Spin Polaization in Kohn-Sham calculations

Ronald Cohen

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Sep 11, 2019, 11:37:40 AM9/11/19

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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

Vladimir Rybkin

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Sep 12, 2019, 6:45:40 AM9/12/19

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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 lost.

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.

Yours,

Vladimir

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

Ron Cohen

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Sep 12, 2019, 7:04:56 AM9/12/19

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Yes, but unfortunately it seems the results are wrong. The spin-polarized kohn-sham equations are not solved using UKS and RELAX_MULTIPLICITY. For an insulator the integrated spin must be an integer, but it is not in cp2k. The results obtained with quantum espresso for the same system are as expected. It is an insulator with integrated spin exactly 2.0, but cp2k gives 2.04. If the ks equations are not being solved, it is not a dft calculation, and the solution is not the minimum energy solution.

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Ronald Cohen

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Sep 12, 2019, 7:12:02 AM9/12/19

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I do not understand how you get a non-integer spin if you fill states one electron at a time for up and down states. Perhaps I do not understand ‘Integrated absolute spin density is non-integer.’ Thank you,

Ron

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> On Sep 12, 2019, at 06:45, Vladimir Rybkin <rybk...@gmail.com> wrote:
>

hut...@chem.uzh.ch

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Sep 12, 2019, 7:15:37 AM9/12/19

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Hi

as Vladimir wrote, the value printed is the integrated ABSOLUTE
spin value. The integrated spin value is integer and given by
construction. The printed absolute value gives additional information
on localization of the different spins.

regards

Juerg Hutter
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Juerg Hutter Phone : ++41 44 635 4491
Institut für Chemie C FAX : ++41 44 635 6838
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Date: 09/12/2019 01:12PM
Subject: Re: [CP2K:12210] Re: Spin Polaization in Kohn-Sham calculations

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Ronald Cohen

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Sep 12, 2019, 7:22:10 AM9/12/19

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Oh I understand. Of course that need not be integer. So the printed multiplicity when relax multiplicity is on is incorrect. What about the number of electrons? It prints a renormalization when Multiplicity =3 and also shows the same number of up anddien when multiplicity =1 even with relax multiplicity on. I can send that output if you like. Thank you! Ron

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hut...@chem.uzh.ch

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Sep 12, 2019, 7:29:10 AM9/12/19

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Hi

the renormalization is just information from the initial guess.
The superposition of atomic densities can result in initial
densities that are not representing the requested spin state.
A rescaling is used to fix that. As you can see in the output, all
of this happens before KS interations start.

regards

Juerg Hutter
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Juerg Hutter Phone : ++41 44 635 4491
Institut für Chemie C FAX : ++41 44 635 6838
Universität Zürich E-mail: hut...@chem.uzh.ch
Winterthurerstrasse 190
CH-8057 Zürich, Switzerland
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Date: 09/12/2019 01:22PM
Subject: Re: [CP2K:12212] Re: Spin Polaization in Kohn-Sham calculations

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Ronald Cohen

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Sep 12, 2019, 8:21:19 AM9/12/19

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Dear Juerg,

Thank you so much. Here is what I get using the latest version on github:

When I have in the input:

UKS T

# MULTIPLICITY 3

RELAX_MULTIPLICITY 3

&KIND O2

BASIS_SET DZVP-MOLOPT-GTH-q6

ELEMENT O

POTENTIAL GTH-PBE-q6

&POTENTIAL

2 4

0.2445543000000000E+00 2 -0.1666721480000000E+02 0.2487311320000000E+01

2

0.2209559200000000E+00 1 0.1833745811000000E+02

0.2113324700000000E+00 0

&END POTENTIAL

MAGNETIZATION 2

&END KIND

The output shows:

DFT| Multiplicity 1

DFT| Number of spin states 2

Spin 1

Number of electrons: 38

Number of occupied orbitals: 38

Number of molecular orbitals: 40

Spin 2

Number of electrons: 38

Number of occupied orbitals: 38

Number of molecular orbitals: 40

Number of orbital functions: 210

Number of independent orbital functions: 210

and this number of electrons is repeated, even though there is a moment:

grep -B 3 "Number of electrons:" Opt.out

Spin 1

Number of electrons: 38

--

Spin 2

Number of electrons: 38

--

Spin 1

Number of electrons: 38

--

Spin 2

Number of electrons: 38

--

Spin 1

Number of electrons: 38

--

Spin 2

Number of electrons: 38

--

…

When I have this in the input:

UKS T

MULTIPLICITY 3

RELAX_MULTIPLICITY 3

I see:

DFT| Multiplicity 3

DFT| Number of spin states 2

and

grep -B 1 -A 2 "Re-scal" Opt.out.1

Spin 1

Re-scaling the density matrix to get the right number of electrons for spin 1