diff --git a/Notebooks/F12_matrix.ipynb b/Notebooks/F12_matrix.ipynb
index adab92c..903c6ea 100644
--- a/Notebooks/F12_matrix.ipynb
+++ b/Notebooks/F12_matrix.ipynb
@@ -827,7 +827,7 @@
     "                    let int_value = \n",
     "                      integral_value ki kj\n",
     "                    in\n",
-    "(*   Printf.printf \"%d %d %e %e\\n%!\" i j det_value int_value; *)\n",
+    "(*   Printf.printf \"%d %d %e %e\\n%!\" i j det_value int_value;  *)\n",
     "                    (i,j,det_value,int_value)\n",
     "                  end\n",
     "            ) det_list\n",
@@ -842,7 +842,7 @@
     "        else\n",
     "          let i, j, d, v = result.(k) in\n",
     "          let e = abs_float (d -. v) in\n",
-    "          if e > emax then\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",
@@ -881,6 +881,7 @@
     "  done;\n",
     "  result\n",
     "\n",
+    "\n",
     "let array_4_init d1 d2 d3 d4 f =\n",
     "  let result = \n",
     "      Bigarray.(Genarray.create Float64 fortran_layout) [| d1;d2;d3;d4 |]\n",
@@ -896,6 +897,24 @@
     "  done;\n",
     "  result\n",
     "\n",
+    "\n",
+    "let array_5_init d1 d2 d3 d4 d5 f =\n",
+    "  let result = \n",
+    "      Bigarray.(Genarray.create Float64 fortran_layout) [| d1;d2;d3;d4;d5 |]\n",
+    "  in\n",
+    "  for m=1 to d5 do\n",
+    "    for l=1 to d4 do\n",
+    "      for k=1 to d3 do\n",
+    "        for j=1 to d2 do\n",
+    "          for i=1 to d1 do\n",
+    "             result.{i,j,k,l,m} <- f i j k l m\n",
+    "          done\n",
+    "        done\n",
+    "      done\n",
+    "    done\n",
+    "  done;\n",
+    "  result\n",
+    "\n",
     "(* ----- *)"
    ]
   },
@@ -919,7 +938,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "png_image \"0_1_11.png\""
+    "let _ = png_image \"0_1_11.png\""
    ]
   },
   {
@@ -1099,7 +1118,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "png_image \"0_1_22.png\""
+    "let _ = png_image \"0_1_22.png\""
    ]
   },
   {
@@ -1256,7 +1275,7 @@
    },
    "outputs": [],
    "source": [
-    "png_image \"0_2_22.png\""
+    "let _ = png_image \"0_2_22.png\""
    ]
   },
   {
@@ -1371,7 +1390,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "png_image \"1_1_11.png\""
+    "let _ = png_image \"1_1_11.png\""
    ]
   },
   {
@@ -1560,7 +1579,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "png_image \"1_1_12.png\""
+    "let _ = png_image \"1_1_12.png\""
    ]
   },
   {
@@ -1647,6 +1666,109 @@
     "let _ = check 0 integral_value 1 1 1 2"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "let m_1112_1H_2Fa = \n",
+    "  array_3_init mo_num mo_num mo_num (fun i j k ->\n",
+    "      sum mos_cabs (fun a ->\n",
+    "        h_one j a Spin.Alfa *. f_two a i j k Spin.Alfa Spin.Alfa ))\n",
+    "\n",
+    "    \n",
+    "let m_1112_1H_2Fb = \n",
+    "  array_3_init mo_num mo_num mo_num (fun i j k ->\n",
+    "      sum mos_cabs (fun a ->\n",
+    "        h_one j a Spin.Beta *. f_two a i j k Spin.Alfa Spin.Beta ))\n",
+    "\n",
+    "\n",
+    "let m_1112_2Ha_2Fa =\n",
+    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "      h_two j m a m Spin.Alfa Spin.Alfa *.\n",
+    "      f_two a i j k Spin.Alfa Spin.Alfa \n",
+    "    )\n",
+    "  )\n",
+    "\n",
+    "\n",
+    "let m_1112_2Hb_2Fa =\n",
+    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "      h_two j m a m Spin.Alfa Spin.Beta *.\n",
+    "      f_two a i j k Spin.Alfa Spin.Alfa \n",
+    "    )\n",
+    "  )\n",
+    "\n",
+    "let m_1112_2Ha_2Fb =\n",
+    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "      h_two j m a m Spin.Alfa Spin.Alfa *.\n",
+    "      f_two a i j k Spin.Alfa Spin.Beta \n",
+    "    )\n",
+    "  )\n",
+    "\n",
+    "\n",
+    "let m_1112_2Hb_2Fb =\n",
+    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "      h_two j m a m Spin.Alfa Spin.Beta *.\n",
+    "      f_two a i j k Spin.Alfa Spin.Beta \n",
+    "    )\n",
+    "  )\n",
+    "\n",
+    "\n",
+    "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_j, mos_j' =\n",
+    "      let alfa = \n",
+    "        let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
+    "        let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
+    "        Bitstring.to_list (Bitstring.logand i j)\n",
+    "      in\n",
+    "      let beta  = \n",
+    "        let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
+    "        let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
+    "        Bitstring.to_list (Bitstring.logand i j)\n",
+    "      in\n",
+    "      match s with\n",
+    "      | Spin.Alfa -> alfa, beta\n",
+    "      | Spin.Beta -> beta, alfa\n",
+    "    in\n",
