MGRID vs KPOINTS for small systems

[Sebastian Hütter]

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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