Modeling of the relationship between the structure and physico-chemical properties of hydrocarbons based on spectral graph theory

Medvedev D.Y., Skvortsova M.I., Solomonova E.V.

MIREA - Russian Technological University (M.V. Lomonosov Institute of Fine Chemical Technologies), 86 Vernadsky Ave., Moscow, 119571, Russia Medvedev Dmitry Yurievich, e-mail: Skvortsova Maria Ivanovna, e-mail: Solomonova Ekaterina Valeryevna, e-mail:

The problem of mathematical modeling of the relationship between the structure and properties of chemical compounds is the most important task of modern theoretical and computer chemistry. The main purpose of constructing such models is to predict the properties of chemical compounds directly by their structure, using the resulting equation, bypassing the experiment. Most often in such studies, molecules are represented in the form of graphs, and invariants of these graphs are used to quantitatively describe the structure of molecules. It should be noted that in this case, problems arise in choosing the method of constructing molecular graphs, their invariants, as well as the type of equation describing the structure-property relationship from an infinite set of possible options.

It is shown that for a number of physico-chemical properties of alkanes (boiling point, molar volume, molar refraction, heat of vaporization, critical temperature, critical pressure, surface tension), sufficiently accurate structure-property coupling models can be constructed, in which only spectral type invariants calculated as molecular parameters are used. for the corresponding molecular graphs. These invariants are defined using some symmetric functions of the eigenvalues of certain graph matrices. In particular, adjacency, distance, Kirchhoff, etc. matrices are considered as such matrices. Both linear and nonlinear models are constructed for matrices of each type. It is established that the best result in such modeling is given by the adjacency matrix of the graph. Based on the statistical analysis of the frequency of occurrence of various invariants in the constructed correlations, the most "popular" parameters are identified and a qualitative explanation of these facts is proposed. In addition, it is shown that the use of all invariants of all the considered matrices for constructing correlations simultaneously makes it possible to improve the results obtained for each matrix separately.

The proposed approach to the construction of "structure-property" correlations allows generalization by expanding the list of both spectral invariants used and molecular graph matrices. The developed method of modeling the structure-property relationship can be applied to organic compounds of any class and any properties measured quantitatively.


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