diff --git a/Notebooks/F12_matrix.ipynb b/Notebooks/F12_matrix.ipynb
index b53e52d..8b1b0c6 100644
--- a/Notebooks/F12_matrix.ipynb
+++ b/Notebooks/F12_matrix.ipynb
@@ -156,7 +156,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "let hf =  HartreeFock.make ~guess:`Hcore  simulation  ;;\n",
+    "let hf =  HartreeFock.make ~guess:`Hcore ~max_scf:1 simulation  ;;\n",
     "\n",
     "let mo_basis = MOBasis.of_hartree_fock hf"
    ]
@@ -865,22 +865,20 @@
     "$i,j$ : orbital indices of MOs occupied in $|I\\rangle$.\n",
     "\n",
     "\\begin{align}\n",
-    "\\sum_{a} \\left( \n",
-    "        \\sum_{i} \\sum_{j}\n",
-    "            \\left(h_{ia} +  \\langle i j || a j \\rangle \\right) \n",
-    "            \\left(f_{ai} +   \\left[ a j || i j \\right] \\right) + \n",
-    "        \\sum_{i} \\sum_{\\bar{j}}\n",
-    "            \\left(h_{ia} +  \\langle i \\bar{j} | a \\bar{j} \\rangle \\right) \n",
-    "            \\left(f_{ai} +   \\left[ a \\bar{j} | i \\bar{j} \\right] \\right) \n",
-    "    \\right) + \\\\\n",
-    "\\sum_{\\bar{a}} \\left(\n",
-    "        \\sum_{\\bar{i}} \\sum_{\\bar{j}}\n",
-    "            \\left(h_{\\bar{i}\\bar{a}} +  \\langle \\bar{i} \\bar{j} || \\bar{a} \\bar{j} \\rangle \\right) \n",
-    "            \\left(f_{\\bar{a}\\bar{i}} +   \\left[ \\bar{a} \\bar{j} || \\bar{i} \\bar{j} \\right] \\right) + \n",
-    "        \\sum_{\\bar{i}} \\sum_{j}\n",
-    "            \\left(h_{\\bar{i}\\bar{a}} +  \\langle \\bar{i} j | \\bar{a} j \\rangle \\right)\n",
-    "            \\left(f_{\\bar{a}\\bar{i}} +   \\left[ \\bar{a} j | \\bar{i} j \\right] \\right) \n",
-    "        \\right) \n",
+    "\\sum_{a} \\sum_{i}\n",
+    "        \\left( h_{ia} +\n",
+    "            \\sum_{j} \\langle i j || a j \\rangle +\n",
+    "            \\sum_{\\bar{j}} \\langle i \\bar{j} | a \\bar{j} \\rangle \\right) \n",
+    "        \\left( f_{ai} +\n",
+    "            \\sum_{j}  \\left[ a j || i j \\right] + \n",
+    "            \\sum_{\\bar{j}}  \\left[ a \\bar{j} | i \\bar{j} \\right] \\right) + \\\\\n",
+    "\\sum_{\\bar{a}}  \\sum_{\\bar{i}}\n",
+    "        \\left( h_{ia} +\n",
+    "            \\sum_{j} \\langle \\bar{i} j | \\bar{a} j \\rangle +\n",
+    "            \\sum_{\\bar{j}} \\langle \\bar{i} \\bar{j} || \\bar{a} \\bar{j} \\rangle \\right) \n",
+    "        \\left( f_{ai} +\n",
+    "            \\sum_{j}  \\left[ \\bar{a} j | \\bar{i} j \\right] + \n",
+    "            \\sum_{\\bar{j}}  \\left[ \\bar{a} \\bar{j} || \\bar{i} \\bar{j} \\right] \\right)  \n",
     "\\end{align}"
    ]
   },
@@ -893,29 +891,28 @@
     "let integral_value ki kj = \n",
     "   (* Alpha-Beta *)\n",
     "   let s, s' = Spin.(Alfa, Beta) in \n",
-    "   List.fold_left (fun accu j -> accu +. \n",
+    "   let mos_a, mos_b = mos_a ki, mos_b ki in\n",
+    "   List.fold_left (fun accu a -> accu +.\n",
     "       List.fold_left (fun accu i -> accu +. \n",
-    "           List.fold_left (fun accu a ->\n",
-    "               accu +.( (h_one i a s  +. h_two i j a j s s') *. \n",
-    "                        (f_one a i s  +. f_two a j i j s s') )\n",
-    "                    +.( (h_one j a s' +. h_two i j i a s s') *. \n",
-    "                        (f_one a j s' +. f_two i a i j s s') )\n",
-    "             ) 0. mos_cabs\n",
-    "         ) 0. (mos_a ki)\n",
-    "     ) 0. (mos_b ki)\n",
+    "           (h_one i a s  +.\n",
+    "               List.fold_left (fun accu j -> accu +. h_two i j a j s s ) 0. mos_a +. \n",
+    "               List.fold_left (fun accu j -> accu +. h_two i j a j s s') 0. mos_b ) *. \n",
+    "           (f_one a i s  +.\n",
+    "               List.fold_left (fun accu j -> accu +. f_two a j i j s s ) 0. mos_a +.\n",
+    "               List.fold_left (fun accu j -> accu +. f_two a j i j s s') 0. mos_b )\n",
+    "         ) 0. mos_a\n",
+    "     ) 0. mos_cabs\n",
     "   +.\n",
-    "   (* Alpha-Alpha / Beta-Beta *)\n",
-    "   List.fold_left (fun accu (mos,s) -> \n",
-    "     let s' = s in accu +. \n",
-    "     List.fold_left (fun accu j -> accu +. \n",
-    "         List.fold_left (fun accu i -> accu +. \n",
