A mathematical relationship between the number of isomers of alkenes and alkynes: A result established from the enumeration of isomers of alkenes from alkyl biradicals

Abstract

A simple and fast algorithm for enumerating alkene isomers is described. This algorithm is based on a 2-step hypothetical chemical reaction. In the first step, an alkane molecule loses two protons becoming an alkyl biradical. In the second step, two alkyl biradicals react to form an alkene molecule. By using two sequential recursive algorithms, the number of computational terms in the enumeration process is much less than when using the Henze-Blair algorithm. By using this simple algorithm, the numbers of constitutional isomers of alkenes and alkynes for carbon content greater than 30 are easily enumerated. In addition, through this algorithm, a mathematical relationship between the number of constitutional isomers of alkenes and alkynes has been established for the first time.