[zjdai]

Noncollinear states with a transverse y component can converge while reverse spatial-block assembly violates full spinor Hermiticity. The production fix removes the extra conjugation in ModuleGint::merge_hr_part_to_hR.

Linked Issue

Fixes #8121

What's changed?

Retain the one-assignment Gint correction and add two compact O2 SCF regressions, scf_nspin4_nsoc_hr and scf_nspin4_soc_hr. Both use the existing O fully relativistic pseudopotential and minimal 1s1p orbitals, an 18-bohr cell, a 2.3-bohr bond, Gamma 1x1x1, PBE/LCAO, 15 Ry, scf_thr=1e-7, scf_nmax=50, xy initial moments and no DeltaSpin constraint.

Each case includes complete raw 16x16 H(R)/S(R) references at R=0 and uses the existing matrix comparator without changing its tolerances. Only the two case directories and their CASES_CPU.txt entries are added; no archive or duplicated PP/orbital data is included.

Unit Tests and/or Case Tests for my changes

Fresh runs with the GNU 11.4 and IntelLLVM 2025.3 builds exercised both final cases twice, using four MPI ranks and one OpenMP thread. All eight SCF calculations converged in 34/35 steps and passed the existing H/S comparisons. Cross-build maximum H differences are about 1.00e-13 Ry; the sparse positions match. Program calculation time is 1.05-1.65 s per case locally, or 4.18-5.03 s including MPI and other external overhead.

The unfixed parent converges for both inputs but fails both H comparisons, with errors about 1.97e-2 Ry; S comparisons pass. References are byte copies of the corrected build's raw converged SCF outputs, without projections, averaging or truncation.

The GitHub OpenMPI/OpenBLAS CPU integration and unit-test job also passed for commit d0442d4. Both new cases executed with four MPI ranks and one OpenMP thread and passed the existing H(R), S(R), total-energy and energy-per-atom comparisons: NSOC took 4.137 s and SOC took 4.202 s. CPU CI log.

Governance Notes

I have read AGENTS.md and docs/developers_guide/agent_governance.md. No documentation update required: INPUT interfaces and output formats are unchanged, and each fixture has a short README. These compact parameters protect the assembly regression; they do not certify material-property convergence or all SCF endpoint covariance relations.

[mohanchen]

Thanks for your fix!

[zjdai]

Added the reviewed compact O2 cases in c085dde:

• tests/03_NAO_multik/scf_nspin4_nsoc_hr
• tests/03_NAO_multik/scf_nspin4_soc_hr

Download the exact reviewed ZIP (10,257 bytes). The archive is included in the commit; PP/orbital resources are reused from the repository.

The existing collector passes both fixed-build H/S references and detects the pre-fix H errors. The PR description now records the rotation diagnostics and the remaining difference between the NSOC last-SCF Hamiltonian and the Hamiltonian rebuilt from the final converged density; it does not claim that all SCF endpoint covariance checks passed.

[ABACUS-PR-BOT]

Static review of 3e557eef16a3 supports the spatial-transpose correction in merge_hr_part_to_hR; independent direct-quadrature checks reproduce the old B_y Hermiticity error.

Non-blocking follow-up to the existing test discussion: please include the focused replacement regression, or demonstrate a retained case that fails with the old conjugation, with exact commands/results.

No ABACUS build, MPI/GPU runtime, or SCF validation was performed.