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 Carbon () is a chemical element; it has chemical symbol, symbol C and atomic number 6. It is nonmetallic and tetravalence, tetravalent—meaning that its atoms are able to form up to four covalent bonds due to its valence shell exhibiting 4 ...

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. 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: *The

molecular orbital In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding ...

energies for the π system are paired, that is for an orbital of energy

E=\alpha +x\beta

there is one of energy

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. *The population or

electron density Electron density or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial variables and is typical ...

at all sites is equal to unity in the

ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than 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 A non-bonding orbital, also known as ''non-bonding molecular orbital'' (NBMO), is a molecular orbital whose occupation by electrons neither increases nor decreases the bond order between the involved atoms. Non-bonding orbitals are often designa ...

). 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 the assignment of all coefficients and then normalize them. This procedure permits the prediction of reactivity patterns and can be exploited to calculate Dewar's reactivity numbers for all sites.

References

Theoretical chemistry Molecular physics {{molecular-physics-stub