Future prospects for the Xα method

Abstract

Recent work to eliminate the effect of the muffin-tin approximation has shown that this makes an important improvement in Xα results for diatomic molecules, though it is less important for atoms with many neighbors. Various aspects of the Xα method itself, not involving the muffin-tin approximation, are discussed. It is pointed out that for the Hellmann Feynman and virial theorems to hold for the Xα method, with α's varying from one atom to another, it is sufficient if the α's change values from those appropriate to one atom to those for another on the surfaces of spheres small enough so that the charge density is practically constant over the surface of such a sphere. This means that the spheres should be smaller than those usually used for the muffin-tin method. It is shown that one can get approximately the correct exchange correlation for any atom, except the very lightest ones, if a value of α equal to 0.7772 is used within a sphere of radius rα, somewhat smaller than the radius of maximum radial charge density in the L shell, and a value of 2/3 is used everywhere outside these spheres. Except for the very light atoms, this would fulfill the requirements for the Hellmann Feynman and virial theorems to hold. There is a discussion of spin polarization in molecules. The value of 0.7772 for hydrogen would imply that it is to be treated in a spin-polarized way, which would imply that an antiferromagnetic type of structure for the H2 molecule, somewhat similar to that proposed many years ago by Coulson and Fischer, should be used. Some magnetic problems are discussed, and in particular a procedure is outlined for using the Xα method to find the Heisenberg exchange integral in an antiferromagnetic substance like NiO. Calculations of this quantity have not yet been completed.