[CP2K-user] [CP2K:22244] Calcite crystal RPBE force convergence

['Kit Joll' via cp2k]

Dear CP2K developers,

I am writing to ask for advice on a reproducible force-consistency issue 
that we see for bulk calcite, CaCO₃, using CP2K/Quickstep GPW.

For a periodic cell at zero external electric field, the sum of the forces 
over all atoms should vanish to the accuracy of the force evaluation, even 
when the geometry is not relaxed. For the same 30-atom calcite frame, 
Quantum ESPRESSO gives a net force sum close to numerical zero, whereas 
CP2K gives a residual of order 1e-4 Ha/Bohr. In the attached representative 
CP2K output, for example, the force sum is

Fx = 3.49e-5 Ha/Bohr
Fy = 1.13e-4 Ha/Bohr
Fz = -5.39e-5 Ha/Bohr

with a total net force of about 1.30e-4 Ha/Bohr.

This residual is small compared with typical individual atomic forces, but 
in our tests the same force-consistency issue contaminates finite-field 
response properties. Our intended workflow requires numerical derivatives 
of the forces with respect to external electric-field components, for 
example for atomic polar tensors and related higher-order response 
quantities. Other systems, including bulk water, transition-metal 
oxide/water interfaces, and cation solutions, behave well with the same 
CP2K finite-field workflow, so the problem appears to be specific to CaCO₃, 
or to this particular combination of pseudopotential, Gaussian basis, and 
GPW grid.

The attached figure shows cutoff convergence for the energy per atom and 
for the zero-field net force sum. The top row is CP2K, using fixed 
REL_CUTOFF = 120 Ry and NGRIDS = 4 while varying the MGRID CUTOFF. The 
bottom row is Quantum ESPRESSO for the same structure. I include the QE 
result mainly as a translational-invariance sanity check, not as a strict 
force reference, since the pseudopotentials are different. QE gives a 
near-zero net force sum across the tested cutoffs, while CP2K retains a 
much larger residual. The CP2K energy also shows noticeable oscillations 
with increasing MGRID cutoff, which makes me suspect a grid/multigrid or 
Gaussian-grid-coupling contribution, although I am not sure.

Could you advise which CP2K settings or tests would be most appropriate to 
diagnose this? In particular, I would be grateful for advice on whether 
this could be related to any of the following:

   - 
   
   the Ca/O/C pseudopotentials or basis sets, and their use with RPBE;
   - 
   
   GPW multigrid effects or Gaussian-grid coupling;
   - 
   
   Pulay/grid force terms;
   - 
   
   CUTOFF, REL_CUTOFF, NGRIDS, or less obvious QS thresholds;
   - 
   
   SCF/OT convergence settings.
   
The attached input uses TZV2P-MOLOPT-PBE-GTH basis sets, GTH-PBE 
pseudopotentials, RPBE, EPS_SCF = 1e-9, OUTER_SCF EPS_SCF = 1e-9, 
EPS_DEFAULT = 1e-18, OT/CG with 3PNT line search, CUTOFF = 2500 Ry, 
REL_CUTOFF = 120 Ry, and NGRIDS = 4.

I have attached a representative CP2K input/output pair for one frame. The 
same qualitative behaviour is observed across the other tested calcite 
geometries.

Thank you very much for your time. I would really appreciate any 
suggestions for further tests or settings to try.

Best wishes,
Kit

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