Spectra of Tetrahedral Complexes

Introduction

Tetrahedral cobalt(II) species often appear deep blue, whereas aqueous octahedral Co²⁺ is commonly pale pink. The difference is not a change in cobalt's d count: Co²⁺ remains d⁷. Geometry changes both the energy levels and the intensity rules. Tetrahedral symmetry lacks an inversion centre, allowing metal-like d orbitals to mix with other orbital character and giving spin-allowed ligand-field bands more intensity than in an ideal octahedron.

Core explanation

In a tetrahedral field, the twofold e set lies lower than the threefold t₂ set, opposite the ordering convention for octahedral t₂g/e g. The splitting Δ t is usually smaller than the corresponding octahedral splitting for comparable metal–ligand interactions, often roughly estimated as 4/9 Δₒ within a simple electrostatic model. That ratio is a rule of thumb, not a universal measurement, because coordination number, bond length and covalency change between geometries. The relatively small Δ t makes tetrahedral first-row complexes usually high spin.

Co²⁺ is d⁷. Its free-ion ^4F ground term splits under T d into ^4A₂(F), ^4T₁(F) and ^4T₂(F), while ^4P gives ^4T₁(P). In the usual tetrahedral Co²⁺ ordering, ^4A₂(F) is ground. The three principal quartet-to-quartet targets are ^4T₂(F), ^4T₁(F) and ^4T₁(P). All preserve S=3/2. The lowest transition can fall in the near infrared, while the upper transitions contribute to visible colour; a visible-only measurement may therefore show fewer than three complete bands.

There are no g subscripts on tetrahedral state labels because T d has no inversion operation. A strict Laporte parity prohibition is inapplicable, and orbitals with metal d and metal p or ligand character of compatible T d symmetry can mix. The resulting d–d transition dipoles are usually larger than those for centrosymmetric octahedral g→g transitions. “Laporte allowed” is sometimes said informally, but absence of a parity prohibition does not mean every transition is equally strong; spin, detailed point-group symmetry and orbital overlap still matter.

The chloride–water balance around Co²⁺ illustrates the colour contrast. In a suitable chloride-rich environment, tetrahedral [CoCl₄]²⁻ can form and appears strongly blue; in water-rich conditions, octahedral aqua species are often pinker and less intense. This is a chemical equilibrium as well as a spectral phenomenon. Temperature and chloride concentration can shift the composition, so an observed colour is evidence about the dominant species only after considering solution conditions.

Tetrahedral spectra need an appropriate term-energy model. An octahedral d⁷ Tanabe–Sugano diagram cannot simply be read with g labels erased, because the orbital ordering and state correlations differ. Orgel electron–hole relationships help qualitative comparison, but quantitative Δ t and B should come from tetrahedral assignments or a justified mapping. The P-derived upper transition includes electron-repulsion information, so it need not equal Δ t; using a single visible maximum as “the splitting” can be badly misleading.

Magnetic data provide an independent check: high-spin tetrahedral Co²⁺ has three unpaired electrons, giving a spin-only estimate √15≈3.87 μ B. Real observed moments may exceed that because orbital and spin–orbit contributions are appreciable. An observed moment above 3.87 is therefore not by itself proof of a fourth unpaired electron or wrong oxidation state. Pairing a magnetic result with band pattern and known coordination number is more reliable.

Step-by-step reasoning

Use charge balance to establish Co²⁺ d⁷ and structural evidence to confirm tetrahedral geometry. Write the lower e/upper t₂ ordering and ^4A₂(F) ground term. Assign possible spin-allowed targets ^4T₂(F), ^4T₁(F) and ^4T₁(P), noting that the first may be in the near infrared. Expect no strict g→g parity restriction. Compare visible and near-IR bands, molar absorptivity and magnetic behaviour before extracting Δ t or B.

