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

Vladimir Rybkin rybk... at gmail.com
Thu Sep 12 10:45:40 UTC 2019

Dear Ron,

regarding the first point. CP2K does spin polarization in molecular quantum 
chemistry style: either with spin-unrestricted KS (UKS, or LSD) or with 
restricted open-shell (ROKS). The first option assumes different (spatial) 
orbitals for different spins: orbitals for alpha- and beta-channels are 
found independently and are in general different. That's why Sz and S^2 are 
no more good quantum numbers. Integrated absolute spin density is 
non-integer. In the ROKS scheme, spatial orbitals are fixed the same so 
that the spin symmetry does not break, but some variational flexibility is 

The RELAX_MULTIPLICITY  keyword means, that CP2K should find the electronic 
state according to the aufbau principle. It does exactly this. The 
MULTIPLICITY 1 message is perhaps a "bug" of the output. It prints the 
default multiplicity (1) rather than the one that it will going to find 
according to aufbau.



среда, 11 сентября 2019 г., 17:37:40 UTC+2 пользователь 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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