The valence connection index delta (v)(i) is not suitable for the inorganic compounds that have complicated oxidation states (for example, S2- S-0 S2+ S4+ S6+) and the organic compounds that include many types of heteroatoms such as F, Cl, Br, I, O, S, N, etc. In order to circumvent this problem, we defined the valence connection index delta (v)(i) of heteroatoms. It is discovered that the scope of vertex valence, delta (v)(i) is affected not only by the nature of the heteroatoms i (through the main quantum number n(i), the family number N-i: the number of Valence electrons Z(i), etc), but also by the conditions under which the bond is formed (through the binding hydrogen atom number h(i) and other atom number m(i), hybridization mode L-p, etc). delta (v)(i) has explicit physical meanings, and shows linear relationship with Pauling electronegativities. By using the novel index of vertex, different hybridization states for the same atom can be distinguished. The improved Molecular topological index (n)chi (h) (n = 0, 1, 2) is defined delta (v)(i) the (1)chi (h) of ClmSi(OR)(n) (m + n = 4) halogeno-benzene and halogeno-phenol, (n)chi (h) (n = 0, 1, 2) of nitrogen-containing heterocycles and derivatives of alkanes. By using these (n)chi (h)'s, good results have been obtained in predicting the physicochemical properties and biological activities (toxicity) of organic compounds. The results are much better than those of the topological (1)chi (v) and (1)chi (-) which are formed by delta (v)(i) and delta (i) (-). It has been demonstrated that (n)chi (h) is clear in physical meaning and easy to compute.
