Force constants and electron density distributions in coordination polyhedra in molecules and crystals are modeled using Hartree-Fock molecular orbital methods. Model bond-stretching force constants calculated for coordination polyhedra in a series of nitride, oxide and sulfide molecules are ~ 10-20% larger than obtained with spectroscopic methods. Well-developed correlations obtain between the force constants and minimum energy bond lengths, effective nuclear charges and polyhedral compressibilities of molecules and crystals. Model electron density distributions calculated for a large number of molecules with MOn (n = 1, 2,3,4 or 6) coordination polyhedra show that the MO bonds of a given type vary in a regular way with the value of the electron density at bond critical points, bonded radii and the curvatures of the electron density. The bonded interactions in the polyhedra are examined in terms of criteria set forth by Bader and Essen (1984) and Cremer and Kraka (1984).