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Mathematical transformations of recurrent relations for different types of homologues
Author(s) -
Zenkevich Igor G.
Publication year - 2016
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.2796
Subject(s) - homologous series , row , series (stratigraphy) , row and column spaces , mathematics , order (exchange) , combinatorics , basis (linear algebra) , property (philosophy) , pure mathematics , computer science , chemistry , crystallography , geometry , biology , paleontology , finance , database , economics , philosophy , epistemology
Most of discrete properties A of individual organic compounds belonging to single‐row homologous series ( RX → RCH 2 X → … → R ( CH 2 ) n X ) or multi‐row series ( R k Y → [ RCH 2 ] k Y → … [ R ( CH 2 ) n ] k Y , k > 1) can 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). Copyright © 2016 John Wiley & Sons, Ltd.