diff --git a/source/source_hamilt/module_gint/gint_common.cpp b/source/source_hamilt/module_gint/gint_common.cpp
index 4f34657640..c466a817b0 100644
--- a/source/source_hamilt/module_gint/gint_common.cpp
+++ b/source/source_hamilt/module_gint/gint_common.cpp
@@ -210,10 +210,10 @@ void merge_hr_part_to_hR(const std::vector<hamilt::HContainer<double>>& hr_gint_
                             + std::complex<double>(clx_i[is], clx_j[is]) * mat_nspin2->get_value(irow, icol);
                         }
                     }
-                    //fill the lower triangle matrix at -R by conjugate transpose of upper at R
-                    // This ensures H(-R) = H(R)^dagger, required for Hermiticity of H(k).
-                    // For real matrices (is=0,3), conj has no effect.
-                    // For complex matrices (is=1,2), conj is essential.
+                    // Transpose only the spatial indices within this fixed spin block.
+                    // The real Pauli-channel matrices obey V_mu(-R) = V_mu(R)^T.
+                    // Full spinor Hermiticity also exchanges the spin indices; the
+                    // conjugate coefficients are already in the opposite spin block.
                     if (iat1 < iat2)
                     {
                         auto lower_mat = lower_ap->find_matrix(-R_index);
@@ -221,7 +221,7 @@ void merge_hr_part_to_hR(const std::vector<hamilt::HContainer<double>>& hr_gint_
                         {
                             for (int icol = 0; icol < upper_mat->get_col_size(); ++icol)
                             {
-                                lower_mat->get_value(icol, irow) = std::conj(upper_mat->get_value(irow, icol));
+                                lower_mat->get_value(icol, irow) = upper_mat->get_value(irow, icol);
                             }
                         }
                     }
diff --git a/tests/03_NAO_multik/CASES_CPU.txt b/tests/03_NAO_multik/CASES_CPU.txt
index a85a0938ec..c1a91cb6ce 100644
--- a/tests/03_NAO_multik/CASES_CPU.txt
+++ b/tests/03_NAO_multik/CASES_CPU.txt
@@ -69,3 +69,5 @@ get_pchg_k
 get_s
 scf_deltaspin2
 scf_deltaspin4
+scf_nspin4_nsoc_hr
+scf_nspin4_soc_hr
diff --git a/tests/03_NAO_multik/pr8183_o2_hr_tests.zip b/tests/03_NAO_multik/pr8183_o2_hr_tests.zip
new file mode 100644
index 0000000000..7e6c7b9a4f
Binary files /dev/null and b/tests/03_NAO_multik/pr8183_o2_hr_tests.zip differ
diff --git a/tests/03_NAO_multik/scf_nspin4_nsoc_hr/INPUT b/tests/03_NAO_multik/scf_nspin4_nsoc_hr/INPUT
new file mode 100644
index 0000000000..d6504b7303
--- /dev/null
+++ b/tests/03_NAO_multik/scf_nspin4_nsoc_hr/INPUT
@@ -0,0 +1,22 @@
+INPUT_PARAMETERS
+suffix            autotest
+calculation       scf
+symmetry          0
+pseudo_dir        ../../PP_ORB
+orbital_dir       ../../PP_ORB
+gamma_only        0
+ecutwfc           20
+scf_thr           1e-6
+scf_nmax          50
+noncolin          1
+nspin             4
+lspinorb          0
+basis_type        lcao
+ks_solver         scalapack_gvx
+dft_functional    pbe
+smearing_method   gauss
+smearing_sigma    0.02
+mixing_type       pulay
+mixing_beta       0.4
+mixing_gg0        3.0
+out_hsr           1 12
diff --git a/tests/03_NAO_multik/scf_nspin4_nsoc_hr/KPT b/tests/03_NAO_multik/scf_nspin4_nsoc_hr/KPT
new file mode 100644
index 0000000000..c289c0158a
--- /dev/null
+++ b/tests/03_NAO_multik/scf_nspin4_nsoc_hr/KPT
@@ -0,0 +1,4 @@
+K_POINTS
+0
+Gamma
+1 1 1 0 0 0
diff --git a/tests/03_NAO_multik/scf_nspin4_nsoc_hr/README b/tests/03_NAO_multik/scf_nspin4_nsoc_hr/README
new file mode 100644
index 0000000000..31b5d893f3
--- /dev/null
+++ b/tests/03_NAO_multik/scf_nspin4_nsoc_hr/README
@@ -0,0 +1,8 @@
+Self-consistent nspin=4 O2 H(R)/S(R) regression, without SOC.
+Two O atoms separated by 2.3 bohr along z in a 20-bohr cubic cell.
+Existing fully relativistic O PP and minimal 6-bohr 1s1p orbitals; PBE, 20 Ry, Gamma 1x1x1.
+Both initial moments are (1/sqrt(2),1/sqrt(2),0) muB; no DeltaSpin constraint.
+Full SCF reaches 1e-6 within 50 steps and retains a finite y magnetization.
+Complete raw complex references cover the nspin=4 interatomic H(R) export fix.
+The pre-fix build converges but fails the H comparison against the fixed-build reference.
