[CP2K-user] [CP2K:22255] Calcite crystal RPBE force convergence
Thomas Kühne
tkuehne at gmail.com
Wed May 27 22:27:23 UTC 2026
Dear Kit,
thank you for the additional finite-field checks. Your observation was exactly the useful diagnostic: the
residual is odd in the applied field, proportional to the field strength, and parallel to the field direction.
This points to the periodic Berry-phase electric-field force contribution rather than to the GAPW_XC
grid issue.
I have prepared a CP2K patch that enforces the acoustic sum rule on the isolated periodic electric-field
force contribution for neutral periodic cells. With your +1.25e-4 a.u. calcite case, the force sum changes
from
(-6.11e-9, 7.87e-9, 1.02476e-4) Ha/Bohr
to
(-6.11e-9, 7.87e-9, -3.02e-9) Ha/Bohr,
with the total force sum reduced to about 1.0e-8 Ha/Bohr.
The energy is unchanged within numerical noise. This confirms that the remaining finite-field force-sum
residual was a center-of-mass component of the periodic electric-field force, distinct from the original
XC/grid force issue.
A smaller reproducer would still be useful for adding a lightweight regression test, since the full calcite case
is too expensive for the regular CP2K test suite.
Best,
Thomas
> Am 27.05.2026 um 14:10 schrieb 'Kit Joll' via cp2k <cp2k at googlegroups.com>:
>
> Dear Thomas,
>
> Thank you again for the helpful suggestions. I have now repeated the finite-field calculation with both signs of the field and with the field magnitude halved.
>
> All four calculations used the same input settings, cell, coordinates, GAPW_XC / GAPW_ACCURATE_XCINT setup, XC grid settings, basis sets and pseudopotentials. The only changes were the PERIODIC_EFIELD INTENSITY and POLARISATION. The effective field is along z, with E_z = INTENSITY * POLARISATION_z. I have attached the four corresponding input/output pairs. The attachment filenames indicate the actual field values (the PROJECT_NAME inside the input files is just a leftover label).
>
> The resulting force sums are:
>
> E_z / a.u. Sum F_x Sum F_y Sum F_z (Sum F_z) / E_z
> -2.5e-4 -6.1085e-09 7.8702e-09 -2.04936242e-04 0.819744968
> -1.25e-4 -6.1090e-09 7.8708e-09 -1.02473941e-04 0.819791528
> +1.25e-4 -6.1100e-09 7.8720e-09 1.02475947e-04 0.819807576
> +2.5e-4 -6.1104e-09 7.8725e-09 2.04962359e-04 0.819849436
>
> So the absolute z-component of the force-sum residual approximately halves when the field is halved, while the ratio Sum F_z / E_z remains essentially constant at about 0.8198. The residual also changes sign when the field direction is reversed. The transverse components remain at the zero-field level, around 1e-8 Ha/Bohr.
>
> The central finite-difference slopes are very similar for the two field magnitudes:
>
> [ F_z(+1.25e-4) - F_z(-1.25e-4) ] / [2 * 1.25e-4] = 0.819799552
>
> [ F_z(+2.5e-4) - F_z(-2.5e-4) ] / [2 * 2.5e-4] = 0.819797202
>
> This seems to confirm your suggested diagnostic: the remaining force-sum residual is odd in the field, proportional to the applied field, and parallel to the field direction. It therefore looks distinct from the original XC/grid force issue.
>
> Would you recommend any further diagnostic at this point, or would it be useful for me to prepare a more minimal test case for the periodic-electric-field force contribution?
>
> All the best,
> Kit
>
> On Tuesday, May 26, 2026 at 7:15:40 PM UTC+1 Thomas Kühne wrote:
>> Dear Kit,
>>
>> I agree with your interpretation. The important point is that the residual is now almost entirely parallel to the applied periodic field. In your z-field calculation,
>>
>> FORCES| Sum -6.11045615E-09 7.87254948E-09 2.04962359E-04
>>
>> the x and y components remain at the zero-field accuracy, whereas the z component is of the order of the applied field strength. This strongly suggests that
>> we are no longer looking at the same XC/grid egg-box issue that was cured by GAPW_XC + GAPW_ACCURATE_XCINT. Rather, the remaining term seems
>> to originate from the finite-field/Berry-phase force contribution itself.