+    "    \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",
+    "   \n",
+    "    let result = \n",
+    "     sum mos_j (fun j -> \n",
+    "       m_1112_1H_2Fa.{i,j,k} +. \n",
+    "       sum mos_i  (fun m -> m_1112_2Ha_2Fa.{i,j,k,m}) +.\n",
+    "       sum mos_i' (fun m -> m_1112_2Hb_2Fa.{i,j,k,m})) +.\n",
+    "     sum mos_j' (fun j ->\n",
+    "       m_1112_1H_2Fb.{i,j,k} +. \n",
+    "       sum mos_i  (fun m -> m_1112_2Hb_2Fb.{i,j,k,m}) +.\n",
+    "       sum mos_i' (fun m -> m_1112_2Ha_2Fb.{i,j,k,m}))\n",
+    "    in\n",
+    "    \n",
+    "    match phase with\n",
+    "    | Phase.Pos -> result\n",
+    "    | Phase.Neg -> -. result\n",
+    "   \n",
+    "   \n",
+    "\n",
+    "let _ = check 0 integral_value 1 1 1 2"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -1662,7 +1784,7 @@
    },
    "outputs": [],
    "source": [
-    "png_image \"1_1_21.png\""
+    "let _ = png_image \"1_1_21.png\""
    ]
   },
   {
@@ -1748,6 +1870,109 @@
     "let _ = check 0 integral_value 1 1 2 1"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "let m_1121_2Ha_1F = \n",
+    "  array_3_init mo_num mo_num mo_num (fun i j k ->\n",
+    "      sum mos_cabs (fun a ->\n",
+    "        h_two i j k a Spin.Alfa Spin.Alfa *. f_one a j Spin.Alfa))\n",
+    "\n",
+    "    \n",
+    "let m_1121_2Hb_1F = \n",
+    "  array_3_init mo_num mo_num mo_num (fun i j k ->\n",
+    "      sum mos_cabs (fun a ->\n",
+    "        h_two i j k a Spin.Alfa Spin.Beta *. f_one a j Spin.Beta))\n",
+    "\n",
+    "\n",
+    "let m_1121_2Ha_2Fa =\n",
+    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "      h_two i j k a Spin.Alfa Spin.Alfa *.\n",
+    "      f_two m a m j Spin.Alfa Spin.Alfa \n",
+    "    )\n",
+    "  )\n",
+    "\n",
+    "\n",
+    "let m_1121_2Hb_2Fa =\n",
+    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "      h_two i j k a Spin.Alfa Spin.Beta *.\n",
+    "      f_two m a m j Spin.Alfa Spin.Alfa \n",
+    "    )\n",
+    "  )\n",
+    "\n",
+    "let m_1121_2Ha_2Fb =\n",
+    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "      h_two i j k a Spin.Alfa Spin.Alfa *.\n",
+    "      f_two m a m j Spin.Alfa Spin.Beta \n",
+    "    )\n",
+    "  )\n",
+    "\n",
+    "\n",
+    "let m_1121_2Hb_2Fb =\n",
+    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "      h_two i j k a Spin.Alfa Spin.Beta *.\n",
+    "      f_two m a m j Spin.Alfa Spin.Beta \n",
+    "    )\n",
+    "  )\n",
+    "\n",
+    "\n",
+    "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_j, mos_j' =\n",
+    "      let alfa = \n",
+    "        let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
+    "        let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
+    "        Bitstring.to_list (Bitstring.logand i j)\n",
+    "      in\n",
+    "      let beta  = \n",
+    "        let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
+    "        let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
+    "        Bitstring.to_list (Bitstring.logand i j)\n",
+    "      in\n",
+    "      match s with\n",
+    "      | Spin.Alfa -> alfa, beta\n",
+    "      | Spin.Beta -> beta, alfa\n",
+    "    in\n",
+    "    \n",
+    "    let mos_i, mos_i' =\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",
+    "     sum mos_j (fun j -> \n",
+    "       m_1121_2Ha_1F.{i,j,k} +. \n",
+    "       sum mos_i  (fun m -> m_1121_2Ha_2Fa.{i,j,k,m}) +.\n",
+    "       sum mos_i' (fun m -> m_1121_2Ha_2Fb.{i,j,k,m})) +.\n",
+    "     sum mos_j' (fun j ->\n",
+    "       m_1121_2Hb_1F.{i,j,k} +. \n",
+    "       sum mos_i  (fun m -> m_1121_2Hb_2Fb.{i,j,k,m}) +.\n",
+    "       sum mos_i' (fun m -> m_1121_2Hb_2Fa.{i,j,k,m}))\n",
+    "    in\n",
+    "    \n",
+    "    match phase with\n",
+    "    | Phase.Pos -> result\n",
+    "    | Phase.Neg -> -. result\n",
+    "   \n",
+    "   \n",
+    "\n",
+    "let _ = check 0 integral_value 1 1 2 1"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -1761,7 +1986,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "png_image \"1_1_22.png\""
+    "let _ = png_image \"1_1_22.png\""
    ]
   },
   {
@@ -1774,9 +1999,10 @@
     "    \\hat{T}_{ij}^{ma} \\hat{T}_{ma}^{kj} - \n",
     "    \\hat{T}_{lj}^{ka} \\hat{T}_{ia}^{lj} + \\\\\n",
     "\\sum_{\\bar{j}} \\sum_{\\bar{a}} \\sum_{m}\n",
-    "    \\hat{T}_{i\\bar{j}}^{m\\bar{a}} \\hat{T}_{m\\bar{a}}^{k\\bar{j}} + \n",
-    "    \\hat{T}_{i\\bar{j}}^{a\\bar{m}} \\hat{T}_{a\\bar{m}}^{k\\bar{j}} -\n",
-    "    \\hat{T}_{l\\bar{j}}^{k\\bar{a}} \\hat{T}_{i\\bar{a}}^{l\\bar{j}}\n",
+    "    \\hat{T}_{i\\bar{j}}^{m\\bar{a}} \\hat{T}_{m\\bar{a}}^{k\\bar{j}} - \n",
+    "    \\hat{T}_{l\\bar{j}}^{k\\bar{a}} \\hat{T}_{i\\bar{a}}^{l\\bar{j}} +\n",