+Only R=0 is present. This tests the export convention, not material convergence or intercell Bloch phases.
diff --git a/tests/03_NAO_multik/scf_nspin4_nsoc_hr/STRU b/tests/03_NAO_multik/scf_nspin4_nsoc_hr/STRU
new file mode 100644
index 0000000000..96603e21aa
--- /dev/null
+++ b/tests/03_NAO_multik/scf_nspin4_nsoc_hr/STRU
@@ -0,0 +1,22 @@
+ATOMIC_SPECIES
+O 15.999 O_ONCV_PBE_FR-1.0.upf
+
+NUMERICAL_ORBITAL
+O_gga_6au_60Ry_1s1p.orb
+
+LATTICE_CONSTANT
+20.0
+
+LATTICE_VECTORS
+1 0 0
+0 1 0
+0 0 1
+
+ATOMIC_POSITIONS
+Direct
+
+O
+0.0
+2
+0.5 0.5 0.4425 0 0 0 mag 0.7071067811865475 0.7071067811865475 0
+0.5 0.5 0.5575 0 0 0 mag 0.7071067811865475 0.7071067811865475 0
diff --git a/tests/03_NAO_multik/scf_nspin4_nsoc_hr/hrs1_nao.csr.ref b/tests/03_NAO_multik/scf_nspin4_nsoc_hr/hrs1_nao.csr.ref
new file mode 100644
index 0000000000..a62446058c
--- /dev/null
+++ b/tests/03_NAO_multik/scf_nspin4_nsoc_hr/hrs1_nao.csr.ref
@@ -0,0 +1,75 @@
+ --- Ionic Step 1 ---
+ # print H matrix in real space H(R)
+ 1 # number of spin directions
+ 1 # spin index, E_Fermi = -6.59889 eV
+ 16 # number of localized basis
+ 1 # number of Bravais lattice vector R
+
+ user_defined_lattice
+ 10.5835
+ 1 0 0
+ 0 1 0
+ 0 0 1
+ O
+ 2
+ Direct
+ 0.5 0.5 0.4424999999992
+ 0.5 0.5 0.5575000000008
+
+ #----------------------------------------------------------------------#
+ #                               CSR Format                             #
+ # The outer loop corresponds to the number of Bravais lattice vectors. #
+ # The first line contains the index of the Bravais lattice vector      #
+ # (Rx, Ry, Rz), followed by the number of non-zero elements.           #
+ # The subsequent lines consist of three blocks of data, which are      #
+ # values, column indices, row pointers.                                #
+ #----------------------------------------------------------------------#
+
+ 0 0 0 176
+ # CSR values
+ (-2.007633384794e+00,0.000000000000e+00) (-4.362949235670e-02,4.362947017816e-02) (-4.159497162204e-01,0.000000000000e+00) (1.259652625142e-03,-1.259682213725e-03) (-1.103721312843e-09,0.000000000000e+00) (-1.109394672457e-09,-1.109362693949e-09)
+ (-1.005948197227e+00,0.000000000000e+00) (-8.822139488821e-03,8.822117336488e-03) (1.094900063890e+00,0.000000000000e+00) (9.771130281636e-03,-9.771100798884e-03) (-1.103717922653e-09,0.000000000000e+00) (-1.109395077935e-09,-1.109362059317e-09)
+ (-4.362949235670e-02,-4.362947017816e-02) (-2.007633404793e+00,0.000000000000e+00) (1.259652625142e-03,1.259682213725e-03) (-4.159497439845e-01,0.000000000000e+00) (-1.109394672457e-09,1.109362693949e-09) (1.103714868562e-09,0.000000000000e+00)
+ (-8.822139488821e-03,-8.822117336488e-03) (-1.005948217119e+00,0.000000000000e+00) (9.771130281636e-03,9.771100798884e-03) (1.094900091226e+00,0.000000000000e+00) (-1.109395077935e-09,1.109362059317e-09) (1.103717050219e-09,0.000000000000e+00)
+ (-4.159497162204e-01,0.000000000000e+00) (1.259652625142e-03,-1.259682213725e-03) (-1.157369969289e+00,0.000000000000e+00) (-1.805578229644e-02,1.805574267800e-02) (-1.417147887359e-09,0.000000000000e+00) (-1.428456578452e-09,-1.428414588965e-09)
+ (-1.094900063871e+00,0.000000000000e+00) (-9.771130286489e-03,9.771100793936e-03) (8.106170895977e-01,0.000000000000e+00) (1.679599918853e-03,-1.679560416061e-03) (-1.417148743788e-09,0.000000000000e+00) (-1.428456283077e-09,-1.428414962515e-09)
+ (1.259652625142e-03,1.259682213725e-03) (-4.159497439845e-01,0.000000000000e+00) (-1.805578229644e-02,-1.805574267800e-02) (-1.157370007515e+00,0.000000000000e+00) (-1.428456578452e-09,1.428414588965e-09) (1.417147509629e-09,0.000000000000e+00)
+ (-9.771130286489e-03,-9.771100793936e-03) (-1.094900091246e+00,0.000000000000e+00) (1.679599918853e-03,1.679560416061e-03) (8.106171273558e-01,0.000000000000e+00) (-1.428456283077e-09,1.428414962515e-09) (1.417146927015e-09,0.000000000000e+00)
+ (-1.103721771670e-09,0.000000000000e+00) (-1.109394671601e-09,-1.109362694177e-09) (-1.417148053652e-09,0.000000000000e+00) (-1.428456579193e-09,-1.428414590375e-09) (-7.929900020956e-01,0.000000000000e+00) (-5.659068868439e-02,5.659067608671e-02)
+ (-5.563390342022e-10,0.000000000000e+00) (-1.103717975597e-09,0.000000000000e+00) (-1.109395052813e-09,-1.109362081886e-09) (1.417148528001e-09,0.000000000000e+00) (1.428456236039e-09,1.428415005041e-09) (-4.152966155347e-01,0.000000000000e+00)
+ (-5.960410685548e-03,5.960398075592e-03) (-5.563390026505e-10,0.000000000000e+00) (-1.109394671601e-09,1.109362694177e-09) (1.103714409736e-09,0.000000000000e+00) (-1.428456579193e-09,1.428414590375e-09) (1.417147343336e-09,0.000000000000e+00)
+ (-5.659068868439e-02,-5.659067608671e-02) (-7.929900036338e-01,0.000000000000e+00) (5.563393474512e-10,0.000000000000e+00) (-1.109395052813e-09,1.109362081886e-09) (1.103717071435e-09,0.000000000000e+00) (1.428456236039e-09,-1.428415005041e-09)
