Formula periodic table for acyclic hydrocarbon isomer classes: combinatorially averaged graph invariants

Abstract

The overall isomer classes of acyclic hydrocarbons C_nH_2m with classical valence structures can be presented in the form of a formula “periodic table’' with n and m identifying rows and columns, respectively. Such a table may be used to reflect property trends of isomer classes. A general approach is presented for obtaining isomer-class averages of specified molecular properties, and the approach is extended to deal with mean square-deviations, so as to estimate the property overlap between the different isomer classes. Here the properties considered include graph diameters, molecular branching, counts of bonds of different multiplicities, and counts of sites of different hybridizations. Contour plots in the “periodic table’' illustrate overall property trends for families of up to about 10¹² structural isomers (as arise for isomer classes of up to n=25 carbon atoms). Evidently, an overall view of various property trends of acyclic hydrocarbon isomer classes is possible.

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