Coordination Compounds & Crystal Field Theory Cheat Sheet

A printable reference covering coordination number, ligand charge, oxidation state, crystal field splitting, magnetic behavior, and isomerism for grades 11-12.

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Coordination compounds contain a central metal ion bonded to surrounding ligands through coordinate covalent bonds. This cheat sheet helps students name complexes, find oxidation states, predict geometry, and connect structure to color and magnetism. These ideas are important in transition metal chemistry, biochemistry, catalysis, and materials science. The core ideas include coordination number, ligand charge, crystal field splitting, and electron pairing. In octahedral complexes, the $d$ orbitals split into lower-energy $t_{2g}$ orbitals and higher-energy $e_g$ orbitals. The size of the splitting energy $\Delta_o$ helps determine whether a complex is high spin or low spin. Magnetic behavior depends on the number of unpaired electrons, often estimated using $\mu = \sqrt{n(n+2)}$ BM.

Key Facts

The oxidation state of the metal is found from $x + \sum \text{ligand charges} = \text{overall charge of complex}$ .
The coordination number is the number of donor atoms directly bonded to the central metal ion.
Common geometries include linear for $\text{CN}=2$ , tetrahedral or square planar for $\text{CN}=4$ , and octahedral for $\text{CN}=6$ .
In an octahedral field, the crystal field splitting is $\Delta_o = E(e_g) - E(t_{2g})$ .
The crystal field stabilization energy for octahedral complexes is $\text{CFSE} = (-0.4x + 0.6y)\Delta_o$ , where $x$ is the number of $t_{2g}$ electrons and $y$ is the number of $e_g$ electrons.
A high-spin complex forms when $\Delta_o < P$ , so electrons occupy higher-energy orbitals before pairing.
A low-spin complex forms when $\Delta_o > P$ , so electrons pair in lower-energy orbitals before occupying higher-energy orbitals.
The spin-only magnetic moment is estimated by $\mu = \sqrt{n(n+2)}$ BM, where $n$ is the number of unpaired electrons.

Vocabulary

Coordination compound: A compound containing a central metal atom or ion bonded to surrounding ligands through coordinate covalent bonds.
Ligand: An ion or molecule that donates at least one lone pair to a central metal ion.
Coordination number: The number of ligand donor atoms directly attached to the central metal ion.
Crystal field splitting: The separation of metal $d$ orbitals into different energy levels due to repulsions from surrounding ligands.
Spectrochemical series: An ordering of ligands from weak field to strong field based on how much they split the metal $d$ orbitals.
Chelate: A complex formed when a multidentate ligand bonds to the same metal ion through two or more donor atoms.

Common Mistakes to Avoid

Forgetting ligand charges when finding oxidation state is wrong because neutral and charged ligands affect the metal charge differently.
Confusing coordination number with the number of ligands is wrong because one ligand can donate through more than one atom, as in bidentate ligands.
Assuming every $\text{CN}=4$ complex is tetrahedral is wrong because some $d^8$ metal ions form square planar complexes.
Pairing electrons too early in a high-spin complex is wrong because weak-field ligands have $\Delta_o < P$ , so electrons spread out before pairing.
Using $\Delta_o$ for tetrahedral complexes without adjustment is wrong because tetrahedral splitting is smaller, approximately $\Delta_t \approx \frac{4}{9}\Delta_o$ .

Practice Questions

1 Find the oxidation state of cobalt and the coordination number in $[\text{Co}(\text{NH}_3)_5\text{Cl}]^{2+}$ .
2 For an octahedral $d^6$ complex, compare the number of unpaired electrons in a high-spin case and a low-spin case.
3 Calculate the spin-only magnetic moment for a complex with $n=3$ unpaired electrons using $\mu = \sqrt{n(n+2)}$ BM.
4 Explain why a strong-field ligand can make a transition metal complex low spin even when the same metal ion is high spin with a weak-field ligand.

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