Lesson 6 · 30 min

Colour and the spectrochemical series

Nickel(II) is green in water, blue-violet with ammonia and violet with ethylenediamine. The absorption band sits at Δo, and changing the ligand moves the colour along the spectrochemical series.

In this lesson

Explain that a complex shows the complement of the light it absorbs, and read the band maximum from a spectrum
For d¹, d³ and d⁸ ions, obtain Δo from the lowest-energy band and convert between nm, cm⁻¹ and kJ/mol
Order ligands by the spectrochemical series and predict which way the colour moves when a ligand is changed
Explain why d⁰ and d¹⁰ ions are colourless and high-spin d⁵ ions only faintly coloured

Ruby and emerald owe their colours to the same impurity: a trace of $\ce{Cr^3+}$ . In ruby it replaces $\ce{Al^3+}$ in corundum ( $\ce{Al2O3}$ ); in emerald it replaces $\ce{Al^3+}$ in beryl. Both times it sits in an octahedron of six oxygen atoms — only the ligand field in emerald is slightly weaker. That small difference makes one stone fiery red and the other grass green. A test tube plays the same trick: $\ce{Ni^2+}$ is green in water, turns blue-violet when ammonia is added and violet with ethylenediamine.

Predict first

$\ce{NH3}$ splits the d orbitals of $\ce{Ni^2+}$ more than $\ce{H2O}$ does (a larger Δo). When green $\ce{[Ni(H2O)6]^2+}$ becomes $\ce{[Ni(NH3)6]^2+}$ , which way do the absorption bands move?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

To longer wavelengths (towards the red) To shorter wavelengths (towards the blue) They stay put and only grow stronger The bands disappear

We see the complement of what is absorbed

As white light passes through a solution, the wavelengths taken up by d–d transitions disappear, and what remains mixes into the colour we see. With a single band we see roughly the complement of the absorbed colour: $\ce{[Ti(H2O)6]^3+}$ (d¹) absorbs only blue-green light near 493 nm, so it looks violet.

For d¹, d³ and d⁸ ions the lowest-energy band corresponds exactly to lifting one electron from t₂g to eg — it equals Δo. The spectrum therefore measures Δo directly: read off the wavelength of maximum absorption and convert it to an energy.

\tilde{\nu}_\text{max} = \frac{1}{\lambda_\text{max}},\qquad \Delta_\text{o} = N_\text{A}\,h\,c\,\tilde{\nu}_\text{max}

Wavenumber ν̃ is proportional to energy, so spectroscopists quote Δo directly in cm⁻¹: 1 cm⁻¹ corresponds to 0.011 96 kJ/mol, and with λ in nm, ν̃ = 10⁷/λ cm⁻¹.

$\lambda_\text{max}$: wavelength at the maximum of the lowest-energy d–d band
$\tilde{\nu}_\text{max}$: the corresponding wavenumber, usually in cm⁻¹
$N_\text{A}hc$: 0.1196 J m mol⁻¹: converts energy per photon to energy per mole

Chromium(III) complexes (d³): the lowest-energy band is Δo
Complex	λmax / nm	Δo / cm⁻¹	Δo / (kJ/mol)	Colour
[CrF₆]³⁻	671	14 900	178	green
[Cr(H₂O)₆]³⁺	575	17 400	208	grey blue-violet
[Cr(C₂O₄)₃]³⁻	570	17 544	210	deep purple
[Cr(NH₃)₆]³⁺	464	21 550	258	yellow-orange
[Cr(en)₃]³⁺	458	21 850	261	yellow-orange
[Cr(CN)₆]³⁻	375	26 700	319	pale yellow

Source: Band maxima: A. B. P. Lever, Inorganic Electronic Spectroscopy, 2nd ed. (1984), as quoted by Housecroft & Sharpe; conversions computed by the coordination kernel of this site.

