Controlling orbital collapse from inside and outside a transition element

We report a study of bimodal behaviour of atomic wavefunctions for a transition element (Cr) and how this behaviour can be controlled and even turned into single-mode character either by (i) varying the effective nuclear charge for nonintegral values, or (ii) placing the atom in a spherical cavity of adjustable radius. Our conclusions have relevance to the emergence of valence instabilities for transition metals in the solid state. Also it is shown that the very existence of the bimodal wavefunctions provides an explanation for the frequently experienced instability of self-consistent field algorithms when a double-valley potential occurs, and suggestions are made on how to improve the numerical procedure for such calculations.