+    "\\sum_{\\bar{j}} \\sum_{a} \\sum_{\\bar{m}}\n",
+    "    \\hat{T}_{i\\bar{j}}^{a\\bar{m}} \\hat{T}_{a\\bar{m}}^{k\\bar{j}} \n",
     "$\n",
     "\n",
     "$j,l$ : orbital indices of MOs occupied both in $|I\\rangle$  and $|J\\rangle$.\n",
@@ -1786,16 +2012,16 @@
     "$a$ : orbital indices of CABS MOs\n",
     "\n",
     "\\begin{align}\n",
-    "%    \\sum_{a} \\sum_{j} \\sum_{m}\n",
-    "%      \\langle i j || m a \\rangle  \\left[ m a || k j \\right]  + \n",
-    "%    \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{m} \n",
-    "%      \\langle i \\bar{j} | m \\bar{a} \\rangle  \\left[ m \\bar{a} | k \\bar{j} \\right] - \\\\\n",
-    "%    \\sum_{a} \\sum_{j} \\sum_{l}\n",
-    "%      \\langle l j || k a \\rangle  \\left[ i a || l j \\right]  - \n",
-    "%    \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{l} \n",
-    "%      \\langle l \\bar{j} | k \\bar{a} \\rangle  \\left[ i \\bar{a} | l \\bar{j} \\right] + \\\\\n",
-    "%    \\sum_{a} \\sum_{\\bar{j}} \\sum_{\\bar{m}} \n",
-    "%      \\langle i \\bar{j} | a \\bar{m} \\rangle  \\left[ a \\bar{m} | k \\bar{j} \\right] \\\\\n",
+    "    \\sum_{a} \\sum_{j} \\sum_{m}\n",
+    "      \\langle i j || m a \\rangle  \\left[ m a || k j \\right]  - \\\\\n",
+    "    \\sum_{a} \\sum_{j} \\sum_{l}\n",
+    "      \\langle l j || k a \\rangle  \\left[ i a || l j \\right]  + \\\\\n",
+    "    \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{m}\n",
+    "      \\langle i \\bar{j} | m \\bar{a} \\rangle  \\left[ m \\bar{a} | k \\bar{j} \\right]  + \\\\\n",
+    "    \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{l}\n",
+    "      \\langle l \\bar{j} | k \\bar{a} \\rangle  \\left[ i \\bar{a} | l \\bar{j} \\right] - \\\\\n",
+    "    \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{\\bar{m}}\n",
+    "      \\langle i \\bar{j} | a \\bar{m} \\rangle  \\left[ a \\bar{m} | k \\bar{j} \\right]  \n",
     "\\end{align}"
    ]
   },
@@ -1807,6 +2033,47 @@
    },
    "outputs": [],
    "source": [
+    "let m_1122_oa =\n",
+    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "      h_two l j k a Spin.Alfa Spin.Alfa *.\n",
+    "      f_two i a l j Spin.Alfa Spin.Alfa \n",
+    "    )\n",
+    "  )\n",
+    "\n",
+    "let m_1122_va =\n",
+    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "      h_two i j m a Spin.Alfa Spin.Alfa *.\n",
+    "      f_two m a k j Spin.Alfa Spin.Alfa \n",
+    "    )\n",
+    "  )\n",
+    "\n",
+    "let m_1122_o =\n",
+    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "      h_two l j k a Spin.Alfa Spin.Beta *.\n",
+    "      f_two i a l j Spin.Alfa Spin.Beta \n",
+    "    )\n",
+    "  )\n",
+    "\n",
+    "let m_1122_v =\n",
+    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "      h_two i j m a Spin.Alfa Spin.Beta *.\n",
+    "      f_two m a k j Spin.Alfa Spin.Beta \n",
+    "    )\n",
+    "  )\n",
+    "\n",
+    "let m_1122_v2 =\n",
+    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "      h_two i j a m Spin.Alfa Spin.Beta *.\n",
+    "      f_two a m k j Spin.Alfa Spin.Beta \n",
+    "    )\n",
+    "  )\n",
+    "\n",
+    "\n",
     "let integral_value ki kj = \n",
     "    let i, k, s, phase =\n",
     "          match Excitation.of_det ki kj with\n",
@@ -1853,32 +2120,26 @@
     "    in\n",
     "\n",
     "    let result = \n",
-    "       let s' = Spin.other s in\n",
-    "        sum mos_cabs (fun a -> \n",
     "        sum mos_j    (fun j -> \n",
     "        sum mos_virt (fun m -> \n",
-    "             h_two i j m a s s   *.  f_two m a k j s s \n",
-    "        ))) +.\n",
-    "        sum mos_cabs (fun a -> \n",
+    "          m_1122_va.{i,j,k,m}\n",
+    "        )) +.\n",
     "        sum mos_j'   (fun j -> \n",
     "        sum mos_virt (fun m -> \n",
-    "             h_two i j m a s s'  *.  f_two m a k j s s' \n",
-    "        )))   +.\n",
-    "        sum mos_cabs  (fun a -> \n",
+    "          m_1122_v.{i,j,k,m}\n",
+    "        ))   +.\n",
     "        sum mos_j'    (fun j -> \n",
     "        sum mos_virt' (fun m -> \n",
-    "             h_two i j a m s s'  *.  f_two a m k j s s'\n",
-    "        )))   -.\n",
-    "        sum mos_cabs (fun a -> \n",
+    "          m_1122_v2.{i,j,k,m}\n",
+    "        ))   -.\n",
     "        sum mos_j    (fun j -> \n",
     "        sum mos_j    (fun l -> if l = i then 0. else\n",
-    "             h_two l j k a s s   *.  f_two i a l j s s \n",
-    "        ))) -. \n",
-    "        sum mos_cabs (fun a -> \n",
+    "          m_1122_oa.{i,j,k,l}\n",
+    "        )) -. \n",
     "        sum mos_j'   (fun j -> \n",
     "        sum mos_j    (fun l -> if l = i then 0. else\n",
