[CP2K-user] [CP2K:22446] GAPW_XC + r2SCAN: analytic forces and stress disagree with finite differences (CP2K 2026.2)

[Thomas Kühne]

Dear Wei,

in the July revision c92cc08 you used, the GAPW_XC meta-GGA tau
potential was integrated with the original orbital products, whereas the 
XC kinetic-energy density was constructed from the soft orbitals. This 
makes the operator and analytic derivatives inconsistentwith the XC 
energy. The correction is already included in PR #5749: 
https://github.com/cp2k/cp2k/pull/5749 Please use a build containing 
this PR.

Since our last Al exchange, I have also extended the basis and 
numerical controls. An important finding is that EPS_DEFAULT 5E-11
still gives a derived EPS_PGF_ORB of about 7E-6. I found appreciable
primitive-screening sensitivity in equivalent representations
of the enlarged Al basis. With explicit EPS_PGF_ORB 1E-8, these
representations differ by about 0.12 meV/A in Al force-vector RMS.
Tightening from 1E-8 to 1E-10 gives an Al force-vector RMS change
below 0.003 meV/A in the matched PBE-potential controls. 

For Al, raising the PP cutoff from 800 to 1200 Ry changes the forces by
only 0.05 meV/A RMS. Refining the AE quadrature from 110/100 to 194/160
gives 0.10 meV/A, whereas enlarging the AE basis from 70 to 159 functions
gives 8.3 meV/A. However, the 159-function basis is an extension, not an 
optimized production basis. At EPS_PGF_ORB 1E-8, the last PP basis
step from 113 to 154 functions still changes the Al forces by 6.0 meV/A.

The Al-potential trend remains clear. With r2SCAN as the
functional throughout, the enlarged PP basis and the same expanded
Al-only AE reference, PBE-GTH-q3 gives an Al force-vector RMS
difference of about 172 meV/A, compared with about 282 meV/A
for the earlier SCAN-GTH-q3 baseline on the initial 302-atom
geometry. O, P and Zn are unchanged. I.e., PBE-GTH-q3 performs
better in this comparison, despite not being fitted for r2SCAN.

The roughly 0.17 eV/A residual with PBE remains after the
tighter screening. Therefore, a potential-transferability or frozen-core
contribution remains plausible ...

Best regards,
Thomas

> Am 17.10.2026 um 11:39 schrieb liu wei <whisper256136 at gmail.com>:
> 
> Dear CP2K developers and users,
> 
> While testing METHOD GAPW_XC with r2SCAN in CP2K 2026.2 (git:c92cc08), I found that the analytic forces and stress
> do not agree with RUN_TYPE DEBUG finite differences, whereas GAPW, and GAPW_XC with PBE, pass the same check. I may
> be missing something in my setup, so I would be grateful if you could take a look. All inputs and outputs, a short
> analysis script (numpy only) and a README with the full tables are attached (cp2k_GAPW_XC_mGGA_report.zip).
> 
> **Setup**
> 
> 302-atom ZnO–P2O5–Al2O3 glass (cubic, a = 16.06 Å, Γ point), TZVP-MOLOPT-SCAN-GTH + GTH-SCAN for all elements,
> `MGGA_X_R2SCAN` + `MGGA_C_R2SCAN` (libxc) + D3(BJ), CUTOFF 1100 / REL_CUTOFF 60, EPS_SCF 1e-7, analytical stress.
> RUN_TYPE DEBUG checks one Al, O, P and Zn atom and the stress tensor. Between the inputs, only METHOD,
> GAPW_ACCURATE_XCINT, FORCE_PAW or the functional changes. Without FORCE_PAW, O and Zn are PAW kinds and Al and P are
> treated by GPW.
> 
> **Results** (analytic − finite difference; force: max over x, y, z, meV/Å; stress: GPa)
> 
> | functional | METHOD | ACCURATE_XCINT | Al | O | P | Zn | ΔS diagonal | ΔS off-diagonal |
> |---|---|---|---|---|---|---|---|---|
> | r2SCAN | GAPW | T | 0.02 | 0.03 | 0.23 | 0.03 | 0.004 | 0.001 |
> | r2SCAN | GAPW | F | 0.02 | 0.03 | 0.23 | 0.04 | 0.004 | 0.001 |
> | r2SCAN | **GAPW_XC** | T | 11.5 | 91.5 | 23.3 | **410** | **+23.7** | 0.008 |
> | r2SCAN | **GAPW_XC** | F | 18.2 | 261 | 37.6 | **458** | **+28.8** | 0.004 |
> | PBE | GAPW_XC | T | 0.03 | 0.01 | 0.23 | 0.00 | 0.005 | 0.001 |
> | PBE | GAPW_XC | F | 0.02 | 0.01 | 0.23 | 0.00 | 0.004 | 0.001 |
> 
> - The checked forces are 2000–3600 meV/Å, so the Zn error is about 20 %. The stress error is an isotropic shift
>   of the diagonal; the off-diagonal components agree.
> - The *finite-difference* forces of GAPW_XC and GAPW agree to within 2.6 meV/Å (with and without
>   ACCURATE_XCINT), so the GAPW_XC energy itself looks fine; only the analytic derivatives seem to be affected.
> - The largest errors are on the PAW kinds (Zn, then O). Adding `FORCE_PAW` (so Al and P also become PAW atoms)
>   does not change the numbers.
> - So the problem seems specific to the combination GAPW_XC + meta-GGA, and does not depend on
>   GAPW_ACCURATE_XCINT.
> 
> In the v2026.2 regtests, the GAPW_XC finite-difference checks (`regtest-acc-1/h2o-gapw_xc-force-1.inp`,
> `h2o-gapw_xc-stress-debug-1.inp`) use PBE, and the meta-GGA (TPSS) checks use GAPW with USE_FINER_GRID, so I could
> not find a test that covers this combination. I have not tested the current master, other meta-GGAs or a smaller
> system.
> 
> My questions:
> 
> 1. Is this a known issue, or is GAPW_XC not meant to be used with meta-GGA forces and stress?
> 2. If it is a bug, would a small reproducer help (for example H2O with TPSS, based on `h2o-gapw_xc-force-1.inp`)?
>    I would be happy to prepare one, or to open a GitHub issue.
> 
> For now I use GAPW (or GPW with USE_FINER_GRID), which pass the same checks.
> 
> Thank you very much for your time and for CP2K.
> 
> Best regards,
> Wei LIU
> 
> 
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> <cp2k_GAPW_XC_mGGA_report.zip>

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