Application of the ANB-matrices and their Modifications in Mathematical Chemistry

Author: mikheil gverdtsiteli
Co-authors: K.Giorgadze
Keywords: matrix, topologic index, correlation
Annotation:

Among 60 topologic indeces (molecular discriptors) seven are constructed by Georgian mathematical chemistry school. Three topologic indeces, constructed on the basic of ANB-, QANB- and GANB-matrices, are the most efficient. The diagonal elements of ANB-matrix are the atomic numbers of the chemical elements, nondiagonal elements are the multiplicities of the chemical bonds. Within the scope of ANB-matrices method about 60 chemical systems were investigated and about 200 correlation equations are derived. QANB- and GANB- matrices are constructed on the basis of molecular models and it is new approach in mathematical chemistry. The range of GANB- matrix is two and it can be used for ABn type molecules. The first diagonal element is ZA, the second - nZB (thus, n B atoms are considered as one quasi-atom). Monodiagonal elements are n (thus, n simple bonds are considered as one quasi-bond). Within the scope of GANB- matrices method about 20 chemical systems are considered and about 60 correlation equations are derived. All correlations are satisfactory. The results are represented in one small monography, 20 scientific articles and two thesises.