# 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(NH$_3$)$_2$]$^+$
* linear: dicyanoaurate(I), [Au(CN)$_2$]$^−$
* tetrahedral: tetrachloronickelate(II), [NiCl$_4$]$^{2−}$
* tetrahedral: tetracarbonylnickel, Ni(CO)$_4$
* tetrahedral: tetrahydridoborate(III), [BH$_4$]$^−$
* tetrahedral: tetrahydroxozincate(II), [Zn(OH)$_4$]$^{2−}$
* square planar: tetraamminecopper(II), [Cu(NH$_3$)$_4$]$^{2+}$
* square planar: tetracyanonickelate(II), [Ni(CN)$_4$]$^{2−}$
* square planar: cisplatin, cis-diamminedichloroplatinum(II), PtCl$_2$(NH$_3$)$_2$
* octahedral: hexaaquacopper(II), [Cu(H$_2$O)$_6$]$^{2+}$
* 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

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

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 Sc$^{3+}$ are colourless because Sc$^{3+}$ (electron configuration: [Ar]3s$^2$3d$^0$) 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 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 Zn$^{2+}$ and Cu$^+$ (electron configuration: [Ar]3s$^2$3d$^{10}$) are colourless because the d orbitals of Zn$^{2+}$ 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, 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, 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 t$_2$ 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.