diff --git a/source/source_lcao/module_hcontainer/hcontainer.cpp b/source/source_lcao/module_hcontainer/hcontainer.cpp
index 837458744bd..d1c03a634fd 100644
--- a/source/source_lcao/module_hcontainer/hcontainer.cpp
+++ b/source/source_lcao/module_hcontainer/hcontainer.cpp
@@ -38,7 +38,9 @@ HContainer<T>::HContainer(const HContainer<T>& HR_in, T* data_array)
     this->allocated_size = 0;
     this->atom_pairs = HR_in.atom_pairs;
     // data of HR_in will not be copied, please call add() after this constructor to copy data.
-    this->allocate(this->wrapper_pointer, true);
+    // Only zero memory when allocating fresh data (data_array==nullptr);
+    // when wrapping existing data (data_array!=nullptr), preserve the original content.
+    this->allocate(this->wrapper_pointer, data_array == nullptr);
     // tmp terms not copied
 }
 
diff --git a/tests/03_NAO_multik/scf_out_hsr_spin2/INPUT b/tests/03_NAO_multik/scf_out_hsr_spin2/INPUT
new file mode 100644
index 00000000000..5502dad86c8
--- /dev/null
+++ b/tests/03_NAO_multik/scf_out_hsr_spin2/INPUT
@@ -0,0 +1,32 @@
+INPUT_PARAMETERS 
+#Parameters (1.General)
+suffix            autotest
+calculation       scf
+
+nbands            6
+symmetry          0
+pseudo_dir        ../../PP_ORB
+orbital_dir       ../../PP_ORB
+gamma_only        0
+
+nspin             2
+
+#Parameters (2.Iteration)
+ecutwfc           20
+scf_thr           1e-8
+scf_nmax          1
+
+#Parameters (3.Basis)
+basis_type        lcao
+
+#Parameters (4.Smearing)
+smearing_method   gauss
+smearing_sigma    0.002
+
+#Parameters (5.Mixing)
+mixing_type       broyden
+mixing_beta       0.7
+mixing_gg0        0.0
+
+out_mat_hs2       1 5
+ks_solver         scalapack_gvx
diff --git a/tests/03_NAO_multik/scf_out_hsr_spin2/KPT b/tests/03_NAO_multik/scf_out_hsr_spin2/KPT
new file mode 100644
index 00000000000..e769af76382
--- /dev/null
+++ b/tests/03_NAO_multik/scf_out_hsr_spin2/KPT
@@ -0,0 +1,4 @@
+K_POINTS
+0
+Gamma
+2 1 1 0 0 0
diff --git a/tests/03_NAO_multik/scf_out_hsr_spin2/README b/tests/03_NAO_multik/scf_out_hsr_spin2/README
new file mode 100644
index 00000000000..860dbd92051
--- /dev/null
+++ b/tests/03_NAO_multik/scf_out_hsr_spin2/README
@@ -0,0 +1 @@
+test the output of H(R)/S(R) matrix with nspin=2; Note: delete OUT folder before testing!
diff --git a/tests/03_NAO_multik/scf_out_hsr_spin2/STRU b/tests/03_NAO_multik/scf_out_hsr_spin2/STRU
new file mode 100644
index 00000000000..78f469ab645
--- /dev/null
+++ b/tests/03_NAO_multik/scf_out_hsr_spin2/STRU
@@ -0,0 +1,22 @@
+ATOMIC_SPECIES
+Si 14 Si_dojo_nsoc.upf upf201
+
+NUMERICAL_ORBITAL
+Si_dojo_6au_sz.orb
+
+LATTICE_CONSTANT
+15.3  // add lattice constant
+
+LATTICE_VECTORS
+0.0 0.5 0.5
+0.5 0.0 0.5
+0.5 0.5 0.0
+
+ATOMIC_POSITIONS
+Direct 
+
+Si	// Element type	
+0.0	// magnetism
+2	
+0.00 0.00 0.00 1 1 1 mag 1.0
+0.25 0.25 0.25 1 1 1 mag -1.0
diff --git a/tests/03_NAO_multik/scf_out_hsr_spin2/hrs1_nao.csr.ref b/tests/03_NAO_multik/scf_out_hsr_spin2/hrs1_nao.csr.ref
new file mode 100644
index 00000000000..de17e412592
--- /dev/null
+++ b/tests/03_NAO_multik/scf_out_hsr_spin2/hrs1_nao.csr.ref
@@ -0,0 +1,229 @@
+ --- Ionic Step 1 ---
+ # print H matrix in real space H(R)
+ 2 # number of spin directions
+ 1 # spin index
+ 8 # number of localized basis
+ 13 # number of Bravais lattice vector R
+
+ user_defined_lattice
+ 8.09641
+ 0 0.5 0.5
+ 0.5 0 0.5
+ 0.5 0.5 0
+ Si
+ 2
+ Direct
+ 0 0 0
+ 0.25 0.25 0.25
+
+ #----------------------------------------------------------------------#
+ #                               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.                                #
+ #----------------------------------------------------------------------#
+
+ -1 0 0 48
+ # CSR values
+ -1.11792e-04 7.16241e-04 -3.82452e-06 -7.16241e-04 -3.37629e-02 8.00872e-03
+ 8.00872e-03 -8.00872e-03 -7.16241e-04 2.12235e-03 -2.46427e-05 -2.57041e-03
+ -5.50669e-03 -1.91945e-03 -1.96652e-02 1.96652e-02 -3.82452e-06 2.46427e-05
