Index method of finding the independent routes of complex chemical reactions

Abstract

The route is a vector such that multiplication of its components by the corresponding step of the complex reaction mechanism with subsequent summation of the steps leads to the overall reaction equation that does not contain intermediates [1].The concept of "reaction route" has been intro duced in classical works by J. Horiuti [1] and M.I. Temkin [2] while developing a steady state reac tion theory. The route theory played an important role in construction of complex reaction kinetics theory [2]. The concept of "route" and its application have again attracted much attention in analysis of complex reactions of metal complex catalysis [3].When formulating the steady state reaction theory, Temkin [2] has suggested graphical interpretation of the complex reaction mechanism. This approach has been used for exclusion of intermediates and con struction of general kinetic equations for the cases when the stationarity equation set is linear with respect to the intermediates. This is the case when all elemen tary reactions are first order in intermediates. This "linearity" has considerably limited the application of the graph theory.A general description of chemical reaction schemes based on the graph theory has been intro duced by A.I. Volpert [4]. A specific feature here is the fact that all results can be used for arbitrary nonlinear reaction mechanisms.Real complex reaction mechanisms often involve a large number of substances and reactions between them [5]. Intermediates are formed and consumed in the course of reaction. At the initial instant of time, their concentrations are zero. The vertex index is the minimum order of the derivative with respect to con centration nonzero at the initial instant of time [4]. In other words, information on indices characterizes intermediates on the basis of the rate of their involve ment in the course of a complex reaction.Any of the sets found according to the algorithm described in [2] can be selected as the route basis. A question arises as to how to select a route basis each component of which is characterized by a part of a complex reaction mechanism that has physicochemi cal meaning. In this context, the rate of involvement of a substance in the reaction provides important specific information for selection of the basic route. This can be of importance for finding a unique solution of inverse problems of identification of complex reaction mechanisms [6].This brings up a question of constructing algo rithms for route selection based on information on vertex indices. The present study is aimed at creating an algorithm for independent route basis selection, using the information on vertex indices of the chemi cal reaction graph. The major result is one to one cor respondence between the graph cycles and index matrix. Thus, taking into account the theorem relating the route basis and the cycle basis [7] leads to the appropriate algorithm.Let us describe the algorithm of searching for inde pendent routes and deriving overall equations of com plex chemical reactions.(1) Construction...