diff --git a/Notebooks/F12_matrix.ipynb b/Notebooks/F12_matrix.ipynb
index 5ee5b29..b53e52d 100644
--- a/Notebooks/F12_matrix.ipynb
+++ b/Notebooks/F12_matrix.ipynb
@@ -284,6 +284,9 @@
     "let mos_cabs = \n",
     "  Util.list_range (mo_num+1) aux_num\n",
     "  \n",
+    "let mos_abs = \n",
+    "  Util.list_range 1 aux_num\n",
+    "  \n",
     "let mos_in = \n",
     "  Util.list_range 1 mo_num\n",
     "\n",
@@ -653,17 +656,18 @@
     "      [ List.map (fun hole -> \n",
     "          List.map (fun particle ->\n",
     "                  Determinant.single_excitation Spin.Alfa hole particle ki\n",
-    "              ) mos_cabs\n",
+    "              ) mos_abs\n",
     "          ) mos_a\n",
     "      ;\n",
     "        List.map (fun hole -> \n",
     "          List.map (fun particle ->\n",
     "                  Determinant.single_excitation Spin.Beta hole particle ki\n",
-    "              ) mos_cabs\n",
+    "              ) mos_abs\n",
     "          ) mos_b \n",
     "      ]\n",
     "      |> List.concat\n",
     "      |> List.concat\n",
+    "      |> List.filter (fun x -> Determinant.is_none x = false)\n",
     "      |> List.map (fun x -> Determinant.set_phase Phase.Pos x)\n",
     "  in\n",
     "  \n",
@@ -677,9 +681,9 @@
     "                if hole' > hole && particle' < particle then\n",
     "                  Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Alfa hole' particle' ki)\n",
     "                else None\n",
-    "                      ) mos_cabs\n",
+    "                      ) mos_abs\n",
     "                  ) mos_a \n",
-    "              ) mos_cabs\n",
+    "              ) mos_abs\n",
     "          ) mos_a\n",
     "        ; \n",
     "        List.map (fun hole ->  (* Beta-Beta *)\n",
@@ -689,9 +693,9 @@
     "                if hole' > hole && particle' < particle then\n",
     "                  Some (Determinant.double_excitation Spin.Beta hole particle Spin.Beta hole' particle' ki)\n",
     "                else None\n",
-    "                      ) mos_cabs\n",
+    "                      ) mos_abs\n",
     "                  ) mos_b \n",
-    "              ) mos_cabs\n",
+    "              ) mos_abs\n",
     "          ) mos_b\n",
     "        ;\n",
     "        List.map (fun hole ->  (* Alpha-Beta *)\n",
@@ -699,9 +703,9 @@
     "            List.map (fun hole' -> \n",
     "              List.map (fun particle' ->\n",
     "                  Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Beta hole' particle' ki)\n",
-    "                      ) mos_cabs\n",
+    "                      ) mos_abs\n",
     "                  ) mos_b \n",
-    "              ) mos_cabs\n",
+    "              ) mos_abs\n",
     "          ) mos_a\n",
     "      ]\n",
     "      |> List.concat\n",
@@ -760,10 +764,10 @@
     "  |> List.sort_uniq compare\n",
     "  \n",
     "  (* Filter out all determinants with incorrect numbers of electrons in the CABS *)\n",
-    "  |> List.filter good_cabs\n",
+    "  |> List.filter good_cabs \n",
     "  \n",
     "  (* Filter out all determinants with incorrect excitation numbers *)\n",
-    "  |> List.filter good_lr\n",
+    "  |> List.filter good_lr \n",
     "  \n",
     "  \n",
     "let compute_HaaF ki alphas kj =\n",
@@ -785,30 +789,48 @@
     "          | 0 -> det_I\n",
     "          | n -> Array.sub det_I 0 n\n",
     "    in\n",
-    "    Printf.printf \"Checking...\\n%!\";\n",
     "    let result =\n",
+    "        Printf.printf \"Checking ... \\n%!\";\n",
+    "        let percent = ref 0 in\n",
     "        Array.mapi (fun i ki -> \n",
+    "            let p = (10 * (i+1))/(Array.length det_list) in\n",
+    "            if p <> !percent then\n",
+    "                ( percent := p ; Printf.printf \" - %3d %%\\n%!\" (p*10) );\n",
     "            Array.mapi (fun j kj -> \n",
-    "                if i > j then 0. else\n",
-    "                if Determinant.degree ki kj <> exc then 0. else\n",
+    "                if i > j then (0,0,0.,0.) else\n",