+ -4.45692e-04 -2.46427e-05 -5.50669e-03 -1.96652e-02 -1.91945e-03 1.96652e-02
+ 7.16241e-04 -2.57041e-03 2.46427e-05 2.12235e-03 5.50669e-03 1.96652e-02
+ 1.96652e-02 -1.91945e-03 -1.12382e-04 7.21513e-04 3.79778e-06 -7.21513e-04
+ -7.21513e-04 2.16956e-03 2.43147e-05 -2.61966e-03 3.79778e-06 -2.43147e-05
+ -4.48512e-04 2.43147e-05 7.21513e-04 -2.61966e-03 -2.43147e-05 2.16956e-03
+ # CSR column indices
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7
+ # CSR row pointers
+ 0 8 16 24 32 36 40 44 48
+
+ -1 0 1 32
+ # CSR values
+ -1.11792e-04 7.16241e-04 7.16241e-04 3.82452e-06 -7.16241e-04 2.12235e-03
+ 2.57041e-03 2.46427e-05 -7.16241e-04 2.57041e-03 2.12235e-03 2.46427e-05
+ 3.82452e-06 -2.46427e-05 -2.46427e-05 -4.45692e-04 -1.12382e-04 7.21513e-04
+ 7.21513e-04 -3.79778e-06 -7.21513e-04 2.16956e-03 2.61966e-03 -2.43147e-05
+ -7.21513e-04 2.61966e-03 2.16956e-03 -2.43147e-05 -3.79778e-06 2.43147e-05
+ 2.43147e-05 -4.48512e-04
+ # CSR column indices
+ 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
+ 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7
+ # CSR row pointers
+ 0 4 8 12 16 20 24 28 32
+
+ -1 1 0 32
+ # CSR values
+ -1.11792e-04 -3.82452e-06 7.16241e-04 -7.16241e-04 -3.82452e-06 -4.45692e-04
+ 2.46427e-05 -2.46427e-05 -7.16241e-04 -2.46427e-05 2.12235e-03 -2.57041e-03
+ 7.16241e-04 2.46427e-05 -2.57041e-03 2.12235e-03 -1.12382e-04 3.79778e-06
+ 7.21513e-04 -7.21513e-04 3.79778e-06 -4.48512e-04 -2.43147e-05 2.43147e-05
+ -7.21513e-04 2.43147e-05 2.16956e-03 -2.61966e-03 7.21513e-04 -2.43147e-05
+ -2.61966e-03 2.16956e-03
+ # CSR column indices
+ 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
+ 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7
+ # CSR row pointers
+ 0 4 8 12 16 20 24 28 32
+
+ 0 -1 0 48
+ # CSR values
+ -1.11792e-04 7.16241e-04 -7.16241e-04 -3.82452e-06 -3.37629e-02 8.00872e-03
+ -8.00872e-03 8.00872e-03 -7.16241e-04 2.12235e-03 -2.57041e-03 -2.46427e-05
+ -5.50669e-03 -1.91945e-03 1.96652e-02 -1.96652e-02 7.16241e-04 -2.57041e-03
+ 2.12235e-03 2.46427e-05 5.50669e-03 1.96652e-02 -1.91945e-03 1.96652e-02
+ -3.82452e-06 2.46427e-05 -2.46427e-05 -4.45692e-04 -5.50669e-03 -1.96652e-02
+ 1.96652e-02 -1.91945e-03 -1.12382e-04 7.21513e-04 -7.21513e-04 3.79778e-06
+ -7.21513e-04 2.16956e-03 -2.61966e-03 2.43147e-05 7.21513e-04 -2.61966e-03
+ 2.16956e-03 -2.43147e-05 3.79778e-06 -2.43147e-05 2.43147e-05 -4.48512e-04
+ # CSR column indices
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7
+ # CSR row pointers
+ 0 8 16 24 32 36 40 44 48
+
+ 0 -1 1 32
+ # CSR values
+ -1.11792e-04 7.16241e-04 3.82452e-06 7.16241e-04 -7.16241e-04 2.12235e-03
+ 2.46427e-05 2.57041e-03 3.82452e-06 -2.46427e-05 -4.45692e-04 -2.46427e-05
+ -7.16241e-04 2.57041e-03 2.46427e-05 2.12235e-03 -1.12382e-04 7.21513e-04
+ -3.79778e-06 7.21513e-04 -7.21513e-04 2.16956e-03 -2.43147e-05 2.61966e-03
+ -3.79778e-06 2.43147e-05 -4.48512e-04 2.43147e-05 -7.21513e-04 2.61966e-03
+ -2.43147e-05 2.16956e-03
+ # CSR column indices
+ 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
+ 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7
+ # CSR row pointers
+ 0 4 8 12 16 20 24 28 32
+
+ 0 0 -1 48
+ # CSR values
+ -1.11792e-04 3.82452e-06 -7.16241e-04 -7.16241e-04 -3.37629e-02 -8.00872e-03
+ -8.00872e-03 -8.00872e-03 3.82452e-06 -4.45692e-04 2.46427e-05 2.46427e-05
+ 5.50669e-03 -1.91945e-03 -1.96652e-02 -1.96652e-02 7.16241e-04 -2.46427e-05
+ 2.12235e-03 2.57041e-03 5.50669e-03 -1.96652e-02 -1.91945e-03 -1.96652e-02
+ 7.16241e-04 -2.46427e-05 2.57041e-03 2.12235e-03 5.50669e-03 -1.96652e-02
+ -1.96652e-02 -1.91945e-03 -1.12382e-04 -3.79778e-06 -7.21513e-04 -7.21513e-04
+ -3.79778e-06 -4.48512e-04 -2.43147e-05 -2.43147e-05 7.21513e-04 2.43147e-05
+ 2.16956e-03 2.61966e-03 7.21513e-04 2.43147e-05 2.61966e-03 2.16956e-03
+ # CSR column indices
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7
+ # CSR row pointers
+ 0 8 16 24 32 36 40 44 48
