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

A novel molecular polynomial, P-x(G, x), representing the connectivity between all pairs of atoms in a molecule is introduced. The connectivity index X is obtained directly from the first derivative of this polynomial, P'(x)(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, P'(x)(G, x not equal 0). Significant improvements compared to the X index are obtained when the novel descriptors are used in QSPR studies. The physicochemical and structural interpretations of these indices are also advanced. (C) 1999 Elsevier Science B.V. All rights reserved.