Recurrent approximation of densities and refractive indices of the homologs of different series

Abstract

Approximation of the refractive indices and relative densities of the homologues of organic compounds, as well as of other physicochemical constants, is possible with the use of linear recurrent relations A(n + 1) = aA(n) + b (A = nD20 or d420, n is the number of carbon atoms in the molecule) not only for a separate homologous series, but also for their combination. The basic problem of this approximation is the estimation of the unknown constants of the highest homologs according to the data for the better described simplest compounds. The accuracy of recurrent estimations for the series with the homologous differences CH2 and, especially, CF2 is higher than at the application of ACD software. Mathematical transformation of initial recurrent relation at the condition a < 1 is reduced to the equivalent equation A(n + 1) = αan + β, where the physicochemical sense of coefficients can be easily interpreted. Similar exponential functions have not been applied earlier to the approximation of the constants of homologs belonging to different series.