The topologically derived, nonempirical molecular connectivity index, chi, for several classes of compounds is shown to be parabolically related to the biological activities of these compounds. Similar nonlinear relationships were previously shown between the octanol-water partition coefficients, expressed as log P, of the compounds and their biological activities. These and previous studies indicate that many physiochemical properties presently used in structure-activity studies may be intermediaries between the nonempirical molecular structure encoded in chi and measured biological activities.