diff --git a/Notebooks/F12_matrix.ipynb b/Notebooks/F12_matrix.ipynb
index 903c6ea..99a9fd7 100644
--- a/Notebooks/F12_matrix.ipynb
+++ b/Notebooks/F12_matrix.ipynb
@@ -98,7 +98,9 @@
     "#install_printer MOClass.pp ;;\n",
     "let pp_mo ppf t = MOBasis.pp ~start:1 ~finish:0 ppf t ;;\n",
     "#install_printer pp_mo;;\n",
+    "(*\n",
     "#install_printer DeterminantSpace.pp;;\n",
+    "*)\n",
     "#install_printer SpindeterminantSpace.pp;;\n",
     "#install_printer Bitstring.pp;;\n"
    ]
@@ -123,8 +125,8 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "let basis_filename  = \"/home/scemama/qp2/data/basis/sto-3g\" \n",
-    "let aux_basis_filename = \"/home/scemama/qp2/data/basis/6-31g\" \n",
+    "let basis_filename  = \"/home/scemama/qp2/data/basis/6-31g\" \n",
+    "let aux_basis_filename = \"/home/scemama/qp2/data/basis/cc-pvdz\" \n",
     "let nuclei = Nuclei.of_zmt_string \"c\" \n",
     "let frozen_core = false\n",
     "let multiplicity = 1\n",
@@ -513,7 +515,9 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "scrolled": false
+   },
    "outputs": [],
    "source": [
     "let ci = CI.make ~n_states:state in_space\n",
@@ -803,6 +807,7 @@
    "outputs": [],
    "source": [
     "let check n integral_value exc cabs lexc rexc =\n",
+    "  let cpudet, cpuint = ref 0., ref 0. in\n",
     "  let det_list =\n",
     "      match n with\n",
     "        | 0 -> det_I\n",
@@ -822,10 +827,16 @@
     "                  begin\n",
     "                    let alphas = generate_alphas ki kj exc cabs lexc rexc in\n",
     "                    let det_value =\n",
-    "                      compute_HaaF ki alphas kj\n",
+    "                      let t0 = Unix.gettimeofday () in\n",
+    "                      let result = compute_HaaF ki alphas kj in\n",
+    "                      cpudet := !cpudet +. Unix.gettimeofday () -. t0;\n",
+    "                      result\n",
     "                    in\n",
     "                    let int_value = \n",
-    "                      integral_value ki kj\n",
+    "                      let t0 = Unix.gettimeofday () in\n",
+    "                      let result = integral_value ki kj in\n",
+    "                      cpuint := !cpuint +. Unix.gettimeofday () -. t0;\n",
+    "                      result\n",
     "                    in\n",
     "(*   Printf.printf \"%d %d %e %e\\n%!\" i j det_value int_value;  *)\n",
     "                    (i,j,det_value,int_value)\n",
@@ -854,9 +865,9 @@
     "  (*\n",
     "      Printf.printf \"OK: %e\\n%!\" error\n",
     "      *)\n",
-    "      Printf.printf \"OK: (%d, %d) | %e %e | %e\\n%!\" i j d v error\n",
+    "      Printf.printf \"OK: (%d, %d) | %e %e | %e  |  cpu : %f  %f\\n%!\" i j d v error !cpudet !cpuint\n",
     "  else\n",
-    "      Printf.printf \"Failed: (%d, %d) | %e %e | %e\\n%!\" i j d v error\n",
+    "      Printf.printf \"Failed: (%d, %d) | %e %e | %e  |  cpu : %f %f\\n%!\" i j d v error !cpudet !cpuint\n",
     "\n",
     "    \n",
     "let sum l f = List.fold_left (fun accu i -> accu +. f i) 0. l"
@@ -1006,7 +1017,9 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "scrolled": false
+   },
    "outputs": [],
    "source": [
     "let m_0111_1H_1F = \n",
@@ -1197,7 +1210,7 @@
     "   ) 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",
+    "  check 100 integral_value 0 1 2 2\n",
     "    "
    ]
