A quest for an optimal missing descriptor is started here, a descriptor that can include information on van der Waals and hydrogen bond interactions. This quest is centered on the construction of special molecular connectivity terms that make use of an empirical parameter, the dielectric constant, and three different "ad hoc" parameters indirectly related to the dielectric constant that should render molecular connectivity terms able to describe also noncovalent interactions. The molar mass Al was also used, as an empirical parameter, to derive molecular connectivity terms strongly related to the mass of the compounds. Derived st semiempirical molecular connectivity terms were used to model 11 different properties of a wide heterogeneous range of solvents. for which chi indices alone and their linear combinations are insufficient descriptors: boiling points. melting points, refractive indices, density, viscosities, flashpoint values, elutropic values, UV cutoff values, dipolar moments, magnetic susceptibility, and the same dielectric constant. Achieved modelings are quite fair, and with the exclusion of the refractive indices all of them needed semiempirical terms. mainly based on supramolecular connectivity indices of different forms. Further, a common term, within the "double sieve" approximation for the melting points, has been detected for the boiling and melting tc temperatures, Two types of valence molecular connectivity indices have been used all along the modeling: chi(y) indices based on delta(v) valence and chi(z) indices based on delta(z) valence numbers. This last kind of chi(z) index plays an important role in X terms for the flashpoints: and melting points only.