# MGRID vs KPOINTS for small systems

Sebastian Hütter sebastia... at ovgu.de
Fri Dec 1 14:17:12 UTC 2017

```Hi all,

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).