Hellmann-Feynman and Virial Theorems in the X α Method

Abstract

It is proved that the Xα method leads rigorously to the Hellmann‐Feynman and virial theorems. The proof of the virial theorem is general, not limited to the scaling argument used in earlier discussions. These proofs hold only if α is a constant, independent of nuclear positions. If α has one value inside one atomic sphere, another in another sphere, there are small correction terms, so that if one wishes the theorems to be rigorously applicable, it is best to use the same α everywhere. Discussion of the van der Waals force indicates that the Xα method should give a satisfactory treatment of this force.