+
+ 0 0 0 40
+ # CSR values
+ -5.43126e-01 -3.37629e-02 -8.00872e-03 8.00872e-03 8.00872e-03 8.04017e-01
+ 5.50669e-03 -1.91945e-03 1.96652e-02 1.96652e-02 8.04017e-01 -5.50669e-03
+ 1.96652e-02 -1.91945e-03 -1.96652e-02 8.04017e-01 -5.50669e-03 1.96652e-02
+ -1.96652e-02 -1.91945e-03 -3.37629e-02 5.50669e-03 -5.50669e-03 -5.50669e-03
+ -4.69258e-01 -8.00872e-03 -1.91945e-03 1.96652e-02 1.96652e-02 8.75227e-01
+ 8.00872e-03 1.96652e-02 -1.91945e-03 -1.96652e-02 8.75227e-01 8.00872e-03
+ 1.96652e-02 -1.96652e-02 -1.91945e-03 8.75227e-01
+ # CSR column indices
+ 0 4 5 6 7 1 4 5 6 7 2 4 5 6 7 3
+ 4 5 6 7 0 1 2 3 4 0 1 2 3 5 0 1
+ 2 3 6 0 1 2 3 7
+ # CSR row pointers
+ 0 5 10 15 20 25 30 35 40
+
+ 0 0 1 48
+ # CSR values
+ -1.11792e-04 3.82452e-06 7.16241e-04 7.16241e-04 3.82452e-06 -4.45692e-04
+ -2.46427e-05 -2.46427e-05 -7.16241e-04 2.46427e-05 2.12235e-03 2.57041e-03
+ -7.16241e-04 2.46427e-05 2.57041e-03 2.12235e-03 -3.37629e-02 5.50669e-03
+ 5.50669e-03 5.50669e-03 -1.12382e-04 -3.79778e-06 7.21513e-04 7.21513e-04
+ -8.00872e-03 -1.91945e-03 -1.96652e-02 -1.96652e-02 -3.79778e-06 -4.48512e-04
+ 2.43147e-05 2.43147e-05 -8.00872e-03 -1.96652e-02 -1.91945e-03 -1.96652e-02
+ -7.21513e-04 -2.43147e-05 2.16956e-03 2.61966e-03 -8.00872e-03 -1.96652e-02
+ -1.96652e-02 -1.91945e-03 -7.21513e-04 -2.43147e-05 2.61966e-03 2.16956e-03
+ # CSR column indices
+ 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ # CSR row pointers
+ 0 4 8 12 16 24 32 40 48
+
+ 0 1 -1 32
+ # CSR values
+ -1.11792e-04 -7.16241e-04 3.82452e-06 -7.16241e-04 7.16241e-04 2.12235e-03
+ -2.46427e-05 2.57041e-03 3.82452e-06 2.46427e-05 -4.45692e-04 2.46427e-05
+ 7.16241e-04 2.57041e-03 -2.46427e-05 2.12235e-03 -1.12382e-04 -7.21513e-04
+ -3.79778e-06 -7.21513e-04 7.21513e-04 2.16956e-03 2.43147e-05 2.61966e-03
+ -3.79778e-06 -2.43147e-05 -4.48512e-04 -2.43147e-05 7.21513e-04 2.61966e-03
+ 2.43147e-05 2.16956e-03
+ # CSR column indices
+ 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
+ 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7
+ # CSR row pointers
+ 0 4 8 12 16 20 24 28 32
+
+ 0 1 0 48
+ # CSR values
+ -1.11792e-04 -7.16241e-04 7.16241e-04 -3.82452e-06 7.16241e-04 2.12235e-03
+ -2.57041e-03 2.46427e-05 -7.16241e-04 -2.57041e-03 2.12235e-03 -2.46427e-05
+ -3.82452e-06 -2.46427e-05 2.46427e-05 -4.45692e-04 -3.37629e-02 -5.50669e-03
+ 5.50669e-03 -5.50669e-03 -1.12382e-04 -7.21513e-04 7.21513e-04 3.79778e-06
+ 8.00872e-03 -1.91945e-03 1.96652e-02 -1.96652e-02 7.21513e-04 2.16956e-03
+ -2.61966e-03 -2.43147e-05 -8.00872e-03 1.96652e-02 -1.91945e-03 1.96652e-02
+ -7.21513e-04 -2.61966e-03 2.16956e-03 2.43147e-05 8.00872e-03 -1.96652e-02
+ 1.96652e-02 -1.91945e-03 3.79778e-06 2.43147e-05 -2.43147e-05 -4.48512e-04
+ # CSR column indices
+ 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ # CSR row pointers
+ 0 4 8 12 16 24 32 40 48
+
+ 1 -1 0 32
+ # CSR values
+ -1.11792e-04 -3.82452e-06 -7.16241e-04 7.16241e-04 -3.82452e-06 -4.45692e-04
+ -2.46427e-05 2.46427e-05 7.16241e-04 2.46427e-05 2.12235e-03 -2.57041e-03
+ -7.16241e-04 -2.46427e-05 -2.57041e-03 2.12235e-03 -1.12382e-04 3.79778e-06
+ -7.21513e-04 7.21513e-04 3.79778e-06 -4.48512e-04 2.43147e-05 -2.43147e-05
+ 7.21513e-04 -2.43147e-05 2.16956e-03 -2.61966e-03 -7.21513e-04 2.43147e-05
+ -2.61966e-03 2.16956e-03
+ # CSR column indices
+ 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
+ 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7
+ # CSR row pointers
+ 0 4 8 12 16 20 24 28 32
+
+ 1 0 -1 32
+ # CSR values
+ -1.11792e-04 -7.16241e-04 -7.16241e-04 3.82452e-06 7.16241e-04 2.12235e-03
+ 2.57041e-03 -2.46427e-05 7.16241e-04 2.57041e-03 2.12235e-03 -2.46427e-05
+ 3.82452e-06 2.46427e-05 2.46427e-05 -4.45692e-04 -1.12382e-04 -7.21513e-04
+ -7.21513e-04 -3.79778e-06 7.21513e-04 2.16956e-03 2.61966e-03 2.43147e-05
+ 7.21513e-04 2.61966e-03 2.16956e-03 2.43147e-05 -3.79778e-06 -2.43147e-05
+ -2.43147e-05 -4.48512e-04
+ # CSR column indices
