Spectrochemical Series

The idea: ligands tune the d-orbital gap

Drop a bare transition-metal ion in space and its five d-orbitals all have the same energy — they are degenerate. Surround it with six ligands at the corners of an octahedron and that degeneracy breaks. The two orbitals that point straight at the ligands (d_z² and d_x²−y², together called the e_g set) feel more electron–electron repulsion and rise in energy. The three orbitals that point between the ligands (d_xy, d_xz, d_yz, the t_2g set) drop. The energy gap between them is the crystal-field splitting, Δ_o (also written 10 Dq).

Here is the punchline the spectrochemical series captures: the size of Δ_o depends almost entirely on which ligand you use. Swap chloride for ammonia on the same metal in the same oxidation state and Δ_o jumps. Swap ammonia for cyanide and it jumps again. Rank every common ligand by the Δ_o it produces and you get a single, nearly metal-independent ordering — the spectrochemical series:

WEAK FIELD  ← small Δo                                   large Δo →  STRONG FIELD

 I⁻ < Br⁻ < S²⁻ < SCN⁻ < Cl⁻ < NO₃⁻ < F⁻ < OH⁻ < ox²⁻ < H₂O
     < NCS⁻ < CH₃CN < NH₃ < en < bipy < phen < NO₂⁻ < CN⁻ < CO

      π-DONORS            σ-only          π-ACCEPTORS
   (push Δo down)     (neutral)        (push Δo up)

That single line of ligands explains a huge fraction of inorganic color and magnetism. Everything downstream — which wavelength a complex absorbs, what color you see, how many unpaired electrons it carries — falls out of where its ligands sit on this scale.

Why the order is what it is: σ, π-donation, π-back-bonding

Pure electrostatics (the original crystal-field picture) gets the rough trend but fails on the details — it cannot explain why neutral CO outsplits the F⁻ anion. The modern explanation is the molecular-orbital ligand-field model, in which three effects feed into Δ_o:

• σ-donation. A ligand's lone pair points at the e_g orbitals and pushes them up. Stronger σ-donors → larger Δ_o. This is why NH₃ (good σ-donor) beats H₂O.
• π-donation (weak-field end). Halides and oxygen donors have filled p or lone-pair orbitals of π symmetry. These push the t_2g set up, shrinking the gap. The heavier the halide, the more diffuse and the stronger the π-donation: I⁻ > Br⁻ > Cl⁻ > F⁻ — exactly the weak-field tail of the series.
• π-back-bonding (strong-field end). CO, CN⁻, NO₂⁻ and phenanthroline carry empty π* orbitals. The filled metal t_2g donates electron density into them, which lowers t_2g and enlarges Δ_o. This single effect is why the strong-field champions are π-acceptors, not the most negatively charged ligands.

So the series reads left-to-right as: π-donors (Δ down) → σ-only donors (neutral) → π-acceptors (Δ up). Reading the position of a ligand tells you its bonding character at a glance.

From Δ to the color you see

A d–d transition promotes one electron from t_2g to e_g. The photon it absorbs has exactly the energy Δ_o:

Δo = h·c / λ        →        λ_absorbed = h·c / Δo

The complex looks like the complement of the color it absorbs. A complex that absorbs orange light (~600 nm) looks blue; one that absorbs blue–violet (~430 nm) looks yellow-orange. So as a ligand climbs the series:

• Δ_o rises → absorbed photon is more energetic → λ_absorbed shifts toward the blue (shorter wavelength).
• The observed color shifts the opposite way.

The classic teaching set is the same metal with a ligand walk-up. [Cr(H₂O)₆]³⁺ absorbs around 575 nm and looks violet; replace water with the stronger-field ethylenediamine to make [Cr(en)₃]³⁺ and Δ_o rises, the absorption moves toward ~455 nm, and the complex turns yellow. Same metal, same oxidation state — only the ligand changed, and the color tracked the spectrochemical series exactly.

