Simple Approximation of Any Constants of Homologues Using Single Recurrent Function

摘要

The dependencies of various physicochemical constants of organic compounds (A) vs. number of carbon atoms in the molecule within homologous series [A = f(n_C)] are non-linear. However the simplest recurrent equation A(n+1) = a A(n) + b, connecting any A-values for homologues with the values of the same constants for previous members of series, indicates practically 'ideal' linear character for most of all known properties of organic compounds. This fact permits us to approximate (or to extrapolate) any physicochemical data within any homologous series using the standard approach without special search of complex algebraic functions. Principal mathematical properties of the function A(n+1) = a A(n) + b are considered.