+ (-1.417147426619e-09,0.000000000000e+00) (-5.960410685548e-03,-5.960398075592e-03) (-4.152966171227e-01,0.000000000000e+00) (5.563390573209e-10,0.000000000000e+00) (-5.563390325043e-10,0.000000000000e+00) (-7.929899958025e-01,0.000000000000e+00)
+ (-5.659068715897e-02,5.659067761213e-02) (-5.563390037131e-10,0.000000000000e+00) (-4.152966092416e-01,0.000000000000e+00) (-5.960409160130e-03,5.960399601017e-03) (5.563393491491e-10,0.000000000000e+00) (-5.659068715897e-02,-5.659067761213e-02)
+ (-7.929900099269e-01,0.000000000000e+00) (5.563390562583e-10,0.000000000000e+00) (-5.960409160130e-03,-5.960399601017e-03) (-4.152966234158e-01,0.000000000000e+00) (-1.005948197227e+00,0.000000000000e+00) (-8.822139488821e-03,8.822117336488e-03)
+ (-1.094900063871e+00,0.000000000000e+00) (-9.771130286489e-03,9.771100793936e-03) (-1.103717975597e-09,0.000000000000e+00) (-1.109395052813e-09,-1.109362081886e-09) (-2.007633384900e+00,0.000000000000e+00) (-4.362949233026e-02,4.362947020412e-02)
+ (4.159497166290e-01,0.000000000000e+00) (-1.259652726087e-03,1.259682112809e-03) (-1.103719043688e-09,0.000000000000e+00) (-1.109394720880e-09,-1.109362663299e-09) (-8.822139488821e-03,-8.822117336488e-03) (-1.005948217119e+00,0.000000000000e+00)
+ (-9.771130286489e-03,-9.771100793936e-03) (-1.094900091246e+00,0.000000000000e+00) (-1.109395052813e-09,1.109362081886e-09) (1.103717071435e-09,0.000000000000e+00) (-4.362949233026e-02,-4.362947020412e-02) (-2.007633404686e+00,0.000000000000e+00)
+ (-1.259652726087e-03,-1.259682112809e-03) (4.159497435759e-01,0.000000000000e+00) (-1.109394720880e-09,1.109362663299e-09) (1.103715812279e-09,0.000000000000e+00) (1.094900063890e+00,0.000000000000e+00) (9.771130281636e-03,-9.771100798884e-03)
+ (8.106170895977e-01,0.000000000000e+00) (1.679599918853e-03,-1.679560416061e-03) (1.417148528001e-09,0.000000000000e+00) (1.428456236039e-09,1.428415005041e-09) (4.159497166290e-01,0.000000000000e+00) (-1.259652726087e-03,1.259682112809e-03)
+ (-1.157369969757e+00,0.000000000000e+00) (-1.805578218067e-02,1.805574279352e-02) (1.417147670354e-09,0.000000000000e+00) (1.428457107906e-09,1.428413982774e-09) (9.771130281636e-03,9.771100798884e-03) (1.094900091226e+00,0.000000000000e+00)
+ (1.679599918853e-03,1.679560416061e-03) (8.106171273558e-01,0.000000000000e+00) (1.428456236039e-09,-1.428415005041e-09) (-1.417147426619e-09,0.000000000000e+00) (-1.259652726087e-03,-1.259682112809e-03) (4.159497435759e-01,0.000000000000e+00)
+ (-1.805578218067e-02,-1.805574279352e-02) (-1.157370007047e+00,0.000000000000e+00) (1.428457107906e-09,-1.428413982774e-09) (-1.417147726848e-09,0.000000000000e+00) (-1.103717922653e-09,0.000000000000e+00) (-1.109395077935e-09,-1.109362059317e-09)
+ (-1.417148743788e-09,0.000000000000e+00) (-1.428456283077e-09,-1.428414962515e-09) (-4.152966155347e-01,0.000000000000e+00) (-5.960410685548e-03,5.960398075592e-03) (-5.563390037131e-10,0.000000000000e+00) (-1.103718927573e-09,0.000000000000e+00)
+ (-1.109394720796e-09,-1.109362654618e-09) (1.417147693483e-09,0.000000000000e+00) (1.428457108364e-09,1.428413982235e-09) (-7.929900020457e-01,0.000000000000e+00) (-5.659068869637e-02,5.659067607414e-02) (-5.563389220589e-10,0.000000000000e+00)
+ (-1.109395077935e-09,1.109362059317e-09) (1.103717050219e-09,0.000000000000e+00) (-1.428456283077e-09,1.428414962515e-09) (1.417146927015e-09,0.000000000000e+00) (-5.960410685548e-03,-5.960398075592e-03) (-4.152966171227e-01,0.000000000000e+00)
+ (5.563390562583e-10,0.000000000000e+00) (-1.109394720796e-09,1.109362654618e-09) (1.103715928394e-09,0.000000000000e+00) (1.428457108364e-09,-1.428413982235e-09) (-1.417147703719e-09,0.000000000000e+00) (-5.659068869637e-02,-5.659067607414e-02)
+ (-7.929900036834e-01,0.000000000000e+00) (5.563391892780e-10,0.000000000000e+00) (-5.563390026505e-10,0.000000000000e+00) (-4.152966092416e-01,0.000000000000e+00) (-5.960409160130e-03,5.960399601017e-03) (-5.563389220892e-10,0.000000000000e+00)
+ (-7.929899957526e-01,0.000000000000e+00) (-5.659068717096e-02,5.659067759957e-02) (5.563390573209e-10,0.000000000000e+00) (-5.960409160130e-03,-5.960399601017e-03) (-4.152966234158e-01,0.000000000000e+00) (5.563391892477e-10,0.000000000000e+00)
+ (-5.659068717096e-02,-5.659067759957e-02) (-7.929900099765e-01,0.000000000000e+00)
+ # CSR column indices
+ 0 1 2 3 4 5 8 9 10 11 12 13 0 1 2 3
+ 4 5 8 9 10 11 12 13 0 1 2 3 4 5 8 9
+ 10 11 12 13 0 1 2 3 4 5 8 9 10 11 12 13
+ 0 1 2 3 4 5 6 8 9 10 11 12 13 14 0 1
+ 2 3 4 5 7 8 9 10 11 12 13 15 4 6 7 12
+ 14 15 5 6 7 13 14 15 0 1 2 3 4 5 8 9
+ 10 11 12 13 0 1 2 3 4 5 8 9 10 11 12 13
+ 0 1 2 3 4 5 8 9 10 11 12 13 0 1 2 3
+ 4 5 8 9 10 11 12 13 0 1 2 3 4 5 6 8