High-spin vs low-spin: Δ competes with the pairing energy

For octahedral d⁴ through d⁷ configurations there is a genuine fork. The first three electrons go into the three t_2g orbitals singly (Hund's rule). The fourth electron has two options:

Option A — pair up inside t2g        cost = P  (pairing energy)
Option B — go up to the empty eg     cost = Δo (the splitting)

  if  Δo < P   →  electron climbs to eg   →  HIGH-SPIN  (max unpaired e⁻)
  if  Δo > P   →  electron pairs in t2g    →  LOW-SPIN   (min unpaired e⁻)

The pairing energy P — the extra electrostatic and exchange cost of forcing two electrons into one orbital — runs roughly 200–300 kJ/mol for first-row metals. Weak-field ligands keep Δ_o below that and you get high-spin; strong-field ligands push Δ_o above it and you get low-spin. The spectrochemical series is therefore also a high-spin / low-spin predictor: anything left of about H₂O tends to be high-spin, anything from NH₃ rightward (especially CN⁻, CO) tends to be low-spin.

The textbook pair is iron(II), d⁶. [Fe(H₂O)₆]²⁺ is high-spin with four unpaired electrons (paramagnetic, μ ≈ 5.1 μ_B); [Fe(CN)₆]⁴⁻ is low-spin with zero unpaired electrons (diamagnetic). Identical metal, identical charge, opposite magnetism — decided entirely by where the ligand sits on the series.

Ligand-by-ligand data

Real Δ_o values, mostly referenced to a common metal so the trend is clean. (1000 cm⁻¹ ≈ 11.96 kJ/mol.)

Complex	Ligand class	Δo (cm⁻¹)	Δo (kJ/mol)	Spin / color
[CrCl₆]³⁻	π-donor (weak)	~13,600	~163	high-spin, green
[Cr(H₂O)₆]³⁺	σ + weak π-donor	17,400	208	high-spin, violet
[Cr(NH₃)₆]³⁺	σ-donor	21,600	258	yellow
[Cr(en)₃]³⁺	chelating σ-donor	21,900	262	yellow
[Cr(CN)₆]³⁻	π-acceptor (strong)	26,600	318	yellow
[Co(H₂O)₆]²⁺	weak field, d⁷	9,300	111	high-spin, pink
[Co(NH₃)₆]³⁺	strong field, d⁶	22,900	274	low-spin, orange
[Fe(CN)₆]³⁻	π-acceptor, d⁵	~35,000	~419	low-spin, red

Two patterns jump out. First, on the same metal (Cr³⁺), Δ_o climbs monotonically from Cl⁻ → H₂O → NH₃ → en → CN⁻, exactly tracing the series. Second, oxidation state matters enormously: Co(II) with water gives Δ_o ≈ 111 kJ/mol (high-spin), while Co(III) — only one electron different in charge — with the moderate ligand ammonia reaches 274 kJ/mol and goes low-spin.

The numbers that make it click

A few quantitative anchors worth carrying around:

• The visible window in Δ. Visible light spans roughly 400–700 nm, i.e. photon energies of ~170 to ~300 kJ/mol. That is exactly the Δ_o range of common first-row complexes — which is why transition-metal complexes are the showcase of inorganic color. A Δ_o of 240 kJ/mol corresponds to λ ≈ 500 nm.
• [Ti(H₂O)₆]³⁺, the cleanest case. A single d-electron, one absorption band at λ_max ≈ 500 nm. That band is Δ_o: 20,300 cm⁻¹ ≈ 243 kJ/mol. The complex absorbs green and looks purple.
• Metal-row scaling. Δ rises about 50% per row going down a group. For the same ligands, Δ(4d) ≈ 1.5 × Δ(3d) and Δ(5d) ≈ 1.5 × Δ(4d). Combined with higher oxidation states, this is why 4d/5d metals (Rh³⁺, Pd²⁺, Pt²⁺, Ir³⁺) are almost universally low-spin.
• Oxidation-state scaling. Δ_o(M³⁺) ≈ 1.5 × Δ_o(M²⁺) for the same metal and ligands. Higher charge pulls ligands closer, increasing repulsion at the e_g orbitals.
• Crystal-field stabilization energy (CFSE). Each t_2g electron sits 0.4 Δ_o below the barycenter; each e_g electron sits 0.6 Δ_o above it. Low-spin d⁶ (all six in t_2g) has CFSE = −2.4 Δ_o — the most stable configuration possible, which is why low-spin d⁶ ions like Co³⁺ and Pt⁴⁺ are kinetically inert.

