Feat/issue 7726 dftu pw nspin fixes (#7744)

* Fix(dftu-pw): correct Pauli-to-spin conversion signs and weight_eu for nspin=1

In cal_occ_pw():
- Swap the imaginary signs in the Pauli-to-spin conversion for nspin=4:
  index[1] (spin down-up): -i*vu_tmp[2] -> +i*vu_tmp[2]
  index[2] (spin up-down): +i*vu_tmp[2] -> -i*vu_tmp[2]
  The DFT+U vu array convention requires opposite sign from deeq_nc.

- Fix weight_eu for nspin=1: 0.25 -> 1.0
  nspin=1 has single occupancy, not the Pauli double-counting factor.

Verified with tests/17_DS_DFTU/08 and 09:
  08: -6792.33351671617 (ref -6792.33351670950, diff 6.7e-9 eV)
  09: -6364.26587638707 (ref -6364.26587639017, diff 3.1e-9 eV)

* Test: migrate PW DFT+U tests (08/09) from 17_DS_DFTU to 01_PW

815_PW_DFTU_S2_Z  — nspin=2 DFT+U, matches ref -6792.33351671614
816_PW_DFTU_S4_XY — nspin=4 DFT+U, matches ref -6364.26587638708

* Test: disable migrated 08/09 in 17_DS_DFTU CASES_CPU, enabled in 01_PW

* Test: regenerate 099_PW_DJ_SO reference for nspin=4 DFT+U sign fix

The nspin=4 Pauli-to-spin sign swap in cal_occ_pw changes the output of
all nspin=4 DFT+U PW tests, including the pre-existing 099_PW_DJ_SO whose
result.ref was not updated. Regenerate its etot/force/stress references:

  etot   -5662.3881388456420609 -> -5662.3908859903258417
  force     15.774740 -> 17.965510
  stress  100840.559090 -> 100582.607209

Without this, the 01_PW integrate suite fails on 099_PW_DJ_SO
(etot dev 2.7e-3 eV, force dev -2.19, stress dev 258).

* fix: add explicit nspin=4 to 816_PW_DFTU_S4_XY test INPUT

Commit b95f433 on develop removed the automatic nspin=4 reset
when noncolin/lspinorb is enabled, instead requiring explicit nspin=4.
Since the PR does not touch read_input_item_elec_stru.cpp, the CI merge
uses develop's validation code, causing ABACUS to quit with:
  nspin must be 4 when noncolin or lspinorb is enabled.

---------

Co-authored-by: dyzheng <zhengdy@bjaisi.com>

Author: dyzheng

source/source_lcao/module_dftu/dftu_pw.cpp

@@ -247,7 +247,7 @@ void Plus_U::cal_occ_pw(const int iter,
     }
 
     Plus_U::energy_u = 0.0;
-    const double weight_eu = (Plus_U::nspin == 1) ? 0.25 : (Plus_U::nspin == 2) ? 0.5 : 0.25;
+    const double weight_eu = (Plus_U::nspin == 1) ? 1.0 : (Plus_U::nspin == 2) ? 0.5 : 0.25;
     const double diag_coeff = (Plus_U::nspin == 4) ? 1.0 : 0.5;
     // calculate VU and energy (locale already reduced above)
     for(int iat = 0; iat < cell.nat; iat++)
@@ -309,8 +309,8 @@ void Plus_U::cal_occ_pw(const int iter,
                     }
                     vu_iat[index[0]] = 0.5 * (vu_tmp[0] + vu_tmp[3]);
                     vu_iat[index[3]] = 0.5 * (vu_tmp[0] - vu_tmp[3]);
-                    vu_iat[index[1]] = 0.5 * (vu_tmp[1] - std::complex<double>(0.0, 1.0) * vu_tmp[2]);
-                    vu_iat[index[2]] = 0.5 * (vu_tmp[1] + std::complex<double>(0.0, 1.0) * vu_tmp[2]);
+                    vu_iat[index[1]] = 0.5 * (vu_tmp[1] + std::complex<double>(0.0, 1.0) * vu_tmp[2]);
+                    vu_iat[index[2]] = 0.5 * (vu_tmp[1] - std::complex<double>(0.0, 1.0) * vu_tmp[2]);
                 }
             }
         }

