Chemical combinatorics for alkane-isomer enumeration and more
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Standard combinatorial enumeration techniques for alkanes are considered with a view to the extension to a widened range of chemically interesting features. As one brief point it is noted that these standard techniques naturally associate to generational schemes and thence have nomenclatural interpretations, which may be made to achieve some similarity to the standard IUPAC nomenclature. Our primary focus is the illustration that such combinatorial techniques are sufficient to enable computation of several graph-theoretic structural invariants averaged over (different types of) isomer classes. Such averages (and associated isomer counts) are tabulated for structural isomers for up to N = 40 carbons, where there are ∼1014 isomers (though the computational methodology should rather readily extend to at least W = 80 where there should be ∼1028 isomers). The averages for invariants are utilized to estimate several physicochemical properties averaged over these same isomer classes. The properties currently so considered are heat of formation, index of refraction, and magnetic susceptibility. Further, various asymptotic results for counts, mean invariants, and mean properties are noted, so that the exact graph-theoretic data are extrapolated with high accuracy to arbitrarily large alkanes.
