diff --git a/source/module_cell/klist.cpp b/source/module_cell/klist.cpp
index 3f6e89ac73..1c42184d7e 100644
--- a/source/module_cell/klist.cpp
+++ b/source/module_cell/klist.cpp
@@ -483,7 +483,7 @@ bool K_Vectors::read_kpoints(const std::string &fn)
         }
     }
 
-    this->nks = this->nkstot;
+    this->nkstot_full = this->nks = this->nkstot;
 
 	ModuleBase::GlobalFunc::OUT(GlobalV::ofs_running,"nkstot",nkstot);
     return 1;
@@ -546,7 +546,7 @@ void K_Vectors::update_use_ibz( void )
     ModuleBase::TITLE("K_Vectors","update_use_ibz");
     assert( nkstot_ibz > 0 );
 
-	// update nkstot
+    // update nkstot
     this->nkstot = this->nkstot_ibz;
 
 	ModuleBase::GlobalFunc::OUT(GlobalV::ofs_running,"nkstot now",nkstot);
@@ -1035,6 +1035,8 @@ void K_Vectors::mpi_k(void)
 
     Parallel_Common::bcast_int(nkstot);
 
+    Parallel_Common::bcast_int(nkstot_full);
+
     Parallel_Common::bcast_int(nmp, 3);
 
     Parallel_Common::bcast_double(koffset, 3);
diff --git a/source/module_cell/klist.h b/source/module_cell/klist.h
index bf9a5abbea..cd37f0529f 100644
--- a/source/module_cell/klist.h
+++ b/source/module_cell/klist.h
@@ -23,8 +23,9 @@ class K_Vectors
     std::vector<int> ibz2bz;					// mohan added 2009-05-18
 
     int nks;						// number of k points in this pool(processor, up+dw)
-    int nkstot;						// total number of k points
-    int nkstot_ibz;
+    int nkstot;						/// total number of k points, equal to nkstot_ibz after reducing k points
+    int nkstot_ibz;             /// number of k points in IBZ
+    int nkstot_full;    /// number of k points in full k mesh
 
     int nmp[3];						// Number of Monhorst-Pack
 
diff --git a/source/module_io/input_conv.cpp b/source/module_io/input_conv.cpp
index f4745461dc..a7d62b5115 100644
--- a/source/module_io/input_conv.cpp
+++ b/source/module_io/input_conv.cpp
@@ -570,9 +570,9 @@ void Input_Conv::Convert(void)
         Exx_Abfs::Jle::Ecut_exx = INPUT.exx_opt_orb_ecut;
         Exx_Abfs::Jle::tolerence = INPUT.exx_opt_orb_tolerence;
 
-        // EXX does not support any symmetry analyse, force symmetry setting to -1
-        if (INPUT.calculation != "nscf")
-            ModuleSymmetry::Symmetry::symm_flag = -1;
+        // EXX does not support symmetry=1
+        if (INPUT.calculation != "nscf" && INPUT.symmetry == "1")
+            ModuleSymmetry::Symmetry::symm_flag = 0;
     }
 #endif // __LCAO
 #endif // __EXX
diff --git a/source/module_ri/Exx_LRI.hpp b/source/module_ri/Exx_LRI.hpp
index 05fd00ffe6..297dae100f 100644
--- a/source/module_ri/Exx_LRI.hpp
+++ b/source/module_ri/Exx_LRI.hpp
@@ -78,7 +78,7 @@ void Exx_LRI<Tdata>::init(const MPI_Comm &mpi_comm_in, const K_Vectors &kv_in)
 				throw std::domain_error(std::string(__FILE__)+" line "+std::to_string(__LINE__));	break;
 		}
 	};
-	this->abfs_ccp = Conv_Coulomb_Pot_K::cal_orbs_ccp( this->abfs, info.ccp_type, get_ccp_parameter(), this->info.ccp_rmesh_times,  p_kv->nks );
+    this->abfs_ccp = Conv_Coulomb_Pot_K::cal_orbs_ccp(this->abfs, info.ccp_type, get_ccp_parameter(), this->info.ccp_rmesh_times, p_kv->nkstot_full);
 
 
 	for( size_t T=0; T!=this->abfs.size(); ++T )
diff --git a/source/module_ri/RI_2D_Comm.hpp b/source/module_ri/RI_2D_Comm.hpp
index 081f1fad9a..738260c790 100644
--- a/source/module_ri/RI_2D_Comm.hpp
+++ b/source/module_ri/RI_2D_Comm.hpp
@@ -18,6 +18,13 @@
 #include <string>
 #include <stdexcept>
 
