Investigation of Dimerization Reaction of Ethylene within the Scope of Quasi-ANB-Matrices Method

Author: mikheil gverdtsiteli
Co-authors: -
Keywords: ethylene, dimerization, cyclodimerization
Annotation:

The schemes of dimerization and cyclodimerization reactions of ethylene are: 2CH2=CH2  – CH2 – CH2 – CH2 – CH2 – (1) For investigation of chemical reactions in mathematical chemistry the method of quasi-ANB-matrices ( ) is efficiently used. Quasi-ANB-matrix is modified contiguity matrix of molecular graph. Its diagonal elements are the sum of atomic numbers of the elements, which structural fragments contain; nondiagonal elements are the multiplicities of the chemical bonds between these structural fragments. Thus, quasi-ANB-matrix can be constructed on the basis of molecular model, that is exceptional case in mathematical chemistry. The simplest model is elaborated for (1) reaction: 2A = A  A – A – A – A (3) where: A = CH2. (4) represents this reaction in the form of -matrices: Consider the expression: r = f – i (5) where: r is the change of determinant of -matrices during the reaction; f – the determinant of -matrix for final state; i – for initial state. For (4) r >0. The value of  is proportional to the complexity of the system.   comp.M (6) So, the reaction of ethylene dimerization (1) proceeds with the increase of the complexity of the system. This result is general for addition reaqctions.