Shapes of Coordination Compounds

The overall three-dimensional shape of a coordination entity is determined primarily by its coordination number (Section 5.4), and for two-, four-, and six-coordinate complexes the correlation is generally reliable.

A coordination number of 2 gives a linear geometry, with the two ligands on directly opposite sides of the metal at a bond angle of $180^{\circ}$. This is common for certain $d^{10}$ metal ions in the $+1$ oxidation state, such as $\text{Ag}^+$ in $[\text{Ag}(\text{NH}_3)_2]^+$ or $\text{Au}^+$ in $[\text{Au}(\text{CN})_2]^-$ (the very ion used industrially to extract gold, Section 5.18).

A coordination number of 6 almost always gives an octahedral geometry: six ligands positioned symmetrically at the vertices of an octahedron around the central metal, with bond angles of $90^{\circ}$ between adjacent ligands and $180^{\circ}$ between opposite ligands. This is overwhelmingly the most common geometry among transition-metal complexes — $[\text{Co}(\text{NH}_3)_6]^{3+}$, $[\text{Fe}(\text{CN})_6]^{4-}$, $[\text{CoF}_6]^{3-}$, and $[\text{Cr}(\text{en})_3]^{3+}$ are all octahedral.

A coordination number of 4 is the one genuinely ambiguous case, since two distinct geometries — tetrahedral and square planar — are both possible, and predicting which one a given complex adopts requires knowing the metal's d-electron count and the field strength of the ligands, not the coordination number alone. Tetrahedral geometry (bond angles of roughly $109.5^{\circ}$) is generally favoured when the metal has no strong electronic preference for square planar geometry, or when the ligands are weak-field and/or sterically bulky — $[\text{Ni}(\text{CO})_4]$ (Ni in the zero oxidation state, $d^{10}$) and $[\text{NiCl}_4]^{2-}$ ($\text{Ni}^{2+}$, $d^8$, weak-field $\text{Cl}^-$) are both tetrahedral. Square planar geometry (all four ligands and the metal coplanar, bond angles of $90^{\circ}$ and $180^{\circ}$) is characteristically favoured by $d^8$ metal ions paired with strong-field ligands, since the strong field forces the metal's single normally-unpaired d-electron to pair up, freeing an orbital that permits a $dsp^2$-hybridized square planar arrangement instead — $[\text{Ni}(\text{CN})_4]^{2-}$ (same $\text{Ni}^{2+}$, $d^8$, but strong-field $\text{CN}^-$ instead of $\text{Cl}^-$) is square planar, as are essentially all complexes of $\text{Pd}^{2+}$, $\text{Pt}^{2+}$, and $\text{Au}^{3+}$ (all $d^8$), which show a very strong intrinsic preference for square planar geometry almost regardless of ligand field strength. …