Spin polarized KS with Relax_multiplicity does not converge

[Laura Scalfi]

Dear Cp2k forum,

We are trying to run a graphene sheet with a Fe defect (containing 1 Fe atom and 4 N atoms, 155 atoms in total), using spin polarized Kohn-Sham (UKS). We managed to run fixed multiplicities of 1, 3 and 5 using the keywords UKS and MULTIPLICITY and the orbital transformation algorithm. However, we would like to let the multiplicity relax using RELAX_MULTIPLICITY keyword and we haven’t been able to make any energy calculation converge yet.

We are using DIAGONALIZATION instead of OT, with ADDED_MOS 500 and a Fermi-Dirac smearing with temperature 300 K. As of now we succeded to get convergence for DIAGONALIZATION – using the standard algorithm – (I) without UKS, (II) with UKS and a fixed MULTIPLICITY of 1, and (III) with UKS and RELAX_MULTIPLICITY starting from a multiplicity of 1 (but, however large the RELAX_MULTIPLICITY, we did not observe any switching of spin).

Note that, even for the multiplicity 1, the SCF loop converges on a value higher than one found earlier in the loop (see below), and we therefore are not sure whether we can trust this.

###############################################

SCF WAVEFUNCTION OPTIMIZATION

Step Update method Time Convergence Total energy Change

------------------------------------------------------------------------------

1 NoMix/Diag. 0.40E+00 1.0 0.94554597 -1011.7340994699 -1.01E+03

2 Broy./Diag. 0.40E+00 1.5 0.98949973 -984.4304450815 2.73E+01

3 Broy./Diag. 0.40E+00 1.5 1.00114938 -1018.8335907387 -3.44E+01

4 Broy./Diag. 0.40E+00 1.5 0.75169399 -1001.3444674373 1.75E+01

5 Broy./Diag. 0.40E+00 1.5 0.71210144 -1019.8272742272 -1.85E+01

6 Broy./Diag. 0.40E+00 1.4 0.91325270 -1013.4277794778 6.40E+00

7 Broy./Diag. 0.40E+00 1.4 0.50466440 -1029.6824961219 -1.63E+01

8 Broy./Diag. 0.40E+00 1.5 0.33674220 -1021.0650257790 8.62E+00

...

40 Broy./Diag. 0.40E+00 1.4 0.00002151 -1017.3149228922 1.08E-04

41 Broy./Diag. 0.40E+00 1.4 0.00001546 -1017.3151997206 -2.77E-04

42 Broy./Diag. 0.40E+00 1.4 0.00000072 -1017.3150173627 1.82E-04

*** SCF run converged in 42 steps ***

########################################################

The fixed multiplicity of 3 is very hard to converge (we only managed with specific parameters of Broyden mixing, after 500 iteration steps, and the total spin moment (Mulliken population analysis) was not consistent with the given multiplicity). The RELAX_MULTIPLICITY case, starting from multiplicity 3 or 11, never converges (we set it to 1e-5, but different values up to 0.5 don’t change anything).

We tried Pulay mixing but we got an error of bad conditioning, and Direct_p_mixing seems to worsen the convergence. We also tried using the method OT instead of STANDARD, with CG minimizer or DIIS (as done in a test case with O2), and in all cases it never converged and the OT eigensolver never converged at each step.

Does anyone can suggest other parameters/methods to use or point out if there is a mistake in our simulations? We attach here a typical input file.

Thank you very much,

Sincerely,

Laura

[Marcella Iannuzzi]

Dear Laura

When using diagonalization+smearing the multiplicity is never fixed by default. Are you sure that you are fixing the multiplicity?

The relax_multiplicity makes no sense in this case and probably it is only creating discontinuous changes in the electronic distribution, which prevent the convergence.

Spin polarised systems are notoriously harder to converge.

Often the initial guess has a significant influence on the final result.

In general using mixing it is normal to see lower values in energy along the iterative loop, because the densities used to calculate the hamiltonian are not single solutions of the diagonalization algorithm.

0.40E+00 for alpha is very large, in particular if there are convergence issues

Regards

Marcella

[Maximilian Becker]

Dear Marcella,

Thank you for your help. We have tested the diagonalization + smearing on the O2 molecule and indeed the total spin was free to change. We then ran these settings for our graphene+Fe system and we had unexpected results. Whatever multiplicity we start from (1, 3, 7...) the total spin converged to 0 and also the integrated total spin was close to zero. However, using OT and restricting the multiplicities for each simulation, we find a more stable configuration for the triplet instead of the singlet (-1017.356 Ha versus -1017.345 Ha). In OT we also found non-zero spin density on our Iron atom (0.5) even in the singlet case, while for the diagonalization + smearing we find no spin moment on all atoms. Although our OT results do not include electronic smearing, they seem to agree with other calculations done with VASP. Do you think these qualitatively fairly different results are to be expected and do you have an advice on which ones to trust more?

PS: There is a significant difference in energies between OT and DIAG + smearing ( -1017.345 to -1017.315 ). We assume it is due to the smearing and not beacuse OT finds a more stable configuration. Could you confirm this is true?

PPS : For each step when starting from a triplet, we still got different number of electrons in each channel although the total spin was 0 in the end (Mulliken population analysis), is this a printing error simply?

Spin 1
│

│ Number of electrons:                                                       1123
│ Number of occupied orbitals:                                               1124
│ Number of molecular orbitals:                                              2123
│
│ Spin 2
│
│ Number of electrons:                                                       1121
│ Number of occupied orbitals:                                               1124
│ Number of molecular orbitals:                                              2121
│
│ Number of orbital functions:                                               6651
│ Number of independent orbital functions:                                   6651

Regards,

Max and Laura

[Marcella Iannuzzi]

Dear Max and Laura, 

Using OT the Multiplicity is constraint by the number of electrons assigned to each channel at the very beginning. 

The total energy obtained with smearing contains also the entropic term and cannot be compared directly with the energy obtained without smearing. 

Reducing the temperature of the Fermi-Dirac smearing progressively to a small value, one can estimate the entropic contribution.

If you do not need smearing, you could run only OT calculations with different multiplicities and compare the energies. 

The printed values you report are just taken from the initial settings, i.e. , that value for number of electrons is not calculated on the actual density.

Regards

Marcella