diff --git a/gpu4pyscf/df/tests/test_df_hessian.py b/gpu4pyscf/df/tests/test_df_hessian.py
index 08ac27af..3cf63cc0 100644
--- a/gpu4pyscf/df/tests/test_df_hessian.py
+++ b/gpu4pyscf/df/tests/test_df_hessian.py
@@ -114,6 +114,7 @@ class KnownValues(unittest.TestCase):
     def test_hessian_rhf(self):
         print('-----testing DF RHF Hessian----')
         mf = _make_rhf(mol_sph)
+        mf.conv_tol_cpscf = 1e-7
         hobj = mf.Hessian()
         hobj.set(auxbasis_response=2)
         h = hobj.kernel()
@@ -123,6 +124,7 @@ def test_hessian_rhf(self):
     def test_hessian_lda(self):
         print('-----testing DF LDA Hessian----')
         mf = _make_rks(mol_sph, 'LDA')
+        mf.conv_tol_cpscf = 1e-7
         hobj = mf.Hessian()
         hobj.set(auxbasis_response=2)
         h = hobj.kernel()
@@ -132,6 +134,7 @@ def test_hessian_lda(self):
     def test_hessian_gga(self):
         print('-----testing DF PBE Hessian----')
         mf = _make_rks(mol_sph, 'PBE')
+        mf.conv_tol_cpscf = 1e-7
         hobj = mf.Hessian()
         hobj.set(auxbasis_response=2)
         h = hobj.kernel()
@@ -141,6 +144,7 @@ def test_hessian_gga(self):
     def test_hessian_hybrid(self):
         print('-----testing DF B3LYP Hessian----')
         mf = _make_rks(mol_sph, 'b3lyp')
+        mf.conv_tol_cpscf = 1e-7
         hobj = mf.Hessian()
         hobj.set(auxbasis_response=2)
         h = hobj.kernel()
@@ -150,6 +154,7 @@ def test_hessian_hybrid(self):
     def test_hessian_mgga(self):
         print('-----testing DF M06 Hessian----')
         mf = _make_rks(mol_sph, 'm06')
+        mf.conv_tol_cpscf = 1e-7
         hobj = mf.Hessian()
         hobj.set(auxbasis_response=2)
         h = hobj.kernel()
@@ -159,6 +164,7 @@ def test_hessian_mgga(self):
     def test_hessian_rsh(self):
         print('-----testing DF wb97 Hessian----')
         mf = _make_rks(mol_sph, 'wb97')
+        mf.conv_tol_cpscf = 1e-7
         hobj = mf.Hessian()
         hobj.set(auxbasis_response=2)
         h = hobj.kernel()
@@ -171,6 +177,7 @@ def test_hessian_D3(self):
 
         mf = dft.rks.RKS(pmol, xc='B3LYP', disp='d3bj').density_fit(auxbasis=auxbasis0)
         mf.conv_tol = 1e-12
+        mf.conv_tol_cpscf = 1e-7
         mf.grids.level = grids_level
         mf.verbose = 1
         mf.kernel()
@@ -186,6 +193,7 @@ def test_hessian_D4(self):
 
         mf = dft.rks.RKS(pmol, xc='B3LYP', disp='d4').density_fit(auxbasis=auxbasis0)
         mf.conv_tol = 1e-12
+        mf.conv_tol_cpscf = 1e-7
         mf.grids.level = grids_level
         mf.verbose = 1
         mf.kernel()
@@ -198,6 +206,7 @@ def test_hessian_D4(self):
     def test_hessian_cart(self):
         print('-----testing DF Hessian (cartesian)----')
         mf = _make_rks(mol_cart, 'b3lyp')
+        mf.conv_tol_cpscf = 1e-7
         hobj = mf.Hessian()
         hobj.set(auxbasis_response=2)
         h = hobj.kernel()
diff --git a/gpu4pyscf/lib/tests/test_to_gpu.py b/gpu4pyscf/lib/tests/test_to_gpu.py
index 587b3102..7e485b89 100644
--- a/gpu4pyscf/lib/tests/test_to_gpu.py
+++ b/gpu4pyscf/lib/tests/test_to_gpu.py
@@ -88,9 +88,10 @@ def test_df_RHF(self):
         assert numpy.abs(lib.fp(g) - -0.01641213202225146) < 1e-7
 
         mf = scf.RHF(mol).density_fit().run()
+        mf.conv_tol_cpscf = 1e-7
         hobj = mf.Hessian().to_gpu()
         h = hobj.kernel()
-        assert numpy.abs(lib.fp(h) - 2.198079352288524) < 1e-7
+        assert numpy.abs(lib.fp(h) - 2.198079352288524) < 1e-4
 
     @pytest.mark.skipif(pyscf_24, reason='requires pyscf 2.5 or higher')
     def test_df_b3lyp(self):
@@ -104,9 +105,10 @@ def test_df_b3lyp(self):
         assert numpy.abs(lib.fp(g) - -0.04079190644707999) < 1e-7
 
         mf = rks.RKS(mol, xc='b3lyp').density_fit().run()
+        mf.conv_tol_cpscf = 1e-7
         hobj = mf.Hessian().to_gpu()
         h = hobj.kernel()
-        assert numpy.abs(lib.fp(h) - 2.1527804103141848) < 1e-7
+        assert numpy.abs(lib.fp(h) - 2.1527804103141848) < 1e-4
 
     @pytest.mark.skipif(pyscf_24, reason='requires pyscf 2.5 or higher')
     def test_df_RKS(self):
@@ -121,6 +123,7 @@ def test_df_RKS(self):
         assert numpy.abs(lib.fp(g) - -0.034343799164131) < 1e-5
 
         mf = rks.RKS(mol, xc='wb97x').density_fit().run()
+        mf.conv_tol_cpscf = 1e-7
         hobj = mf.Hessian().to_gpu()
         h = hobj.kernel()
         assert numpy.abs(lib.fp(h) - 2.187025544697092) < 1e-4