orbital hybridization
/ hy-bri-dy-ZAY-shun /
Carbon's atomic orbitals are one round 2s and three dumbbell-shaped 2p orbitals pointing along x, y and z. Yet methane has four identical bonds pointing symmetrically to the corners of a tetrahedron. How do mismatched atomic orbitals give equivalent bonds? Hybridisation is the answer: the atom blends its atomic orbitals into a new set of equivalent hybrid orbitals that point in just the right directions to bond.
Mixing one s and one p orbital gives two sp hybrids 180 degrees apart (linear, as in BeCl2 or the carbons of CO2); one s and two p give three sp2 hybrids at 120 degrees (trigonal planar, as in BF3); one s and three p give four sp3 hybrids at 109.5 degrees (tetrahedral, as in CH4). The number of hybrid orbitals always equals the number of atomic orbitals you mixed in, and it matches the number of electron regions VSEPR counts. Any leftover, unhybridised p orbitals stay free to form pi bonds sideways. The older schemes sp3d and sp3d2, invoked for five and six bonds, are now regarded as poor descriptions because the d orbitals barely participate; the geometry is real but the bonding is better described by delocalised molecular orbitals.
Hybridisation is the part of valence-bond theory that links a Lewis structure and a VSEPR shape to a bonding picture: count the electron regions, read off the hybridisation, and you know the directions the bonds point. It is genuinely useful for the light main-group elements, but it is best understood as a mathematical convenience for shaping orbitals to a known geometry, not as a physical cause of the shape. Honestly, hybridisation does not happen first and then dictate the geometry; we choose the hybrids that match the geometry the molecule already adopts.
Ethene-like sp2 carbon shows the idea cleanly: three sp2 hybrids form three sigma bonds in a plane at 120 degrees, while the one leftover p orbital, untouched by hybridisation, overlaps sideways to make the pi bond of the C=C double bond.
sp2 carbon: three in-plane sigma bonds plus one leftover p orbital for the pi bond.
Hybridisation is a model fitted to a known geometry, not the cause of it; and the sp3d / sp3d2 schemes for hypervalent atoms are now considered misleading, since the d orbitals contribute very little.