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Ozone is bent, with two equivalent O–O bonds of approximate bond order $1.5$. Its useful localized orbital hybridization description is $s{p}^2$ at all three oxygens. Two hybrids at the central oxygen form sigma bonds and a third contains a lone pair; the three perpendicular p orbitals form a three-centre four-electron pi bond.

The three pi orbitals are bonding, nonbonding and antibonding, filled as ${\pi }_{\mathrm{b}}^2{\pi }_{\mathrm{nb}}^2{\pi }_{\ast }^0$. The terminal-centred nonbonding orbital is the Homo, conventionally $1a_2$; the delocalized antibonding orbital is the LUMO, $2b_1$. The two principal resonance structures, ${}^{-}\mathrm{O}-{\mathrm{O}}^{+}=\mathrm{O}$ and $\mathrm{O}={\mathrm{O}}^{+}-{\mathrm{O}}^{-}$, distribute the extra pi bond across the two links.

The 18 valence electrons comprise four sigma-bond electrons, ten in five sigma-framework lone pairs, and four in the pi system. This gives a paired ground-state model. More accurate treatments include electron correlation; the simple bond-order picture is not an exact charge-density calculation.^[ref]

One consistent localized orbital hybridization description uses the Lewis structuresFor methyldiazonium, take C as $s{p}^3$ and both N atoms as $sp$. For diazomethane, the double-bond resonance contributor suggests C as $s{p}^2$, central N as $sp$, and terminal N as $s{p}^2$. The central N uses two opposite $sp$ hybrids for the linear C–N–N sigma bond framework. In the localized double-bond picture, terminal N uses one $s{p}^2$ hybrid for its sigma bond, two for lone pairs, and its remaining p atomic orbital for a pi bond.

These labels specify an approximate bonding construction, not uniquely measurable atomic properties. An alternative representation takes terminal N as $sp$, with one $sp$ lone pair and one p lone pair; the latter can participate in the delocalized C–N–N $\pi$ system. It describes the same resonance more explicitly. Neither construction requires an unpaired electron or a bent central N.

Gallium phosphide forms a tetrahedral network of polar covalent bonds, with electron density displaced toward phosphorus. The alternating diamond-related structure is the zinc blende structure: each Ga has four P neighbours and each P has four Ga neighbours. A local orbital hybridization picture combines outward-pointing s,p-derived orbitals into four approximately $s{p}^3$ bond directions; in the crystal these interactions form extended occupied bonding bands.

Since ${\chi }_{\mathrm{Allen}}(\mathrm{P})-{\chi }_{\mathrm{Allen}}(\mathrm{Ga})=2.25-1.76=0.49>0$, P attracts shared electron density more strongly. Write ${\mathrm{Ga}}^{\delta +}-{\mathrm{P}}^{\delta -}$ to indicate an ionic contribution superposed on covalent bonds. Formal oxidation states Ga($+3$) and P($-3$) are electron-assignment labels, not proof of completely transferred charges or a purely ionic crystal.

Neither atom requires $3d$ hybrids for these four bonds. The Ga $3d^{10}$ shell is filled and relatively core-like; the relevant Ga valence orbitals are $4s,4p$. P uses principally $3s,3p$; its empty $3d$ orbitals are too high in energy to be a necessary bonding set. Detailed band calculations may include d-state mixing or core–valence effects, but that does not turn the tetrahedral bonding into an expanded-valence d-hybrid construction.

Opposite parity of same-centre s orbitals and axial p orbitals makes their left and right nearest-neighbour hopping integrals opposite in sign. Their Bloch wave sum is consequently odd in wavevector and vanishes at the zone centre and boundary. Away from those points, orbital hybridization repels coupled levels and can produce an avoided crossing.