Application of recurrent relations in chemistry

Abstract

AbstractAs it was previously demonstrated, mathematical properties of simplest first‐order recurrent relations A(n + 1) = aA(n) + b provide important advantages at their applications in chemistry, namely in the approximation of monotonous variations of different physicochemical properties of homologues of various series of organic compounds. Besides that it was empirically revealed the unique ‘chemical’ property of recurrences that is the application of single equations of this kind to constants of different series. To explain this high ‘approximating ability’ of recurrences it was proved first time that numerical sequences that obey high‐order recurrence in a limiting case can be approximated by first‐order recurrence. Consequently, this fact explains us the existence of close analogy between first‐order recurrent approximation of recursive numerical sequences (Fibonacci, Padovan, Lucas and Perrin sequences are considered as examples) and physicochemical constants of homologues. This analogy is considered as not ‘chemically’ correct proof, but reasonable explanation of the applicability of single recurrent equations to constants of different homologous series. The mentioned properties of recurrences seem to be the reason of their high approximating ability in relation to different chemical variables. Recurrent relations can be recommended as universal approach in processing of not only various sets of physicochemical constants of homologues, but also properties or processes characterized by equidistant values of arguments. Copyright © 2010 John Wiley & Sons, Ltd.