Mathematical chemistry is the area of research engaged in the novel and nontrivial applications of mathematics to chemistry; it concerns itself principally with the mathematical modeling of chemical phenomena.[1] Mathematical chemistry has also sometimes been called computer chemistry, but should not be confused with computational chemistry.
Major areas of research in mathematical chemistry include chemical graph theory, which deals with topics such as the mathematical study of isomerism and the development of topological descriptors or indices which find application in quantitative structure-property relationships; chemical aspects of group theory, which finds applications in stereochemistry and quantum chemistry; and topological aspects of chemistry.
The term was coined in 1970s, although the history of the approach may be traced back into 18th century. Some of the early periodical publications specializing in the field are MATCH Communications in Mathematical and in Computer Chemistry, first published in 1975, and the Journal of Mathematical Chemistry, first published in 1987.
The basic models for mathematical chemistry are molecular graph and topological index
Mathematical Chemistry Research Unit
My interest in mathematical questions from chemistry began in the early 80s from work on the symmetry groups of crystals. Through that work I established scholarly contact with chemists and became invoved with the formation of the Mathematical Chemistry Research Unit at the University of Saskatchewan. The unit is co-directed by Prof. Paul Mezey from the Department of Chemistry and myself. Its purpose is to facilitate collaborative work between mathematicians and chemists.
Asymptotic Properties
One of the current projects of the Mathematical Chemistry Research Unit that is of particular interest to me involves certain asymptotic linearity phenomena observed in the laboratory setting with families of hydrocarbons. The driving force behind this project is Prof. Shigeru Arimoto who has been studying these and related phenomena since 1978 and gave the first proof of the Asymptotic Linearity Theorem in 1987 which is fundamental to elucidate the mechanism of additivity phenomena in physico-chemical network systems. He has formulated the mathematical notion of a Repeat Space which he and collaborators used to explain the observed asymptotic linearities. These results suggested a multitude of other questions which we are investigating. I will sketch the mathematical setting below. Let q and r be fixed natural numbers.
Let Q-r, ..., Q-1, Q0, Q1, ..., Qr be fixed q by q complex matrices which satisfy Q-j* = Qj, for -r < j < r. For each natural number n define the qn by qn block Toeplitz matrix Tn by
Tn= Q0. Q-1 . . . Q-r .0 . . . . . . . . . . . . . 0
Q1. Q0. Q-1 . . . Q-r 0 . . . . . . . . . . .0
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Qr. Qr-1
. 0 . Qr . Qr-1 . . . . . . . . . . Q-r 0 . . 0
-.Journal of Mathematical Chemistry
Publisher Springer Netherlands
ISSN 0259-9791 (Print) 1572-8897 (Online)
Subject Collection Chemistry and Materials Science
Subject Chemistry and Materials Science, Mathematics and Statistics, Chemistry, Physical Chemistry, Theoretical and Computational Chemistry and Math. Applications in Chemistry
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