This paper describes a study of the topology of the electron density and its Laplacian for the molecules VF5, VMe(5), VH5, CrF6, CrMe(6), CrOF4, MoOF4, CrO2F2, CrO2F42- and CrOF5- all of which, except VF5, CrF6, and CrOF5- have a non-VSEPR geometry. It is shown that in each case the interaction of the ligands with the metal atom core causes it to distort to a nonspherical shape. In particular, the Laplacian of the electron density reveals the formation of local concentrations of electron density in the outer shell of the core, which have a definite geometrical arrangement such as four in a tetrahedral. arrangement or five in a square pyramidal or trigonal bipyramidal and six in an octahedral arrangement. Ligands that are predominately covalently bonded are found opposite regions of charge depletion between these core charge concentrations. In VH5, VMe(5), CrOF4, and MoOF4, these core charge concentrations have a square pyramidal arrangement, and the regions of charge depletions have the corresponding inverse square pyramidal arrangement so that these molecules have a square pyramidal geometry rather than a trigonal prism geometry. In CrMe(6), there are five core charge concentrations with a trigonal bipyramidal arrangement so that the regions of charge depletion have a trigonal prismatic arrangement and the molecule has the corresponding trigonal prism geometry rather than an octahedral geometry. In contrast, molecules in which the only ligand is the more ionically bound fluorine are less affected by core distortion and have VSEPR-predicted structures. The unexpected bond angles in CrO2F2 and the preference of CrO2F42- for a cis structure are also discussed in terms of the pattern of core charge concentrations.