+ 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
+ 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7
+ # CSR row pointers
+ 0 4 8 12 16 20 24 28 32
+
+ 1 0 0 48
+ # CSR values
+ -1.11792e-04 -7.16241e-04 -3.82452e-06 7.16241e-04 7.16241e-04 2.12235e-03
+ 2.46427e-05 -2.57041e-03 -3.82452e-06 -2.46427e-05 -4.45692e-04 2.46427e-05
+ -7.16241e-04 -2.57041e-03 -2.46427e-05 2.12235e-03 -3.37629e-02 -5.50669e-03
+ -5.50669e-03 5.50669e-03 -1.12382e-04 -7.21513e-04 3.79778e-06 7.21513e-04
+ 8.00872e-03 -1.91945e-03 -1.96652e-02 1.96652e-02 7.21513e-04 2.16956e-03
+ -2.43147e-05 -2.61966e-03 8.00872e-03 -1.96652e-02 -1.91945e-03 1.96652e-02
+ 3.79778e-06 2.43147e-05 -4.48512e-04 -2.43147e-05 -8.00872e-03 1.96652e-02
+ 1.96652e-02 -1.91945e-03 -7.21513e-04 -2.61966e-03 2.43147e-05 2.16956e-03
+ # CSR column indices
+ 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ # CSR row pointers
+ 0 4 8 12 16 24 32 40 48
+
diff --git a/tests/03_NAO_multik/scf_out_hsr_spin2/hrs2_nao.csr.ref b/tests/03_NAO_multik/scf_out_hsr_spin2/hrs2_nao.csr.ref
new file mode 100644
index 00000000000..d4aa39c5b68
--- /dev/null
+++ b/tests/03_NAO_multik/scf_out_hsr_spin2/hrs2_nao.csr.ref
@@ -0,0 +1,229 @@
+ --- Ionic Step 1 ---
+ # print H matrix in real space H(R)
+ 2 # number of spin directions
+ 2 # spin index
+ 8 # number of localized basis
+ 13 # number of Bravais lattice vector R
+
+ user_defined_lattice
+ 8.09641
+ 0 0.5 0.5
+ 0.5 0 0.5
+ 0.5 0.5 0
+ Si
+ 2
+ Direct
+ 0 0 0
+ 0.25 0.25 0.25
+
+ #----------------------------------------------------------------------#
+ #                               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.                                #
+ #----------------------------------------------------------------------#
+
+ -1 0 0 48
+ # CSR values
+ -1.12382e-04 7.21513e-04 -3.79778e-06 -7.21513e-04 -3.37629e-02 5.50669e-03
+ 5.50669e-03 -5.50669e-03 -7.21513e-04 2.16956e-03 -2.43147e-05 -2.61966e-03
+ -8.00872e-03 -1.91945e-03 -1.96652e-02 1.96652e-02 -3.79778e-06 2.43147e-05
+ -4.48512e-04 -2.43147e-05 -8.00872e-03 -1.96652e-02 -1.91945e-03 1.96652e-02
+ 7.21513e-04 -2.61966e-03 2.43147e-05 2.16956e-03 8.00872e-03 1.96652e-02
+ 1.96652e-02 -1.91945e-03 -1.11792e-04 7.16241e-04 3.82452e-06 -7.16241e-04
+ -7.16241e-04 2.12235e-03 2.46427e-05 -2.57041e-03 3.82452e-06 -2.46427e-05
+ -4.45692e-04 2.46427e-05 7.16241e-04 -2.57041e-03 -2.46427e-05 2.12235e-03
+ # CSR column indices
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7
+ # CSR row pointers
+ 0 8 16 24 32 36 40 44 48
+
+ -1 0 1 32
+ # CSR values
+ -1.12382e-04 7.21513e-04 7.21513e-04 3.79778e-06 -7.21513e-04 2.16956e-03
+ 2.61966e-03 2.43147e-05 -7.21513e-04 2.61966e-03 2.16956e-03 2.43147e-05
+ 3.79778e-06 -2.43147e-05 -2.43147e-05 -4.48512e-04 -1.11792e-04 7.16241e-04
+ 7.16241e-04 -3.82452e-06 -7.16241e-04 2.12235e-03 2.57041e-03 -2.46427e-05
+ -7.16241e-04 2.57041e-03 2.12235e-03 -2.46427e-05 -3.82452e-06 2.46427e-05
+ 2.46427e-05 -4.45692e-04
+ # CSR column indices
+ 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
+ 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7
+ # CSR row pointers
+ 0 4 8 12 16 20 24 28 32
+
+ -1 1 0 32
+ # CSR values
+ -1.12382e-04 -3.79778e-06 7.21513e-04 -7.21513e-04 -3.79778e-06 -4.48512e-04
+ 2.43147e-05 -2.43147e-05 -7.21513e-04 -2.43147e-05 2.16956e-03 -2.61966e-03
+ 7.21513e-04 2.43147e-05 -2.61966e-03 2.16956e-03 -1.11792e-04 3.82452e-06
+ 7.16241e-04 -7.16241e-04 3.82452e-06 -4.45692e-04 -2.46427e-05 2.46427e-05
+ -7.16241e-04 2.46427e-05 2.12235e-03 -2.57041e-03 7.16241e-04 -2.46427e-05
+ -2.57041e-03 2.12235e-03
+ # CSR column indices
+ 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
+ 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7
+ # CSR row pointers
+ 0 4 8 12 16 20 24 28 32
+
+ 0 -1 0 48
+ # CSR values
+ -1.12382e-04 7.21513e-04 -7.21513e-04 -3.79778e-06 -3.37629e-02 5.50669e-03
