The model Hamiltonian describing the partially delocalized f-electron system has been generalized to include both hybridization and band-f exchange Coulomb interaction. A method has been developed to calculate the parameters appearing in such a model Hamiltonian from first principles. This enables us to calculate f-electron-based electronic and magnetic phenomena of pertinent materials on a quantitative basis. Calculations have been done for cerium monopnictides and monochalcogenides. Results are in agreement with experiment on various unusual behaviors of these materials, such as anomalous crystal-field splitting and anisotropic magnetic ordering, all of which are caused by the interactions between f electrons and band electrons. In contrast to the earlier version of this theory that included only hybridization effects and produced range parameters (two-ion ''exchange'' coupling) that failed by an order of magnitude in matching the phenomenologically determined parameters which provide agreement with experiment, the present first-principles theory calculations which also include band-f Coulomb exchange provide excellent agreement with the phenomenologically required magnitude.