+    "                if Determinant.degree ki kj <> exc then (0,0,0.,0.) else\n",
     "                let alphas = generate_alphas ki kj exc cabs lexc rexc in\n",
     "                let det_value =\n",
     "                  compute_HaaF ki alphas kj\n",
     "                in\n",
-    "                integral_value ki kj -. det_value \n",
+    "                let int_value = \n",
+    "                  integral_value ki kj\n",
+    "                in\n",
+    "                (i,j,det_value,int_value)\n",
     "            ) det_list\n",
     "        ) det_list\n",
     "        |> Array.to_list\n",
     "        |> Array.concat\n",
     "  in\n",
-    "  let error = \n",
-    "      Array.fold_left (fun accu x -> accu +. x *. x) 0. result\n",
-    "      /. (float_of_int @@ Array.length result)\n",
+    "  let i,j,d,v = \n",
+    "      let rec aux k imax jmax emax dmax vmax = \n",
+    "        if k = -1 then\n",
+    "          imax, jmax, dmax, vmax\n",
+    "        else\n",
+    "          let i, j, d, v = result.(k) in\n",
+    "          let e = abs_float (d -. v) in\n",
+    "          if e > emax then\n",
+    "            aux (k-1) i j e d v\n",
+    "          else\n",
+    "            aux (k-1) imax jmax emax dmax vmax\n",
+    "      in\n",
+    "      aux (n-1) 0 0 0. 0. 0.\n",
     "  in\n",
+    "  let error = abs_float (d -. v) in\n",
     "  if error < epsilon_float then\n",
     "      Printf.printf \"OK: %e\\n%!\" error\n",
     "  else\n",
-    "      Printf.printf \"Failed: %e\\n%!\" error\n",
+    "      Printf.printf \"Failed: (%d, %d) | %e %e | %e\\n%!\" i j d v error\n",
     "\n",
     "    "
    ]
@@ -817,7 +839,198 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# 0 2 22"
+    "******"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 1. 0 1 11"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "png_image \"0_1_11.png\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$i,j$ : 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",
+    "\\end{align}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "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",
+    "       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",
+    "   +.\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",
+    "     \n",
+    "let _ =\n",
+    "  check 0 integral_value 0 1 1 1\n",
+    "    "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 2. 0 1 22"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "png_image \"0_1_22.png\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$i,j$ : orbital indices of MOs   occupied in $|I\\rangle$.\n",
+    "\n",
+    "$k$   : orbital indices of MOs unoccupied in $|I\\rangle$.\n",
+    "\n",
+    "\\begin{align}\n",
+    "\\sum_{a} \\sum_{k} \\sum_{i} \\sum_{j<i}\n",
+    "            \\langle i j || a k \\rangle \n",
+    "             \\left[ a k || i j \\right] + \n",
+    "\\sum_{a} \\sum_{\\bar{k}} \\sum_{i} \\sum_{\\bar{j}}\n",
+    "            \\langle i \\bar{j} | a \\bar{k} \\rangle \n",
+    "             \\left[ a \\bar{k} | i \\bar{j} \\right]  + \\\\\n",
+    "\\sum_{\\bar{a}} \\sum_{k} \\sum_{\\bar{i}} \\sum_{j}\n",
+    "            \\langle \\bar{i} j | \\bar{a} k \\rangle \n",
+    "             \\left[ \\bar{a} k | \\bar{i} j \\right] + \n",
+    "\\sum_{\\bar{a}} \\sum_{\\bar{k}} \\sum_{\\bar{i}} \\sum_{\\bar{j}<\\bar{i}}\n",
+    "            \\langle \\bar{i} \\bar{j} || \\bar{a} \\bar{k} \\rangle \n",
+    "             \\left[ \\bar{a} \\bar{k} || \\bar{i} \\bar{j} \\right] \n",
+    "\\end{align}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "let integral_value ki kj = \n",
+    "   (* mos unoccupied in both I and J *)\n",
+    "   let mos_virt_a, mos_virt_b = \n",
+    "     Array.init mo_num (fun i -> Some (i+1)) , \n",
+    "     Array.init mo_num (fun i -> Some (i+1)) \n",
+    "   in\n",
+    "   List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n",
+    "   List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n",
+    "   List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n",
+    "   List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n",