+ 9 10 11 12 13 14 0 1 2 3 4 5 7 8 9 10
+ 11 12 13 15 4 6 7 12 14 15 5 6 7 13 14 15
+ # CSR row pointers
+ 0 12 24 36 48 62 76 82 88 100 112 124 136 150 164 170
+ 176
+
diff --git a/tests/03_NAO_multik/scf_nspin4_nsoc_hr/result.ref b/tests/03_NAO_multik/scf_nspin4_nsoc_hr/result.ref
new file mode 100644
index 0000000000..4d4ce3a028
--- /dev/null
+++ b/tests/03_NAO_multik/scf_nspin4_nsoc_hr/result.ref
@@ -0,0 +1,5 @@
+etotref -861.0910298473461
+etotperatomref -430.5455149237
+CompareHR_pass 0
+CompareSR_pass 0
+totaltimeref 2.77
diff --git a/tests/03_NAO_multik/scf_nspin4_nsoc_hr/sr_nao.csr.ref b/tests/03_NAO_multik/scf_nspin4_nsoc_hr/sr_nao.csr.ref
new file mode 100644
index 0000000000..084e88d70e
--- /dev/null
+++ b/tests/03_NAO_multik/scf_nspin4_nsoc_hr/sr_nao.csr.ref
@@ -0,0 +1,44 @@
+ --- Ionic Step 1 ---
+ # print S matrix in real space S(R)
+ 1 # number of spin directions
+ 1 # spin index
+ 16 # number of localized basis
+ 1 # number of Bravais lattice vector R
+
+ user_defined_lattice
+ 10.5835
+ 1 0 0
+ 0 1 0
+ 0 0 1
+ O
+ 2
+ Direct
+ 0.5 0.5 0.4424999999992
+ 0.5 0.5 0.5575000000008
+
+ #----------------------------------------------------------------------#
+ #                               CSR Format                             #
+ # The outer loop corresponds to the number of Bravais lattice vectors. #
+ # The first line contains the index of the Bravais lattice vector      #
+ # (Rx, Ry, Rz), followed by the number of non-zero elements.           #
+ # The subsequent lines consist of three blocks of data, which are      #
+ # values, column indices, row pointers.                                #
+ #----------------------------------------------------------------------#
+
+ 0 0 0 40
+ # CSR values
+ (1.000000000000e+00,0.000000000000e+00) (3.122772551440e-01,0.000000000000e+00) (-3.769119232454e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (3.122772551440e-01,0.000000000000e+00) (-3.769119232454e-01,0.000000000000e+00)
+ (1.000000000000e+00,0.000000000000e+00) (3.769119232454e-01,0.000000000000e+00) (-2.556149750289e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (3.769119232454e-01,0.000000000000e+00) (-2.556149750289e-01,0.000000000000e+00)
+ (1.000000000000e+00,0.000000000000e+00) (2.212660810968e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (2.212660810968e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (2.212660810968e-01,0.000000000000e+00)
+ (1.000000000000e+00,0.000000000000e+00) (2.212660810968e-01,0.000000000000e+00) (3.122772551440e-01,0.000000000000e+00) (3.769119232454e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (3.122772551440e-01,0.000000000000e+00)
+ (3.769119232454e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (-3.769119232454e-01,0.000000000000e+00) (-2.556149750289e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (-3.769119232454e-01,0.000000000000e+00)
+ (-2.556149750289e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (2.212660810968e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (2.212660810968e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00)
+ (2.212660810968e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (2.212660810968e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00)
+ # CSR column indices
+ 0 8 10 1 9 11 2 8 10 3 9 11 4 12 5 13
+ 6 14 7 15 0 2 8 1 3 9 0 2 10 1 3 11
+ 4 12 5 13 6 14 7 15
+ # CSR row pointers
+ 0 3 6 9 12 14 16 18 20 23 26 29 32 34 36 38
+ 40
+
diff --git a/tests/03_NAO_multik/scf_nspin4_soc_hr/INPUT b/tests/03_NAO_multik/scf_nspin4_soc_hr/INPUT
new file mode 100644
index 0000000000..f87c10e214
--- /dev/null
+++ b/tests/03_NAO_multik/scf_nspin4_soc_hr/INPUT
@@ -0,0 +1,22 @@
+INPUT_PARAMETERS
+suffix            autotest
+calculation       scf
+symmetry          0
+pseudo_dir        ../../PP_ORB
+orbital_dir       ../../PP_ORB
+gamma_only        0
+ecutwfc           20
+scf_thr           1e-6
+scf_nmax          50
+noncolin          1
+nspin             4
+lspinorb          1
+basis_type        lcao
+ks_solver         scalapack_gvx
+dft_functional    pbe
+smearing_method   gauss
+smearing_sigma    0.02
+mixing_type       pulay
+mixing_beta       0.4
+mixing_gg0        3.0
+out_hsr           1 12
diff --git a/tests/03_NAO_multik/scf_nspin4_soc_hr/KPT b/tests/03_NAO_multik/scf_nspin4_soc_hr/KPT
new file mode 100644
index 0000000000..c289c0158a
--- /dev/null
+++ b/tests/03_NAO_multik/scf_nspin4_soc_hr/KPT
@@ -0,0 +1,4 @@
+K_POINTS
+0
+Gamma
+1 1 1 0 0 0
diff --git a/tests/03_NAO_multik/scf_nspin4_soc_hr/README b/tests/03_NAO_multik/scf_nspin4_soc_hr/README
new file mode 100644
index 0000000000..0405d8145e
--- /dev/null
+++ b/tests/03_NAO_multik/scf_nspin4_soc_hr/README
@@ -0,0 +1,8 @@
+Self-consistent nspin=4 O2 H(R)/S(R) regression, with SOC.
