A-level Chemistry/OCR (Salters)/Complexes

A complex is a compound in which a central metal atom is surrounded ligands that form dative covalent bonds with it. Complexes are discussed in Chemical Ideas Section 11.6: The d block: complex formation.

Examples of complex geometry

• 
  linear:
  diamminesilver(I), [Ag(NH₃)₂]⁺
• 
  linear:
  dicyanoaurate(I), [Au(CN)₂]⁻
• 
  tetrahedral:
  tetrachloronickelate(II), [NiCl₄]²⁻
• 
  tetrahedral:
  tetracarbonylnickel, Ni(CO)₄
• 
  tetrahedral:
  tetrahydridoborate(III), [BH₄]⁻
• 
  tetrahedral:
  tetrahydroxozincate(II), [Zn(OH)₄]²⁻
• 
  square planar:
  tetraamminecopper(II), [Cu(NH₃)₄]²⁺
• 
  square planar:
  tetracyanonickelate(II), [Ni(CN)₄]²⁻
• 
  square planar:
  cisplatin, cis-diamminedichloroplatinum(II), PtCl₂(NH₃)₂
• 
  octahedral:
  hexaaquacopper(II), [Cu(H₂O)₆]²⁺
• 
  octahedral:
  hexacyanoiron(III), [Fe(CN)₆]³⁻

Why are transition metal complexes usually coloured?

You might like to look at the spectroscopy page to remind yourself of how and why light interacts with electrons in molecules. You could also have a look at the atomic orbitals page to see what shape d orbitals are.

Partially-filled d orbitals split by ligands

In a nutshell, transition metal complexes are coloured because their central transition metal atoms have a partially-filled d subshell that is split by the surrounding ligands. Partially-filled means at least one d orbital is half-filled or empty and at least one d orbital is half-filled or full, i.e. that the d subshell contains between 1 and 9 electrons. Split means that the within the d subshell, there are now different energy levels, whereas without the ligands, the five d orbitals that make up the d subshell all have the same energy.

This is really a university-level topic

For the purpose of exams, students of Salters A-Level Chemistry are not required to understand how or why ligands cause the d subshell to split, just that it happens. Students who go on to study chemistry at university will learn about the interactions between metal atoms and ion with ligands in much greater detail, where they will encounter crystal field theory (electrostatic effects of ligands on d orbitals) and ligand field theory (covalent bonding of ligands to metal atoms and ions).

Ligands split d orbitals

Without ligands, all five d orbitals have equal energy.

A complex needs ligands to be coloured. Without ligands, all five d orbitals are equal in energy (degenerate is a word often used here — it simply means of the same energy). When ligands are present, some of the d orbitals become higher in energy than before, and some become lower. This happens because some of the d orbitals are nearer the ligands than others so they experience more repulsion from the ligand electrons and thus have a higher energy.

An empty d shell cannot absorb visible photons

Empty d shells have no electrons to absorb photons

A coloured complex needs partially-filled d orbitals. Empty d orbitals cannot produce colour because they lack electrons. Electrons are needed to move from a lower-energy d orbital to a higher-energy d-orbital by absorbing a photon of visible light. Complexes of Sc³⁺ are colourless because Sc³⁺ (electron configuration: [Ar]3s²3d⁰) has empty d orbitals.

The same is also true of all elements that come before Ti in the periodic table — none of these have any electrons in their d orbitals. For instance, K has d orbitals but they are unoccupied and as such, complexes of K cannot absorb photons promoting a d electron from a d orbital to a higher energy one, since K doesn't have any d electrons.

A full d shell cannot absorb visible photons

If all d orbitals are full, d electrons have nowhere to go once they gain energy.

If a complex has an empty d shell, there are no electrons to move. If a complex has a full d shell, there are no vacancies in any d orbitals for an electron to move into. Complexes of Zn²⁺ and Cu⁺ (electron configuration: [Ar]3s²3d¹⁰) are colourless because the d orbitals of Zn²⁺ and Cu⁺ are full.

How do ligands split d orbitals?

We noted above that the presence of ligands around a transition metal atom or ion splits the five d orbitals into two groups, one group higher in energy and one group lower in energy than they were before the ligands arrived. Chemical Ideas p. 271 offers a short and sweet explanation which is ideal for revision and exams. This section attempts to present a deeper explanation. It is more detailed than the Salters Advanced Chemistry specification requires, but this may be exactly what you want to know if you're interested.

Ligand electrons repel d electrons

Ligands have lone pairs of electrons that they use to bond to transition metal atoms or ions. The presence of these ligand electrons repels the transition metal's electrons in its d orbitals. The metal d electrons can't go anywhere to avoid the repulsion, so the only effect is that their energy increases.

Ligands affect different d orbitals differently

Ligands do not affect each of the five d orbitals to the same extent. A d orbital that brings its electrons close to the ligands will increase a great deal in energy. A d orbital occupies space away from the ligands will increase in energy a little, but not as much. As you can probably imagine, the exact positioning of the ligands determines which d orbitals they will affect the most.

Splitting in octahedral complexes

In an octahedral complex, two d orbitals become higher in energy and three become lower in energy. The two higher-energy d orbitals are given the label e_g and the three lower-energy d orbitals are labelled t_2g.

In an octahedral complex, the d_z² and d_x²−y² orbitals are increased in energy the most. We refer to the d_z² and d_x²−y² orbitals collectively as the e_g d orbitals.

The images below illustrate the orbitals d_z² (left) and d_x²−y² (right) and their positioning within an octahedral complex. The central transition metal atom or ion is grey, the six ligands are red and the orbitals are yellow.

Let us continue to consider an octahedral complex. The remaining d orbitals, d_xy, d_xz and d_yz see their energy increase to a lesser extent. We refer to the d_xy, d_xz and d_yz orbitals collectively as the t_2g d orbitals.

The images below illustrate these three orbitals in relation to the central metal atom and ligands in an octahedral complex. Compare these images of the t_2g orbitals with those of the e_g above. You may be able to see that the t_2g orbitals are, on average, further away from the ligands than the e_g orbitals. This is the reason for splitting.

Splitting in tetrahedral complexes

In a tetrahedral complex, three d orbitals increase in energy while two decrease. The three higher-energy d orbitals are given the label t₂ and the two lower-energy d orbitals are labelled e. This is the opposite order of energy to that found in octahedral complexes.

In a tetrahedral complex, the d_xy, d_xz and d_yz orbitals are increased in energy the most. We refer to the d_xy, d_xz and d_yz orbitals collectively as the t₂ d orbitals.

The remaining d orbitals, d_z² and d_x²−y², see their energy increase to a lesser extent. We refer to the d_z² and d_x²−y² orbitals collectively as the e d orbitals.

e_g and t_2g

You should know the labels e_g and t_2g; they are mathematical constructs derived from group theory. Chemists later borrowed the labels as they refer to the molecular symmetry and are useful for determining behavior, orbital splitting, and properties of molecules.