Ionic waves

Adding the contributions from these ionic wave functions to the ground state of the H2 molecule gives... 

The MPIB and VIB [35] models attempt to improve the aeeuraey of the earlier models and to overcome some of the difficulties associated with the use of Hartree-Fock wave functions. We have already stated some of the advantages of using the density functional approach to obtain ionic wave-functions they were amply demonstrated by the PIB model which replaced the Hartree-Fock equation with a density functional implementation of the Dirac equation [21]. The MPIB is so called because it also adopts the density functional approach to obtain ionic charge densities (specifically anon-relativistic version derived from the Herman-Skillman [48],but replaces the potential inside the Watson shell with the spherical average of the potential due to the rest of the material, IF (r)[36] ... 

At very large R, the exact wave function will have one electron near the left proton and one near the right, as in Eq. (19), which we will refer to as the covalent part of the wave function. The other terms of (18) have both electrons near one proton and none near the other, thus creating an ionic wave function. At R = 00, these ionic terms lead... 

To improve further the molecular orbital wave-function, we may invoke configuration interaction (C.I.), i.e. linearly combine the bonding configuration Vab(l)Vab(2) with the antibonding configuration )/ (1) )/ (2). Covalent-ionic resonance improves the Heitler-London valence-bond function, This resonance involves linearly combining the covalent wave-function a(l)b(2) + b(l)a(2) with the wave-functions a(l)a(2) and b(l)b(2) for the ionic valence-bond structures A B" and A B . For Hj, the appropriate ionic wave-function is... 

This identification is based on a simple model for the open-shell ionized system, in which the ionic Hartree-Fock wave function is not allowed to relax upon ionization but is instead constructed from the frozen MOs of the neutral system. A more satisfactory procedure would be to relax the MOs of the ionized system - that is, to calculate the ionic wave function by the standard (open-shell) Hartree-Fbck procedure. This approach is known as the ASCF method since the IPs are obtained as the difference between SCF (Hartree-Fock) energies of the neutral and ionic systems ... 

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