-    "             h_two l j k a s s'  *.  f_two i a l j s s'\n",
-    "        ))) \n",
+    "          m_1122_o.{i,j,k,l}\n",
+    "        )) \n",
     "    in\n",
     "    match phase with\n",
     "    | Phase.Pos -> result\n",
@@ -1903,7 +2164,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "png_image \"1_2_22.png\""
+    "let _ = png_image \"1_2_22.png\""
    ]
   },
   {
@@ -1973,11 +2234,79 @@
     "let _ = check 0 integral_value 1 2 2 2"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "let m_1222a =\n",
+    "  array_3_init mo_num mo_num mo_num (fun i j k ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "    sum mos_cabs (fun b -> if b > a then 0. else\n",
+    "      h_two i j a b Spin.Alfa Spin.Alfa *.\n",
+    "      f_two a b k j Spin.Alfa Spin.Alfa \n",
+    "    )\n",
+    "    )\n",
+    "  )\n",
+    "\n",
+    "let m_1222 =\n",
+    "  array_3_init mo_num mo_num mo_num (fun i j k ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "    sum mos_cabs (fun b ->\n",
+    "      h_two i j a b Spin.Alfa Spin.Beta *.\n",
+    "      f_two a b k j Spin.Alfa Spin.Beta \n",
+    "    )\n",
+    "    )\n",
+    "  )\n",
+    "  \n",
+    "\n",
+    "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",
+    "   (* MOs unoccupied in both I and J *)\n",
+    "    let mos_j, mos_j' =\n",
+    "      let alfa = \n",
+    "        let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
+    "        let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
+    "        Bitstring.to_list (Bitstring.logand i j)\n",
+    "      in\n",
+    "      let beta  = \n",
+    "        let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
+    "        let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
+    "        Bitstring.to_list (Bitstring.logand i j)\n",
+    "      in\n",
+    "      match s with\n",
+    "      | Spin.Alfa -> alfa, beta\n",
+    "      | Spin.Beta -> beta, alfa\n",
+    "    in\n",
+    "\n",
+    "    let result = \n",
+    "        sum mos_j    (fun j ->  m_1222a.{i,j,k} ) +.\n",
+    "        sum mos_j'   (fun j ->  m_1222.{i,j,k} )\n",
+    "    in\n",
+    "    match phase with\n",
+    "    | Phase.Pos -> result\n",
+    "    | Phase.Neg -> -. result\n",
+    "     \n",
+    "\n",
+    "let _ = check 0 integral_value 1 2 2 2\n",
+    "\n",
+    "\n"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# 9. *2 1 12*"
+    "# 9. 2 1 12"
    ]
   },
   {
@@ -1986,7 +2315,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "png_image \"2_1_12.png\""
+    "let _ = png_image \"2_1_12.png\""
    ]
   },
   {
@@ -2001,9 +2330,7 @@
     "\n",
     "$\\sum_{a} \n",
     "    \\hat{T}_{i}^{a} \\hat{T}_{aj}^{kl} +\n",
-    "    \\hat{T}_{j}^{a} \\hat{T}_{ai}^{lk} +\n",
-    "    \\hat{T}_{i}^{a} \\hat{T}_{a\\bar{j}}^{k\\bar{l}} + \n",
-    "    \\hat{T}_{j}^{a} \\hat{T}_{a\\bar{i}}^{l\\bar{k}} \n",
+    "    \\hat{T}_{j}^{a} \\hat{T}_{ia}^{kl} \n",
     "$\n",
     "\n",
     "\n",
@@ -2011,14 +2338,16 @@
     "\\sum_{a}\n",
     "    \\left( h_{ia} + \\sum_{n} \\langle i n || a n \\rangle + \\sum_{\\bar{n}} \\langle i \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ a j || k l \\right] + \\\\\n",
     "\\sum_{a}\n",
-    "    \\left( h_{ja} + \\sum_{n} \\langle j n || a n \\rangle + \\sum_{\\bar{n}} \\langle j \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ a i || l k \\right] \n",
+    "    \\left( h_{ja} + \\sum_{n} \\langle j n || a n \\rangle + \\sum_{\\bar{n}} \\langle j \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ i a || k l \\right] \n",
     "$$"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "scrolled": true
+   },
    "outputs": [],
    "source": [
     "let integral_value ki kj = \n",
@@ -2034,20 +2363,27 @@
     "          | Spin.Alfa -> mos_a ki, mos_b ki\n",
     "          | Spin.Beta -> mos_b ki, mos_a ki\n",
     "        in\n",
+    "        \n",
+    "        let mos2, mos2' =\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",
-    "           let s'' = Spin.other s in\n",
     "       sum mos_cabs (fun a -> \n",
+    "           let s'' = Spin.other s in\n",
     "             ( h_one i a s +.\n",
-    "               sum mos  (fun n -> h_two n i n a s s) +.\n",
-    "               sum mos' (fun n -> h_two n i n a s'' s) \n",
-    "             ) *. f_two j a l k s' s\n",
+    "               sum mos  (fun n -> h_two i n a n s s  ) +.\n",
+    "               sum mos' (fun n -> h_two i n a n s s'') \n",
+    "             ) *. f_two a j k l s s'\n",
     "             ) +.\n",
     "       sum mos_cabs (fun a -> \n",
-    "             ( h_one j a s +.\n",
-    "               sum mos  (fun n -> h_two n j n a s s) +.\n",
