diff --git a/source/source_estate/elecstate_pw.cpp b/source/source_estate/elecstate_pw.cpp
index 7edb7b6bcf..641def5dc4 100644
--- a/source/source_estate/elecstate_pw.cpp
+++ b/source/source_estate/elecstate_pw.cpp
@@ -8,6 +8,7 @@
 #include "source_base/timer.h"
 #include "source_hamilt/module_xc/xc_functional.h"
 #include "source_io/module_parameter/parameter.h"
+#include "source_lcao/module_deltaspin/spin_constrain.h"
 #include "source_pw/module_pwdft/vnl_pw.h"
 
 namespace elecstate {
@@ -56,6 +57,14 @@ ElecStatePW<T, Device>::~ElecStatePW()
     delmem_complex_op()(this->wfcr_another_spin);
 }
 
+template<typename T, typename Device>
+double ElecStatePW<T, Device>::get_spin_constrain_energy()
+{
+    spinconstrain::SpinConstrain<std::complex<double>>& sc
+        = spinconstrain::SpinConstrain<std::complex<double>>::getScInstance();
+    return sc.cal_escon();
+}
+
 template<typename T, typename Device>
 void ElecStatePW<T, Device>::init_rho_data() 
 {
diff --git a/source/source_estate/elecstate_pw.h b/source/source_estate/elecstate_pw.h
index 623704e178..53e39917a5 100644
--- a/source/source_estate/elecstate_pw.h
+++ b/source/source_estate/elecstate_pw.h
@@ -36,6 +36,8 @@ class ElecStatePW : public ElecState
 
     virtual void cal_tau(const psi::Psi<T, Device>& psi);
 
+    double get_spin_constrain_energy() override;
+
     //! calculate becsum for uspp
     void cal_becsum(const psi::Psi<T, Device>& psi);
 
