Monopole electron-density deformations for first-and second-row atoms are obtained using Hirshfeld partitioning of near Hartree-Fock-limit electron densities for 28 diatomics. The k-refinement model [Coppens, Guru Row, Leung, Stevens, Becker & Yang (1979). Acta Cryst. A35, 63-72] is applied to these monopole deformations and its success in modelling them is gauged by means of deformation radial distribution plots, r2 DELTA-rho-(r), and kappa-and charge-transfer values. The kappa-refinement procedure proves to be remarkably successful in modelling the monopole deformations in this work. This in large part explains the successful application of the kappa-refinement model to X-ray diffraction data, where it is capable of yielding an excellent point-charge model of the electrostatic potential in molecules and crystals.