+    "   \n",
+    "   let mos_virt_a, mos_virt_b = \n",
+    "     Array.to_list mos_virt_a |> Util.list_some,\n",
+    "     Array.to_list mos_virt_b |> Util.list_some\n",
+    "   in\n",
+    "   \n",
+    "   (* Alpha-Beta *)\n",
+    "   let s, s' = Spin.(Alfa, Beta) in\n",
+    "   List.fold_left (fun accu j -> accu +. \n",
+    "       List.fold_left (fun accu i -> accu +. \n",
+    "           List.fold_left (fun accu k -> accu +. \n",
+    "               List.fold_left (fun accu a ->\n",
+    "                   accu +. h_two i j a k s s'  *. f_two a k i j s s'\n",
+    "                 ) 0. mos_cabs\n",
+    "             ) 0. mos_virt_b\n",
+    "         ) 0. (mos_a ki)\n",
+    "     ) 0. (mos_b ki)\n",
+    "   +.\n",
+    "   List.fold_left (fun accu j -> accu +. \n",
+    "       List.fold_left (fun accu i -> accu +. \n",
+    "           List.fold_left (fun accu k -> accu +. \n",
+    "               List.fold_left (fun accu a ->\n",
+    "                   accu +. h_two i j a k s s'  *. f_two a k i j s s'\n",
+    "                 ) 0. mos_cabs\n",
+    "             ) 0. mos_virt_a\n",
+    "         ) 0. (mos_b ki)\n",
+    "     ) 0. (mos_a ki)\n",
+    "   +.\n",
+    "   (* Alpha-Alpha / Beta-Beta *)\n",
+    "   List.fold_left (fun accu (mos_virt,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",
+    "             if i < j then accu else\n",
+    "                 List.fold_left (fun accu k -> accu +. \n",
+    "                     List.fold_left (fun accu a -> \n",
+    "                           accu +. h_two i j a k s s'  *. f_two a k i j s s'\n",
+    "                       ) 0. mos_cabs\n",
+    "                   ) 0. mos_virt\n",
+    "           ) 0. mos\n",
+    "       ) 0. mos\n",
+    "     ) 0. [ (mos_virt_a,mos_a ki,Spin.Alfa) ; (mos_virt_b,mos_b ki,Spin.Beta)]\n",
+    "     \n",
+    "let _ =\n",
+    "  check 0 integral_value 0 1 2 2\n",
+    "    "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 3. 0 2 22"
    ]
   },
   {
@@ -835,13 +1048,22 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "$i,j$ : orbital indices of MOs occupied in $|I\\rangle$.\n",
+    "$i,j$ : orbital indices of MOs   occupied in $|I\\rangle$.\n",
     "\n",
-    "$$\n",
-    "\\sum_{j} \\sum_{i<j} \\sum_{b}\\sum_{a<b}\n",
-    "    \\langle i j || a b \\rangle \n",
-    "    \\left[ ab || ij \\right]\n",
-    "$$"
+    "\\begin{align}\n",
+    "\\sum_{a} \\sum_{b>a} \\sum_{i} \\sum_{j<i}\n",
+    "            \\langle i j || a b \\rangle \n",
+    "             \\left[ a b || i j \\right] + \n",
+    "\\sum_{a} \\sum_{\\bar{b}} \\sum_{i} \\sum_{\\bar{j}}\n",
+    "            \\langle i \\bar{j} | a \\bar{b} \\rangle  \n",
+    "             \\left[ a \\bar{b} | i \\bar{j} \\right]  + \\\\\n",
+    "\\sum_{\\bar{a}} \\sum_{b} \\sum_{\\bar{i}} \\sum_{j}\n",
+    "            \\langle \\bar{i} j | \\bar{a} b \\rangle  \n",
+    "             \\left[ \\bar{a} b | \\bar{i} j \\right] + \n",
+    "\\sum_{\\bar{a}} \\sum_{\\bar{b}>\\bar{a}} \\sum_{\\bar{i}} \\sum_{\\bar{j}<\\bar{i}}\n",
+    "            \\langle \\bar{i} \\bar{j} || \\bar{a} \\bar{b} \\rangle \n",
+    "             \\left[ \\bar{a} \\bar{b} || \\bar{i} \\bar{j} \\right] \n",
+    "\\end{align}"
    ]
   },
   {
@@ -880,7 +1102,7 @@
     "     ) 0. [ (mos_a ki,Spin.Alfa) ; (mos_b ki,Spin.Beta)]\n",
     "     \n",
     "let _ =\n",
-    "  check 10 integral_value 0 2 2 2\n",
+    "  check 100 integral_value 0 2 2 2\n",
     "    "
    ]
   },
@@ -888,7 +1110,156 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# 1 2 22"
+    "# 4. *1 1 11*"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "png_image \"1_1_11.png\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n",
+    "\n",
+    "$j$ : 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",
+    "\\end{align}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "let integral_value ki kj = \n",
+    "    let i, k, s, phase =\n",
+    "          match Excitation.of_det ki kj with\n",
+    "          | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
