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An '''alternant hydrocarbon''' is any [[conjugated system|conjugated hydrocarbon system]] which does not possess an [[Cycloalkane|odd-membered ring]]. For such systems it is possible to undertake a starring process, in which the [[carbon]] atoms are divided into two sets: all the carbons in one set are marked with a star such that no two starred or unstarred atoms are bonded to each other. Here the starred set contains the highest number of atoms.<ref>{{cite book |title= The Vocabulary And Concepts Of Organic Chemistry|last= Orchin|first=Milton |year= 2005|publisher= [[John Wiley & Sons]] |isbn= 9780471680284|pages=73–74 }}</ref> When this condition is met, the [[secular determinant]] in the [[Huckel method|Huckel approximation]] has a simpler form, since cross-diagonal elements between atoms in the same set are necessarily 0.

Alternant hydrocarbons display three very interesting properties:<ref name=Jones>{{cite book |title= Physical and Mechanistic Organic Chemistry|last= Yardley Jones|first=Richard Arnold |year= 1979|publisher= [[Cambridge University Press]] |isbn= 9780521295963|pages=105–111 }}</ref>
*The [[molecular orbital]] energies for the π system are paired, that is for an orbital of energy <math>E=\alpha +x\beta</math> there is one of energy <math>E=\alpha-x\beta</math>.
*The coefficients of two paired molecular orbitals are the same at the same site, except for a sign change in the unstarred set.
*The population or [[electron density]] at all sites is equal to unity in the [[ground state]], so the distribution of π electrons is uniform across the whole molecule.

Moreover, if the alternant hydrocarbon contains an odd number of atoms then there must be an unpaired orbital with zero bonding energy (a [[non-bonding orbital]]).<ref>{{cite book |title= March's Advanced Organic Chemistry: Reactions, Mechanisms, And Structure|last= Smith|first=Michael|last2=March|first2=Jerry |year= 2007|publisher= [[John Wiley & Sons]] |isbn= 9780471720911|pages=69–71 }}</ref> For this orbital, the coefficients on the atomic sites can be written down without calculation: the coefficient on all the orbitals belonging to the smaller (unstarred) set are 0, and the sum of the coefficients of the (starred) orbitals around them must also be 0. Simple algebra allows to assign all coefficients and then [[normalized vector|normalize them]].<ref name=Jones /> This procedure permits to predict reactivity patterns and can be exploited to calculate [[Dewar reactivity number|Dewar's reactivity numbers]] for all sites.

== References ==
<references/>

[[Category:Theoretical chemistry]]
[[Category:Molecular physics]]

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