Chemistry · Ch 5 — Chemical Bonding
Overlap of atomic orbitals
Overlap of atomic orbitals
The strength of a covalent bond is governed by how much its two contributing atomic orbitals overlap — a GREATER extent of overlap gives a STRONGER bond — and how much overlap is geometrically possible in turn depends on each orbital's own shape, size and symmetry. On the basis of the GEOMETRY of that overlap, covalent bonds are classified into two types. A sigma (σ) bond forms when the orbital overlap lies directly ALONG the internuclear (bond) axis; it can arise from three combinations — two 's' orbitals overlapping (e.g. H2's s-s overlap), one 's' and one 'p' orbital overlapping end-on (e.g. HF's s-p overlap), or two 'p' orbitals overlapping end-on along that same axis (e.g. F2's p-p σ overlap, using each fluorine's half-filled orbital). A pi (π) bond, by contrast, forms when two 'p' orbitals overlap SIDEWAYS (laterally) rather than end-on, so the resulting bond lies PERPENDICULAR to the internuclear axis rather than along it. Because end-on (σ) overlap is inherently more extensive/direct than the sideways overlap of a π bond, a σ bond is …
What this figure shows. A potential-energy-vs-internuclear-distance curve for two approaching H atoms with opposite electron spins. Far apart, the system's energy is (arbitrarily) taken as zero, since there is no interaction. As the atoms approach, attractive forces dominate and the potential energy steadily decreases, reaching a minimum at the equilibrium internuclear distance (this minimum-energy separation IS the H–H bond length, 74 pm, and the depth of the minimum below zero corresponds to the bond's dissociation energy, 438 kJ mol⁻¹); pushing the atoms closer than this minimum makes repulsive forces dominate and the curve rises steeply again. A second curve, for two H atoms approaching with PARALLEL spins, shows energy rising monot …
Worked out. Three worked sigma-overlap examples, each end-on along the internuclear (z) axis: (a) s-s overlap in H2 — the two hydrogen orbitals overlap directly to give a σ bond. (b) p-p σ overlap in F2 — each fluorine atom () has one half-filled orbital, and the two orbitals overlap end-on along the internuclear axis to give a σ(2pz) bond. (c) s-p σ overlap in HF — hydrogen's half-filled orbital overlaps end-on with fluorine's half-filled orbital. Separately, a π overlap is illustrated as two half-filled p orbitals (one from each atom) overlapping sideways/laterally rather than end-on, so the resulting bond lies perp …