RealQM 2nd Row of Periodic Table: Na to Argon

We now proceed to the second row of the periodic table where to speed up computation the electrons in inner shells of an atom are homogenised to a common charge density and we keep individual electrons only in the outermost shell acting as the valence shell in formation of molecules by interaction with other atoms. 

RealQM gives the following ground state energies with display of electron distribution over shells from inner to outer:  

• Ne (2+8):                   -128      (-128.5) (code)
• Ne (2+4+4):               -128      (-128.5) (code)
• Na (2+4+4+1):         -161.8    (-162.4) (code)
• Mg (2+4+4+2):         -199.4   (-200.3)  (code)
• Al  (2+4+4+2+1):     -242.4   (-242.7) (code)
• Si  (2+8+4):               -290      (-290)   (code)
• P (2+8+4+1):            -342      (-342)  (code)
• S  (2+8+4+2):          -396      (-399)   (code)       
• Cl (2+8+4+3):         - 461      (-461.4) (code)
• Ar (2+8+8):             -528       (-529)   (code) 
• K (2+8+8+1):          -601      (-602)   (code)
• Xe (2+8+18+18+8) -7458    (-7438) (code)

We see good agreement between RealQM and reference values in parenthesis. 

We see that the number of valence electrons in the outermost shell ranges from 1 to 4  (except for the noble gases Xe), which is different from stdQM with 1 to 8 valence electrons according to the "octet rule". 

We see that the 2+4+4 configuration for Neon gives about the same energy as a 2+8 configuration  suggesting that 4+4 for inner shells is the same as 8.

We note that atoms with 1-2 valence electrons are metals/metalloids and those with 3 are non-metals. This gives a very simple non-standard classification. Metals with 1-2 valence electrons have small ionization energies and those with 3 large ionization energies. 

Molecules naturally form by combining metals with non-metals such as NaCl, which will be explored in an upcoming post. 

In the above computations we have kept a full 3d resolution of all shells, with spherical charge homogenisation of inner shells to speed up. A further speed up opening to large molecules will be made by resolving inner shells in spherical symmetry and only valence shells in full 3d.  

We note that the RealQM is very simple (3 lines essentially) and and as such is essentially ab initio.  We compare with stdQM computations using Hartree-Fock or Density Functional Theory which are very complicated and thus not ab initio. 

PS It is not yet clear exactly when to stop iterations and so the number of iterations can be used to arrive exactly at reference values, if desired. Further study of stop criterion is needed.