Fix time-reversal symmetry in plane-wave basis Hartree matrix elements v_h and dump_hartree - #46
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hamilt::v_h passed kp_trev(k) to transform_k2g, which applies the sign
flip sg=-1 and places the plane-wave coefficients at -S*g. Combined with
the separate real-space conjugation of the orbital, this double-applies
the sign and produces the per-k density inverted about the FFT grid
origin, n_{Sk}(-r) instead of n_{Sk}(r).
For crystals whose inversion center is not at the grid origin (e.g.
diamond Si, inversion center at the bond midpoint), the time-reversed
half of the BZ is then misregistered relative to the non-TR half. The
total charge (G=0) is preserved, but the G!=0 structure partially
cancels, halving the Hartree matrix elements (e.g. Si Gamma band 3:
2.65 eV vs QE 5.30 eV). Only the plane-wave v_h path is affected; the
THC J[Dm] path used for HF/GW energies is correct.
Fix: pass false to transform_k2g in both v_h overloads. Time reversal is
already applied via the real-space conjugation of the orbital (full-
density path) and is unnecessary for |psi|^2 (diagonal-density path).
This matches the idiom used elsewhere (unfold_bz.cpp): spatial rotation
via transform_k2g(false, ...) and time reversal via a separate conj.
Test: new fixture qe_si333_sym (diamond Si, 3x3x3, force_symmorphic ->
27 kpts reduce to 4 IBZ with 13 time-reversal pairs and no inversion op)
with two check_Hartree sections (full and diagonal density). Before fix
||J - J2|| = 0.098 (FAIL); after fix O(1e-7). Existing LiH/GaAs fixtures
do not catch this: LiH's inversion center is at the origin (masks the
misregistration) and the GaAs fixture has no TR pairs.
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Problem
coqui.post_proc.dump_hartree(plane-wave Hartree matrix elementsVH_skij) was wrong for systems with time-reversal symmetry but no symmorphic inversion (inversion about the grid origin), such as silicon with inversion center at (1/8, 1/8, 1/8).Fix
Updated
src/hamiltonian/v_h.hppconj(FFT[c @ -S·g])(r) = u₋ₛₖ(-r)→ densityn_{Sk}(-r)(inverted about the origin)conj(FFT[c @ +S·g])(r) = u₋ₛₖ(r)→ densityn_{Sk}(r)(correct)Same as
coqui/src/mean_field/symmetry/unfold_bz.cpp
Lines 141 to 142 in 3f807e4
Test
New fixture
qe_si333_sym(diamond Si, 3×3×3,force_symmorphic = .true.) + twocheck_Hartreesections.J: from the THC ERIs (hf.evaluate)J2: from the plane-wave path (hamilt::Vhartree→v_h, the code under test)si333_sym(full ρ)si333_sym_diag(diagonal ρ)Existing LiH/GaAs fixtures do not cover this because LiH inversion center at origin; GaAs does not use symmetry.