-    "               sum mos' (fun n -> h_two n j n a s'' s) \n",
-    "             ) *. f_two i a k l s' s\n",
+    "           let s'' = Spin.other s' in\n",
+    "             ( h_one j a s' +.\n",
+    "               sum mos2 (fun n -> h_two j n a n s' s' ) +.\n",
+    "               sum mos2'  (fun n -> h_two j n a n s' s'') \n",
+    "             ) *. f_two i a k l s s'\n",
     "             ) \n",
     "        in\n",
     "\n",
@@ -2059,6 +2395,122 @@
     "let _ = check 0 integral_value 2 1 1 2"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n",
+    "\n",
+    "$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$  and $|J\\rangle$.\n",
+    "\n",
+    "$n$ : orbital indices of MOs occupied in $|I\\rangle$\n",
+    "\n",
+    "$\\sum_{a} \n",
+    "    \\hat{T}_{i}^{a} \\hat{T}_{aj}^{kl} +\n",
+    "    \\hat{T}_{j}^{a} \\hat{T}_{ia}^{kl} \n",
+    "$\n",
+    "\n",
+    "\n",
+    "$$\n",
+    "\\sum_{a}\n",
+    "    \\left( h_{ia} + \\sum_{n} \\langle i n || a n \\rangle + \\sum_{\\bar{n}} \\langle i \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ a j || k l \\right] + \\\\\n",
+    "\\sum_{a}\n",
+    "    \\left( h_{ja} + \\sum_{n} \\langle j n || a n \\rangle + \\sum_{\\bar{n}} \\langle j \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ i a || k l \\right] \n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "let m_2112_1H_2Fa =\n",
+    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "        h_one i a Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Alfa +.\n",
+    "        h_one j a Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Alfa )\n",
+    "    )\n",
+    "\n",
+    "let m_2112_1H_2Fb =\n",
+    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "        h_one i a Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Beta +.\n",
+    "        h_one j a Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Beta)\n",
+    "    )\n",
+    "\n",
+    "let m_2112_2Ha_2Fa =\n",
+    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "        h_two i n a n Spin.Alfa Spin.Alfa *.\n",
+    "        f_two a j k l Spin.Alfa Spin.Alfa )\n",
+    "    )\n",
+    "    \n",
+    "let m_2112_2Hb_2Fa =\n",
+    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "        h_two i n a n Spin.Alfa Spin.Beta *.\n",
+    "        f_two a j k l Spin.Alfa Spin.Alfa )\n",
+    "    )\n",
+    "    \n",
+    "let m_2112_2Ha_2Fb =\n",
+    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "        h_two i n a n Spin.Alfa Spin.Alfa *.\n",
+    "        f_two a j k l Spin.Alfa Spin.Beta )\n",
+    "    )\n",
+    "    \n",
+    "let m_2112_2Hb_2Fb =\n",
+    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "        h_two i n a n Spin.Alfa Spin.Beta *.\n",
+    "        f_two a j k l Spin.Alfa Spin.Beta )\n",
+    "    )\n",
+    "    \n",
+    "let integral_value ki kj = \n",
+    "    let i, j, k, l, s, s', phase =\n",
+    "          match Excitation.of_det ki kj with\n",
+    "          | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
+    "            hole, hole', particle, particle', spin, spin', phase\n",
+    "          | _ -> assert false\n",
+    "    in\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",
+    "       if s = s' then\n",
+    "         m_2112_1H_2Fa.{i,j,k,l} +. \n",
+    "         sum mos  (fun n ->\n",
+    "             m_2112_2Ha_2Fa.{i,j,k,l,n} +. m_2112_2Ha_2Fa.{j,i,l,k,n}\n",
+    "         ) +.\n",
+    "         sum mos' (fun n ->\n",
+    "             m_2112_2Hb_2Fa.{i,j,k,l,n} +. m_2112_2Hb_2Fa.{j,i,l,k,n}\n",
+    "         ) \n",
+    "       else\n",
+    "         m_2112_1H_2Fb.{i,j,k,l} +.\n",
+    "         sum mos  (fun n ->\n",
+    "             m_2112_2Ha_2Fb.{i,j,k,l,n} +. m_2112_2Hb_2Fb.{j,i,l,k,n}\n",
+    "         ) +.\n",
+    "         sum mos' (fun n ->\n",
+    "             m_2112_2Hb_2Fb.{i,j,k,l,n} +. m_2112_2Ha_2Fb.{j,i,l,k,n}\n",
+    "         ) \n",
+    "     in\n",
+    "\n",
+    "    match phase with\n",
+    "    | Phase.Pos -> result\n",
+    "    | Phase.Neg -> -. result\n",
+    "     \n",
+    "\n",
+    "let _ = check 0 integral_value 2 1 1 2\n",
+    "\n",
+    "\n"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -2072,7 +2524,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "png_image \"2_1_21.png\""
+    "let _ = png_image \"2_1_21.png\""
    ]
   },
   {
@@ -2083,7 +2535,7 @@
     "\n",
     "$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$  and $|J\\rangle$.\n",
     "\n",
-    "$n$ : orbital indices of MOs occupied in $|I\\rangle$\n",
+    "$n$ : orbital indices of MOs occupied in $|J\\rangle$\n",
     "\n",
     "$\\sum_{a} \n",
     "    \\hat{T}_{ij}^{al} \\hat{T}_{a}^{k} +\n",
