MGRID vs KPOINTS for small systems
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Sebastian Hütter
Dec 1, 2017, 9:17:12 AM12/1/17
to cp2k
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:
vs.
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
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
&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: -16.51116548922202The 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
hut...@chem.uzh.ch
Dec 1, 2017, 9:37:13 AM12/1/17
to cp...@googlegroups.com
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...@chem.uzh.ch
Winterthurerstrasse 190
CH-8057 Zürich, Switzerland
---------------------------------------------------------------
-----cp...@googlegroups.com wrote: -----
To: cp2k <cp...@googlegroups.com>
From: Sebastian Hütter
Sent by: cp...@googlegroups.com
Date: 12/01/2017 03:17PM
Subject: [CP2K:9757] MGRID vs KPOINTS for small systems
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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...@chem.uzh.ch
Winterthurerstrasse 190
CH-8057 Zürich, Switzerland
---------------------------------------------------------------
-----cp...@googlegroups.com wrote: -----
To: cp2k <cp...@googlegroups.com>
From: Sebastian Hütter
Sent by: cp...@googlegroups.com
Date: 12/01/2017 03:17PM
Subject: [CP2K:9757] MGRID vs KPOINTS for small systems
You received this message because you are subscribed to the Google Groups "cp2k" group.
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Sebastian Hütter
Dec 2, 2017, 1:06:39 PM12/2/17
to cp2k
Hi,
thank you. The way I understood it is that to get better results, I can either increase the volume of real-space the integration happens over (MULTIPLE_UNIT_CELLS), or can move to a model in the reciprocal lattice and sample the 1st BZ at high(er) resolution? That means that for such a small system, what I effectively did in my test was the same as if I used a too coarse k-point grid? The thing that confused me was that most energies were very similar, just that one term wildly different.
For my test system, I need 27 supercells to get the kpt energies, but even more for correct stresses - but at about 1/10th the computation time and a little less memory/proc that could be worth it. But now I have all quantities output for the replicated atoms as well, making things a bit harder to use... guess I'll stick with k-point sampling. Is there a break-even point regarding volume or atom/electron count where one method is generally faster than the other?
As a related question, is there a way to specify an M-P grid using point spacing instead of point counts?
Best regards,
Sebastian
thank you. The way I understood it is that to get better results, I can either increase the volume of real-space the integration happens over (MULTIPLE_UNIT_CELLS), or can move to a model in the reciprocal lattice and sample the 1st BZ at high(er) resolution? That means that for such a small system, what I effectively did in my test was the same as if I used a too coarse k-point grid? The thing that confused me was that most energies were very similar, just that one term wildly different.
For my test system, I need 27 supercells to get the kpt energies, but even more for correct stresses - but at about 1/10th the computation time and a little less memory/proc that could be worth it. But now I have all quantities output for the replicated atoms as well, making things a bit harder to use... guess I'll stick with k-point sampling. Is there a break-even point regarding volume or atom/electron count where one method is generally faster than the other?
As a related question, is there a way to specify an M-P grid using point spacing instead of point counts?
Best regards,
Sebastian
hut...@chem.uzh.ch
Dec 4, 2017, 3:33:16 AM12/4/17
to cp...@googlegroups.com
Hi
the actual grid sizes is calculated from the plane wave energy cutoff
and optimal sizes for 3-d FFTs. Defining grid spacings would result
in similar results, but the actual grid spacing in the calculation would
most likely differ from the input.
Energy cutoffs are the standard units for accuracy in electronic structure
calculations.
regards
Juerg
--------------------------------------------------------------
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
---------------------------------------------------------------
-----cp...@googlegroups.com wrote: -----To: cp2k <cp...@googlegroups.com>
Date: 12/02/2017 07:06PM
Subject: Re: [CP2K:9763] MGRID vs KPOINTS for small systems
the actual grid sizes is calculated from the plane wave energy cutoff
and optimal sizes for 3-d FFTs. Defining grid spacings would result
in similar results, but the actual grid spacing in the calculation would
most likely differ from the input.
Energy cutoffs are the standard units for accuracy in electronic structure
calculations.
regards
Juerg
--------------------------------------------------------------
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
---------------------------------------------------------------
Date: 12/02/2017 07:06PM
Subject: Re: [CP2K:9763] MGRID vs KPOINTS for small systems
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