Heterolytic cleavage is the unsymmetrical splitting of a covalent bond in which one atom keeps both bonding electrons (becoming an anion) while the other keeps none (becoming a cation); the more electronegative atom is always the one that ends up as the anion, shown with a curved arrow pointing toward it. Unlike homolysis, heterolysis needs no special energetic trigger and readily occurs at room temperature under polar/ionic conditions -- it always requires less energy than homolytic cleavage of the same bond, since it only relocates an intact electron pair rather than genuinely separating one.
Carbocation formation. When the leaving atom/group is more electronegative than carbon (e.g. Br in tert-butyl bromide, (CH3)3C-Br, hydrolysing to (CH3)3C+ + Br−), carbon is left electron-deficient as a carbocation. A carbocation's positively-charged carbon is sp2 hybridised, giving it a planar (trigonal) shape with an empty p-orbital perpendicular to the plane of its three sigma bonds -- this empty orbital is why it carries a positive charge, and its two lobes (above and below the plane) let an attacking nucleophile approach from either face. Carbocation stability rises with alkyl substitution (inductive +I donation plus hyperconjugation from each added alkyl group):
+C(CH3)3>+CH(CH3)2>+CH2CH3>+CH3(3∘>2∘>1∘>methyl)
Carbanion formation. When carbon retains the bonding pair as the more electronegative atom in the bond (e.g. an α-C-H bond of an aldehyde, deprotonated by OH− in aldol condensation), the result is a carbanion. A carbanion's carbon is sp3 hybridised, with the extra lone pair occupying one of the four sp3 orbitals -- giving it a pyramidal shape, analogous to ammonia's lone pair. Carbanion stability runs in the opposite direction to carbocation stability, since alkyl groups are electron-donating and so destabilise an already electron-rich centre:
−C(CH3)3<−CH(CH3)2<−CH2CH3<−CH3(methyl is the most stable, 3∘ the least)
An alkyl free radical, by contrast, may be either pyramidal or planar; when planar it resembles a carbocation's sp2 geometry, except its p-orbital holds one unpaired electron rather than being completely empty.