Alternate and non alternant hydrocarbons
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An alternant hydrocarbon is any conjugated hydrocarbon system which does not possess an odd-membered ring.
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An alternant hydrocarbon is any conjugated hydrocarbon system which does not possess an 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.[1] When this condition is met, the secular determinant in the Hückel 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:[2]
The molecular orbital energies for the π system are paired, that is for an orbital of energy {\displaystyle E=\alpha +x\beta } {\displaystyle E=\alpha +x\beta } there is one of energy {\displaystyle E=\alpha -x\beta } {\displaystyle E=\alpha -x\beta }.
The coefficients of two paired molecular orbitals are the same at the same site, except for a sign change in the unstarred set.
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