+    "            hole, particle, spin, phase\n",
+    "          | _ -> assert false\n",
+    "    in\n",
+    "\n",
+    "    let mos, mos' =\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",
+    "\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",
+    "    in\n",
+    "    match phase with\n",
+    "    | Phase.Pos -> result\n",
+    "    | Phase.Neg -> -. result\n",
+    "     \n",
+    "\n",
+    "let _ = check 50 integral_value 1 1 1 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "let ki = det_I.(0)\n",
+    "let kj = det_I.(0)\n",
+    "\n",
+    "\n",
+    "let _ =\n",
+    "    let alphas =\n",
+    "        generate_alphas ki kj 0 1 2 2\n",
+    "    in\n",
+    "    compute_HaaF ki alphas kj\n",
+    "\n",
+    "let _ = integral_value ki kj"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 5. *1 1 12*"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "png_image \"1_1_12.png\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 6. *1 1 21*"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "png_image \"1_1_21.png\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 7. *1 1 22*"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "png_image \"1_1_22.png\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 8. 1 2 22 "
    ]
   },
   {
@@ -923,42 +1294,232 @@
    "outputs": [],
    "source": [
     "let integral_value ki kj = \n",
-    "   let h, p, s, phase =\n",
-    "       match Excitation.of_det ki kj with\n",
-    "       | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
-    "         hole, particle, spin, phase\n",
-    "       | _ -> assert false\n",
+    "    let h, p, s, phase =\n",
+    "          match Excitation.of_det ki kj with\n",
+    "          | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
+    "            hole, particle, spin, phase\n",
+    "          | _ -> assert false\n",
     "    in\n",
-    "   \n",
-    "   let mos, mos' =\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",
     "\n",
-    "   (* Alpha-Beta *)\n",
-    "   let s' = Spin.other s in\n",
-    "   List.fold_left (fun accu j -> accu +. \n",
-    "       List.fold_left (fun accu b -> accu +. \n",
-    "           List.fold_left (fun accu a ->\n",
-    "               accu +. h_two h j a b s s'  *. f_two a b p j s s'\n",
+    "    let mos, mos' =\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",
+    "\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 b ->\n",
+    "               accu +. List.fold_left (fun accu a ->\n",
+    "                   accu +. h_two h j a b s s'  *. f_two a b p j s s'\n",
+    "                 ) 0. mos_cabs\n",
     "             ) 0. mos_cabs\n",
-    "         ) 0. mos_cabs\n",
-    "     ) 0. mos' \n",
-    "   +.\n",
-    "   (* Alpha-Alpha / Beta-Beta *)\n",
-    "     let s' = s in \n",
-    "     List.fold_left (fun accu j -> accu +. \n",
-    "       List.fold_left (fun accu b -> accu +. \n",
-    "           List.fold_left (fun accu a -> \n",
-    "               if b > a then accu else\n",
-    "                 accu +. h_two h j a b s s'  *. f_two a b p j s s'\n",
-    "             ) 0. mos_cabs\n",
-    "         ) 0. mos_cabs\n",
-    "       ) 0. mos \n",
+    "         ) 0. mos' \n",
+    "       +.\n",
+    "       (* Alpha-Alpha / Beta-Beta *)\n",
+    "       List.fold_left (fun accu j ->\n",
+    "           let s' = s in \n",
+    "           accu +. List.fold_left (fun accu b ->\n",
+    "             accu +. List.fold_left (fun accu a -> \n",
+    "                 if b > a then accu else\n",
+    "                   accu +. h_two h j a b s s'  *. f_two a b p j s s'\n",
+    "               ) 0. mos_cabs\n",
+    "           ) 0. mos_cabs\n",
+    "         ) 0. mos \n",
+    "    in\n",
+    "    match phase with\n",
+    "    | Phase.Pos -> result\n",
+    "    | Phase.Neg -> -. result\n",
     "     \n",
     "\n",
-    "let _ = check 10 integral_value 1 2 2 2"
