Alkane isomer combinatorics: Stereostructure enumeration and graph-invariant and molecular-property distributions

Combinatoric manipulative methodology to characterize different isomer-clas s features is extended and illustrated in application to alkane isomers. St ereoisomeric enumerations and various molecular-property characteristics fo r structural-isomer classes are made. For a range of carbon-atom counts N w e enumerate the following: the mean number of diastereomers per N-carbon st ructural isomer; the mean number of stereoisomers per N-carbon diastereomer ; and the mean number of "conformers" per N-carbon stereoisomer. Also we co nsider distributions of several graph-theoretic properties, characterizing the distributions in terms of averages, variances, covariances, and extrema l values. The results for these graph-theoretic invariants are used to pred ict (via substructural cluster expansion) some molecular properties (heats of formation and magnetic susceptibilities) averaged over these classes. Th e associated proper standard deviations as well as the extremal values for these cluster-expansion approximants are also obtained, and correspondent e xtremal structures are identified. Thence combinatoric techniques to deal n eatly with astronomical numbers (even if greater than a mole) of different molecular structures and some associated physical and chemical properties a re developed.