+Two O atoms separated by 2.3 bohr along z in a 20-bohr cubic cell.
+Existing fully relativistic O PP and minimal 6-bohr 1s1p orbitals; PBE, 20 Ry, Gamma 1x1x1.
+Both initial moments are (1/sqrt(2),1/sqrt(2),0) muB; no DeltaSpin constraint.
+Full SCF reaches 1e-6 within 50 steps and retains a finite y magnetization.
+Complete raw complex references cover the nspin=4 interatomic H(R) export fix.
+The pre-fix build converges but fails the H comparison against the fixed-build reference.
+Only R=0 is present. This tests the export convention, not material convergence or intercell Bloch phases.
diff --git a/tests/03_NAO_multik/scf_nspin4_soc_hr/STRU b/tests/03_NAO_multik/scf_nspin4_soc_hr/STRU
new file mode 100644
index 0000000000..96603e21aa
--- /dev/null
+++ b/tests/03_NAO_multik/scf_nspin4_soc_hr/STRU
@@ -0,0 +1,22 @@
+ATOMIC_SPECIES
+O 15.999 O_ONCV_PBE_FR-1.0.upf
+
+NUMERICAL_ORBITAL
+O_gga_6au_60Ry_1s1p.orb
+
+LATTICE_CONSTANT
+20.0
+
+LATTICE_VECTORS
+1 0 0
+0 1 0
+0 0 1
+
+ATOMIC_POSITIONS
+Direct
+
+O
+0.0
+2
+0.5 0.5 0.4425 0 0 0 mag 0.7071067811865475 0.7071067811865475 0
+0.5 0.5 0.5575 0 0 0 mag 0.7071067811865475 0.7071067811865475 0
diff --git a/tests/03_NAO_multik/scf_nspin4_soc_hr/hrs1_nao.csr.ref b/tests/03_NAO_multik/scf_nspin4_soc_hr/hrs1_nao.csr.ref
new file mode 100644
index 0000000000..6fd6d52e74
--- /dev/null
+++ b/tests/03_NAO_multik/scf_nspin4_soc_hr/hrs1_nao.csr.ref
@@ -0,0 +1,93 @@
+ --- Ionic Step 1 ---
+ # print H matrix in real space H(R)
+ 1 # number of spin directions
+ 1 # spin index, E_Fermi = -6.5989 eV
+ 16 # number of localized basis
+ 1 # number of Bravais lattice vector R
+
+ user_defined_lattice
+ 10.5835
+ 1 0 0
+ 0 1 0
+ 0 0 1
+ O
+ 2
+ Direct
+ 0.5 0.5 0.4424999999992
+ 0.5 0.5 0.5575000000008
+
+ #----------------------------------------------------------------------#
+ #                               CSR Format                             #
+ # The outer loop corresponds to the number of Bravais lattice vectors. #
+ # The first line contains the index of the Bravais lattice vector      #
+ # (Rx, Ry, Rz), followed by the number of non-zero elements.           #
+ # The subsequent lines consist of three blocks of data, which are      #
+ # values, column indices, row pointers.                                #
+ #----------------------------------------------------------------------#
+
+ 0 0 0 256
+ # CSR values
+ (-2.007633651031e+00,0.000000000000e+00) (-4.371846988445e-02,4.371846993221e-02) (-4.159492095343e-01,0.000000000000e+00) (1.147628562737e-03,-1.147628458939e-03) (2.040454953921e-05,0.000000000000e+00) (-1.659204589595e-06,-6.562798408203e-09)
+ (2.040775135279e-05,0.000000000000e+00) (6.565586288042e-09,1.659205492058e-06) (-1.005948080350e+00,0.000000000000e+00) (-8.912562325061e-03,8.912562356481e-03) (1.094899885270e+00,0.000000000000e+00) (9.884921529837e-03,-9.884921570493e-03)
+ (9.448370689697e-08,0.000000000000e+00) (-3.551267249028e-05,-6.563543443739e-09) (9.768552351893e-08,0.000000000000e+00) (6.566331181920e-09,3.551267339317e-05) (-4.371846988445e-02,-4.371846993221e-02) (-2.007633650912e+00,0.000000000000e+00)
+ (1.147628562737e-03,1.147628458939e-03) (-4.159492089157e-01,0.000000000000e+00) (1.649505976100e-06,6.562798408203e-09) (-2.040454951763e-05,0.000000000000e+00) (6.565586288042e-09,1.649505073637e-06) (-2.040775133256e-05,0.000000000000e+00)
+ (-8.912562325061e-03,-8.912562356481e-03) (-1.005948080390e+00,0.000000000000e+00) (9.884921529837e-03,9.884921570493e-03) (1.094899885356e+00,0.000000000000e+00) (3.550297532761e-05,6.563543443739e-09) (-9.448369482362e-08,0.000000000000e+00)
+ (6.566331181920e-09,3.550297442473e-05) (-9.768551139170e-08,0.000000000000e+00) (-4.159492095343e-01,0.000000000000e+00) (1.147628562737e-03,-1.147628458939e-03) (-1.157370327208e+00,0.000000000000e+00) (-1.820408861115e-02,1.820408873295e-02)
+ (-3.337439016156e-05,0.000000000000e+00) (8.972997652376e-04,-8.630859735441e-09) (-3.337020594404e-05,0.000000000000e+00) (8.634551560830e-09,-8.972997640220e-04) (-1.094899885299e+00,0.000000000000e+00) (-9.884921527379e-03,9.884921572981e-03)
