Pseudopotentials, the Sizes of Atoms and Their s—p Splittings

The pseudopotential has made an important contribution to our understanding of the electronic structure of solids. It is here applied to free atoms. The strongly attractive real potential inside the atomic core of completed shells is nearly all cancelled off in the pseudopotential, resulting for instance in 1s-like nodeless pseudowavefunctions for the valence electron in all the alkali atoms. This gives a natural means of comparing atoms from different rows of the periodic table. The method is applied to the sizes of atoms, in particular to the increase of size with row in the periodic table, and the effect of a soft core as in the noble metals. It explains various qualitative trends with row and valency through the periodic table. It also gives an illuminating picture of the s—p energy differences, which determine in large measure the tendency to covalency and other effects in solids.