Hybridisation Involving d Orbitals and Shapes of Molecules

The $sp$, $sp^2$ and $sp^3$ hybridisation schemes account for every case where a central atom is surrounded by two, three or four electron pairs — but some central atoms, especially those from period 3 and beyond that have energetically accessible $d$ orbitals, are surrounded by five or six electron pairs. Accommodating this many pairs requires bringing $d$ orbitals into the hybridisation scheme as well.

$sp^3d$ hybridisation. One $s$ orbital, three $p$ orbitals and one $d$ orbital mix to give five equivalent $sp^3d$ hybrid orbitals, oriented toward the corners of a trigonal bipyramid — three equatorial positions at $120^{\circ}$ to one another, and two axial positions at $90^{\circ}$ to the equatorial plane. Phosphorus in $\text{PCl}_5$ is $sp^3d$ hybridised: phosphorus's ground-state configuration ($[\text{Ne}] 3s^2 3p^3$) is promoted so that all five valence electrons occupy separate orbitals ($3s^1 3p^3 3d^1$), which mix into five $sp^3d$ hybrids, each overlapping with a chlorine orbital. This directly reproduces the trigonal bipyramidal shape predicted by VSEPR theory, including the genuine axial/equatorial inequivalence discussed there.

$sp^3d^2$ hybridisation. One $s$ orbital, three $p$ orbitals and two $d$ orbitals mix to give six equivalent $sp^3d^2$ hybrid orbitals, oriented toward the six corners of a regular octahedron, all at $90^{\circ}$ to their four nearest neighbours. Sulphur in $\text{SF}_6$ is $sp^3d^2$ hybridised: sulphur's ground-state configuration ($[\text{Ne}] 3s^2 3p^4$) is promoted so that all six valence electrons occupy separate orbitals ($3s^1 3p^3 3d^2$), which mix into six $sp^3d^2$ hybrids, each overlapping with a fluorine orbital to give the perfectly symmetric octahedral $\text{SF}_6$ molecule, with every F–S–F bond angle between adjacent fluorines equal to $90^{\circ}$. …