A convenient way of describing conjugated hydrocarbon systems that is helpful in predicting properties is the alternant/nonalternant classification. A conjugated hydrocarbon is alternant if:

• Stars (asterisks) can be placed on alternating p-centers with no two stars adjacent

It is nonalternant if

• two or more adjacent centers receive stars

Alternant systems can be further subclassified:

• The system is even alternant if equal numbers of starred and unstarred carbons occur

• It is odd alternant if the numbers in the two sets are not equal; since we always maximize the number of stars, this means that odd alternant systems will have more starred than unstarred atoms

In the graphic below, A, like all linear systems, is an alternant hydrocarbon. The ones with even numbers of atoms are even alternant, with odd numbers, they are odd alternant.

Structure B, naphthalene, is an even alternant species, having five starred and five unstarred carbons. Azulene (C) is a nonalternant; any way of placing stars on alternate carbons eventually leads to two adjacent stars. In this case, starring was started at the top bridgehead. Try some other starting points yourself. Tropylium, D, also is nonalternant, as are all odd rings.

In alternant species, no carbons in the same set (starred or unstarred) have overlapping p orbitals. (Draw the p-MOs of hexatriene (A) and convince yourself of this.)

• Therefore, in the Huckel theory description, all H_ii = a integrals and all H_ij = b integrals are the same.

• The consequence of this is that all charge densities are zero.

Even alternant molecules have equal numbers of bonding and antibonding orbitals, symmetrically distributed, and no nonbonding orbital.

• When neutral, these species have all bonding orbitals full.

Odd alternant structures have equal numbers of bonding and antibonding orbitals, but also have a nonbonding orbital with E = a.

• The nonbonding orbital has non-zero coefficients only at the starred atoms, and the sum of the coefficients of the starred atoms attached to a given unstarred atom must equal zero.

• Along with the requirement that the sum of the squares of the coefficients must equal one, this allows computation of the coefficients in the nonbonding orbital.

Another interesting difference in properties is illustrated by the two diradicals, E and F. E is even alternant.

• This means that it has a resonance structure in which the electrons all can be paired, using one more double bond than shown to start.

F is odd alternant; one cannot write a resonance structure with more double bonds than the number of nonstarred atoms.

• This in turn means that no resonance structures exist in which the spins are paired.