+ -5.50669e-03 5.50669e-03 -7.21513e-04 2.16956e-03 -2.61966e-03 -2.43147e-05
+ -8.00872e-03 -1.91945e-03 1.96652e-02 -1.96652e-02 7.21513e-04 -2.61966e-03
+ 2.16956e-03 2.43147e-05 8.00872e-03 1.96652e-02 -1.91945e-03 1.96652e-02
+ -3.79778e-06 2.43147e-05 -2.43147e-05 -4.48512e-04 -8.00872e-03 -1.96652e-02
+ 1.96652e-02 -1.91945e-03 -1.11792e-04 7.16241e-04 -7.16241e-04 3.82452e-06
+ -7.16241e-04 2.12235e-03 -2.57041e-03 2.46427e-05 7.16241e-04 -2.57041e-03
+ 2.12235e-03 -2.46427e-05 3.82452e-06 -2.46427e-05 2.46427e-05 -4.45692e-04
+ # CSR column indices
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7
+ # CSR row pointers
+ 0 8 16 24 32 36 40 44 48
+
+ 0 -1 1 32
+ # CSR values
+ -1.12382e-04 7.21513e-04 3.79778e-06 7.21513e-04 -7.21513e-04 2.16956e-03
+ 2.43147e-05 2.61966e-03 3.79778e-06 -2.43147e-05 -4.48512e-04 -2.43147e-05
+ -7.21513e-04 2.61966e-03 2.43147e-05 2.16956e-03 -1.11792e-04 7.16241e-04
+ -3.82452e-06 7.16241e-04 -7.16241e-04 2.12235e-03 -2.46427e-05 2.57041e-03
+ -3.82452e-06 2.46427e-05 -4.45692e-04 2.46427e-05 -7.16241e-04 2.57041e-03
+ -2.46427e-05 2.12235e-03
+ # CSR column indices
+ 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
+ 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7
+ # CSR row pointers
+ 0 4 8 12 16 20 24 28 32
+
+ 0 0 -1 48
+ # CSR values
+ -1.12382e-04 3.79778e-06 -7.21513e-04 -7.21513e-04 -3.37629e-02 -5.50669e-03
+ -5.50669e-03 -5.50669e-03 3.79778e-06 -4.48512e-04 2.43147e-05 2.43147e-05
+ 8.00872e-03 -1.91945e-03 -1.96652e-02 -1.96652e-02 7.21513e-04 -2.43147e-05
+ 2.16956e-03 2.61966e-03 8.00872e-03 -1.96652e-02 -1.91945e-03 -1.96652e-02
+ 7.21513e-04 -2.43147e-05 2.61966e-03 2.16956e-03 8.00872e-03 -1.96652e-02
+ -1.96652e-02 -1.91945e-03 -1.11792e-04 -3.82452e-06 -7.16241e-04 -7.16241e-04
+ -3.82452e-06 -4.45692e-04 -2.46427e-05 -2.46427e-05 7.16241e-04 2.46427e-05
+ 2.12235e-03 2.57041e-03 7.16241e-04 2.46427e-05 2.57041e-03 2.12235e-03
+ # CSR column indices
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7
+ # CSR row pointers
+ 0 8 16 24 32 36 40 44 48
+
+ 0 0 0 40
+ # CSR values
+ -4.69258e-01 -3.37629e-02 -5.50669e-03 5.50669e-03 5.50669e-03 8.75227e-01
+ 8.00872e-03 -1.91945e-03 1.96652e-02 1.96652e-02 8.75227e-01 -8.00872e-03
+ 1.96652e-02 -1.91945e-03 -1.96652e-02 8.75227e-01 -8.00872e-03 1.96652e-02
+ -1.96652e-02 -1.91945e-03 -3.37629e-02 8.00872e-03 -8.00872e-03 -8.00872e-03
+ -5.43126e-01 -5.50669e-03 -1.91945e-03 1.96652e-02 1.96652e-02 8.04017e-01
+ 5.50669e-03 1.96652e-02 -1.91945e-03 -1.96652e-02 8.04017e-01 5.50669e-03
+ 1.96652e-02 -1.96652e-02 -1.91945e-03 8.04017e-01
+ # CSR column indices
+ 0 4 5 6 7 1 4 5 6 7 2 4 5 6 7 3
+ 4 5 6 7 0 1 2 3 4 0 1 2 3 5 0 1
+ 2 3 6 0 1 2 3 7
+ # CSR row pointers
+ 0 5 10 15 20 25 30 35 40
+
+ 0 0 1 48
+ # CSR values
+ -1.12382e-04 3.79778e-06 7.21513e-04 7.21513e-04 3.79778e-06 -4.48512e-04
+ -2.43147e-05 -2.43147e-05 -7.21513e-04 2.43147e-05 2.16956e-03 2.61966e-03
+ -7.21513e-04 2.43147e-05 2.61966e-03 2.16956e-03 -3.37629e-02 8.00872e-03
+ 8.00872e-03 8.00872e-03 -1.11792e-04 -3.82452e-06 7.16241e-04 7.16241e-04
+ -5.50669e-03 -1.91945e-03 -1.96652e-02 -1.96652e-02 -3.82452e-06 -4.45692e-04
+ 2.46427e-05 2.46427e-05 -5.50669e-03 -1.96652e-02 -1.91945e-03 -1.96652e-02
+ -7.16241e-04 -2.46427e-05 2.12235e-03 2.57041e-03 -5.50669e-03 -1.96652e-02
+ -1.96652e-02 -1.91945e-03 -7.16241e-04 -2.46427e-05 2.57041e-03 2.12235e-03
+ # CSR column indices
+ 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ # CSR row pointers
+ 0 4 8 12 16 24 32 40 48
+
+ 0 1 -1 32
+ # CSR values
+ -1.12382e-04 -7.21513e-04 3.79778e-06 -7.21513e-04 7.21513e-04 2.16956e-03
+ -2.43147e-05 2.61966e-03 3.79778e-06 2.43147e-05 -4.48512e-04 2.43147e-05
+ 7.21513e-04 2.61966e-03 -2.43147e-05 2.16956e-03 -1.11792e-04 -7.16241e-04
+ -3.82452e-06 -7.16241e-04 7.16241e-04 2.12235e-03 2.46427e-05 2.57041e-03
+ -3.82452e-06 -2.46427e-05 -4.45692e-04 -2.46427e-05 7.16241e-04 2.57041e-03
+ 2.46427e-05 2.12235e-03
