Racah parameters B and nephelauxetic ratios β

d–d bands of chromium(III) and nickel(II) complexes, with the Δo, Racah parameter B and β = B(complex)/B(free ion) computed from them. The values of β rank the nephelauxetic series.


$\ce{[CrF6]^3-}$	14900	22700	—	14900	896	0.98	35442	solved from ν₁ and ν₂
$\ce{[Cr(H2O)6]^3+}$	17400	24600	—	17400	729	0.79	38529	solved from ν₁ and ν₂
$\ce{[Cr(C2O4)3]^3-}$	17544	23866	—	17544	613	0.67	37964	solved from ν₁ and ν₂
$\ce{[Cr(NH3)6]^3+}$	21550	28500	—	21550	657	0.72	46011	solved from ν₁ and ν₂
$\ce{[Cr(en)3]^3+}$	21850	28500	—	21850	622	0.68	46383	solved from ν₁ and ν₂
$\ce{[Cr(CN)6]^3-}$	26700	32200	—	26700	490	0.53	55252	solved from ν₁ and ν₂
$\ce{[Ni(H2O)6]^2+}$	8500	13800	25300	8500	907	0.86	—	sum rule ν₂ + ν₃ = 15B + 3Δo
$\ce{[Ni(NH3)6]^2+}$	10750	17500	28200	10750	897	0.85	—	sum rule ν₂ + ν₃ = 15B + 3Δo
$\ce{[Ni(en)3]^2+}$	11200	18350	29000	11200	917	0.87	—	sum rule ν₂ + ν₃ = 15B + 3Δo

Δo is the first band; B is computed with the site’s Tanabe–Sugano kernel. The free-ion B is one fifteenth of the separation of the F and P terms (centres of gravity weighted by 2J + 1) in the NIST atomic spectra; the textbook values of 918 and 1041 cm⁻¹ differ from these by less than 2 %.

Sources

A. B. P. Lever, Inorganic Electronic Spectroscopy, 2nd ed., Elsevier (1984): band maxima (as quoted in C. E. Housecroft & A. G. Sharpe, Inorganic Chemistry, 5th ed., 2018) and the d³/d⁸ energy expressions.
A. Kramida, Yu. Ralchenko, J. Reader and NIST ASD Team, NIST Atomic Spectra Database, version 5.12 (2024): Cr IV and Ni III levels, which give free-ion B = 917 cm⁻¹ (Cr³⁺) and 1056 cm⁻¹ (Ni²⁺).

Used in these lessons

Electronic spectra: Δo and B from the bands