Non-Kekule molecule
A non-Kekule molecule is a conjugated hydrocarbon that cannot be assigned classical Kekule structures. Since non-Kekule molecules have two or more formal radical centers, their spin-spin interactions can cause conductivity or ferromagnetism, and applications to functional materials are expected. However, as these molecules are quite reactive and most of them are easily decomposed or polymerized at room temperature, strategies for stabilization are needed for their practical use. Synthesis and observation of these reactive molecules are generally accomplished by matrix-isolation methods.
The simplest non-Kekule molecules are biradicals.

# Biradicals
A biradical in organic chemistry is an even-electron chemical compound with two free radical
centres which act independently of each other and not to be confused with diradicals in general.
The first biradical was synthesized by Wilhelm Schlenk in 1915 following the same methodology as Moses Gomberg's triphenylmethyl radical.  The so-called Schlenk-Brauns hydrocarbons are:
It was established for the first time by Eugene Muller that these compounds are paramagnetic with a triplet ground state with the aid of a Gouy balance.
Another well studied biradical is trimethylenemethane or TMM:
This molecule can be obtained from photolysis of an diazo precursor with expulsion of nitrogen or from photolysis of 2-methylenecyclobutanone with expulsion of carbon monoxide. In 1966 Paul Dowd determined with electron spin resonance that this compound also has a triplet state. In a crystalline host the 6 hydrogen atoms in TMM are identical. Recombination of the two radicals to a cyclopropane full valence compound is only possible when the triplet state converts to the higher energy singlet state first.
Non-Kekule quinodimethanes are biradicaloids of a six-membered ring with methylene substituents. Non-Kekule polynuclear aromatics are composed of several fused six-membered rings. The synthesis of Triangulene, the simplest non-Kekule polynuclear aromatic, was first tried by Eric Clar in 1953, but it was not even observed until the syntheses of trioxytriangulene by Richard J. Bushby in 1995 and kinetically stabilized triangulene by Kazuhiro Nakasuji in 2001. A related class of biradicals are para-benzynes.
When the two nonbonding electrons are situated on the same atom the molecule is a carbene.

# Classification of non-Kekule molecules
Non-Kekule molecules with two formal radical centers (non-Kekule diradicals) can be classified into non-disjoint and disjoint by the shape of their two non-bonding molecular orbitals (NBMOs).
Both NBMOs of molecules with non-disjoint characteristics such as trimethylenemethane (TMM) have electron density at the same atom. According to Hund's rule, each orbital is filled with one electron with parallel spin, avoiding the Coulomb repulsion by filling one orbital with two electrons. Therefore, such molecules with non-disjoint NBMOs are expected to prefer a triplet ground state.
In contrast, the NBMOs of the molecules with disjoint characteristics such as tetramethyleneethane (TME) can be described without having electron density at the same atom. With such MOs, the destabilization factor by the Coulomb repulsion becomes much smaller than with non-disjoint type molecules, and therefore the relative stability of the singlet ground state to the triplet ground state will be nearly equal, or even reversed because of exchange interaction.