Fix a dimension bug in direct_spin1_cyl_sym. Update example for issue p…

…yscf#2291

examples/mcscf/18-o2_spatial_spin_symmetry.py

@@ -7,42 +7,53 @@
 
 from pyscf import gto, scf, mcscf, fci
 
-#
-# Starting from a triplet SCF calculation
-#
 mol = gto.M(atom='O; O 1 1.2', basis='ccpvdz', spin=2, symmetry=1)
 mf = scf.RHF(mol).run()
 norb = 4
-nelec = 6
+nelec = 6 # leads to 4 alpha electrons and 2 beta electons due to spin=2 (Sz=1)
 mc = mcscf.CASSCF(mf, norb, nelec)
 try:
     mc.kernel()
-except IndexError as e:
+except RuntimeError as e:
     print('When symmetry is enabled, FCI solver optimize the wfn of A1g symmetry by default.')
-    print('In this CAS space, wfn of A1g symmetry does not exist.  This leads to error')
+    print('In this CAS space, wfn of A1g (Sigma^+_g) symmetry for Sz=1 does not exist.')
     print(e)
 
-# Ground state is A2g
+# Target the ground state is A2g (Sigma^-_g) with Sz=0.
+# Specify 3 alpha electrons and 3 beta electrons for CASSCF calculation.
+# The Sz value for CASCI/CASSCF does not have to be the same to the mol.spin.
+nelec = (3, 3)
+mc = mcscf.CASSCF(mf, norb, nelec)
 mc.fcisolver.wfnsym = 'A2g'
 mc.kernel()
-
 #
-# Starting from a singlet SCF calculation
+# Print out the largest CI coefficients
 #
-# SCF calculation for singlet state does not converge if mol.symmetry is
-# enabled.  Starting from a symmetry-broken SCF initial guess, the CASSCF
-# solver can converge to the solution with correct symmetry, with more
-# iterations.
-mol = gto.M(atom='O; O 1 1.2', basis='ccpvdz', spin=0)
-mf = scf.RHF(mol).run()
-nalpha = 4
-nbeta = 2
-mc = mcscf.CASSCF(mf, norb, (nalpha,nbeta))
-mc.kernel()
+for c, deta, detb in fci.addons.large_ci(mc.ci, norb, nelec, tol=.01, return_strs=False):
+    print(deta.tolist(), detb.tolist(), c)
 
 #
-# Print out the largest CI coefficients
+# The default FCI solver utilize the D2h symmetry to mimic the cylindrical symmetry.
+# It may incorrectly remove the initial guess of A2g symmetry with Sz=1 or Sz=-1 .
+# direct_spin1_cyl_sym can be used to solve this problem. This module is
+# designed for the cylindrical symmetry. By specifying the different Sz and
+# wfnsym, the CASSCF can produce three degenerated results.
 #
-for c, deta, detb in fci.addons.large_ci(mc.ci, norb, (nalpha, nbeta),
-                                         tol=.01, return_strs=False):
-    print(deta.tolist(), detb.tolist(), c)
+from pyscf.fci import direct_spin1_cyl_sym
+nelec = (4, 2)  # Sz=1
+mc = mcscf.CASSCF(mf, norb, nelec)
+mc.fcisolver = direct_spin1_cyl_sym.FCI(mol)
+mc.fcisolver.wfnsym = 'A2g'
+mc.kernel()
+
+nelec = (3, 3)  # Sz=0
+mc = mcscf.CASSCF(mf, norb, nelec)
+mc.fcisolver = direct_spin1_cyl_sym.FCI(mol)
+mc.fcisolver.wfnsym = 'A2g'
+mc.kernel()
+
+nelec = (2, 4)  # Sz=-1
+mc = mcscf.CASSCF(mf, norb, nelec)
+mc.fcisolver = direct_spin1_cyl_sym.FCI(mol)
+mc.fcisolver.wfnsym = 'A2g'
+mc.kernel()

pyscf/fci/direct_spin1_symm.py

@@ -310,6 +310,13 @@ def get_init_guess_cyl_sym(norb, nelec, nroots, hdiag, orbsym, wfnsym=0):
             addra1, sign_a = _sv_associated_det(strsa[addra], degen_mapping)
             addrb1, sign_b = _sv_associated_det(strsb[addrb], degen_mapping)
             if wfnsym in (1, 4) and addra == addra1 and addrb == addrb1:
+                # Remove the A1 repr from initial guess.
+                # The product of two E reprs can produce A1, A2 and another E repr.
+                # addra == addra1 and addrb == addrb1  can be found in the A1 repr.
+                # However, this may also incorrectly remove the A2 repr, see the
+                # explanation in issue #2291.
+                # In this case, the direct_spin1_cyl_sym solver can be used to
+                # solve A2. See example mcscf/18-o2_spatial_spin_symmetry.py
                 continue
             x = ca[:,None] * cb
 

pyscf/fci/test/test_spin1_cyl_sym.py

@@ -221,6 +221,22 @@ def test_incomplete_orbsym(self):
         with self.assertRaises(lib.exceptions.PointGroupSymmetryError):
             sol.kernel(h1, h2, no, ne, orbsym=orbsym)
 
+    # issue 2291
+    def test_triplet_degeneracy(self):
+        mol = gto.M(atom='O; O 1 1.2', basis='631g', spin=2, symmetry=1)
+        mf = mol.RHF().run()
+
+        def casci(nelec):
+            norb = 4
+            mc = mcscf.CASCI(mf, norb, nelec)
+            mc.fcisolver = direct_spin1_cyl_sym.FCI(mol)
+            mc.fcisolver.wfnsym = 'A2g'
+            mc.kernel()
+            return mc.e_tot
+        self.assertAlmostEqual(casci((4, 2)), -149.56827649707, 9)
+        self.assertAlmostEqual(casci((3, 3)), -149.56827649707, 9)
+        self.assertAlmostEqual(casci((2, 4)), -149.56827649707, 9)
+
 if __name__ == "__main__":
     print("Full Tests for spin1-symm")
     unittest.main()

pyscf/lib/mcscf/fci_contract.c

@@ -1003,7 +1003,7 @@ void FCIcontract_2e_cyl_sym(double *eris, double *ci0, double *ci1,
                                         strb_ir = IRREP_OF(strb_l, strb_g);
                                         mb = nbs[strb_ir];
                                 }
-                                if (nas[intera_ir] > 0 && nas[interb_ir] > 0 &&
+                                if (nas[intera_ir] > 0 && nbs[interb_ir] > 0 &&
                                     (ma > 0 || mb > 0)) {
 // clinka for intera*ai -> stra.
 pick_link_by_irrep(clinka, linka+linka_loc[intera_ir], nas[intera_ir], nlinka, ai_ir);