The algebraic modelling of chemical structures: On the development of three-dimensional molecular descriptors

Abstract

A novel approach to algebraic modelling of molecular structures is proposed. Structures of molecules are characterized by a single number derived from the topographic (geometric) distance matrix of the molecule. The topographic distance matrix is obtained in the following way. The idealized structure of a molecule is set up and then processed by the molecular mechanics method. This computation gives the optimum (minimum-energy) molecular geometry which is used for computing the topographic distance matrix. The half-sum of the elements of the topographic distance matrix is named the three-dimensional (3-D) Wiener number because of its formal similarity with the twodimensional (2-D) Wiener number which is equal to the half-sum of elements in the graph-theoretical distance matrix. The 3-D Wiener number is used to build, as an illustrative example, the 3-D structure-property model for predicting boiling points of alkanes. The comparison between the models based on the 2-D and 3-D Wiener numbers and the connectivity index is also discussed.