Generalisation of the viril theorem and related theorems for jellia with arbitrary background densities and application to special geometries and profiles. II. Application to spherical shell, plane slab and void; work function

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Abstract
For pt.I see ibid., vol.15, p.4807 (1982). Starting from the virial and Budd-Vannimenus theorems for electrons bounded by a jellium background of constant density within an arbitrary volume, the special case of a spherical jellium shell is considered. Two limits are treated: a plane slab and a spherical void. In both cases kinetic and potential energy- and via these quantities also momentum and pair distribution-are related to each other and to the total charge distribution. From the case of a plane slab a further limit, the semi-infinite jellium, is obtained. Surface theorems, connecting the surface energy with certain semi-moments of the total charge density or of the electrostatic potential inside the jellium, are derived. With the help of the generalised Budd-Vannimenus theorem, expressions for the work function of a sample with arbitrary geometry and especially of a plane slab are derived.