diff --git a/source/source_estate/test/CMakeLists.txt b/source/source_estate/test/CMakeLists.txt
index b9118b01a5..ae09357ac8 100644
--- a/source/source_estate/test/CMakeLists.txt
+++ b/source/source_estate/test/CMakeLists.txt
@@ -51,6 +51,7 @@ AddTest(
     ../elecstate.cpp
     ../occupy.cpp
     ../module_charge/charge_mpi.cpp
+    ../../source_lcao/module_deltaspin/spin_constrain.cpp
     ../../source_psi/psi.cpp
     ../../source_base/module_device/memory_op.cpp
 )
diff --git a/source/source_lcao/module_deltaspin/spin_constrain.cpp b/source/source_lcao/module_deltaspin/spin_constrain.cpp
index b4048b5e9f..df8b4b20b3 100644
--- a/source/source_lcao/module_deltaspin/spin_constrain.cpp
+++ b/source/source_lcao/module_deltaspin/spin_constrain.cpp
@@ -45,7 +45,7 @@ template <typename TK>
 double SpinConstrain<TK>::cal_escon()
 {
     this->escon_ = 0.0;
-    if (!this->is_Mi_converged)
+    if (this->lambda_.empty() || this->Mi_.empty())
     {
         return this->escon_;
     }
diff --git a/source/source_lcao/module_deltaspin/spin_constrain.h b/source/source_lcao/module_deltaspin/spin_constrain.h
index 4785e8dfe8..474cef6716 100644
--- a/source/source_lcao/module_deltaspin/spin_constrain.h
+++ b/source/source_lcao/module_deltaspin/spin_constrain.h
@@ -79,7 +79,7 @@ inline ModuleBase::Vector3<double> pauli_to_moment(const std::complex<double> oc
 {
     return ModuleBase::Vector3<double>(
         weight * (occ[1] + occ[2]).real(),
-        -weight * (occ[1] - occ[2]).imag(),
+        weight * (occ[1] - occ[2]).imag(),
         weight * (occ[0] - occ[3]).real()
     );
 }
diff --git a/tests/17_DS_DFTU/14_PW_DS_S4_XYZ/result.ref b/tests/17_DS_DFTU/14_PW_DS_S4_XYZ/result.ref
index f63986cceb..97fc3aaca4 100644
--- a/tests/17_DS_DFTU/14_PW_DS_S4_XYZ/result.ref
+++ b/tests/17_DS_DFTU/14_PW_DS_S4_XYZ/result.ref
@@ -1,3 +1,3 @@
-etotref -6366.562922988214
-etotperatomref -3183.2814614941
-totaltimeref 4.23
+etotref -6369.19895097706
+etotperatomref -3184.59947548853
+totaltimeref 1.0
diff --git a/tests/17_DS_DFTU/15_PW_DS_S4_Z/result.ref b/tests/17_DS_DFTU/15_PW_DS_S4_Z/result.ref
index 07523240a6..3c6f1a967e 100644
--- a/tests/17_DS_DFTU/15_PW_DS_S4_Z/result.ref
+++ b/tests/17_DS_DFTU/15_PW_DS_S4_Z/result.ref
@@ -1,3 +1,3 @@
-etotref -6366.562433916121
-etotperatomref -3183.2812169581
-totaltimeref 4.26
+etotref -6369.198273166801
+etotperatomref -3184.5991365834007
+totaltimeref 1.0
diff --git a/tests/17_DS_DFTU/16_PW_DS_S4_XY/result.ref b/tests/17_DS_DFTU/16_PW_DS_S4_XY/result.ref
index c2ed3287e2..d5b3da693e 100644
--- a/tests/17_DS_DFTU/16_PW_DS_S4_XY/result.ref
+++ b/tests/17_DS_DFTU/16_PW_DS_S4_XY/result.ref
@@ -1,3 +1,3 @@
-etotref -6366.562695059035
-etotperatomref -3183.2813475295
-totaltimeref 4.19
+etotref -6369.198274098935
+etotperatomref -3184.5991370494676
+totaltimeref 1.0
diff --git a/tests/17_DS_DFTU/19_PW_DFTU_DS_S4_XY/result.ref b/tests/17_DS_DFTU/19_PW_DFTU_DS_S4_XY/result.ref
index ed294b0414..e40be3f01b 100644
--- a/tests/17_DS_DFTU/19_PW_DFTU_DS_S4_XY/result.ref
+++ b/tests/17_DS_DFTU/19_PW_DFTU_DS_S4_XY/result.ref
@@ -1,3 +1,3 @@
-etotref -6355.9841673819892094
-etotperatomref -3177.9920836910
-totaltimeref 5.88
+etotref -6360.5554588729937677
+etotperatomref -3180.277729436497
+totaltimeref 1.0
diff --git a/tests/17_DS_DFTU/21_PW_DFTU_DS_S4_Z/result.ref b/tests/17_DS_DFTU/21_PW_DFTU_DS_S4_Z/result.ref
index 1810d27088..b06c7ee03a 100644
--- a/tests/17_DS_DFTU/21_PW_DFTU_DS_S4_Z/result.ref
+++ b/tests/17_DS_DFTU/21_PW_DFTU_DS_S4_Z/result.ref
@@ -1,3 +1,3 @@
-etotref -6355.9834051938123594
-etotperatomref -3177.9917025969
-totaltimeref 5.46
+etotref -6360.5554655414534864
+etotperatomref -3180.2777327707267
+totaltimeref 1.0
diff --git a/tests/17_DS_DFTU/41_PW_DS_S4_Thr10_XY/result.ref b/tests/17_DS_DFTU/41_PW_DS_S4_Thr10_XY/result.ref
index acf31e682c..8d127ea729 100644
--- a/tests/17_DS_DFTU/41_PW_DS_S4_Thr10_XY/result.ref
+++ b/tests/17_DS_DFTU/41_PW_DS_S4_Thr10_XY/result.ref
@@ -1,3 +1,3 @@
-etotref -6366.564253345298
-etotperatomref -3183.2821266726
-totaltimeref 7.03
+etotref -6369.198254647004
+etotperatomref -3184.599127323502
+totaltimeref 1.0