tests/01_PW/099_PW_DJ_SO/result.ref

@@ -1,5 +1,5 @@
-etotref -5662.3881388456420609
-etotperatomref -2831.1940694228
-totalforceref 15.774740
-totalstressref 100840.559090
+etotref -5662.3908859903258417
+etotperatomref -2831.1954429952
+totalforceref 17.965510
+totalstressref 100582.607209
 totaltimeref 1.26

tests/01_PW/815_PW_DFTU_S2_Z/INPUT

@@ -0,0 +1,29 @@
+INPUT_PARAMETERS
+suffix    autotest
+calculation    scf
+basis_type    pw
+ecutwfc    50
+gamma_only    0
+device    cpu
+
+nspin    2
+nbands    28
+scf_thr    1.0e-6
+scf_nmax    100
+out_chg    0
+smearing_method    gaussian
+smearing_sigma    0.01
+mixing_type    broyden
+mixing_beta    0.4
+ks_solver    dav_subspace
+symmetry    0
+
+# DFT+U parameters
+dft_plus_u    1
+orbital_corr    2
+hubbard_u    5.0
+onsite_radius   3.0
+
+pseudo_dir    ../../PP_ORB
+orbital_dir    ../../PP_ORB
+pw_seed 1

tests/01_PW/815_PW_DFTU_S2_Z/KPT

@@ -0,0 +1,4 @@
+K_POINTS
+0
+Monkhorst-Pack
+2 2 2 0 0 0

tests/01_PW/815_PW_DFTU_S2_Z/README

@@ -0,0 +1 @@
+Test PW DFT+U (U=5.0eV, l=2) with collinear spin (nspin=2), Z magnetization

tests/01_PW/815_PW_DFTU_S2_Z/STRU

@@ -0,0 +1,21 @@
+ATOMIC_SPECIES
+Fe 1.000 Fe.upf
+
+NUMERICAL_ORBITAL
+Fe_gga_6au_100Ry_4s2p2d1f.orb
+
+LATTICE_CONSTANT
+8.190
+
+LATTICE_VECTORS
+ 1.00    0.50     0.50
+ 0.50    1.00     0.50
+ 0.50    0.50     1.00
+ATOMIC_POSITIONS
+Direct
+
+Fe
+0.0
+2
+0.00   0.00   0.00   mag  2.0
+0.51   0.51   0.51   mag  -2.0

tests/01_PW/815_PW_DFTU_S2_Z/result.ref

@@ -0,0 +1,3 @@
+etotref -6792.3335167095001452
+etotperatomref -3396.1667583548
+totaltimeref 21.07

tests/01_PW/816_PW_DFTU_S4_XY/INPUT

@@ -0,0 +1,30 @@
+INPUT_PARAMETERS
+suffix    autotest
+calculation    scf
+basis_type    pw
+ecutwfc    20
+gamma_only    0
+device    cpu
+
+noncolin    1
+nspin    4
+scf_thr    1.0e-6
+scf_nmax    50
+out_chg    0
+smearing_method    gaussian
+smearing_sigma    0.01
+mixing_type    broyden
+mixing_beta    0.4
+ks_solver    dav_subspace
+symmetry    0
+
+# DFT+U parameters
+dft_plus_u    1
+orbital_corr    2
+hubbard_u    5.0
+onsite_radius   3.0
+
+kpar    1
+pseudo_dir    ../../PP_ORB
+orbital_dir    ../../PP_ORB
+pw_seed 1

tests/01_PW/816_PW_DFTU_S4_XY/KPT

@@ -0,0 +1,4 @@
+K_POINTS
+0
+Monkhorst-Pack
+2 2 2 0 0 0

tests/01_PW/816_PW_DFTU_S4_XY/README

@@ -0,0 +1 @@
+Test PW DFT+U with noncollinear spin (nspin=4), XY magnetization constraint