+ (8.106167242772e-01,0.000000000000e+00) (1.824181683226e-03,-1.824181742691e-03) (-2.491285473770e-06,0.000000000000e+00) (-3.948296095405e-05,-8.629429196517e-09) (-2.487101250488e-06,0.000000000000e+00) (8.633121032073e-09,3.948296217002e-05)
+ (1.147628562737e-03,1.147628458939e-03) (-4.159492089157e-01,0.000000000000e+00) (-1.820408861115e-02,-1.820408873295e-02) (-1.157370326683e+00,0.000000000000e+00) (-8.973125150905e-04,8.630859735441e-09) (3.337439003897e-05,0.000000000000e+00)
+ (8.634551560830e-09,-8.973125163060e-04) (3.337020582147e-05,0.000000000000e+00) (-9.884921527379e-03,-9.884921572981e-03) (-1.094899885327e+00,0.000000000000e+00) (1.824181683226e-03,1.824181742691e-03) (8.106167243569e-01,0.000000000000e+00)
+ (3.947020821254e-05,8.629429196517e-09) (2.491285494250e-06,0.000000000000e+00) (8.633121032073e-09,3.947020699656e-05) (2.487101270866e-06,0.000000000000e+00) (2.040454953921e-05,0.000000000000e+00) (1.649505976100e-06,-6.562798408215e-09)
+ (-3.337439016155e-05,0.000000000000e+00) (-8.973125150905e-04,-8.630859734521e-09) (-7.929912985417e-01,0.000000000000e+00) (-5.657017132569e-02,5.676553524700e-02) (1.814239362027e-09,-9.008532559618e-04) (1.413029402079e-05,-1.413030004508e-05)
+ (-9.768718331413e-08,0.000000000000e+00) (-3.551267249068e-05,-6.563543680609e-09) (-2.487099060856e-06,0.000000000000e+00) (3.948296095496e-05,8.629429767333e-09) (-4.152965836409e-01,0.000000000000e+00) (-5.943812771134e-03,6.139214819621e-03)
+ (-4.020663519336e-10,-4.122872387800e-05) (1.414668848397e-05,-1.414669301876e-05) (-1.659204589595e-06,6.562798408215e-09) (-2.040454951763e-05,0.000000000000e+00) (8.972997652376e-04,8.630859734521e-09) (3.337439003897e-05,0.000000000000e+00)
+ (-5.657017132569e-02,-5.676553524700e-02) (-7.929912986101e-01,0.000000000000e+00) (1.413029402079e-05,1.413030004508e-05) (1.800173207030e-09,9.008532559618e-04) (3.550297532722e-05,6.563543680609e-09) (9.768719571270e-08,0.000000000000e+00)
+ (-3.947020821162e-05,-8.629429767333e-09) (2.487099040964e-06,0.000000000000e+00) (-5.943812771134e-03,-6.139214819621e-03) (-4.152965836534e-01,0.000000000000e+00) (1.414668848397e-05,1.414669301876e-05) (-4.006849690799e-10,4.122872387800e-05)
+ (2.040775135288e-05,0.000000000000e+00) (6.565586292503e-09,-1.649505073636e-06) (-3.337020594404e-05,0.000000000000e+00) (8.634551561660e-09,8.973125163060e-04) (1.814239372445e-09,9.008532559618e-04) (1.413029402079e-05,-1.413030004508e-05)
+ (-7.929912985389e-01,0.000000000000e+00) (-5.676553523865e-02,5.657017133163e-02) (-9.448536680329e-08,0.000000000000e+00) (6.566331432918e-09,3.551267339351e-05) (-2.491283284578e-06,0.000000000000e+00) (-8.633121647298e-09,-3.948296217078e-05)
+ (-4.020663672195e-10,4.122872387800e-05) (1.414668848397e-05,-1.414669301876e-05) (-4.152965836385e-01,0.000000000000e+00) (-6.139214804092e-03,5.943812779953e-03) (6.565586292503e-09,-1.659205492059e-06) (-2.040775133247e-05,0.000000000000e+00)
+ (8.634551561660e-09,8.972997640220e-04) (3.337020582147e-05,0.000000000000e+00) (1.413029402079e-05,1.413030004508e-05) (1.800173217447e-09,-9.008532559618e-04) (-5.676553523865e-02,-5.657017133163e-02) (-7.929912986121e-01,0.000000000000e+00)
+ (6.566331432918e-09,3.550297442439e-05) (9.448537885024e-08,0.000000000000e+00) (-8.633121647298e-09,-3.947020699580e-05) (2.491283264282e-06,0.000000000000e+00) (1.414668848397e-05,1.414669301876e-05) (-4.006849843658e-10,-4.122872387800e-05)
+ (-6.139214804092e-03,-5.943812779953e-03) (-4.152965836558e-01,0.000000000000e+00) (-1.005948080350e+00,0.000000000000e+00) (-8.912562325061e-03,8.912562356481e-03) (-1.094899885299e+00,0.000000000000e+00) (-9.884921527379e-03,9.884921572981e-03)
+ (-9.768718331413e-08,0.000000000000e+00) (3.550297532722e-05,-6.563543680609e-09) (-9.448536680329e-08,0.000000000000e+00) (6.566331432918e-09,-3.550297442439e-05) (-2.007633650871e+00,0.000000000000e+00) (-4.371846990086e-02,4.371846991594e-02)