+inline RI::Tensor<double> tensor_conj(const RI::Tensor<double>& t) { return t; }
+inline RI::Tensor<std::complex<double>> tensor_conj(const RI::Tensor<std::complex<double>>& t)
+{
+    RI::Tensor<std::complex<double>> r(t.shape);
+    for (int i = 0;i < t.data->size();++i)(*r.data)[i] = std::conj((*t.data)[i]);
+    return r;
+}
 template<typename Tdata, typename Tmatrix>
 auto RI_2D_Comm::split_m2D_ktoR(const K_Vectors &kv, const std::vector<const Tmatrix*> &mks_2D, const Parallel_Orbitals &pv)
 -> std::vector<std::map<TA,std::map<TAC,RI::Tensor<Tdata>>>>
@@ -42,11 +49,16 @@ auto RI_2D_Comm::split_m2D_ktoR(const K_Vectors &kv, const std::vector<const Tma
 				RI::Tensor<Tdata_m> mk_2D = RI_Util::Matrix_to_Tensor<Tdata_m>(*mks_2D[ik]);
 				const Tdata_m frac = SPIN_multiple
 					* RI::Global_Func::convert<Tdata_m>( std::exp(
-						- ModuleBase::TWO_PI*ModuleBase::IMAG_UNIT * (kv.kvec_c[ik] * (RI_Util::array3_to_Vector3(cell)*GlobalC::ucell.latvec))));
-				if(mR_2D.empty())
-					mR_2D = RI::Global_Func::convert<Tdata>(mk_2D * frac);
-				else
-					mR_2D = mR_2D + RI::Global_Func::convert<Tdata>(mk_2D * frac);
+                        -ModuleBase::TWO_PI * ModuleBase::IMAG_UNIT * (kv.kvec_c[ik] * (RI_Util::array3_to_Vector3(cell) * GlobalC::ucell.latvec))));
+                auto set_mR_2D = [&mR_2D](auto&& mk_frac) {
+                    if (mR_2D.empty())
+                        mR_2D = RI::Global_Func::convert<Tdata>(mk_frac);
+                    else
+                        mR_2D = mR_2D + RI::Global_Func::convert<Tdata>(mk_frac);
+                    };
+                if (static_cast<int>(std::round(SPIN_multiple * kv.wk[ik] * kv.nkstot_full)) == 2)
+                    set_mR_2D(mk_2D * (frac * 0.5) + tensor_conj(mk_2D * (frac * 0.5)));
+                else set_mR_2D(mk_2D * frac);
 			}
 
 			for(int iwt0_2D=0; iwt0_2D!=mR_2D.shape[0]; ++iwt0_2D)
@@ -122,7 +134,7 @@ void RI_2D_Comm::add_Hexx(
 						if(GlobalV::GAMMA_ONLY_LOCAL)
 							lm.set_HSgamma(iwt0, iwt1,
 								RI::Global_Func::convert<double>(H(iw0_b, iw1_b)) * RI::Global_Func::convert<double>(frac),
-                                lm.Hloc.data());
+                                lm.Hloc.data());
 						else
 							lm.set_HSk(iwt0, iwt1,
 								RI::Global_Func::convert<std::complex<double>>(H(iw0_b, iw1_b)) * frac,
diff --git a/tests/integrate/281_NO_KP_HSE/INPUT b/tests/integrate/281_NO_KP_HSE/INPUT
index f4d2a98f60..6ef86684dd 100644
--- a/tests/integrate/281_NO_KP_HSE/INPUT
+++ b/tests/integrate/281_NO_KP_HSE/INPUT
@@ -2,7 +2,7 @@ INPUT_PARAMETERS
 #Parameters (1.General)
 suffix			autotest
 ntype			1
-symmetry		-1
+symmetry		0
 gamma_only      0
 nspin			1
 
diff --git a/tests/integrate/283_NO_KP_HF/INPUT b/tests/integrate/283_NO_KP_HF/INPUT
index 5d68095e47..b9a3432cc8 100644
--- a/tests/integrate/283_NO_KP_HF/INPUT
+++ b/tests/integrate/283_NO_KP_HF/INPUT
@@ -2,7 +2,7 @@ INPUT_PARAMETERS
 #Parameters (1.General)
 suffix			autotest
 ntype			1
-symmetry		-1
+symmetry		0
 gamma_only      0
 nspin			1
 
diff --git a/tests/integrate/284_NO_KP_PBE0/INPUT b/tests/integrate/284_NO_KP_PBE0/INPUT
index a3faac71c0..a4c9daf26c 100644
--- a/tests/integrate/284_NO_KP_PBE0/INPUT
+++ b/tests/integrate/284_NO_KP_PBE0/INPUT
@@ -2,7 +2,7 @@ INPUT_PARAMETERS
 #Parameters (1.General)
 suffix			autotest
 ntype			1
-symmetry		-1
+symmetry		0
 gamma_only      0
 nspin			1
 
