet follows it.

  1. Selection rule: Δ S=0. A transition such as ⁴A_(2g)→²E_g in d³ changes spin and is forbidden in the absence of coupling.
  2. Spin–orbit mixing: H_(SO)=ζ L· S makes the true states mixtures: ψ=ψ(quartet)+λ ψ(doublet). The intensity is ∝λ²∝(ζ/Δ E)².
  3. Heavy metals: ζ≈400–800 cm⁻¹ for 3d ions, 1000–2000 cm⁻¹ for 4d and 3000–5000 cm⁻¹ for 5d ions, so λ² is 10 to 100 times larger.
  4. Added effects: larger Δₒ and greater covalency in 4d/5d complexes bring the doublet and quartet states closer in energy and enhance the mixing; the bands become comparable with spin-allowed ones, so the spin label is a poor quantum number.

this is also why 4d and 5d complexes are almost always low spin, and why the phosphorescence of Ru(II) and Ir(III) complexes is bright enough for OLEDs.

Model answer to Q1(b), 2026 Mains Paper I: solution page 3
Solution page 3 of 26
Read the whole 2026 solution2026 question paper

Coverselectronic spectraSpin-forbidden bands in 4d and 5d complexes

All parts of Question 1