>>
>> For a neutral periodic system I would still expect the total force to vanish, also in a homogeneous Berry-phase electric field, up to numerical noise. The
>> residual is also not simply a physical net-charge force. The system is neutral in terms of the GTH valence charges, and the residual is approximately 0.82
>> times the field strength rather than an obvious integer-charge contribution.
>>
>> I do not think there is a Wannier-localization setting that should fix this. The PERIODIC_EFIELD implementation uses the Berry-phase formulation directly;
>> the printed Wannier/localization controls are not convergence parameters for this force term. Likewise, increasing the XC fine grid should only affect the
>> ordinary XC/grid part. Since the transverse components are already small, and the residual tracks the field direction, I would not expect FINE_GRID_FACTOR
>> alone to remove it completely.
>>
>> Could you please do two quick checks, if convenient?
>>
>> 1. Repeat the same calculation with the field reversed, i.e. INTENSITY -2.5e-4 or POLARISATION 0 0 -1.
>> 2. Repeat with half the field strength, e.g. 1.25e-4 a.u.
>>
>> If the force-sum residual changes sign with the field and scales linearly with its magnitude, that would be very strong evidence that the issue is in the periodic
>> electric-field force contribution rather than in the GAPW/XC integration.
>>
>> At first sight, finite-field force code path looks like a missing or imperfect cancellation between the ionic and electronic Berry-phase force terms under a uniform
>> translation. In other words, it may be a real CP2K bug or at least a limitation of the present PERIODIC_EFIELD force implementation, rather than an
>> input-convergence issue.
>>
>> As a practical workaround for testing internal forces, subtracting the average force from all atoms would remove the spurious center-of-mass acceleration, but
>> I would not present that as a formally clean solution until we understand the origin of the term.
>>
>> Best wishes,
>> Thomas
>>
>>
>>> Am 26.05.2026 um 16:35 schrieb 'Kit Joll' via cp2k <cp... at googlegroups.com <>>:
>>>
>>
>>> Dear Thomas,
>>>
>>> Thank you again for your help. I was able to reproduce your zero-field results to approximately the same accuracy with a master version cloned on Friday 22nd May. I presume the remaining small differences are due to build/library differences.
>>>
>>> However, while the zero-field force sum is now well converged, I am not seeing the same behaviour once a finite periodic electric field is applied.
>>>
>>> For example, using
>>>
>>> METHOD GAPW_XC
>>> GAPW_ACCURATE_XCINT
>>> USE_FINER_GRID T
>>> FINE_GRID_FACTOR 2.0
>>>
>>> together with a periodic Berry-phase electric field of intensity 2.5e-4 a.u. along z, the force sum becomes
>>>
>>> FORCES| Sum -6.11045615E-09 7.87254948E-09 2.04962359E-04
>>> FORCES| Total atomic force 2.04962360E-04
>>>
>>> So the transverse components remain well converged, but the component along the applied field direction returns to the order of 1e-4 Ha/Bohr. I see similar behaviour when applying the field along other directions. The issue also persists when increasing FINE_GRID_FACTOR from 2 to 8: the force-sum error remains orders of magnitude larger along the field axis (however, all components sum do decrease by ~1 order of magnitude relative to FINE_GRID_FACTOR 2).
>>>
>>> Do you know whether there are additional grid, Berry-phase, or Wannier-related settings that need to be converged for finite-field force calculations? Or is there another setting that should be used together with GAPW_XC and GAPW_ACCURATE_XCINT in the presence of a periodic electric field?
>>>
>>> Please find attached a minimal input (start.inp) /output (output.out) pair that reproduces the issue.
>>>
>>> Thank you again for your help and advice.
>>>
>>> All the best,
>>> Kit
>>>
>>> On Thursday, May 21, 2026 at 10:48:00 AM UTC+1 Kit Joll wrote:
>>>> Dear Thomas,
>>>>
>>>> Many thanks for the very quick and detailed reply! This is extremely helpful, and your diagnosis makes a lot of sense given the behaviour we were seeing.
>>>>
>>>> I will try compiling the current CP2K master using the new make_cp2k.sh workflow, run the relevant regression tests, and then first reproduce your zero-field force-sum results on the same calcite frame. After that, I will check whether the same settings also resolve the sensitivity we observe in the finite-field response tensors.
