General Theory of Pseudopotentials

It has previously been shown that the energy levels of valence electrons in atoms, molecules, and solids can be calculated from a weak net effective pseudopotential $V_p$. In $V_p$ most of the large negative potential energy of an electron, when inside the ion core of an atom, has been canceled against the large positive kinetic energy which the electron has there. It has recently been shown that there are several different forms which the pseudopotential can take. The theory is now developed from a different point of view, and it is shown that there exists an even wider class of pseudopotentials which all give the same valence energy levels. One of these, previously derived as an approximation, is now seen to be an exact form of the pseudopotential. Since it is much simpler and more convenient than other forms, its properties are investigated further with a view to its use for detailed numerical calculations. Finally, it is shown how the pseudopotential can be used not only for calculating valence energy levels, but also for the scattering of electrons by phonons and impurities in solids and by the disorder in liquid metals.