[CP2K:9757] MGRID vs KPOINTS for small systems

[hut... at chem.uzh.ch]

Hi

I think there is a misunderstanding.
MGRID is a numerical method for efficient integration, whereas
k-points define a specific approximation to your model
Hamiltonian (integration of the Brillouin zone).

An equivalent approximation to k-points would be MULTIPLE_UNIT_CELLS.
For metals and small unit cells I would expect k-points to be more efficient.

best regards

Juerg

--------------------------------------------------------------
Juerg Hutter                         Phone : ++41 44 635 4491
Institut für Chemie C                FAX   : ++41 44 635 6838
Universität Zürich                   E-mail: hut... at chem.uzh.ch
Winterthurerstrasse 190
CH-8057 Zürich, Switzerland
---------------------------------------------------------------

-----cp... at googlegroups.com wrote: -----
To: cp2k <cp... at googlegroups.com>
From: Sebastian Hütter 
Sent by: cp... at googlegroups.com
Date: 12/01/2017 03:17PM
Subject: [CP2K:9757] MGRID vs KPOINTS for small systems

Hi all,

this may be a very entry-level question, but please help me understand something that currently confuses me.

Let's say we want to calculate static energies and forces of a small unit cell (or very few repetitions) of a metallic crystal, much like the "How to Calculate Energy and Forces" howto. I find that there is a large difference between multigrid method and k-point sampling (when parameters of both have been correctly converged). For all systems I tried this on, most individual energy terms are very close, but the "Core Hamiltonian energy" is about 5-10% higher using MGRID than using KPOINTS. From other sources I know the correct cohesive and isolated atom energies, and I find that only k-point sampling returns the correct value.

Example from 1x1x2 cells Al, basis DZVP-MOLOPT-SR-GTH, potential GTH-PBE-q3, PBE exchange-correlation:
    &MGRID
      NGRIDS 4
      CUTOFF 300
      REL_CUTOFF 50
    &END MGRID
  Overlap energy of the core charge distribution:               0.00000000001890
  Self energy of the core charge distribution:                -45.13516668382051
  Core Hamiltonian energy:                                     10.22296505539078
  Hartree energy:                                              25.42600995275711
  Exchange-correlation energy:                                 -6.48331280168588
  Electronic entropic energy:                                  -0.00263408295383
  Fermi energy:                                                 0.23983128515630

  Total energy:                                               -15.97213856029344
vs.
    &KPOINTS
      SCHEME MONKHORST-PACK 17 17 34    ! converged to 5 decimals around 13 13 26
      FULL_GRID T
      WAVEFUNCTIONS COMPLEX
    &END KPOINTS
  Overlap energy of the core charge distribution:               0.00000000001890
  Self energy of the core charge distribution:                -45.13516668382051
  Core Hamiltonian energy:                                      9.67133497320798
  Hartree energy:                                              25.41644035557356
  Exchange-correlation energy:                                 -6.46349454507014
  Electronic entropic energy:                                  -0.00027958913223
  Fermi energy:                                                 0.25517849633624

  Total energy:                                               -16.51116548922202
The total energy of that particular system should be around -16.51 Ha.

Why is that? I would very much like to use the multigrid solution, as it is a lot faster for such systems - but obviously I can't if the results are off. I have read one post here that recommended using k-points for such systems, but not why, and where one could place a limit of usefulness between the two methods (if that is possible).


Thanks in advance,

Sebastian Hütter  
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