Improvements in the computer enumeration of permutation isomers

Abstract

Several improvements in methods for the computer enumeration of permutation isomers are presented. The unique compositions of monovalent substituents on a given molecular framework are classified into ordered partitions of the total number of substitution sites, enormously reducing the number of calculations that must be performed. Using an algorithm which multiplies symmetric polynomials represented by partitions and which does not use symbolic algebra, it is possible to expand a Polya cycle index polynomial for the group representing the substitution sites on a molecular framework and automatically collect the multinomial terms into their partition representations. The method is illustrated by completely enumerating all the stereo- and constitutional permutation isomers of nonrigid pentane with up to twelve different substituents. Further examples are provided with adamantane, dodecahedrane and rigid and nonrigid biphenyl.