@@ -2135,10 +2587,10 @@
     "          | Spin.Beta -> mos_b kj, mos_a kj, Spin.Alfa\n",
     "        in\n",
     "        sum mos_cabs (fun a -> \n",
-    "             h_two i j k a s s' *.\n",
+    "             h_two j i a k s' s *.\n",
     "             ( f_one a l s' +.\n",
-    "               sum mos  (fun n -> f_two n a n l s' s') +.\n",
-    "               sum mos' (fun n -> f_two n a n l s'' s') \n",
+    "               sum mos  (fun n -> f_two a n l n s' s') +.\n",
+    "               sum mos' (fun n -> f_two a n l n s' s'') \n",
     "             ) \n",
     "             ) \n",
     "        in\n",
@@ -2151,11 +2603,103 @@
     "let _ = check 0 integral_value 2 1 2 1"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "let m_2121_2Ha_1F =\n",
+    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "        h_two i j a l Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa +.\n",
+    "        h_two i j k a Spin.Alfa Spin.Alfa *. f_one a l Spin.Alfa)\n",
+    "    )\n",
+    "\n",
+    "let m_2121_2Hb_1F =\n",
+    "  array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "        h_two i j a l Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa +.\n",
+    "        h_two i j k a Spin.Alfa Spin.Beta *. f_one a l Spin.Alfa)\n",
+    "    )\n",
+    "\n",
+    "let m_2121_2Ha_2Fa =\n",
+    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "        h_two i j a l Spin.Alfa Spin.Alfa *.\n",
+    "        f_two a n k n Spin.Alfa Spin.Alfa )\n",
+    "    )\n",
+    "    \n",
+    "let m_2121_2Hb_2Fa =\n",
+    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "        h_two i j a l Spin.Alfa Spin.Beta *.\n",
+    "        f_two a n k n Spin.Alfa Spin.Alfa )\n",
+    "    )\n",
+    "    \n",
+    "let m_2121_2Ha_2Fb =\n",
+    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "        h_two i j a l Spin.Alfa Spin.Alfa *.\n",
+    "        f_two a n k n Spin.Alfa Spin.Beta )\n",
+    "    )\n",
+    "    \n",
+    "let m_2121_2Hb_2Fb =\n",
+    "  array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n",
+    "    sum mos_cabs (fun a ->\n",
+    "        h_two i j a l Spin.Alfa Spin.Beta *.\n",
+    "        f_two a n k n Spin.Alfa Spin.Beta )\n",
+    "    )\n",
+    "    \n",
+    "let integral_value ki kj = \n",
+    "    let i, j, k, l, s, s', phase =\n",
+    "          match Excitation.of_det ki kj with\n",
+    "          | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
+    "            hole, hole', particle, particle', spin, spin', phase\n",
+    "          | _ -> assert false\n",
+    "    in\n",
+    "    let mos, mos' =\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",
+    "       if s = s' then\n",
+    "         m_2121_2Ha_1F.{i,j,k,l} +. \n",
+    "         sum mos  (fun n ->\n",
+    "             m_2121_2Ha_2Fa.{i,j,k,l,n} +. m_2121_2Ha_2Fa.{j,i,l,k,n}\n",
+    "         ) +.\n",
+    "         sum mos' (fun n ->\n",
+    "             m_2121_2Ha_2Fb.{i,j,k,l,n} +. m_2121_2Ha_2Fb.{j,i,l,k,n}\n",
+    "         ) \n",
+    "       else\n",
+    "         m_2121_2Hb_1F.{i,j,k,l} +.\n",
+    "         sum mos  (fun n ->\n",
+    "             m_2121_2Hb_2Fa.{i,j,k,l,n} +. m_2121_2Hb_2Fb.{j,i,l,k,n}\n",
+    "         ) +.\n",
+    "         sum mos' (fun n ->\n",
+    "             m_2121_2Hb_2Fb.{i,j,k,l,n} +. m_2121_2Hb_2Fa.{j,i,l,k,n}\n",
+    "         ) \n",
+    "     in\n",
+    "\n",
+    "    match phase with\n",
+    "    | Phase.Pos -> result\n",
+    "    | Phase.Neg -> -. result\n",
+    "     \n",
+    "\n",
+    "let _ = check 0 integral_value 2 1 2 1\n",
+    "\n",
+    "\n"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# 11. *2 1 22*"
+    "# *11. 2 1 22*"
    ]
   },
   {
@@ -2164,7 +2708,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "png_image \"2_1_22.png\""
+    "let _ = png_image \"2_1_22.png\""
    ]
   },
   {
@@ -2175,13 +2719,15 @@
     "\n",
     "$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$  and $|J\\rangle$.\n",
     "\n",
-    "$n$ : orbital indices of MOs occupied in $|I\\rangle$\n",
+    "$n$ : orbital indices of MOs occupied in both $|I\\rangle$ and $|J\\rangle$ .\n",
     "\n",
     "$\\sum_{a} \n",
     "    \\hat{T}_{ij}^{am} \\hat{T}_{am}^{kl} +\n",
     "    \\hat{T}_{ij}^{ma} \\hat{T}_{ma}^{kl} -\n",
     "    \\hat{T}_{in}^{al} \\hat{T}_{aj}^{kn} -\n",
-    "    \\hat{T}_{nj}^{ka} \\hat{T}_{ia}^{nl} \n",
+    "    \\hat{T}_{nj}^{ka} \\hat{T}_{ia}^{nl} +\n",
+    "    \\sum_{n}\n",
+    "    \\hat{T}_{i\\bar{n}}^{k\\bar{a}} \\hat{T}_{\\bar{a}j}^{\\bar{n}l}\n",
     "$\n",
     "\n",
     "\n",
@@ -2236,13 +2782,26 @@
     "        \n",
     "        sum mos_cabs (fun a -> \n",
