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At normal pressures and temperatures many of the so-called simple metals (especially the alkali class) possess highly symmetric structures, often Bravais lattices, and in these stabilizing arrangements the measure of cell size greatly exceeds the measure of core space size (essentially the fourth moment of the localized charge density). The breaking of such symmetry can become, however, a physical possibility providing first that a condition governing relative core and cell sizes is met (that the ratio actually increases). Under such conditions, brought about at high and nowadays attainable pressures, these systems have been predicted to take up complex structures including those with pairing states for the ions at sufficiently high compressions. An important element in the ensuing electronic structure is the progressive interstitial localization of electrons where associated valence band-widths actually decline with further increase in density. Single-particle densities of states therefore also increase and enhances the prospect of ordering (charge-densitywaves, electron-pairing and superconductivity, ...) in the initiating many-body problem. The quasi-localized valence electron states supplement the localized (and often highly polarizable) core states and together give rise to a reappearance of fluctuating multipole terms emphasizing again the importance of the role of non-locality in the functional approach to their energetics, and hence also to their structural characteristics. Measured high density structures of the alkali metals are especially interesting because of insights gained from them on the manifestation of non-linear response in the valence electron system, and the bearing this has on the relative contributions of the (state dependent) pairand multi-center interactions as they evolve with pressure. * Supported by the National Science Foundation

New shapes in surfactant self-assembly: from soft to stiff structures and from finite to infinite sizes