Visual explanation

Draw two columns: octahedral Co²⁺ with lower t₂g/upper e g, g labels and short pale absorbance bars; tetrahedral Co²⁺ with lower e/upper t₂, no g labels and taller absorbance bars. In the tetrahedral column place a ^4A₂(F) baseline and three arrows to ^4T₂(F), ^4T₁(F) and ^4T₁(P). Mark the lowest arrow “may be near IR.”

Real-world analogy

Changing the shape of a room can alter both its resonant frequencies and how easily sound escapes. Octahedral-to-tetrahedral change similarly shifts electronic energies and removes an inversion-symmetry barrier to optical intensity. The colour difference therefore combines position and transition probability, not just one energy-gap change.

Real-world example

Adding chloride to an aqueous Co²⁺ system can increase the fraction of blue tetrahedral [CoCl₄]²⁻ relative to pink aqua species. The shift can be reversed by changing water or chloride activity. A spectrum across visible and near-infrared regions, together with the known equilibrium, is more informative than declaring that chloride “turns cobalt blue” as a fixed intrinsic property.

Why?

Why can tetrahedral Co²⁺ d–d absorption be strong despite remaining a ligand-field transition? Without an inversion centre, the ideal octahedral g→g Laporte argument no longer forces the electric-dipole matrix element to zero. Orbital mixing lends substantial intensity to spin-allowed quartet transitions.

Common misconception

“The deep blue colour means Co²⁺ becomes low spin or changes oxidation state.” Tetrahedral Co²⁺ is normally high spin d⁷. Geometry and ligand exchange change its spectra and intensity while cobalt can remain Co(II).

Worked example

A tetrahedral species has formula [CoCl₄]²⁻. Four Cl⁻ ligands contribute −4; overall −2 requires cobalt +2, hence d⁷. The usual tetrahedral ground term is ^4A₂(F), with three spin-allowed target terms ^4T₂(F), ^4T₁(F) and ^4T₁(P). Absence of g labels predicts stronger d–d intensity than an ideal octahedral Co²⁺ analogue. A first observed visible band need not be the lowest transition, because the ^4A₂→^4T₂ energy can lie in the near IR.

Quick check

1. Which tetrahedral d orbital set is lower, e or t₂? Answer: e is lower and t₂ is higher in the usual tetrahedral splitting scheme.

Exam focus

Derive Co oxidation state, d⁷ count and tetrahedral geometry before assigning the ^4A₂ ground term. Look for a possible near-IR first band and avoid treating the strongest visible band as Δ t automatically. Contrast parity rules carefully without claiming all tetrahedral bands are fully allowed.

Advanced insight

Spin–orbit coupling and low-symmetry distortion can split nominally degenerate tetrahedral Co²⁺ states and influence both spectral shape and magnetic moment. The F/P parent notation is still useful, but a quantitative fit can require covalency, configuration interaction and actual geometric distortion beyond the elementary T d model.

Summary

Tetrahedral Co²⁺ is high-spin d⁷ with ^4A₂(F) ground and three principal quartet targets. Its lack of inversion centre makes spin-allowed d–d absorption typically stronger than in octahedral Co²⁺, while lower Δ t and chemical speciation set band positions and observed colour.

Practice questions

1. Name the tetrahedral Co²⁺ target states reached by principal spin-allowed transitions. Answer: ^4T₂(F), ^4T₁(F) and ^4T₁(P), all reached from ^4A₂(F) while conserving quartet multiplicity. 2. Why might a visible-only spectrum show two strong cobalt bands although three are predicted? Answer: The lowest ^4A₂(F)→^4T₂(F) transition can be in the near infrared, outside the visible scan; overlapping or broadening can also hide a band. 3. A blue Co²⁺ solution turns pink on dilution with water. Give a defensible interpretation. Answer: Changing chloride and water activities can shift equilibrium from tetrahedral chlorocobaltate toward more aqua-coordinated, often octahedral Co²⁺ species, changing both band energies and intensities without requiring a cobalt oxidation-state change. 4. Why are tetrahedral state labels written without g/u? Answer: Tetrahedral T d symmetry has no inversion centre, so gerade/ungerade parity is not a valid label.