+ # CSR column indices
+ 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
+ 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7
+ # CSR row pointers
+ 0 4 8 12 16 20 24 28 32
+
+ 0 1 0 48
+ # CSR values
+ -1.12382e-04 -7.21513e-04 7.21513e-04 -3.79778e-06 7.21513e-04 2.16956e-03
+ -2.61966e-03 2.43147e-05 -7.21513e-04 -2.61966e-03 2.16956e-03 -2.43147e-05
+ -3.79778e-06 -2.43147e-05 2.43147e-05 -4.48512e-04 -3.37629e-02 -8.00872e-03
+ 8.00872e-03 -8.00872e-03 -1.11792e-04 -7.16241e-04 7.16241e-04 3.82452e-06
+ 5.50669e-03 -1.91945e-03 1.96652e-02 -1.96652e-02 7.16241e-04 2.12235e-03
+ -2.57041e-03 -2.46427e-05 -5.50669e-03 1.96652e-02 -1.91945e-03 1.96652e-02
+ -7.16241e-04 -2.57041e-03 2.12235e-03 2.46427e-05 5.50669e-03 -1.96652e-02
+ 1.96652e-02 -1.91945e-03 3.82452e-06 2.46427e-05 -2.46427e-05 -4.45692e-04
+ # CSR column indices
+ 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ # CSR row pointers
+ 0 4 8 12 16 24 32 40 48
+
+ 1 -1 0 32
+ # CSR values
+ -1.12382e-04 -3.79778e-06 -7.21513e-04 7.21513e-04 -3.79778e-06 -4.48512e-04
+ -2.43147e-05 2.43147e-05 7.21513e-04 2.43147e-05 2.16956e-03 -2.61966e-03
+ -7.21513e-04 -2.43147e-05 -2.61966e-03 2.16956e-03 -1.11792e-04 3.82452e-06
+ -7.16241e-04 7.16241e-04 3.82452e-06 -4.45692e-04 2.46427e-05 -2.46427e-05
+ 7.16241e-04 -2.46427e-05 2.12235e-03 -2.57041e-03 -7.16241e-04 2.46427e-05
+ -2.57041e-03 2.12235e-03
+ # CSR column indices
+ 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
+ 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7
+ # CSR row pointers
+ 0 4 8 12 16 20 24 28 32
+
+ 1 0 -1 32
+ # CSR values
+ -1.12382e-04 -7.21513e-04 -7.21513e-04 3.79778e-06 7.21513e-04 2.16956e-03
+ 2.61966e-03 -2.43147e-05 7.21513e-04 2.61966e-03 2.16956e-03 -2.43147e-05
+ 3.79778e-06 2.43147e-05 2.43147e-05 -4.48512e-04 -1.11792e-04 -7.16241e-04
+ -7.16241e-04 -3.82452e-06 7.16241e-04 2.12235e-03 2.57041e-03 2.46427e-05
+ 7.16241e-04 2.57041e-03 2.12235e-03 2.46427e-05 -3.82452e-06 -2.46427e-05
+ -2.46427e-05 -4.45692e-04
+ # CSR column indices
+ 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
+ 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7
+ # CSR row pointers
+ 0 4 8 12 16 20 24 28 32
+
+ 1 0 0 48
+ # CSR values
+ -1.12382e-04 -7.21513e-04 -3.79778e-06 7.21513e-04 7.21513e-04 2.16956e-03
+ 2.43147e-05 -2.61966e-03 -3.79778e-06 -2.43147e-05 -4.48512e-04 2.43147e-05
+ -7.21513e-04 -2.61966e-03 -2.43147e-05 2.16956e-03 -3.37629e-02 -8.00872e-03
+ -8.00872e-03 8.00872e-03 -1.11792e-04 -7.16241e-04 3.82452e-06 7.16241e-04
+ 5.50669e-03 -1.91945e-03 -1.96652e-02 1.96652e-02 7.16241e-04 2.12235e-03
+ -2.46427e-05 -2.57041e-03 5.50669e-03 -1.96652e-02 -1.91945e-03 1.96652e-02
+ 3.82452e-06 2.46427e-05 -4.45692e-04 -2.46427e-05 -5.50669e-03 1.96652e-02
+ 1.96652e-02 -1.91945e-03 -7.16241e-04 -2.57041e-03 2.46427e-05 2.12235e-03
+ # CSR column indices
+ 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
+ # CSR row pointers
+ 0 4 8 12 16 24 32 40 48
+
diff --git a/tests/03_NAO_multik/scf_out_hsr_spin2/result.ref b/tests/03_NAO_multik/scf_out_hsr_spin2/result.ref
new file mode 100644
index 00000000000..71acfc8b989
--- /dev/null
+++ b/tests/03_NAO_multik/scf_out_hsr_spin2/result.ref
@@ -0,0 +1,6 @@
+etotref -173.9710010148657
+etotperatomref -86.9855005074
+CompareHR_pass 0
+CompareHR2_pass 0
+CompareSR_pass 0
+totaltimeref 0.25
diff --git a/tests/03_NAO_multik/scf_out_hsr_spin2/srs1_nao.csr.ref b/tests/03_NAO_multik/scf_out_hsr_spin2/srs1_nao.csr.ref
new file mode 100644
index 00000000000..a2217705e9f
--- /dev/null
+++ b/tests/03_NAO_multik/scf_out_hsr_spin2/srs1_nao.csr.ref
@@ -0,0 +1,205 @@
+ --- Ionic Step 1 ---
+ # print S matrix in real space S(R)
+ 1 # number of spin directions
+ 1 # spin index
+ 8 # number of localized basis
+ 13 # number of Bravais lattice vector R
+
+ user_defined_lattice
+ 8.09641
+ 0 0.5 0.5
+ 0.5 0 0.5
+ 0.5 0.5 0
+ Si
+ 2
+ Direct
+ 0 0 0
+ 0.25 0.25 0.25
+
