[CP2K-user] Spin Polaization in Kohn-Sham calculations

[Ronald Cohen]

I do not understand the way CP2K does spin-polarized Kohn-Sham. What ought 
to be done in a crystal
is to have spin up and down channels (called alpha and beta in cp2k), solve 
them in their separate LSDA (or GGA) potentials for each k-point,
find a common Fermi level by integrating the charge to the correct number 
of electrons, compute the new charge and spin densities, 
compute the new spin dependent potential, and iterate. In an insulator one 
should obtain an integer integrated spin, since each spin polarized band 
holds 1
electron. However, in cp2k for insulating O2 (in a cage) , for example, I 
find a converged integrated spin density of 

  Integrated absolute spin density  :                               
2.0381878543

instead of 2. 


In cp2k, one enters a MULTIPLICITY and RELAX_MULTIPLICITY, and I find 
disconcerting messages like: 

Spin 1
 Re-scaling the density matrix to get the right number of electrons for 
spin 1
                  # Electrons              Trace(P)               Scaling 
factor
                           39                40.000                        
0.975

 Spin 2
 Re-scaling the density matrix to get the right number of electrons for 
spin 2
                  # Electrons              Trace(P)               Scaling 
factor
                           37                36.000                        
1.028

There should be nothing like this.

If I do not enter the MULTIPLICITY key word I do not see this message,
but instead see:

Multiplicity                                                             1

and the resulting integrated spin is similar but not identical:

  Integrated absolute spin density  :                               
2.0411999533

Any clarification would be greatly appreciated. I cannot find an 
explanation in the docs.

Sincerely,

Ron

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