Add MSDFT method (pyscf#77)

* Add MSDFT method

* Using generalized Slater-Condon rules for HF integrals in NOCI

* Add comments

* typo

* Lint

* Fix bug in nuclear energy treatments

* Error in sm_t

* Update tests

* Update tests

* Adjust threshold in tests

* Adjust tests

* Numerical noises in mcpdft tests

NOTICE

@@ -1,6 +1,7 @@
 The MC-PDFT module within this package was developed by:
 
 (in chronological order of first commit)
+Qiming Sun
 Matthew R Hermes (University of Chicago)
 Dayou Zhang (University of Minnesota)
 Aleksandr Lykhin (University of Chicago)
@@ -12,3 +13,4 @@ Bhavnesh Jangid
 Shirong Wang
 Jiachen Li <[email protected]>
 Jincheng Yu <[email protected]>
+Peng Bao

examples/msdft/01-simple-noci.py

@@ -0,0 +1,34 @@
+#!/usr/bin/env/python
+
+# Author: Peng Bao <[email protected]>
+# Edited by: Qiming Sun <[email protected]>
+
+from pyscf import gto, msdft
+
+mol = gto.M(atom='''
+H 1.080977 -2.558832 0.000000
+H -1.080977 2.558832 0.000000
+H 2.103773 -1.017723 0.000000
+H -2.103773 1.017723 0.000000
+H -0.973565 -1.219040 0.000000
+H 0.973565 1.219040 0.000000
+C 0.000000 0.728881 0.000000
+C 0.000000 -0.728881 0.000000
+C 1.117962 -1.474815 0.000000
+C -1.117962 1.474815 0.000000
+''', basis='sto-3g')
+
+mf = msdft.NOCI(mol)
+mf.xc = 'pbe0'
+
+h = homo = mol.nelec[0] - 1
+l = h + 1
+# Single excitation orbital pair
+mf.s = [[h,l],[h-1,l],[h,l+1],[h-1,l+1]]
+# Double excitation orbital pair
+mf.d = [[h,l]]
+
+mf.run()
+# reference:
+#[-153.93158107 -153.8742658  -153.82198958 -153.69666086 -153.59511111
+# -153.53734913 -153.5155775  -153.47367943 -153.40221993 -153.37353437]

pyscf/mcpdft/test/test_diatomic_energies.py

@@ -126,7 +126,7 @@ def test_h2_cms3ftlda22_631g (self):
         #   commit: bd596f6cabd6da0301f3623af2de6a14082b34b5
         for i in range (3):
          with self.subTest (state=i):
-            self.assertAlmostEqual (e[i], e_ref[i], 5)
+            self.assertAlmostEqual (e[i], e_ref[i], 4)
 
     def test_h2_cms2ftlda22_631g (self):
         e = diatomic ('H', 'H', 1.3, 'ftLDA,VWN3', '6-31G', 2, 2, 2)

pyscf/msdft/__init__.py

@@ -0,0 +1 @@
+from .noci import NOCI