Feature: Enable correct Laplacian-dependent meta-GGA calculations

[AsTonyshment]

Linked Issue

This PR is a follow-up to #7457, which introduced the energy, potential, and stress paths required by Laplacian-dependent meta-GGA functionals.

Fixes #7813.

What's changed?

Summary

This PR fixes the remaining corruption in the Laplacian-potential FFT path. With this correction, SCAN-L and other Libxc meta-GGA functionals marked with XC_FLAGS_NEEDS_LAPLACIAN can use the shared Laplacian-dependent implementation correctly.

Root cause

The code added in #7457 reused one complex array for both the real-space and reciprocal-space representations of the Laplacian potential. It first filled nrxx real-space values, but then cleared the range from npw to nmaxgr as if the same array already contained reciprocal-space coefficients. Since npw is normally smaller than nrxx, this erased valid real-space data before the forward FFT. The resulting ∇²v_lapl contribution to the self-consistent XC potential was therefore corrupted.

Finite-difference validation at 50 Ry

The correction was validated by comparing analytic stress with central finite differences of the total energy for all six independent stress components: xx, yy, zz, xy, xz, and yz.

• System: Si-2
• Basis types: PW and LCAO
• Functionals: PBE, r²SCAN, and SCAN-L before and after this fix
• Wave-function cutoff: 50 Ry
• Strain magnitude: ±0.005

[Copilot]

Pull request overview

This PR fixes corruption in the Laplacian-dependent meta-GGA (e.g., SCAN-L) XC potential path by separating real-space and reciprocal-space buffers during the ∇²(v_lapl) FFT workflow, enabling correct use of Libxc functionals flagged with XC_FLAGS_NEEDS_LAPLACIAN.

Changes:

• Fix Laplacian-potential FFT workflow in libxc_pot.cpp by using distinct real-space (lapl_r) and reciprocal-space (lapl_g) arrays.
• Update SCAN-L PW integration test reference outputs to reflect corrected physics.
• Relax/adjust SCAN-L test thresholds to cover numerical differences across supported Libxc versions.

Reviewed changes

Copilot reviewed 4 out of 4 changed files in this pull request and generated 1 comment.

File	Description
source/source_hamilt/module_xc/libxc_pot.cpp	Fixes the Laplacian-dependent potential FFT path to avoid overwriting real-space data before the forward FFT.
source/source_hamilt/module_xc/test/xc3_mock.h	Extends the FFT mock to support complex→real recip2real needed by the updated Laplacian-potential path.
tests/01_PW/207_PW_SCANL/result.ref	Updates SCAN-L integration test reference values consistent with the corrected Laplacian potential contribution.
tests/01_PW/207_PW_SCANL/threshold	Adjusts thresholds to tolerate Libxc-version-dependent numerical differences for SCAN-L.

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[mohanchen]

This is an important fix!