+ #----------------------------------------------------------------------#
+ #                               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.                                #
+ #----------------------------------------------------------------------#
+
+ -1 0 0 36
+ # CSR values
+ 1.24971e-05 -1.10936e-04 1.10936e-04 2.55028e-02 -2.68439e-02 -2.68439e-02
+ 2.68439e-02 1.10936e-04 -9.83160e-04 1.02936e-03 2.68439e-02 2.71313e-02
+ 2.95162e-02 -2.95162e-02 4.62036e-05 2.68439e-02 2.95162e-02 2.71313e-02
+ -2.95162e-02 -1.10936e-04 1.02936e-03 -9.83160e-04 -2.68439e-02 -2.95162e-02
+ -2.95162e-02 2.71313e-02 1.24971e-05 -1.10936e-04 1.10936e-04 1.10936e-04
+ -9.83160e-04 1.02936e-03 4.62036e-05 -1.10936e-04 1.02936e-03 -9.83160e-04
+ # CSR column indices
+ 0 1 3 4 5 6 7 0 1 3 4 5 6 7 2 4
+ 5 6 7 0 1 3 4 5 6 7 4 5 7 4 5 7
+ 6 4 5 7
+ # CSR row pointers
+ 0 7 14 19 26 29 32 33 36
+
+ -1 0 1 20
+ # CSR values
+ 1.24971e-05 -1.10936e-04 -1.10936e-04 1.10936e-04 -9.83160e-04 -1.02936e-03
+ 1.10936e-04 -1.02936e-03 -9.83160e-04 4.62036e-05 1.24971e-05 -1.10936e-04
+ -1.10936e-04 1.10936e-04 -9.83160e-04 -1.02936e-03 1.10936e-04 -1.02936e-03
+ -9.83160e-04 4.62036e-05
+ # CSR column indices
+ 0 1 2 0 1 2 0 1 2 3 4 5 6 4 5 6
+ 4 5 6 7
+ # CSR row pointers
+ 0 3 6 9 10 13 16 19 20
+
+ -1 1 0 20
+ # CSR values
+ 1.24971e-05 -1.10936e-04 1.10936e-04 4.62036e-05 1.10936e-04 -9.83160e-04
+ 1.02936e-03 -1.10936e-04 1.02936e-03 -9.83160e-04 1.24971e-05 -1.10936e-04
+ 1.10936e-04 4.62036e-05 1.10936e-04 -9.83160e-04 1.02936e-03 -1.10936e-04
+ 1.02936e-03 -9.83160e-04
+ # CSR column indices
+ 0 2 3 1 0 2 3 0 2 3 4 6 7 5 4 6
+ 7 4 6 7
+ # CSR row pointers
+ 0 3 4 7 10 13 14 17 20
+
+ 0 -1 0 36
+ # CSR values
+ 1.24971e-05 -1.10936e-04 1.10936e-04 2.55028e-02 -2.68439e-02 2.68439e-02
+ -2.68439e-02 1.10936e-04 -9.83160e-04 1.02936e-03 2.68439e-02 2.71313e-02
+ -2.95162e-02 2.95162e-02 -1.10936e-04 1.02936e-03 -9.83160e-04 -2.68439e-02
+ -2.95162e-02 2.71313e-02 -2.95162e-02 4.62036e-05 2.68439e-02 2.95162e-02
+ -2.95162e-02 2.71313e-02 1.24971e-05 -1.10936e-04 1.10936e-04 1.10936e-04
+ -9.83160e-04 1.02936e-03 -1.10936e-04 1.02936e-03 -9.83160e-04 4.62036e-05
+ # CSR column indices
+ 0 1 2 4 5 6 7 0 1 2 4 5 6 7 0 1
+ 2 4 5 6 7 3 4 5 6 7 4 5 6 4 5 6
+ 4 5 6 7
+ # CSR row pointers
+ 0 7 14 21 26 29 32 35 36
+
+ 0 -1 1 20
+ # CSR values
+ 1.24971e-05 -1.10936e-04 -1.10936e-04 1.10936e-04 -9.83160e-04 -1.02936e-03
+ 4.62036e-05 1.10936e-04 -1.02936e-03 -9.83160e-04 1.24971e-05 -1.10936e-04
+ -1.10936e-04 1.10936e-04 -9.83160e-04 -1.02936e-03 4.62036e-05 1.10936e-04
+ -1.02936e-03 -9.83160e-04
+ # CSR column indices
+ 0 1 3 0 1 3 2 0 1 3 4 5 7 4 5 7
+ 6 4 5 7
+ # CSR row pointers
+ 0 3 6 7 10 13 16 17 20
+
+ 0 0 -1 36
+ # CSR values
+ 1.24971e-05 1.10936e-04 1.10936e-04 2.55028e-02 2.68439e-02 2.68439e-02
+ 2.68439e-02 4.62036e-05 -2.68439e-02 2.71313e-02 2.95162e-02 2.95162e-02
+ -1.10936e-04 -9.83160e-04 -1.02936e-03 -2.68439e-02 2.95162e-02 2.71313e-02
+ 2.95162e-02 -1.10936e-04 -1.02936e-03 -9.83160e-04 -2.68439e-02 2.95162e-02
+ 2.95162e-02 2.71313e-02 1.24971e-05 1.10936e-04 1.10936e-04 4.62036e-05
+ -1.10936e-04 -9.83160e-04 -1.02936e-03 -1.10936e-04 -1.02936e-03 -9.83160e-04
+ # CSR column indices
+ 0 2 3 4 5 6 7 1 4 5 6 7 0 2 3 4
+ 5 6 7 0 2 3 4 5 6 7 4 6 7 5 4 6
+ 7 4 6 7
+ # CSR row pointers
+ 0 7 12 19 26 29 30 33 36
+
+ 0 0 0 40
+ # CSR values
+ 1.00000e+00 2.55028e-02 2.68439e-02 -2.68439e-02 -2.68439e-02 1.00000e+00
+ -2.68439e-02 2.71313e-02 -2.95162e-02 -2.95162e-02 1.00000e+00 2.68439e-02
+ -2.95162e-02 2.71313e-02 2.95162e-02 1.00000e+00 2.68439e-02 -2.95162e-02
+ 2.95162e-02 2.71313e-02 2.55028e-02 -2.68439e-02 2.68439e-02 2.68439e-02
+ 1.00000e+00 2.68439e-02 2.71313e-02 -2.95162e-02 -2.95162e-02 1.00000e+00
+ -2.68439e-02 -2.95162e-02 2.71313e-02 2.95162e-02 1.00000e+00 -2.68439e-02
+ -2.95162e-02 2.95162e-02 2.71313e-02 1.00000e+00
+ # CSR column indices
+ 0 4 5 6 7 1 4 5 6 7 2 4 5 6 7 3
