Summary
The implementation in #7457 provides the main SCAN-L stress support, but finite-difference validation still shows a systematic discrepancy between the analytic stress and the energy derivative. The residuals occur in both PW and LCAO calculations and are concentrated in the xy, xz, and yz shear components. This issue tracks that remaining problem separately from #7457.
Test setup
- ABACUS commit:
39449b0e37eea9f0428ce8c81ee2baebb0525bf2
- Functionals: PBE, r²SCAN, and SCAN-L
- Basis sets: PW and LCAO
- Wave-function cutoff: 50 Ry for the comparison below
- Strain components:
xx, yy, zz, xy, xz, and yz
- Central finite-difference step:
0.0050
- FFT grid:
36 × 36 × 36 for all calculations included in the figure
- Residual definition: finite-difference stress minus analytic stress, in kbar
PBE is used to validate the deformation, sign, unit conversion, and analysis procedure. r²SCAN provides a control for the existing kinetic-energy-density-dependent mGGA stress path.
Results
| Basis and functional |
Maximum absolute residual (kbar) |
RMS residual (kbar) |
| PW PBE |
2.171 |
1.499 |
| LCAO PBE |
0.069 |
0.048 |
| PW r²SCAN |
2.549 |
1.728 |
| LCAO r²SCAN |
0.080 |
0.049 |
| PW SCAN-L |
22.092 |
14.348 |
| LCAO SCAN-L |
21.787 |
14.623 |
The signed SCAN-L residuals at 50 Ry are:
| Basis |
xx |
yy |
zz |
xy |
xz |
yz |
| PW |
-3.734 |
-0.040 |
-0.434 |
22.092 |
16.638 |
-21.357 |
| LCAO |
-8.381 |
-2.292 |
-3.405 |
21.787 |
16.207 |
-21.414 |
The same shear-residual pattern appears in both basis sets. Increasing the cutoff from 50 to 75 Ry reduces the maximum absolute residual from 22.092 to 14.794 kbar for PW and from 21.787 to 17.319 kbar for LCAO, but the discrepancy remains much larger than for the controls. For PW at 50 Ry, changing the finite-difference step from 0.0050 to 0.0025, or applying Richardson extrapolation, also does not remove it.
Expected behavior
With sufficiently converged numerical settings, the analytic SCAN-L stress should agree with the derivative of the total energy under homogeneous strain. The residual should decrease systematically with cutoff and grid convergence and should not show a persistent basis-independent pattern in the shear components.
Summary
The implementation in #7457 provides the main SCAN-L stress support, but finite-difference validation still shows a systematic discrepancy between the analytic stress and the energy derivative. The residuals occur in both PW and LCAO calculations and are concentrated in the
xy,xz, andyzshear components. This issue tracks that remaining problem separately from #7457.Test setup
39449b0e37eea9f0428ce8c81ee2baebb0525bf2xx,yy,zz,xy,xz, andyz0.005036 × 36 × 36for all calculations included in the figurePBE is used to validate the deformation, sign, unit conversion, and analysis procedure. r²SCAN provides a control for the existing kinetic-energy-density-dependent mGGA stress path.
Results
The signed SCAN-L residuals at 50 Ry are:
xxyyzzxyxzyzThe same shear-residual pattern appears in both basis sets. Increasing the cutoff from 50 to 75 Ry reduces the maximum absolute residual from 22.092 to 14.794 kbar for PW and from 21.787 to 17.319 kbar for LCAO, but the discrepancy remains much larger than for the controls. For PW at 50 Ry, changing the finite-difference step from
0.0050to0.0025, or applying Richardson extrapolation, also does not remove it.Expected behavior
With sufficiently converged numerical settings, the analytic SCAN-L stress should agree with the derivative of the total energy under homogeneous strain. The residual should decrease systematically with cutoff and grid convergence and should not show a persistent basis-independent pattern in the shear components.