Structure 3.1.10 – Colour of Transition Metal Complexes

Why Transition Complexes Are Coloured

Transition metal complexes exhibit colour due to the unique arrangement of electrons in their d orbitals. When ligands surround a transition metal ion, they cause the degenerate (equal energy) d orbitals to split into two energy levels. This phenomenon is central to Crystal Field Theory and is responsible for the absorption of specific wavelengths of visible light.

Formation of a Complex

• Transition metal ions act as Lewis acids (electron pair acceptors).
• Ligands are molecules or ions with lone pairs that form coordinate covalent bonds with the central metal ion.
• Examples of ligands:
  • Neutral: \( \text{NH}_3 \), \( \text{H}_2\text{O} \)
  • Negative ions: \( \text{Cl}^- \), \( \text{CN}^- \)
• The resulting structure is called a complex ion.

Crystal Field Splitting

When ligands approach the central metal ion, their negative charge repels the electrons in the d orbitals. This causes the d orbitals to split into two groups with different energies — usually referred to as \( e_g \) and \( t_{2g} \) orbitals (though the names are not needed for IB assessment).

• In an isolated transition metal ion, all five d orbitals are degenerate.
• The presence of ligands causes splitting of these orbitals into two energy levels.
• The energy difference between these levels is denoted by \( \Delta E \).

Absorption and Promotion of Electrons

When visible light passes through a solution containing transition metal complexes:

• Electrons in the lower d-orbital level absorb energy corresponding to the gap \( \Delta E \).
• This energy promotes them to the higher d-orbital level.
• The wavelength of light absorbed corresponds to this energy gap.

Factors Affecting Colour

The energy gap \( \Delta E \), and therefore the colour observed, is influenced by several factors:

• Identity of the metal (atomic number and electron configuration).
• Oxidation state of the metal ion (higher charge typically increases \( \Delta E \)).
• Type of ligands — different ligands create different levels of splitting. (e.g., \( \text{CN}^- \) causes more splitting than \( \text{H}_2\text{O} \)).

Understanding Colour in Transition Metal Complexes

When a transition metal complex absorbs visible light, an electron is promoted from a lower-energy d-orbital to a higher-energy d-orbital within the split d-subshell. This electron transition corresponds to a specific frequency and wavelength of light. The light that is absorbed is not observed; instead, we perceive the complementary colour — the part of the visible spectrum that is not absorbed.

The Colour Wheel and Complementary Colours

The colour wheel helps to identify the complementary colour relationships. If a complex absorbs a certain colour of light, the colour we see is directly opposite on the colour wheel. This relationship is essential when analyzing or predicting the observed colour of a solution or complex.

Wavelength, Frequency, and Energy Relationship

We can also calculate the energy or frequency of light absorbed using the following equations from the IB Data Booklet:

• Speed of light: \( c = \lambda f \)
• Energy of a photon: \( E = hf \)

Where:

• \( c = 3.00 \times 10^8 \, \text{m/s} \) (speed of light)
• \( h = 6.63 \times 10^{-34} \, \text{J·s} \) (Planck’s constant)
• \( \lambda \) = wavelength (in meters)
• \( f \) = frequency (in Hz)