-    "               List.fold_left (fun accu a -> \n",
-    "                   accu +.( (h_one i a s +. h_two i j a j s s') *. \n",
-    "                            (f_one a i s +. f_two a j i j s s') )\n",
-    "                   ) 0. mos_cabs\n",
-    "           ) 0. mos\n",
-    "       ) 0. mos\n",
-    "     ) 0. [ (mos_a ki,Spin.Alfa) ; (mos_b ki,Spin.Beta)]\n",
+    "   List.fold_left (fun accu a -> accu +.\n",
+    "       List.fold_left (fun accu i -> accu +. \n",
+    "           (h_one i a s  +.\n",
+    "               List.fold_left (fun accu j -> accu +. h_two i j a j s' s') 0. mos_b +. \n",
+    "               List.fold_left (fun accu j -> accu +. h_two i j a j s' s ) 0. mos_a ) *. \n",
+    "           (f_one a i s  +.\n",
+    "               List.fold_left (fun accu j -> accu +. f_two a j i j s' s ) 0. mos_a +.\n",
+    "               List.fold_left (fun accu j -> accu +. f_two a j i j s' s') 0. mos_b )\n",
+    "         ) 0. mos_b\n",
+    "     ) 0. mos_cabs\n",
     "     \n",
     "let _ =\n",
     "  check 0 integral_value 0 1 1 1\n",
@@ -1110,7 +1107,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# 4. *1 1 11*"
+    "# 4. 1 1 11"
    ]
   },
   {
@@ -1131,12 +1128,11 @@
     "$j$ : orbital indices of MOs occupied both in $|I\\rangle$  and $|J\\rangle$.\n",
     "\n",
     "\\begin{align}\n",
-    "\\sum_{a} \\sum_{j}\n",
-    "            \\left( h_{ia} + \\langle i j || a j \\rangle \\right)\n",
-    "            \\left( f_{ak} +  \\left[ a j || k j \\right] \\right) + \n",
-    "\\sum_{\\bar{j}}\n",
-    "            \\left( h_{ia} + \\langle i \\bar{j} | a \\bar{j} \\rangle \\right) \n",
-    "            \\left( f_{ak} +  \\left[ a \\bar{j} | k \\bar{j} \\right] \\right)\n",
+    "    \\sum_{a} \n",
+    "    \\left( h_{ia} +\\sum_{j} \\langle i j || a j \\rangle +\n",
+    "    \\sum_{\\bar{j}} \\langle i \\bar{j} | a \\bar{j} \\rangle  \\right)\n",
+    "    \\left( f_{ak} +\\sum_{j}  \\left[ a j || k j \\right] + \n",
+    "    \\sum_{\\bar{j}}  \\left[ a \\bar{j} | k \\bar{j} \\right]\\right) \n",
     "\\end{align}"
    ]
   },
@@ -1154,31 +1150,27 @@
     "          | _ -> assert false\n",
     "    in\n",
     "\n",
-    "    let mos, mos' =\n",
+    "    let mos_i, mos_i' =\n",
     "      match s with\n",
     "      | Spin.Alfa -> mos_a ki, mos_b ki\n",
     "      | Spin.Beta -> mos_b ki, mos_a ki\n",
     "    in\n",
+    "    let mos_j, mos_j' =\n",
+    "      match s with\n",
+    "      | Spin.Alfa -> mos_a kj, mos_b kj\n",
+    "      | Spin.Beta -> mos_b kj, mos_a kj\n",
+    "    in\n",
     "\n",
     "    let result = \n",
-    "       (* Alpha-Beta *)\n",
-    "       List.fold_left (fun accu j ->\n",
-    "           let s' = Spin.other s in\n",
-    "           accu +. List.fold_left (fun accu a ->\n",
-    "                   accu +. (h_one i a s +. h_two i j a j s s')\n",
-    "                        *. (f_one a k s +. f_two a j k j s s')\n",
-    "                 ) 0. mos_cabs\n",
-    "         ) 0. mos'\n",
-    "       +.\n",
-    "       (* Alpha-Alpha / Beta-Beta *)\n",
-    "       List.fold_left (fun accu j ->\n",
-    "           if j = i then accu else\n",
-    "           let s' = s in\n",
-    "           accu +. List.fold_left (fun accu a ->\n",
-    "                   accu +. (h_one i a s +. h_two i j a j s s')\n",
-    "                        *. (f_one a k s +. f_two a j k j s s')\n",
-    "                 ) 0. mos_cabs\n",
-    "         ) 0. mos\n",
+    "       let s' = Spin.other s in\n",
+    "       List.fold_left (fun accu a -> accu +.\n",
+    "           (h_one i a s +. \n",
+    "              (List.fold_left (fun accu j -> accu +. h_two i j a j s s ) 0. mos_i ) +.\n",
+    "              (List.fold_left (fun accu j -> accu +. h_two i j a j s s') 0. mos_i') ) *.\n",
+    "           (f_one a k s +. \n",
+    "              (List.fold_left (fun accu j -> accu +. f_two a j k j s s ) 0. mos_j ) +.\n",
+    "              (List.fold_left (fun accu j -> accu +. f_two a j k j s s') 0. mos_j') ) \n",
+    "         ) 0. mos_cabs\n",
     "    in\n",
     "    match phase with\n",
     "    | Phase.Pos -> result\n",