RealQM 1st Ionization Energy of Alkaline Earth Metals

We let RealQM compute the 1st ionization energy of atoms with 2 valence electrons outside an inner shell of radius R (atomic unit) with a net charge of +2 and get the following result with this code + this code:

• R = 0        E = 0.903  Hartree
• R = 0.4     E = 0.711
• R = 0.6     E = 0.509
• R = 0.8     E = 0.373
• R = 1.0     E = 0.270
• R = 1.2     E = 0.192

We compare with the following list values:

• Be            E = 0.4125
• Mg           E = 0.3381
• Ca            E = 0.2707
• Sr             E = 0.2514
• Ba            E = 0.2308
• Ra            E = 0.2336

We see that Be to Ra roughly corresponds to R = 0.7 to 1.1, which can be made more precise by finding the exact R corresponding to a list value such as R =1.0 closely corresponding to Ca. It is also possible to directly let RealQM compute R in spherical symmetry with this code (with spatial scale change of $0.4301$).

The value of this exercise is to show a particular feature of the non-overlapping electron charge densities of RealQM, which makes it possible to model an atom with kernel charge Z only in terms of its V valence electron wave functions/charge densities with support outside a sphere of radius R around the kernel, subject to a kernel charge of Z - V as the net effect outside the sphere of all electrons inside the sphere and the kernel. 

The outside wave functions meet the inner sphere with zero normal derivative as part of the Bernoulli free boundary condition of RealQM.

This opens to very efficient modeling of molecules in terms of only valence electrons as will be demonstrated in upcoming posts.

In StdQM electron wave functions have global support and a reduction to only valence electrons is difficult in terms of   ”electron shielding of the kernel”.