Parametric transform and moment indices in the molecular dynamics of n-alkanes

The integrated molecular transform (FT_m) is a unitary numerical index of structure that is capable of uniquely representing different molecular structure conformations with the exception of enantiomers. Other molecular indices have been derived from FT_m as well as from the normalized molecular moment (M_n), for example, the analogous electronic and charge transforms (FT_e and FT_c) and moments (M_e and M_c). In this study, each of these indices was calculated for up to 10 sampled conformations of each of the C₁–C₁₀ normal alkanes as they were subjected to a standard annealing process. Statistical analyses of the resulting data in the individual series and subsequent box plots, permitting facile examination of those results, indicated that the respective transform indices (FT_m, FT_e, FT_c) are unique, that is, with no statistically significantly overlap across the series. For the M_n and M_e indices, the numerical values for methane overlapped those of ethane in the first instance and both ethane and propane in the second. The M_c index values overlapped in several instances in the series. Inasmuch as the noted molecular indices are based only on parameters of structural origin, these results have profound implications for the correlation and estimation of properties derived not only from a general structure representation, but also for those properties which may be dependent on specific molecular conformations. This includes the potential for indices of molecular flexibility and conformationally dependent atomic electron densities. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 1185–1194, 1998