The spectrochemical series

In 1938 Ryutaro Tsuchida compared the absorption spectra of many cobalt(III) complexes and ranked the ligands by how far they shift the bands; the same order turned out to hold, with few exceptions, for other metals too. Ordered by increasing Δ, this is the spectrochemical series:

$\ce{I-} < \ce{Br-} < \ce{Cl-} < \ce{F-} < \ce{OH-} < \ce{C2O4^2-} \approx \ce{H2O} < \ce{NCS-} < \ce{NH3} < \text{en} < \text{bipy} < \text{phen} < \ce{NO2-} < \ce{CN-} < \ce{CO}$

The halides and $\ce{OH-}$ on the left are π donors that push t₂g up and shrink Δ; $\ce{NH3}$ and en in the middle are σ-only; $\ce{CN-}$ , CO and phen on the right are π acceptors that pull t₂g down and widen Δ. For a given ligand, Δ also grows with the metal’s oxidation state and down a group.

Virtual experiment · UV–vis–NIR 350–1300 nm · 1 cm cuvette

Spectrophotometer: measure the spectrochemical series

Sample Monochromator wavelength · 575 nm

Absorbance A @ 575 nm 0.132

Show the reference spectrum No data yet. Pick a wavelength and press “Read and record”.

Your lowest-energy band maximum λ / nm

Measure it yourself: choose a chromium(III) sample, scan the spectrum, find the lowest-energy maximum and enter its wavelength. Once all six chromium samples are done, the results table lists the spectrochemical series in order of Δo.

Worked example

Why nickel(II) turns from green to violet

The three bands of $\ce{[Ni(H2O)6]^2+}$ , $\ce{[Ni(NH3)6]^2+}$ and $\ce{[Ni(en)3]^2+}$ lie at 8500/13 800/25 300, 10 750/17 500/28 200 and 11 200/18 350/29 000 cm⁻¹. Find Δo for each in kJ/mol and explain the change of colour.

Concept check

Which of these aqua ions is colourless?

\ce{[Cu(H2O)6]^2+}

\ce{[Zn(H2O)6]^2+}

\ce{[Ni(H2O)6]^2+}

\ce{[Co(H2O)6]^2+}

Try the calculation

The lowest-energy band of $\ce{[Cr(NH3)6]^3+}$ lies at 464 nm. Find Δo in kJ/mol.

Model limits

Only in a few cases such as d¹, d³ and d⁸ can Δo be read straight off one band; for other dⁿ ions, repulsion between the d electrons shifts the bands, and Tanabe–Sugano diagrams are needed to untangle them. d–d transitions are restricted by the Laporte rule (both orbitals are d, so parity does not change), which is why octahedral complexes are pale, with ε of only 1–100 L mol⁻¹ cm⁻¹; tetrahedral $\ce{[CoCl4]^2-}$ , with no centre of symmetry, absorbs far more strongly. Mn(VII) in $\ce{MnO4-}$ is d⁰: its intense purple comes from ligand-to-metal charge transfer, not a d–d transition. The solution colours here are computed from band models and colorimetry; band positions are literature values, intensities and widths are teaching fits.

Key takeaways

A complex shows the complement of the light it absorbs; for d¹, d³ and d⁸ ions the lowest-energy band is Δo.
ν̃ = 10⁷/λ(nm) cm⁻¹ and 1 cm⁻¹ = 0.011 96 kJ/mol; the 464 nm band of [Cr(NH₃)₆]³⁺ means 257.8 kJ/mol.
Spectrochemical series: I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < CN⁻ < CO; π donors shrink Δ, π acceptors widen it.
d⁰ and d¹⁰ ions are colourless; high-spin d⁵ d–d bands are spin-forbidden and very faint; tetrahedral complexes and charge-transfer bands absorb far more strongly.

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Data and references

A. B. P. Lever, Inorganic Electronic Spectroscopy, 2nd ed., Elsevier (1984).
R. Tsuchida, “Absorption spectra of co-ordination compounds. I”, Bull. Chem. Soc. Jpn. 13, 388–400 (1938).
Y. Tanabe, S. Sugano, “On the absorption spectra of complex ions I”, J. Phys. Soc. Jpn. 9, 753–766 (1954).
K. Nassau, The Physics and Chemistry of Color, 2nd ed., Wiley (2001) (ruby and emerald).
C. E. Housecroft, A. G. Sharpe, Inorganic Chemistry, 5th ed., Pearson (2018), ch. 20 (electronic spectra of complexes).