Assignment of d-d Transitions in [Co(H₂O)₆]²⁺

Complex Overview

The complex [Co(H₂O)₆]²⁺ is a high-spin octahedral cobalt(II) species with electronic configuration d⁷.

• Metal ion: Co²⁺ → 3d⁷
• Ligand: H₂O (weak field, spectrochemical series: low)
• Geometry: Octahedral
• Spin state: High-spin (t_2g⁵ e_g²)

Note: Water is a weak-field ligand for Co²⁺ → results in high-spin complex with three unpaired electrons (S = 3/2).

Ground and Excited States (Tanabe-Sugano Diagram)

For d⁷ high-spin octahedral complexes, the ground state is:

⁴T_1g(F)

The three spin-allowed d-d transitions are:

1. ⁴T_1g(F) → ⁴T_2g(F)
2. ⁴T_1g(F) → ⁴A_2g(F)
3. ⁴T_1g(F) → ⁴T_1g(P)

Observed Absorption Bands

Wavenumber (cm⁻¹)	Wavelength (nm)	Assignment	Transition
8,000	1,250	ν₁	4T1g(F) → 4T2g(F)
16,000	625	ν₂	4T1g(F) → 4A2g(F)
20,000	500	ν₃	4T1g(F) → 4T1g(P)

Energy Relationships and Δ_o Calculation

In octahedral field:

• ν₁ = Δ_o
• ν₃ ≈ 15/2 B + Δ_o (for ⁴T_1g(P) state)
• ν₂ = energy to ⁴A_2g ≈ 2ν₁ (in weak field, but deviates)

Approximate Δ_o = ν₁ = 8,000 cm⁻¹

ν₂ ≈ 2 × ν₁ = 16,000 cm⁻¹ → matches observed → confirms assignment.

Final Assignment Summary

Band (cm⁻¹)	Transition	Type
8,000	4T1g(F) → 4T2g(F)	Lowest energy, near-IR
16,000	4T1g(F) → 4A2g(F)	Visible (orange-red absorption → pink color)
20,000	4T1g(F) → 4T1g(P)	Highest energy, visible

Color of the Complex

The complex appears pink due to absorption in the green-yellow region (~16,000–20,000 cm⁻¹), transmitting red and blue light.

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Reference: Lever, A.B.P., Electronic Spectra of dⁿ Ions; Tanabe-Sugano diagrams for d⁷ high-spin.