Overall connectivities/topological complexities: A new powerful tool for QSPR/QSAR

Earlier attempts to assess the complexity of molecules are analyzed and sum marized in a number of definitions of general and topological complexity. A concept which specifies topological complexity as overall connectivity, an d generalizes the idea of molecular connectivities of Randic, Kier, and Hal l, is presented. Two overall connectivity indices, TC and TCl, are defined as the connectivity (the sum of the vertex degrees) of all connected subgra phs in the molecular graph. The contributions to TC and TCl, which originat e from all subgraphs having the same number of edges e, form two sets of et h-order overall connectivities, (TC)-T-e and (TCl)-T-e. The total number of subgraphs K is also analyzed as a complexity measure, and the vector of it s eth-order components, K-e, is examined as well. The TC, TCl, and K indice s match very well the increase in molecular complexity with the increase in the number of atoms and, at a constant number of atoms, with the increased degree of branching and cyclicity of the molecular skeleton, as well as wi th the multiplicity of bonds and the presence of heteroatoms. The potential of the three sets of eth-order complexities for applications to QSPR was t ested by the modeling of 10 alkane properties (boiling point, critical temp erature, critical pressure, critical volume, molar volume, molecular refrac tion, heat of formation, heat of vaporization, heat of atomization, and sur face tension), in parallel with Kier and Hall's molecular connectivity indi ces (k)chi. The topological complexity indices were shown to outperform mol ecular connectivity indices in 44 out of the 50 pairs of models compared, i ncluding all models with four and five parameters.