Q6(c)(ii). Orgel-diagram assignment of the bands of [Ni(H₂O)₆]²⁺; 10Dq

1. Terms of the gaseous ion: d⁸ has the triplet terms ³F (ground) and ³P. In an octahedral field ³F→³A_(2g)+³T_(2g)+³T_(1g) and ³P→³T_(1g).
2. Orgel diagram: d⁸ octahedral has the same diagram as d³ octahedral (and d², d⁷ tetrahedral): the ground term is the non-degenerate ³A_(2g), at -12Dq, with ³T_(2g) at -2Dq and ³T_(1g)(F) at +6Dq (before mixing).
3. Spin-allowed bands (Δ S=0): three, from ³A_(2g) to the three triplet excited terms, rising in energy:

1. The ³T_(2g) level contains no ³P character, so the first band gives the field splitting directly: 3pt] 10Dq=ν₁=8500 cm⁻¹, Dq=850 cm⁻¹
2. ν₂/ν₁=13 800/8500=1.62, within the range expected for octahedral Ni(II), which confirms the assignment. Racah parameter: B=(ν₂+ν₃-3ν₁)/15=907 cm⁻¹, lower than in the gaseous ion (nephelauxetic effect). With Dq=850 and B=907 cm⁻¹ the Orgel (Tanabe–Sugano) energies give ν₂=14 100 and ν₃=25 000 cm⁻¹, within about 2 % of the observed bands.
3. Colour: red (725 nm) and violet (395 nm) are absorbed and the green window between them is transmitted: hydrated nickel salts are green. All three bands are Laporte forbidden (d–d, centrosymmetric) and weak.
4. CFSE: t_(2g)⁶e_g²: -12Dq=-10 200 cm⁻¹ (-122 kJ mol⁻¹). This large CFSE adds to the stability of Ni(II) complexes (Irving–Williams order).

Application. the same assignment gives Δₒ for other Ni(II) complexes and so places ligands in the spectrochemical series: [Ni(NH₃)₆]²⁺ has ν₁ higher than the aqua ion and is blue-violet, as ammonia is the stronger field ligand.