Mathematical transformations of recurrent relations for different types of homologues

Abstract

Most of discrete properties A of individual organic compounds belonging to single-row homologous seriescan be approximated with first order linear recurrent relations A(n + 1) = aA(n) + b. The important chemical property of recurrences is the equality of coefficients a and b for various homologous series of similar topology (with the same homologous differences at the constancy of the number of rows). The values of coefficients a and b for single-and multi-rows series even with the same structural fragments X = Y are different.The algorithm of the mutual recalculating of the coefficients of recurrent relations for single-and multi-rows homologous series is proposed and considered. It allows evaluating different physicochemical properties of insufficiently characterized unsymmetrical organic compounds with different alkyl substituents, like C 2 H 5 NHC 3 H 7 , (CH 3 ) 2 B(C 2 H 5 ), (CF 3 )N(C 2 F 5 ) 2 , etc., using the data for better characterized "symmetrical" homologues (illustrated by examples).