Where it shows up

• Hemoglobin and the breath you just took. Deoxyhemoglobin's iron is high-spin Fe(II) bound to a weak-field histidine and porphyrin. When O₂ binds it acts as a moderately strong π-acceptor, the iron flips to low-spin, shrinks slightly, and slips into the porphyrin plane — the conformational trigger that drives cooperative oxygen uptake. The high-spin/low-spin switch literally moves your blood.
• Cobalt's classic color change. Pink [Co(H₂O)₆]²⁺ (weak field) turns deep blue [CoCl₄]²⁻ (tetrahedral, even smaller Δ) on adding concentrated HCl — the basis of cobalt-chloride humidity indicators and "invisible ink."
• Prussian blue and Hexacyanoferrates. The intense blue of [Fe(CN)₆]-based pigments comes from CN⁻ being the second-strongest field ligand, giving low-spin iron and strong metal-to-metal charge transfer.
• Gemstones. Ruby is Cr³⁺ doped into Al₂O₃; the oxide lattice sets Δ_o so that Cr³⁺ absorbs in the yellow-green and transmits red. Emerald is the same Cr³⁺ ion in beryl, where a slightly weaker field shifts the absorption and the gem turns green. Same chromophore, different ligand field, different jewel.
• Spin-crossover materials. Iron(II) complexes engineered so Δ_o ≈ P flip between high- and low-spin with temperature, pressure, or light — candidate switches for molecular memory and thermochromic coatings.

Octahedral vs tetrahedral splitting

	Octahedral (Δo)	Tetrahedral (Δt)
Coordination number	6	4
Lower set	t2g (3 orbitals)	e (2 orbitals)
Upper set	eg (2 orbitals)	t2 (3 orbitals)
Splitting size	baseline	Δt ≈ (4/9) Δo
Ligand orientation	point straight at orbitals	point between orbitals
Typical spin state	high- or low-spin	almost always high-spin
Δ vs pairing energy	can exceed P	Δt < P essentially always

Because no tetrahedral ligand points directly at a d-orbital and there are only four of them, Δ_t is roughly four-ninths of the octahedral value for the same metal and ligands. That value sits below the pairing energy in essentially every real case, which is why low-spin tetrahedral complexes are vanishingly rare — a clean, memorable consequence of the geometry-scaled spectrochemical splitting.

Common misconceptions and pitfalls

• "More negative charge means stronger field." No. If charge were the driver, F⁻ would outsplit neutral CO and NH₃ — it doesn't. π-back-bonding by neutral π-acceptors dominates the strong-field end. Charge is a weak predictor; bonding type is the real one.
• "The color is the wavelength absorbed." The opposite. You see the complement of the absorbed band. A complex that absorbs orange looks blue, not orange.
• "The series predicts the metal's spin no matter what." The ligand sets Δ_o, but the spin outcome only forks for d⁴–d⁷. d¹–d³ and d⁸–d¹⁰ have no high/low-spin ambiguity in octahedral fields — there is only one way to fill them.
• "Δ_o is fixed for a ligand." The order is nearly constant, but the magnitude scales with the metal's identity, row, and oxidation state. Quote Δ_o for a specific complex, never for a ligand alone.
• "Crystal-field theory explains the whole series." Purely electrostatic CFT gets the trend but misplaces π-acceptors. You need ligand-field / MO theory to explain CO and CN⁻ at the top.
• "Strong-field always means intensely colored." Not necessarily. Strong-field, low-spin complexes can be pale if their d–d transitions are Laporte- or spin-forbidden; the most intense colors often come from charge-transfer bands, not d–d transitions at all (e.g. deep purple permanganate, which has no d-electrons to split).