diff --git a/tests/integrate/285_NO_KP_RE_HSE/INPUT b/tests/integrate/285_NO_KP_RE_HSE/INPUT
index daa8e72c94..da713b6d69 100644
--- a/tests/integrate/285_NO_KP_RE_HSE/INPUT
+++ b/tests/integrate/285_NO_KP_RE_HSE/INPUT
@@ -2,7 +2,7 @@ INPUT_PARAMETERS
 #Parameters (1.General)
 suffix			autotest
 ntype			1
-symmetry		-1
+symmetry		0
 gamma_only      0
 nspin			1
 
diff --git a/tests/integrate/286_NO_KP_CR_HSE/INPUT b/tests/integrate/286_NO_KP_CR_HSE/INPUT
index 608d62b8b6..0885c393c9 100644
--- a/tests/integrate/286_NO_KP_CR_HSE/INPUT
+++ b/tests/integrate/286_NO_KP_CR_HSE/INPUT
@@ -2,7 +2,7 @@ INPUT_PARAMETERS
 #Parameters (1.General)
 suffix			autotest
 ntype			1
-symmetry		-1
+symmetry		0
 gamma_only      0
 nspin			1
 
diff --git a/tests/integrate/381_NO_GO_S1_HSE/INPUT b/tests/integrate/381_NO_GO_S1_HSE/INPUT
index f9b41e90c1..03fd12fddc 100644
--- a/tests/integrate/381_NO_GO_S1_HSE/INPUT
+++ b/tests/integrate/381_NO_GO_S1_HSE/INPUT
@@ -3,7 +3,7 @@ INPUT_PARAMETERS
 suffix				autotest
 calculation     	scf
 ntype				2
-symmetry			-1
+symmetry			0
 nspin				1
 pseudo_dir			../../PP_ORB
 orbital_dir			../../PP_ORB
diff --git a/tests/integrate/382_NO_GO_S2_HSE/INPUT b/tests/integrate/382_NO_GO_S2_HSE/INPUT
index 663dad3134..a0ef5a24f4 100644
--- a/tests/integrate/382_NO_GO_S2_HSE/INPUT
+++ b/tests/integrate/382_NO_GO_S2_HSE/INPUT
@@ -3,7 +3,7 @@ INPUT_PARAMETERS
 suffix				autotest
 calculation     	scf
 ntype				2
-symmetry			-1
+symmetry			0
 nspin				2
 pseudo_dir			../../PP_ORB
 orbital_dir			../../PP_ORB
diff --git a/tests/integrate/383_NO_GO_SO_HSE/INPUT b/tests/integrate/383_NO_GO_SO_HSE/INPUT
index 9b06fc9739..6cfc5cb3d0 100644
--- a/tests/integrate/383_NO_GO_SO_HSE/INPUT
+++ b/tests/integrate/383_NO_GO_SO_HSE/INPUT
@@ -3,7 +3,7 @@ INPUT_PARAMETERS
 suffix				autotest
 calculation     	scf
 ntype				2
-symmetry			-1
+symmetry			0
 nspin				4
 lspinorb			1
 noncolin			1
diff --git a/tests/integrate/385_NO_GO_RE_S1_HSE/INPUT b/tests/integrate/385_NO_GO_RE_S1_HSE/INPUT
index 004553fb7a..35b83abed6 100644
--- a/tests/integrate/385_NO_GO_RE_S1_HSE/INPUT
+++ b/tests/integrate/385_NO_GO_RE_S1_HSE/INPUT
@@ -3,7 +3,7 @@ INPUT_PARAMETERS
 suffix				autotest
 calculation     	relax
 ntype				2
-symmetry			-1
+symmetry			0
 nspin				1
 pseudo_dir			../../PP_ORB
 orbital_dir			../../PP_ORB
diff --git a/tests/integrate/386_NO_GO_MD_S1_HSE/INPUT b/tests/integrate/386_NO_GO_MD_S1_HSE/INPUT
index 82ce110b14..b2b7881cfc 100644
--- a/tests/integrate/386_NO_GO_MD_S1_HSE/INPUT
+++ b/tests/integrate/386_NO_GO_MD_S1_HSE/INPUT
@@ -3,7 +3,7 @@ INPUT_PARAMETERS
 suffix				autotest
 calculation     	md
 ntype				2
-symmetry			-1
+symmetry			0
 nspin				1
 pseudo_dir			../../PP_ORB
 orbital_dir			../../PP_ORB