RealQM for Molecules: Valence Electron Reduction

RealQM for molecules can be reduced to detailed 3d model only for the valence electrons by modelling each atom minus its outer valence electron as spherical charge density of a certain radius R + kernel interacting with the valence electrons. 

For example, Sodium Na with 2+8 electrons in two inner shells and 1 valence electron in an outer shell, can be reduced to a net +1 spherical charge density surrounded by a -1 valence electron, thus a reduction from 11 electrons to 1 electron. 

Or Oxygen O can be reduced to a +2 spherical charge density surrounded by 2 valence electrons. An O2 molecule can then be modeled with 2+2 interacting valence electrons.  

What distinguishes an atom is then the radius of the inner spherical electron charge density. 

Dissociation energy (or atomisation energy) of a molecule XY composed of an X and a Y atom can be computed by varying the distance between X and Y from large with the total energy the sum of the energies of X and Y as atoms, to a minimum total energy as the energy of the molecule XY, and the difference between these energies being the dissociation energy. Dissociation energies typically from 0.1 to 0.3 Hartree.

We get the following dissociation energies for XX=X2 molecules with 2 or 1 outer valence electrons with R=0 and typical value R>0: 

• He2 +2kernel  R = 0:           0.1 Hartree    (ref 0.1)      (code)
• O2   +2kernel  R = 1:           0.19 Hartree (ref 0.19)     (code)  
• H2   +1kernel  R = 0:           0.17 Hartree (ref 0.17)     (code)
• Li2  +1kernel  R = 1:           0.05  Hartree (ref 0.04)     (code)
• Na2 +1kernel  R = 1.5:        0.03  Hartree (ref 0.03)     (code) 

In general good agreement, which indicates that indeed full 3d modelling required only for the valence electrons with inner electrons homogenised to spherical charge density + kernel.