of 3,4-dimethylcyclobutene is symmetry allowed whereas only a disrotatory ring opening of 5,6-dimethylcyclohexa-1,3-diene is symmetry allowed. This is because only in these cases would maximum orbital overlap occur in the transition state. Also, the formed product would be in a ground state rather than an excited state. Frontier molecular orbital theory According to the frontier molecular orbital theory, the sigma bond in the ring will open in such a way that the resulting p-orbitals will have the same symmetry as the HOMO of the product. For the 5,6-dimethylcyclohexa-1,3-diene, only a disrotatory mode would result in p-orbitals having the same symmetry as the HOMO of hexatriene. For the 3,4-dimethylcyclobutene, on the other hand, only a conrotatory mode would result in p-orbitals having the same symmetry as the HOMO of butadiene. Mechanism of photochemical reactions If the ring opening of 3,4-dimethylcyclobutene were carried out under photochemical conditions the resulting electrocyclization would be occur through a disrotatory mode instead of a conrotatory mode as can be seen by the correlation diagram for the allowed excited state ring opening reaction. Only a disrotatory mode, in which symmetry about a reflection plane is maintained throughout the reaction, would result in maximum orbital overlap in the transition state. Also, once again, this would result in the formation of a product that is in an excited state of comparable stability to the excited state of the reactant compound. Electrocyclic reactions in biological systems Electrocyclic reactions occur frequently in nature. One of the most common such electrocyclizations is the biosynthesis of vitamin D3. The first step involves a photochemically induced conrotatory ring opening of 7-dehydrocholesterol to form pre vitamin D3. A [1,7]-hydride shift then forms vitamin D3. Another example is in the proposed biosynthesis of aranotin, a naturally occurring oxepine, and its related compounds. Enzymatic epoxidation of phenylalanine-derived diketopiperazine forms the arene oxide, which undergoes a 6π disrotatory ring opening electrocyclization reaction to produce the uncyclized oxepine. After a second epoxidation of the ring, the nearby nucleophilic nitrogen attacks the electrophilic carbon, forming a five membered ring. The resulting ring system is a common ring system found in aranotin and its related compounds. The benzonorcaradiene diterpenoid (A) was rearranged into the benzocycloheptatriene diterpenoid isosalvipuberlin (B) by boiling a methylene chloride solution. This transformation can be envisaged as a disrotatory electrocyclic reaction, followed by two suprafacial 1,5-sigmatropic hydrogen shifts, as shown below. Electrocyclic reactions in organic synthesis An often