Connectivity polynomial and long-range contributions in the molecular connectivity model

A novel molecular polynomial, Pχ(G, x), representing the connectivity between all pairs of atoms in a molecule is introduced. The connectivity index χ is obtained directly from the first derivative of this polynomial, Pχ′(G, x=0). A series of descriptors containing contributions coming from non-bonded atoms in the molecule is derived by variation of x in the polynomial, Pχ′(G, x≠0). Significant improvements compared to the χ index are obtained when the novel descriptors are used in QSPR studies. The physicochemical and structural interpretations of these indices are also advanced.