>>>>
>>>> Thank you also for pointing out the PRINT_LEVEL LOW workaround and the relevant GAPW_XC / GAPW_ACCURATE_XCINT settings. I will report back once I have tested these on our side.
>>>>
>>>>
>>>> Best wishes,
>>>> Kit
>>>>
>>>>
>>>> On Wednesday, May 20, 2026 at 9:00:47 PM UTC+1 Thomas Kühne wrote:
>>>>> Dear Kit,
>>>>> Thank you for the detailed report and for the input/output files. I was able to
>>>>> reproduce the force-sum residual for the provided calcite frame:
>>>>> GPW baseline:
>>>>> Sum F = ( 3.48675295E-05, 1.12518883E-04, -5.39277596E-05 ) Ha/Bohr
>>>>> |Sum F| = 1.29554803E-04 Ha/Bohr
>>>>> The behavior originate from the XC/grid treatment:
>>>>> GPW + USE_FINER_GRID T, FINE_GRID_FACTOR 2.0:
>>>>> |Sum F| = 2.26659720E-05 Ha/Bohr
>>>>>
>>>>> GPW + finer/smoothed XC grid:
>>>>> |Sum F| = 1.10078684E-06 Ha/Bohr
>>>>>
>>>>> GAPW_XC:
>>>>> |Sum F| = 4.20880179E-05 Ha/Bohr
>>>>>
>>>>> GAPW_XC + GAPW_ACCURATE_XCINT:
>>>>> |Sum F| = 1.68750841E-07 Ha/Bohr
>>>>>
>>>>> GAPW + GAPW_ACCURATE_XCINT + USE_FINER_GRID T, FINE_GRID_FACTOR 2.0:
>>>>> |Sum F| = 3.85198029E-08 Ha/Bohr
>>>>>
>>>>> GAPW_XC + GAPW_ACCURATE_XCINT + USE_FINER_GRID T, FINE_GRID_FACTOR 2.0:
>>>>> |Sum F| = 1.04105369E-08 Ha/Bohr
>>>>> This strongly suggests that the residual is dominated by an egg-box/grid-coupling
>>>>> effect in the XC/grid integration rather than by pseudopotentials, basis sets, or
>>>>> SCF noise.
>>>>> For this system, the best tested setting was:
>>>>> &QS
>>>>> EPS_DEFAULT 1.0E-18
>>>>> METHOD GAPW_XC
>>>>> GAPW_ACCURATE_XCINT
>>>>> &END QS
>>>>>
>>>>> &XC
>>>>> DENSITY_CUTOFF 1.0E-10
>>>>> GRADIENT_CUTOFF 1.0E-10
>>>>> TAU_CUTOFF 1.0E-10
>>>>> &XC_GRID
>>>>> FINE_GRID_FACTOR 2.0
>>>>> USE_FINER_GRID T
>>>>> &END XC_GRID
>>>>> &XC_FUNCTIONAL NO_SHORTCUT
>>>>> &GGA_C_PBE
>>>>> &END GGA_C_PBE
>>>>> &GGA_X_RPBE
>>>>> &END GGA_X_RPBE
>>>>> &END XC_FUNCTIONAL
>>>>> &END XC
>>>>> METHOD GAPW with the same GAPW_ACCURATE_XCINT and fine XC grid also performs
>>>>> very well, but in this test GAPW_XC was slightly better and should be the less
>>>>> intrusive change relative to the original GPW calculation.
>>>>> One practical note: GAPW_ACCURATE_XCINT has been improved recently, so I would
>>>>> recommend testing with a recent CP2K master or a release that includes those
>>>>> changes. Also, for this calcite input current master hit a post-SCF output crash
>>>>> with PRINT_LEVEL MEDIUM; using PRINT_LEVEL LOW while keeping explicit
>>>>> &FORCES ON avoided that and still printed the force block.
>>>>> Best wishes,
>>>>> Thomas
>>>
>>>
>>
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>>> <output.out><start.inp>
>>
>
>
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> <Ez_m2p5e-4_output.out><Ez_m1p25e-4_output.out><Ez_p1p25e-4_start.inp><Ez_m1p25e-4_start.inp><Ez_p1p25e-4_output.out><Ez_p2p5e-4_start.inp><Ez_p2p5e-4_output.out><Ez_m2p5e-4_start.inp>
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