Total and Local Quadratic Indices of the Molecular Pseudograph's Atom Adjacency Matrix: Applications to the Prediction of Physical Properties of Organic Compounds

Molecules

关键词: Molecular Vector Space;    Total and Local Quadratic Index;    QSPR;    Physical Property;    Organic Compound;   

DOI  :  10.3390/80900687

来源: mdpi

【 摘 要 】

A novel topological approach for obtaining a family of new molecular descriptors is proposed. In this connection, a vector space E (molecular vector space), whose elements are organic molecules, is defined as a “direct sum“ of different ℜi spaces. In this way we can represent molecules having a total of i atoms as elements (vectors) of the vector spaces ℜi (i=1, 2, 3,..., n; where n is number of atoms in the molecule). In these spaces the components of the vectors are atomic properties that characterize each kind of atom in particular. The total quadratic indices are based on the calculation of mathematical quadratic forms. These forms are functions of the k-th power of the molecular pseudograph's atom adjacency matrix (M). For simplicity, canonical bases are selected as the quadratic forms' bases. These indices were generalized to “higher analogues“ as number sequences. In addition, this paper also introduces a local approach (local invariant) for molecular quadratic indices. This approach is based mainly on the use of a local matrix [M^k(G, F_R)]. This local matrix is obtained from the k-th power (M^k(G)) of the atom adjacency matrix M. M^k(G, F_R) includes the elements of the fragment of interest and those that are connected with it, through paths of length k. Finally, total (and local) quadratic indices have been used in QSPR studies of four series of organic compounds. The quantitative models found are significant from a statistical point of view and permit a clear interpretation of the studied properties in terms of the structural features of molecules. External prediction series and cross-validation procedures (leave-one-out and leave-group-out) assessed model predictability.

【 授权许可】

CC BY   
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.