Stability,continuity, and symmetry of variational wave-functions

Interrelations between the local and the global aspects of the stability, continuity, and symmetry properties of variational wave-functions are discussed. The spherical limit of one-electron diatomic molecules and the Hartree–Fock approximation of the ground state of the two-electron atom are shown to exhibit the various concepts involved in an ab initio, yet sufficiently simple, manner.