+    "let _ = check 50 integral_value 1 2 2 2"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 9. *2 1 12*"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "png_image \"2_1_12.png\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 10. *2 1 21*"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "png_image \"2_1_21.png\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 11. *2 1 22*"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "png_image \"2_1_22.png\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 12. 2 2 22"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "png_image \"2_2_22.png\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n",
+    "\n",
+    "$$\n",
+    "\\sum_{b}\\sum_{a<b}\n",
+    "    \\langle i j || a b \\rangle \n",
+    "    \\left[ ab || kj \\right]\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "let integral_value ki kj = \n",
+    "    let h, h', p, p', s, s', phase =\n",
+    "          match Excitation.of_det ki kj with\n",
+    "          | Excitation.(Double (phase,\n",
+    "              { hole=h ; particle=p ; spin=s },\n",
+    "              { hole=h'; particle=p'; spin=s'}) )  -> h, h', p, p', s, s', phase\n",
+    "          | _ -> assert false\n",
+    "    in\n",
+    "\n",
+    "    let result = \n",
+    "       if s <> s' then (* Alpha-Beta *)\n",
+    "           List.fold_left (fun accu b ->\n",
+    "               accu +. List.fold_left (fun accu a ->\n",
+    "                   accu +. h_two h h' a b s s'  *. f_two a b p p' s s'\n",
+    "                 ) 0. mos_cabs\n",
+    "             ) 0. mos_cabs\n",
+    "       else (* Alpha-Alpha / Beta-Beta *)\n",
+    "           List.fold_left (fun accu b ->\n",
+    "             accu +. List.fold_left (fun accu a -> \n",
+    "                 if b > a then accu else\n",
+    "                   accu +. h_two h h' a b s s'  *. f_two a b p p' s s'\n",
+    "               ) 0. mos_cabs\n",
+    "           ) 0. mos_cabs\n",
+    "    in\n",
+    "    match phase with\n",
+    "    | Phase.Pos -> result\n",
+    "    | Phase.Neg -> -. result\n",
+    "     \n",
+    "\n",
+    "let _ = check 100 integral_value 2 2 2 2"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 13. *3 1 2 2*"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "png_image \"3_1_22.png\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$|J\\rangle = \\hat{T}_{ijm}^{kln}|I\\rangle$\n",
+    "\n",
+    "$$\n",
+    "\\sum_{a} \\langle i j || k a \\rangle  \\left[ m a || n l \\right] \n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "let integral_value ki kj = \n",
+    "    let h1, h2, h3, p1, p2, p3, s1, s2, s3, phase =\n",
+    "          match Excitation.of_det ki kj with\n",
+    "          | Excitation.(Triple (phase,\n",
+    "              { hole=h1 ; particle=p1 ; spin=s1 },\n",
+    "              { hole=h2 ; particle=p2 ; spin=s2 },\n",
+    "              { hole=h3 ; particle=p3 ; spin=s3 }) )  -> h1, h2, h3, p1, p2, p3, s1, s2, s3, phase\n",
+    "          | _ -> assert false\n",
+    "    in\n",
+    "\n",
+    "(*\n",
+    "123\n",
+    "213\n",
+    "231\n",
+    "321\n",
+    "312\n",
+    "132\n",
+    "*)\n",
+    "\n",
+    "    let result = \n",
+    "       List.fold_left (fun accu a -> accu +.\n",
+    "           h_two h1 h2 p1 a s1 s2  *. f_two h3 a p3 p2 s3 s2 -.\n",
+    "           h_two h2 h1 p2 a s2 s1  *. f_two h3 a p3 p1 s3 s1 +.\n",
+    "           h_two h2 h3 p2 a s2 s3  *. f_two h1 a p1 p3 s1 s3 -.\n",
+    "           h_two h3 h2 p3 a s3 s2  *. f_two h1 a p1 p2 s1 s2 +.\n",
+    "           h_two h3 h1 p3 a s3 s1  *. f_two h2 a p2 p1 s2 s1 -.\n",
+    "           h_two h1 h3 p1 a s1 s3  *. f_two h2 a p2 p3 s2 s3 \n",
+    "           ) 0. mos_cabs\n",
+    "    in\n",
+    "    match phase with\n",
+    "    | Phase.Pos -> result\n",
+    "    | Phase.Neg -> -. result\n",
+    "     \n",
+    "\n",
+    "let _ = check 100 integral_value 3 1 2 2"
    ]
   },
   {
@@ -972,7 +1533,7 @@
  "metadata": {
   "celltoolbar": "Raw Cell Format",
   "kernelspec": {
-   "display_name": "OCaml 4.07.1",
+   "display_name": "OCaml default",
    "language": "OCaml",
    "name": "ocaml-jupyter"
   },