+ (4.159492088588e-01,0.000000000000e+00) (-1.147628502068e-03,1.147628519609e-03) (-2.040775300461e-05,0.000000000000e+00) (1.649505978340e-06,-6.562796506286e-09) (-2.040455119023e-05,0.000000000000e+00) (6.565584229014e-09,-1.649505075363e-06)
+ (-8.912562325061e-03,-8.912562356481e-03) (-1.005948080390e+00,0.000000000000e+00) (-9.884921527379e-03,-9.884921572981e-03) (-1.094899885327e+00,0.000000000000e+00) (-3.551267249068e-05,6.563543680609e-09) (9.768719571270e-08,0.000000000000e+00)
+ (6.566331432918e-09,-3.551267339351e-05) (9.448537885024e-08,0.000000000000e+00) (-4.371846990086e-02,-4.371846991594e-02) (-2.007633651071e+00,0.000000000000e+00) (-1.147628502068e-03,-1.147628519609e-03) (4.159492095913e-01,0.000000000000e+00)
+ (-1.659204587355e-06,6.562796506286e-09) (2.040775302449e-05,0.000000000000e+00) (6.565584229014e-09,-1.659205490332e-06) (2.040455121111e-05,0.000000000000e+00) (1.094899885270e+00,0.000000000000e+00) (9.884921529837e-03,-9.884921570493e-03)
+ (8.106167242772e-01,0.000000000000e+00) (1.824181683226e-03,-1.824181742691e-03) (-2.487099060856e-06,0.000000000000e+00) (-3.947020821162e-05,8.629429767333e-09) (-2.491283284578e-06,0.000000000000e+00) (-8.633121647298e-09,3.947020699580e-05)
+ (4.159492088588e-01,0.000000000000e+00) (-1.147628502068e-03,1.147628519609e-03) (-1.157370326603e+00,0.000000000000e+00) (-1.820408867351e-02,1.820408867064e-02) (-3.337020361165e-05,0.000000000000e+00) (8.973125150830e-04,8.630856333448e-09)
+ (-3.337438782724e-05,0.000000000000e+00) (-8.634548019633e-09,-8.973125162994e-04) (9.884921529837e-03,9.884921570493e-03) (1.094899885356e+00,0.000000000000e+00) (1.824181683226e-03,1.824181742691e-03) (8.106167243569e-01,0.000000000000e+00)
+ (3.948296095496e-05,-8.629429767333e-09) (2.487099040964e-06,0.000000000000e+00) (-8.633121647298e-09,3.948296217078e-05) (2.491283264282e-06,0.000000000000e+00) (-1.147628502068e-03,-1.147628519609e-03) (4.159492095913e-01,0.000000000000e+00)
+ (-1.820408867351e-02,-1.820408867064e-02) (-1.157370327287e+00,0.000000000000e+00) (-8.972997652451e-04,-8.630856333448e-09) (3.337020373650e-05,0.000000000000e+00) (-8.634548019633e-09,-8.972997640286e-04) (3.337438795214e-05,0.000000000000e+00)
+ (9.448370689697e-08,0.000000000000e+00) (3.550297532761e-05,-6.563543443739e-09) (-2.491285473770e-06,0.000000000000e+00) (3.947020821254e-05,-8.629429196517e-09) (-4.152965836409e-01,0.000000000000e+00) (-5.943812771134e-03,6.139214819621e-03)
+ (-4.020663672195e-10,-4.122872387800e-05) (1.414668848397e-05,-1.414669301876e-05) (-2.040775300504e-05,0.000000000000e+00) (-1.659204587354e-06,-6.562796513201e-09) (-3.337020361161e-05,0.000000000000e+00) (-8.972997652451e-04,8.630856333175e-09)
+ (-7.929912985971e-01,0.000000000000e+00) (-5.657017132290e-02,5.676553525427e-02) (1.798791334305e-09,-9.008532559618e-04) (1.413029551015e-05,-1.413029855537e-05) (-3.551267249028e-05,6.563543443739e-09) (-9.448369482362e-08,0.000000000000e+00)
+ (-3.948296095405e-05,8.629429196517e-09) (2.491285494250e-06,0.000000000000e+00) (-5.943812771134e-03,-6.139214819621e-03) (-4.152965836534e-01,0.000000000000e+00) (1.414668848397e-05,1.414669301876e-05) (-4.006849843658e-10,4.122872387800e-05)
+ (1.649505978341e-06,6.562796513201e-09) (2.040775302406e-05,0.000000000000e+00) (8.973125150830e-04,-8.630856333175e-09) (3.337020373654e-05,0.000000000000e+00) (-5.657017132290e-02,-5.676553525427e-02) (-7.929912985537e-01,0.000000000000e+00)
+ (1.413029551015e-05,1.413029855537e-05) (1.815620372481e-09,9.008532559618e-04) (9.768552351893e-08,0.000000000000e+00) (6.566331181920e-09,-3.550297442473e-05) (-2.487101250488e-06,0.000000000000e+00) (8.633121032073e-09,-3.947020699656e-05)
+ (-4.020663519336e-10,4.122872387800e-05) (1.414668848397e-05,-1.414669301876e-05) (-4.152965836385e-01,0.000000000000e+00) (-6.139214804092e-03,5.943812779953e-03) (-2.040455119044e-05,0.000000000000e+00) (6.565584227278e-09,1.659205490333e-06)
+ (-3.337438782729e-05,0.000000000000e+00) (-8.634548019361e-09,8.972997640286e-04) (1.798791333875e-09,9.008532559618e-04) (1.413029551015e-05,-1.413029855537e-05) (-7.929912985951e-01,0.000000000000e+00) (-5.676553523156e-02,5.657017133461e-02)