+ 4 5 6 7 0 1 2 3 4 0 1 2 3 5 0 1
+ 2 3 6 0 1 2 3 7
+ # CSR row pointers
+ 0 5 10 15 20 25 30 35 40
+
+ 0 0 1 36
+ # CSR values
+ 1.24971e-05 -1.10936e-04 -1.10936e-04 4.62036e-05 1.10936e-04 -9.83160e-04
+ -1.02936e-03 1.10936e-04 -1.02936e-03 -9.83160e-04 2.55028e-02 -2.68439e-02
+ -2.68439e-02 -2.68439e-02 1.24971e-05 -1.10936e-04 -1.10936e-04 2.68439e-02
+ 2.71313e-02 2.95162e-02 2.95162e-02 4.62036e-05 2.68439e-02 2.95162e-02
+ 2.71313e-02 2.95162e-02 1.10936e-04 -9.83160e-04 -1.02936e-03 2.68439e-02
+ 2.95162e-02 2.95162e-02 2.71313e-02 1.10936e-04 -1.02936e-03 -9.83160e-04
+ # CSR column indices
+ 0 2 3 1 0 2 3 0 2 3 0 1 2 3 4 6
+ 7 0 1 2 3 5 0 1 2 3 4 6 7 0 1 2
+ 3 4 6 7
+ # CSR row pointers
+ 0 3 4 7 10 17 22 29 36
+
+ 0 1 -1 20
+ # CSR values
+ 1.24971e-05 1.10936e-04 1.10936e-04 -1.10936e-04 -9.83160e-04 -1.02936e-03
+ 4.62036e-05 -1.10936e-04 -1.02936e-03 -9.83160e-04 1.24971e-05 1.10936e-04
+ 1.10936e-04 -1.10936e-04 -9.83160e-04 -1.02936e-03 4.62036e-05 -1.10936e-04
+ -1.02936e-03 -9.83160e-04
+ # CSR column indices
+ 0 1 3 0 1 3 2 0 1 3 4 5 7 4 5 7
+ 6 4 5 7
+ # CSR row pointers
+ 0 3 6 7 10 13 16 17 20
+
+ 0 1 0 36
+ # CSR values
+ 1.24971e-05 1.10936e-04 -1.10936e-04 -1.10936e-04 -9.83160e-04 1.02936e-03
+ 1.10936e-04 1.02936e-03 -9.83160e-04 4.62036e-05 2.55028e-02 2.68439e-02
+ -2.68439e-02 2.68439e-02 1.24971e-05 1.10936e-04 -1.10936e-04 -2.68439e-02
+ 2.71313e-02 -2.95162e-02 2.95162e-02 -1.10936e-04 -9.83160e-04 1.02936e-03
+ 2.68439e-02 -2.95162e-02 2.71313e-02 -2.95162e-02 1.10936e-04 1.02936e-03
+ -9.83160e-04 -2.68439e-02 2.95162e-02 -2.95162e-02 2.71313e-02 4.62036e-05
+ # CSR column indices
+ 0 1 2 0 1 2 0 1 2 3 0 1 2 3 4 5
+ 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0
+ 1 2 3 7
+ # CSR row pointers
+ 0 3 6 9 10 17 24 31 36
+
+ 1 -1 0 20
+ # CSR values
+ 1.24971e-05 1.10936e-04 -1.10936e-04 4.62036e-05 -1.10936e-04 -9.83160e-04
+ 1.02936e-03 1.10936e-04 1.02936e-03 -9.83160e-04 1.24971e-05 1.10936e-04
+ -1.10936e-04 4.62036e-05 -1.10936e-04 -9.83160e-04 1.02936e-03 1.10936e-04
+ 1.02936e-03 -9.83160e-04
+ # CSR column indices
+ 0 2 3 1 0 2 3 0 2 3 4 6 7 5 4 6
+ 7 4 6 7
+ # CSR row pointers
+ 0 3 4 7 10 13 14 17 20
+
+ 1 0 -1 20
+ # CSR values
+ 1.24971e-05 1.10936e-04 1.10936e-04 -1.10936e-04 -9.83160e-04 -1.02936e-03
+ -1.10936e-04 -1.02936e-03 -9.83160e-04 4.62036e-05 1.24971e-05 1.10936e-04
+ 1.10936e-04 -1.10936e-04 -9.83160e-04 -1.02936e-03 -1.10936e-04 -1.02936e-03
+ -9.83160e-04 4.62036e-05
+ # CSR column indices
+ 0 1 2 0 1 2 0 1 2 3 4 5 6 4 5 6
+ 4 5 6 7
+ # CSR row pointers
+ 0 3 6 9 10 13 16 19 20
+
+ 1 0 0 36
+ # CSR values
+ 1.24971e-05 1.10936e-04 -1.10936e-04 -1.10936e-04 -9.83160e-04 1.02936e-03
+ 4.62036e-05 1.10936e-04 1.02936e-03 -9.83160e-04 2.55028e-02 2.68439e-02
+ 2.68439e-02 -2.68439e-02 1.24971e-05 1.10936e-04 -1.10936e-04 -2.68439e-02
+ 2.71313e-02 2.95162e-02 -2.95162e-02 -1.10936e-04 -9.83160e-04 1.02936e-03
+ -2.68439e-02 2.95162e-02 2.71313e-02 -2.95162e-02 4.62036e-05 2.68439e-02
+ -2.95162e-02 -2.95162e-02 2.71313e-02 1.10936e-04 1.02936e-03 -9.83160e-04
+ # CSR column indices
+ 0 1 3 0 1 3 2 0 1 3 0 1 2 3 4 5
+ 7 0 1 2 3 4 5 7 0 1 2 3 6 0 1 2
+ 3 4 5 7
+ # CSR row pointers
+ 0 3 6 7 10 17 24 29 36
+
diff --git a/tests/integrate/tools/catch_properties.sh b/tests/integrate/tools/catch_properties.sh
index 21d3bb70cce..337d0fa38b8 100755
--- a/tests/integrate/tools/catch_properties.sh
+++ b/tests/integrate/tools/catch_properties.sh
@@ -419,6 +419,10 @@ fi
 if ! test -z "$has_hs2"  && [  $has_hs2 == 1 ]; then
     python3 $COMPARE_SCRIPT hrs1_nao.csr.ref OUT.autotest/hrs1_nao.csr 8
     echo "CompareHR_pass $?" >>$1
+    if ! test -z "$nspin" && [ "$nspin" -eq 2 ]; then
+        python3 $COMPARE_SCRIPT hrs2_nao.csr.ref OUT.autotest/hrs2_nao.csr 8
+        echo "CompareHR2_pass $?" >>$1
+    fi
     python3 $COMPARE_SCRIPT srs1_nao.csr.ref OUT.autotest/srs1_nao.csr 8
     echo "CompareSR_pass $?" >>$1
 fi