     "            sum mos_virt' (fun m -> \n",
-    "                 h_two i j a m s s' *. f_two a m k l s s' ) +. \n",
+    "                 h_two i j a m s s' *. f_two a m k l s s') +.\n",
+    "            sum mos  (fun n ->\n",
+    "                 h_two i n k a s s  *. f_two a j n l s s' +. \n",
+    "                 h_two j n l a s s  *. f_two a i n k s s' ) +.\n",
+    "            sum mos' (fun n ->\n",
+    "                 h_two i n k a s s' *. f_two a j n l s' s') \n",
+    "                 (*\n",
     "            sum mos_virt (fun m -> \n",
-    "                 h_two i j m a s s' *. f_two m a k l s s' ) -.\n",
+    "                 h_two i j m a s s' *. f_two m a k l s s' )\n",
+    "                 -.\n",
     "            sum mos' (fun n -> \n",
     "                 h_two i n a l s s' *. f_two a j k n s s' ) -.\n",
     "            sum mos (fun n -> \n",
     "                 h_two n j k a s s' *. f_two i a n l s s' )\n",
+    "                 +.\n",
+    "            sum mos' (fun n -> \n",
+    "                 h_two n j a l s s' *. f_two a i k n s s  ) +.\n",
+    "            sum mos (fun n -> \n",
+    "                 h_two n i a k s s' *. f_two a j l n s' s' )\n",
+    "                 *)\n",
     "        )\n",
     "    in\n",
     "\n",
@@ -2251,7 +2810,117 @@
     "        | Phase.Neg -> -. result\n",
     "\n",
     "\n",
-    "let _ = check 0 integral_value 2 1 2 2"
+    "let _ = check 10 integral_value 2 1 2 2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "let ki = det_I.(0)\n",
+    "let kj = det_I.(9)\n",
+    "\n",
+    "let _ = \n",
+    "generate_alphas ki kj 2 1 2 2\n",
+    "|> Array.of_list\n",
+    "|> Array.mapi (fun kk alpha -> \n",
+    "\n",
+    "(*\n",
+    "let _ = Determinant.to_lists ki\n",
+    "let _ = Determinant.to_lists alpha\n",
+    "let _ = Determinant.to_lists kj\n",
+    "\n",
+    "   \n",
+    "let _ = \n",
+    "    Format.printf \"|I> -> |J> : %a\\n@.\" Excitation.pp (Excitation.of_det ki kj);\n",
+    "    Format.printf \"|I> -> |a> : %a\\n@.\" Excitation.pp (Excitation.of_det ki alpha);\n",
+    "    Format.printf \"|a> -> |J> : %a\\n@.\" Excitation.pp (Excitation.of_det alpha kj)\n",
+    "*)\n",
+    "    let i, j, k, l, s, s', phase =\n",
+    "          match Excitation.of_det ki kj with\n",
+    "          | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
+    "              hole, hole', particle, particle', spin, spin', phase\n",
+    "          | _ -> assert false\n",
+    "    in\n",
+    "\n",
+    "\n",
+    "    let integral_value ki kj = \n",
+    " \n",
+    "    (*       \n",
+    "        let i, j, k, l, s, s', phase =\n",
+    "              match Excitation.of_det ki kj with\n",
+    "              | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
+    "                hole, hole', particle, particle', spin, spin', phase\n",
+    "              | _ -> assert false\n",
+    "        in\n",
+    "        let i, a, s, _ = \n",
+    "              match Excitation.of_det ki alpha with\n",
+    "              | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
+    "                hole, particle, spin, phase\n",
+    "              | _ -> assert false\n",
+    "        in\n",
+    "\n",
+    "        let i', j', k', l', t, u, _ =\n",
+    "              match Excitation.of_det ki alpha with\n",
+    "              | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
+    "                hole, hole', particle, particle', spin, spin', phase\n",
+    "              | _ -> assert false\n",
+    "        in\n",
+    "        \n",
+    "        let i'', j'', k'', l'', t', u', _ =\n",
+    "              match Excitation.of_det alpha kj with\n",
+    "              | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n",
+    "                hole, hole', particle, particle', spin, spin', phase\n",
+    "              | _ -> assert false\n",
+    "        in\n",
+    "        *)\n",
+    "        (*\n",
+    "        let j, k, l, s' = \n",
+    "          if i' = a then\n",
+    "            (assert (k' = k) ; j', k', l', t')\n",
+    "          else\n",
+    "             (assert (j'=a) ; assert (l'=k) ; i', l', k', t)\n",
+    "        in\n",
+    "        *)\n",
+    "        \n",
+    "    Format.printf \"|I> -> |J> : %a |\\n@.\" Excitation.pp (Excitation.of_det ki kj) ;\n",
+    "    Format.printf \"|I> -> |a> : %a |\\n@.\" Excitation.pp (Excitation.of_det ki alpha)  ;\n",
+    "    Format.printf \"|a> -> |J> : %a |\\n@.\" Excitation.pp (Excitation.of_det alpha kj);\n",
+    "    \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",
+    "           let k=5 and l=4 in\n",
+    "           let i=1 and j=2 in\n",