+ (6.566331181920e-09,-3.551267339317e-05) (-9.768551139170e-08,0.000000000000e+00) (8.633121032073e-09,-3.948296217002e-05) (2.487101270866e-06,0.000000000000e+00) (1.414668848397e-05,1.414669301876e-05) (-4.006849690799e-10,-4.122872387800e-05)
+ (-6.139214804092e-03,-5.943812779953e-03) (-4.152965836558e-01,0.000000000000e+00) (6.565584227278e-09,1.649505075361e-06) (2.040455121091e-05,0.000000000000e+00) (-8.634548019361e-09,8.973125162994e-04) (3.337438795208e-05,0.000000000000e+00)
+ (1.413029551015e-05,1.413029855537e-05) (1.815620372051e-09,-9.008532559618e-04) (-5.676553523156e-02,-5.657017133461e-02) (-7.929912985565e-01,0.000000000000e+00)
+ # CSR column indices
+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+ # CSR row pointers
+ 0 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240
+ 256
+
diff --git a/tests/03_NAO_multik/scf_nspin4_soc_hr/result.ref b/tests/03_NAO_multik/scf_nspin4_soc_hr/result.ref
new file mode 100644
index 0000000000..50d19046a0
--- /dev/null
+++ b/tests/03_NAO_multik/scf_nspin4_soc_hr/result.ref
@@ -0,0 +1,5 @@
+etotref -861.0913641486368
+etotperatomref -430.5456820743
+CompareHR_pass 0
+CompareSR_pass 0
+totaltimeref 2.86
diff --git a/tests/03_NAO_multik/scf_nspin4_soc_hr/sr_nao.csr.ref b/tests/03_NAO_multik/scf_nspin4_soc_hr/sr_nao.csr.ref
new file mode 100644
index 0000000000..084e88d70e
--- /dev/null
+++ b/tests/03_NAO_multik/scf_nspin4_soc_hr/sr_nao.csr.ref
@@ -0,0 +1,44 @@
+ --- Ionic Step 1 ---
+ # print S matrix in real space S(R)
+ 1 # number of spin directions
+ 1 # spin index
+ 16 # number of localized basis
+ 1 # number of Bravais lattice vector R
+
+ user_defined_lattice
+ 10.5835
+ 1 0 0
+ 0 1 0
+ 0 0 1
+ O
+ 2
+ Direct
+ 0.5 0.5 0.4424999999992
+ 0.5 0.5 0.5575000000008
+
+ #----------------------------------------------------------------------#
+ #                               CSR Format                             #
+ # The outer loop corresponds to the number of Bravais lattice vectors. #
+ # The first line contains the index of the Bravais lattice vector      #
+ # (Rx, Ry, Rz), followed by the number of non-zero elements.           #
+ # The subsequent lines consist of three blocks of data, which are      #
+ # values, column indices, row pointers.                                #
+ #----------------------------------------------------------------------#
+
+ 0 0 0 40
+ # CSR values
+ (1.000000000000e+00,0.000000000000e+00) (3.122772551440e-01,0.000000000000e+00) (-3.769119232454e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (3.122772551440e-01,0.000000000000e+00) (-3.769119232454e-01,0.000000000000e+00)
+ (1.000000000000e+00,0.000000000000e+00) (3.769119232454e-01,0.000000000000e+00) (-2.556149750289e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (3.769119232454e-01,0.000000000000e+00) (-2.556149750289e-01,0.000000000000e+00)
+ (1.000000000000e+00,0.000000000000e+00) (2.212660810968e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (2.212660810968e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (2.212660810968e-01,0.000000000000e+00)
+ (1.000000000000e+00,0.000000000000e+00) (2.212660810968e-01,0.000000000000e+00) (3.122772551440e-01,0.000000000000e+00) (3.769119232454e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (3.122772551440e-01,0.000000000000e+00)
+ (3.769119232454e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (-3.769119232454e-01,0.000000000000e+00) (-2.556149750289e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (-3.769119232454e-01,0.000000000000e+00)
+ (-2.556149750289e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (2.212660810968e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (2.212660810968e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00)
+ (2.212660810968e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00) (2.212660810968e-01,0.000000000000e+00) (1.000000000000e+00,0.000000000000e+00)
+ # CSR column indices
+ 0 8 10 1 9 11 2 8 10 3 9 11 4 12 5 13
+ 6 14 7 15 0 2 8 1 3 9 0 2 10 1 3 11
+ 4 12 5 13 6 14 7 15
+ # CSR row pointers
+ 0 3 6 9 12 14 16 18 20 23 26 29 32 34 36 38
+ 40
+