Q.What is a pi bond?

Within valence bond theory, the specific GEOMETRY of atomic orbital overlap determines whether a covalent bond is classified as sigma or pi.

A sigma (σ) bond results from HEAD-ON (axial) overlap, where the two orbitals overlap directly along the line joining the two nuclei — also called axial overlap. Any overlap involving an s orbital (s-s or s-p) is always sigma, because the spherically-symmetric s orbital overlaps head-on regardless of approach direction; two p orbitals overlapping ALONG the molecular axis (e.g. pₓ-pₓ, if x is the molecular axis) are likewise sigma.

A pi (π) bond results from SIDEWAYS (lateral) overlap, where two p orbitals lie parallel to one another but perpendicular to the internuclear axis, and overlap above/below (or in front of/behind) that axis rather than head-on (e.g. p_y-p_y or p_z-p_z, if x is the molecular axis).

Every single bond is a σ bond; every double bond is one σ plus one π; every triple bond is one σ plus two mutually-perpendicular π bonds. σ bonds, from their larger head-on overlap, are intrinsically STRONGER than π bonds (which have comparatively less effective overlap) — this is why the π component of a double or triple bond is the one that breaks preferentially in addition reactions, while the σ framework of a molecule survives.

Worked through for four small molecules: H₂ forms via s-s overlap (σ); F₂ via p-p axial overlap of each atom's half-filled 2p_z orbital (σ); HF via s-p axial overlap (σ); and O₂ via BOTH an axial p_z-p_z overlap (σ) AND a sideways p_y-p_y overlap (π), giving the O=O double bond and leaving each oxygen's paired 2s/2pₓ electrons as non-bonding lone pairs. This last case — an apparently fully-paired-electron O₂ — is exactly the picture that (wrongly) predicts O₂ should be diamagnetic, a puzzle only Molecular Orbital Theory resolves.