+    "           let n=2 and a=6 in\n",
+    "           let s   = Spin.Alfa\n",
+    "           and s'  = Spin.Alfa\n",
+    "           and s'' = Spin.Beta\n",
+    "           in\n",
+    "           h_two j n l a s s  *. f_two a i n k s s'\n",
+    "        in\n",
+    "\n",
+    "        match phase with\n",
+    "        | Phase.Pos -> result\n",
+    "        | Phase.Neg -> -. result\n",
+    "\n",
+    "in\n",
+    "let a = (compute_HaaF ki [alpha] kj)\n",
+    "and b = (integral_value ki kj)\n",
+    "in\n",
+    "(*\n",
+    "if a <> b then\n",
+    "*)\n",
+    "Format.printf \"%6d %e %e@.\" (kk) a b\n",
+    ")\n",
+    "\n"
    ]
   },
   {
@@ -2489,202 +3158,6 @@
     ")\n",
     "\n"
    ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Packed diagrams"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Diagonal elements"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Two electrons in CABS"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "(* 0 2 22 *)\n",
-    "\n",
-    "\n",
-    "let integral_value ki kj = \n",
-    "   (* Alpha-Beta *)\n",
-    "   let s, s' = Spin.(Alfa, Beta) in\n",
-    "   sum  mos_cabs  (fun a -> \n",
-    "   sum  mos_cabs  (fun b ->  \n",
-    "   sum (mos_a ki) (fun i ->  \n",
-    "   sum (mos_b ki) (fun j ->  \n",
-    "       h_two i j a b s s'  *. f_two a b i j s s'\n",
-    "   ))))\n",
-    "   +.\n",
-    "   (* Alpha-Alpha / Beta-Beta *)\n",
-    "   List.fold_left (fun accu (mos,s) -> \n",
-    "     let s' = s in accu +.\n",
-    "     sum mos_cabs (fun b ->  \n",
-    "     sum mos_cabs (fun a -> if b > a then 0. else\n",
-    "     sum   mos    (fun j ->  \n",
-    "     sum   mos    (fun i -> if i < j then 0. else\n",
-    "        h_two i j a b s s'  *. f_two a b i j s s'\n",
-    "     ))))\n",
-    "   ) 0. [ (mos_a ki,Spin.Alfa) ; (mos_b ki,Spin.Beta)]\n",
-    "     \n",
-    "let _ =\n",
-    "  check 0 integral_value 0 2 2 2\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### One electron in CABS"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "(* 0 1 11 *)\n",
-    "\n",
-    "\n",
-    "let integral_value ki kj = \n",
-    "   (* Alpha-Beta *)\n",
-    "   let s, s' = Spin.(Alfa, Beta) in \n",
-    "   let mos_a, mos_b = mos_a ki, mos_b ki in\n",
-    "   \n",
-    "   sum mos_cabs (fun a ->\n",
-    "      sum mos_a (fun i -> \n",
-    "           (h_one i a s  +.\n",
-    "               sum mos_a (fun j -> h_two i j a j s s ) +.\n",
-    "               sum mos_b (fun j -> h_two i j a j s s') ) *. \n",
-    "           (f_one a i s  +.\n",
-    "               sum mos_a (fun j -> f_two a j i j s s ) +.\n",
-    "               sum mos_b (fun j -> f_two a j i j s s') )\n",
-    "         )\n",
-    "       +.\n",
-    "       sum mos_b (fun i -> \n",
-    "           (h_one i a s  +.\n",
-    "               sum mos_b (fun j -> h_two i j a j s' s') +.\n",
-    "               sum mos_a (fun j -> h_two i j a j s' s ) ) *. \n",
-    "           (f_one a i s  +.\n",
-    "               sum mos_a (fun j -> f_two a j i j s' s ) +.\n",
-    "               sum mos_b (fun j -> f_two a j i j s' s') )\n",
-    "         ) \n",
-    "     ) \n",
-    "     \n",
-    "\n",
-    "(* 0 1 22 *)\n",
-    "\n",
-    "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",
-    "   sum mos_cabs   (fun a ->\n",
-    "   sum (mos_b ki) (fun j ->  \n",
-    "   sum (mos_a ki) (fun i ->  \n",
-    "   sum mos_virt_b (fun k ->  \n",
-    "       h_two i j a k s s'  *. f_two a k i j s s'\n",
-    "   )))\n",
-    "   +.\n",
-    "   sum (mos_a ki) (fun j ->  \n",
-    "   sum (mos_b ki) (fun i ->  \n",
-    "   sum mos_virt_a (fun k ->  \n",
-    "       h_two i j a k s s'  *. f_two a k i j s s'\n",
-    "   )))) \n",
-    "   +.\n",
-    "   (* Alpha-Alpha / Beta-Beta *)\n",
-    "   List.fold_left (fun accu (mos_virt,mos,s) -> \n",
-    "     let s' = s in accu +.\n",
-    "     sum mos (fun j ->  \n",
-    "     sum mos (fun i -> if i < j then 0. else\n",
-    "     sum mos_virt (fun k ->  \n",
-    "     sum mos_cabs (fun a -> \n",
-    "       h_two i j a k s s'  *. f_two a k i j s s'\n",
-    "     )))) \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",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Single excitations"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Two electrons in CABS"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### One electron in CABS"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Double excitations"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Two electrons in CABS"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### One electron in CABS"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {