Hückel's rule

Source: Wikipedia, the free encyclopedia.
π electrons
(4n + 2, for n = 1).

In

quantum mechanical basis for its formulation was first worked out by physical chemist Erich Hückel in 1931.[1][2] The succinct expression as the 4n + 2 rule has been attributed to W. v. E. Doering (1951),[3][4] although several authors were using this form at around the same time.[5]

In agreement with the

LCAO method[5] and by the Pariser–Parr–Pople method
.

Aromatic compounds are more stable than theoretically predicted using hydrogenation data of simple alkenes; the additional stability is due to the delocalized cloud of electrons, called resonance energy. Criteria for simple aromatics are:

  1. the molecule must have 4n + 2 (a so-called "Hückel number") π electrons[7] (2, 6, 10, ...) in a conjugated system of p orbitals (usually on sp2-hybridized atoms, but sometimes sp-hybridized);
  2. the molecule must be (close to) planar (p orbitals must be roughly parallel and able to interact, implicit in the requirement for conjugation);
  3. the molecule must be cyclic (as opposed to linear);
  4. 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).

Monocyclic hydrocarbons

The rule can be used to understand the stability of completely conjugated monocyclic hydrocarbons (known as annulenes) as well as their cations and anions. The best-known example is benzene (C6H6) with a conjugated system of six π electrons, which equals 4n + 2 for n = 1. The molecule undergoes substitution reactions which preserve the six π electron system rather than addition reactions which would destroy it. The stability of this π electron system is referred to as aromaticity. Still, in most cases, catalysts are necessary for substitution reactions to occur.

The

cyclopropenyl cation (C
3H+
3) [9][10] and the triboracyclopropenyl dianion (B
3H2–
3) are considered examples of a two π electron system, which are stabilized relative to the open system, despite the angle strain imposed by the 60° bond angles.[11][12]

Planar ring molecules with 4n π electrons do not obey Hückel's rule, and theory predicts that they are less stable and have

transannular strain. Thus, these systems are either nonaromatic or experience modest aromaticity. This changes when we get to [18]annulene
, with (4×4) + 2 = 18 π electrons, which is large enough to accommodate six interior hydrogen atoms in a planar configuration (3 cis double bonds and 6 trans double bonds). Thermodynamic stabilization, NMR chemical shifts, and nearly equal bond lengths all point to considerable aromaticity for [18]annulene.

The (4n+2) rule is a consequence of the

regular hexagonal molecule.[13][8]

However for cyclobutadiene or cyclooctatrene with regular geometries, the highest molecular orbital pair is occupied by only 2 π electrons forming a less stable open shell. The molecules therefore stabilize by geometrical distortions which separate the degenerate orbital energies so that the last two electrons occupy the same orbital, but the molecule as a whole is less stable in the presence of such a distortion.[8]

Heteroatoms

Hückel's rule can also be applied to molecules containing other atoms such as nitrogen or oxygen. For example pyridine (C5H5N) has a ring structure similar to benzene, except that one -CH- group is replaced by a nitrogen atom with no hydrogen. There are still six π electrons and the pyridine molecule is also aromatic and known for its stability.[14]

Polycyclic hydrocarbons

Hückel's rule is not valid for many compounds containing more than one ring. For example, pyrene and trans-bicalicene contain 16 conjugated electrons (8 bonds), and coronene contains 24 conjugated electrons (12 bonds). Both of these polycyclic molecules are aromatic, even though they fail the 4n + 2 rule. Indeed, Hückel's rule can only be theoretically justified for monocyclic systems.[5]

Three-dimensional rule

Main article: Spherical aromaticity

In 2000, Andreas Hirsch and coworkers in

icosahedral (or other appropriate) symmetry, so the molecular orbitals must be entirely filled. This is possible only if there are exactly 2(n + 1)2 electrons, where n is a nonnegative integer. In particular, for example, buckminsterfullerene, with 60 π-electrons, is non-aromatic, since 60 ÷ 2 = 30, which is not a perfect square.[15]

In 2011, Jordi Poater and Miquel Solà expanded the rule to determine when a

electrons, then the fullerene would display aromatic properties. This follows from the fact that a spherical species having a same-spin half-filled last energy level with the whole inner levels being fully filled is also aromatic.[16]

See also

References

  1. ^
    • S2CID 186218131
      .
    • doi:10.1007/BF01341953
      .
    • S2CID 121787219
      .
  2. ^ Hückel, E. (1938). Grundzüge der Theorie ungesättiger und aromatischer Verbindungen. Berlin: Verlag Chem. pp. 77–85.
  3. ISSN 0002-7863
    .
  4. ^ Doering, W. v. E. (September 1951), Abstracts of the American Chemical Society Meeting, New York, p. 24M
  5. ^
    doi:10.1021/ja01138a038
    .
  6. OCLC 642506595
  7. ^ Ayub, Rabia (2017). "Excited State Aromaticity and Antiaromaticity. Fundamental Studies and Applications" (PDF). Uppsala University. p. 15. Retrieved 26 January 2022.
  8. ^
    ISBN 978-0-205-12770-2
    .
  9. OCLC 642506595
  10. doi:10.1021/ja00707a040
    .
  11. PMID 26765534
    .
  12. PMID 26530854
    .
  13. ISBN 0-7167-3539-3
    .
  14. ^ "Aromatic Heterocycles- Pyridine and Pyrrole". Chemistry Libre Texts. 3 May 2015. p. 15.5. Retrieved 1 March 2022.
  15. PMID 29711706
    ..
  16. PMID 21952479
    ..
Retrieved from "https://en.wikipedia.org/w/index.php?title=Hückel%27s_rule&oldid=1119982180"