Approximation of physicochemical properties of homologs using recurrent and related non-recurrent relations

• Published in: Journal of chemometrics 2012-03, Vol.26 (3-4), p.108-116
• Main Author: Zenkevich, Igor G.
• Format: Article
• Language: English
• Subjects: Approximation; Atoms & subatomic particles; chemical applications; Chemical compounds; homologs; limiting values; Molecules; Organic chemistry; organic compounds; predicting constants for low-stability compounds; recurrent relations; related non-recursive equations; values of physicochemical properties
• ISSN: 0886-9383; 1099-128X
• DOI: 10.1002/cem.1419

A number of updatings, both recurrent and non‐recurrent, can be suggested for recurrent relations A(n) = aA(n − 1) + b recently introduced into chemistry. Among them, the equation A(n) = a[A(n − 1) − A∞] + A∞, where A∞ denotes the limiting values of a physicochemical property at the number of carbon atoms in the molecule hypothetically tending to infinity, appears to be the most convenient and precise. The application of the new relations to evaluating the refractive indices, relative densities, and normal boiling points as examples is considered. The problem of evaluating the limiting values of various physicochemical properties, discussed in chemistry for a long time, should be reconsidered as going beyond pure theory. The concept becomes very important for real evaluation of properties of organic compounds, A(n). The application of recurrent relations simplifies the evaluation of the values of physicochemical properties of organic compounds. This problem seems to be the most important for low‐stability organic compounds, where only single homologs are properly characterized, whereas the experimentally determined properties for the most of them are lacking. Copyright © 2012 John Wiley & Sons, Ltd. Linear recurrent relations A(n) = aA(n−1) + b recently introduced into chemistry provide precise evaluation of the values of most of physicochemical properties of homologs using the data from previous members of series. A number of updatings can be suggested for these recurrences. The equation A(n) = a[A(n−1) − A¥] + A¥, where A¥ denotes the limiting value of physicochemical property at the number of carbon atoms in the molecule hypothetically tending to infinity, appears to be the most convenient.