d orbitals

d orbitals are the five orbitals in a d subshell, the orbitals with angular momentum quantum number l = 2. They first appear in the third shell (3d), and together they hold up to 10 electrons. Four of them are shaped like a four-leaf clover, and the fifth, d_z², has two lobes and a ring. The d orbitals are filled across the transition metals, and the way they split in energy inside complexes explains why transition metal compounds are coloured.

What are d orbitals?

Electrons in an atom are arranged in shells, numbered from n = 1 outwards, and each shell is divided into subshells labelled s, p, d and f. A subshell with quantum number l has 2l + 1 orbitals, and each orbital holds at most two electrons:

Because l can only go up to n − 1, there are no 1d or 2d orbitals: the first d orbitals are 3d. AQA A-level Chemistry expects electron configurations up to Z = 36, krypton, in terms of s, p and d subshells.

The shapes of the d orbitals

The five d orbitals are named d_xy, d_xz, d_yz, d_x²−y² and d_z², after how they sit on the x, y and z axes.

• d_xy, d_xz and d_yz: four lobes lying in the plane named, pointing between the two axes. d_xy lies in the xy plane, and so on.
• d_x²−y²: four lobes in the xy plane pointing along the x and y axes, the same shape as d_xy turned through 45°.
• d_z²: the odd one out, with a lobe above and below along the z axis and a doughnut-shaped ring (torus) around the middle in the xy plane.

Although d_z² looks different, all five d orbitals in the same subshell have the same energy in a free atom. That changes when the atom is surrounded by ligands, as the section on splitting shows.

d orbitals and electron configuration

The 4s subshell fills before 3d. In potassium and calcium the next electrons go into 4s, because for these atoms 3d is higher in energy: it is less penetrating and more shielded from the nucleus. From scandium (Z = 21) to zinc (Z = 30), electrons are added to the 3d subshell. Elements where the last electron enters a d orbital are the transition metals, or d-block elements.

Chromium and copper

Chromium and copper break the pattern. One electron moves from 4s into 3d, because half-filled and completely filled subshells are especially stable. So chromium is 3d⁵ 4s¹ rather than 3d⁴ 4s², and copper is 3d¹⁰ 4s¹ rather than 3d⁹ 4s².

Transition metal ions lose 4s electrons first

When a transition metal forms a positive ion, it loses its 4s electrons first and only then any 3d electrons. Iron is [Ar] 3d⁶ 4s², so Fe²⁺ is [Ar] 3d⁶, not [Ar] 3d⁴ 4s². In AQA's words, the transition metal characteristics of titanium to copper come from an incomplete d sub-level in their atoms or ions. Check any configuration with the Electron Configuration Tool.

Test the filling order in this question from the Atomic Structure course.

d orbital splitting and colour

In a free transition metal ion, the five d orbitals have the same energy. In a complex, ligands surround the ion. Crystal field theory treats the ligands as negative charges that repel the d electrons. In an octahedral complex the six ligands sit on the x, y and z axes, so:

• d_x²−y² and d_z², whose lobes point straight at the ligands, rise in energy. They are called the e_g set.
• d_xy, d_xz and d_yz, whose lobes point between the ligands, are lower. They are the t_2g set.

The energy gap is the crystal field splitting, Δ_oct. When visible light of exactly the right energy hits the complex, a d electron absorbs it and jumps from t_2g to e_g. The light that is not absorbed is transmitted or reflected, and that is the colour you see. AQA A-level describes this as d electrons moving from the ground state to an excited state, with ΔE = hν = hc/λ.

• Changing the ligand, the oxidation state or the coordination number changes ΔE, so the colour changes.
• Strong-field ligands such as CN⁻ give a large splitting; weak-field ligands such as I⁻ and Cl⁻ give a small one. Water and ammonia lie in between, with ammonia the stronger.
• A full or empty d subshell gives no colour. Cu⁺ is d¹⁰, so no d electron can jump up, no visible light is absorbed, and its compounds are white or colourless.
• Tetrahedral complexes split the other way round and by less, because the ligands overlap less with the d orbitals.

Worked examples

Example 1: configuration of an ion

Write the electron configuration of Cr³⁺.

1. Chromium is [Ar] 3d⁵ 4s¹.
2. Remove the 4s electron first, then two 3d electrons.
3. Cr³⁺ is [Ar] 3d³.

Example 2: the size of Δoct from a colour

OpenStax gives the maximum absorbance of [Ti(H₂O)₆]³⁺ at 499 nm, and this wavelength corresponds to Δ_oct. Find the energy gap per ion and per mole. Use h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹ and N_A = 6.02 × 10²³ mol⁻¹.

1. ΔE = hc ÷ λ = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) ÷ (499 × 10⁻⁹) = 3.99 × 10⁻¹⁹ J per ion.
2. Per mole: 3.99 × 10⁻¹⁹ × 6.02 × 10²³ = 2.40 × 10⁵ J mol⁻¹ = 240 kJ mol⁻¹.
3. Ti³⁺ is [Ar] 3d¹, so there is one d electron to make the jump.

Example 3: which ions are coloured?

Common mistakes

• Removing 3d electrons before 4s when forming ions. 4s fills first and empties first.
• Forgetting the chromium and copper exceptions. Cr is 3d⁵ 4s¹ and Cu is 3d¹⁰ 4s¹.
• Saying the colour seen is the colour absorbed. You see the light that is transmitted or reflected, the complementary colour.
• Saying there are 2d orbitals. d orbitals start at n = 3.
• Calling zinc a transition metal at AQA A-level. AQA defines the transition metal properties for Ti to Cu, from an incomplete d sub-level; Zn²⁺ has a full 3d subshell.

Practise with a short timed paper

Transition metal chemistry is in the second year of A-level Chemistry, and orbital shapes and crystal field theory are in first-year university chemistry. The daily A-level Chemistry: Year 2 and University Chemistry: Year 1 papers are short timed papers of 8 questions, with a new one every day. See also electronic structure.

Read next

Chemistry · Atoms and the periodic tableProperties of transition metals: the 4 key propertiesThe 4 properties of transition metals for A-level: complex ions, coloured ions, variable oxidation states and catalysis, all explained by the d sub-level.