Confined systems within arbitrary enclosed surfaces

A new model of electronic confinement in atoms and molecules is presented. This is based on the electronic flux J which is assumed to vanish on some no- tional bounding surface of arbitrary shape. J is necessarily calculated using an approximate wave-function, whose parameters are chosen to satisfy the required surface conditions. This model embraces the results of all previous calculations for which the wave-functions or their derivatives vanish on conveniently-shaped surfaces, but now extends the theory to more general surfaces. Examples in- clude one-centre hydrogen-like atoms, the valence state of Li and the two centre molecular systems H2+ and HeH++ .