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Hückel's rule
open-in-new
<p>In <a href="/facts/Organic_chemistry/djxhxaNg">organic chemistry</a>, Hückel's rule predicts that a <a href="/facts/Plane_(geometry)/tAUtRFcn">planar</a> <a href="/facts/Ring_(chemistry)/EVFmy88Q">ring</a> <a href="/facts/Molecule/N9ljSfFq">molecule</a> will have <a href="/facts/Aromaticity/wK0DzRY6">aromatic</a> properties if it has 4<i>n</i> + 2 <a href="/facts/Pi_electron/3Q6LAGYK">π-electrons</a>, where <i>n</i> is a non-negative <a href="/facts/Integer/PUwwrawx">integer</a>. The <a href="/facts/Quantum_mechanic/BRc3Mzgr">quantum mechanical</a> basis for its formulation was first worked out by physical chemist <a href="/facts/Erich_H%25C3%25BCckel/EmM42Vtp">Erich Hückel</a> in 1931. The succinct expression as the 4<i>n</i> + 2 rule has been attributed to <a href="/facts/William_von_Eggers_Doering/6K1H3qU0">W. v. E. Doering</a> (1951), although several authors were using this form at around the same time. </p><p>In agreement with the <a href="/facts/M%25C3%25B6bius%25E2%2580%2593H%25C3%25BCckel_concept/PtP0Qk0o">Möbius–Hückel concept</a>, a <a href="/facts/Cyclic_compound/TH2ReKIQ">cyclic</a> ring molecule follows Hückel's rule when the number of its π-electrons equals 4<i>n</i> + 2, although clearcut examples are really only established for values of <i>n</i> = 0 up to about <i>n</i> = 6. Hückel's rule was originally based on calculations using the <a href="/facts/H%25C3%25BCckel_method/2F8acMEn">Hückel method</a>, although it can also be justified by considering a <a href="/facts/Particle_in_a_ring/MvcC9BkI">particle in a ring</a> system, by the <a href="/facts/Linear_combination_of_atomic_orbitals_molecular_orbital_method/K7mcdv2L">LCAO method</a> and by the <a href="/facts/Pariser%25E2%2580%2593Parr%25E2%2580%2593Pople_method/wzyeX8zg">Pariser–Parr–Pople method</a>. </p><p>Aromatic compounds are more stable than theoretically predicted using hydrogenation data of simple <a href="/facts/Alkene/RtYcS6kU">alkenes</a>; the additional stability is due to the delocalized cloud of electrons, called <i><a href="/facts/Resonance_(chemistry)/5tymwoIP">resonance</a> energy</i>. Criteria for simple aromatics are: </p> <ol><li>the molecule must have 4<i>n</i> + 2 (a so-called "Hückel number") π electrons (2, 6, 10, ...) in a <a href="/facts/Conjugated_system/Ddx9qzox">conjugated system</a> of p orbitals (usually on sp2-<a href="/facts/Orbital_hybridisation/Fl7sz8Jm">hybridized</a> atoms, but sometimes sp-hybridized);</li> <li>the molecule must be (close to) planar (p orbitals must be roughly parallel and able to interact, implicit in the requirement for conjugation);</li> <li>the molecule must be cyclic (as opposed to linear);</li> <li>the molecule must have a continuous ring of p atomic orbitals (there cannot be any sp3 atoms in the ring, nor do exocyclic p orbitals count).</li></ol>