The inconsistent temperature dependence of nucleation rates, disagreement of theoretical critical or onset supersaturations with experimental data, and insufficiently accurate predictions of nucleation rates are fundamental problems of the classical nucleation theory (CNT) of water vapors, which is a foundation of various multicomponent nucleation models widely used in the aerosol microphysics, physical chemistry, and chemical technology. In the present study, a correction to the CNT obtained from "first principles" has been derived and significant progress has been made in solving the fundamental problem of predicting nucleation rates of water vapors. The modified model with the quantum-mechanical correction incorporated is in very good agreement with experiments over the full range of temperatures (T=210-290K) , saturation ratios (S=2-100) , and nucleation rates (J= approximately 10{1}-10{17} cm-3).