Concept of Hybridisation: sp, sp2 and sp3

VSEPR theory correctly predicts molecular shape, but it says nothing about why a central atom's orbitals — ordinarily an $s$ orbital and three separate, differently-shaped $p$ orbitals — should produce bonds that are all equivalent to one another and point in exactly the directions VSEPR requires. Hybridisation answers this: it is the mixing of a set of atomic orbitals of comparable energy on one atom to generate an equal-sized new set of hybrid orbitals, all identical in shape and energy, oriented in space to match the observed geometry.

$sp$ hybridisation. One $s$ orbital mixes with one $p$ orbital to give two equivalent $sp$ hybrid orbitals, oriented at $180^{\circ}$ to each other — a linear arrangement. Beryllium in $\text{BeCl}_2$ is $sp$ hybridised: beryllium's ground state ($1s^2 2s^2$) is first promoted to $1s^2 2s^1 2p^1$, and the singly occupied $2s$ and $2p$ orbitals mix to form two $sp$ hybrids, each overlapping with a chlorine orbital to form a linear $\text{Cl}-\text{Be}-\text{Cl}$ molecule.

$sp^2$ hybridisation. One $s$ orbital mixes with two $p$ orbitals to give three equivalent $sp^2$ hybrid orbitals, all lying in one plane and oriented at $120^{\circ}$ to one another — a trigonal planar arrangement. Boron in $\text{BF}_3$ is $sp^2$ hybridised: boron's ground state ($1s^2 2s^2 2p^1$) is promoted to $1s^2 2s^1 2p^2$, and the three singly occupied orbitals mix into three $sp^2$ hybrids, each overlapping with a fluorine orbital to give the trigonal planar $\text{BF}_3$ molecule. …