   },
@@ -1256,7 +1269,7 @@
     "   result\n",
     "     \n",
     "let _ =\n",
-    "  check 0 integral_value 0 1 2 2\n",
+    "  check 100 integral_value 0 1 2 2\n",
     "    "
    ]
   },
@@ -1330,7 +1343,7 @@
     "   ) 0. [ (mos_a ki,Spin.Alfa) ; (mos_b ki,Spin.Beta)]\n",
     "     \n",
     "let _ =\n",
-    "  check 0 integral_value 0 2 2 2\n",
+    "  check 100 integral_value 0 2 2 2\n",
     "    "
    ]
   },
@@ -1373,7 +1386,7 @@
     "   ) 0. [ (mos_a ki) ; (mos_b ki)]\n",
     "     \n",
     "let _ =\n",
-    "  check 0 integral_value 0 2 2 2\n",
+    "  check 100 integral_value 0 2 2 2\n",
     "    "
    ]
   },
@@ -1454,14 +1467,14 @@
     "    | Phase.Neg -> -. result\n",
     "     \n",
     "\n",
-    "let _ = check 0 integral_value 1 1 1 1"
+    "let _ = check 100 integral_value 1 1 1 1"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
-    "scrolled": true
+    "scrolled": false
    },
    "outputs": [],
    "source": [
@@ -1562,7 +1575,7 @@
     "    | Phase.Neg -> -. result\n",
     "   \n",
     "let _ =\n",
-    "  check 0 integral_value 1 1 1 1\n",
+    "  check 100 integral_value 1 1 1 1\n",
     "    "
    ]
   },
@@ -1663,7 +1676,7 @@
     "    | Phase.Neg -> -. result\n",
     "     \n",
     "\n",
-    "let _ = check 0 integral_value 1 1 1 2"
+    "let _ = check 100 integral_value 1 1 1 2"
    ]
   },
   {
@@ -1766,7 +1779,7 @@
     "   \n",
     "   \n",
     "\n",
-    "let _ = check 0 integral_value 1 1 1 2"
+    "let _ = check 100 integral_value 1 1 1 2"
    ]
   },
   {
@@ -1867,7 +1880,7 @@
     "    | Phase.Neg -> -. result\n",
     "     \n",
     "\n",
-    "let _ = check 0 integral_value 1 1 2 1"
+    "let _ = check 100 integral_value 1 1 2 1"
    ]
   },
   {
@@ -1970,7 +1983,7 @@
     "   \n",
     "   \n",
     "\n",
-    "let _ = check 0 integral_value 1 1 2 1"
+    "let _ = check 100 integral_value 1 1 2 1"
    ]
   },
   {
@@ -2025,30 +2038,292 @@
     "\\end{align}"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "(*\n",
+    "let ki = det_I.(6)\n",
+    "let kj = det_I.(58)\n",
+    "\n",
+    "let _ = \n",
+    "    Format.printf \"|I> -> |J> : %a |\\n@.\" Excitation.pp (Excitation.of_det ki kj) ;\n",
+    "generate_alphas ki kj 1 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",
+    "\n",
+    "    let integral_value ki kj = \n",
+    "    \n",
+    "      let exc0 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in\n",
+    "      let exc1 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in \n",
+    "      let exc2 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in \n",
+    " \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",
+    "      let spin = function\n",
+    "        | Spin.Alfa -> 0\n",
+    "        | _ -> 1\n",
+    "      in\n",
+    "        exc0.(i).(spin s ) <- \"i\" \n",
+    "      ; exc0.(k).(spin s ) <- \"k\" \n",
+    "      ;\n",
+    "      let s0 = s in\n",
+    "    \n",
+    "      let i, j, k, l, s, s', p1 =\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",
+    "      if exc0.(i).(spin s ) =  \"-\" then exc0.(i).(spin s ) <- \"n\";\n",
+    "      if exc0.(j).(spin s') =  \"-\" then exc0.(j).(spin s') <- \"n\";\n",
+    "      if exc0.(k).(spin s ) =  \"-\" then exc0.(k).(spin s ) <- if k > mo_num then \"a\" else \"m\";\n",
+    "      if exc0.(l).(spin s') =  \"-\" then exc0.(l).(spin s') <- if l > mo_num then \"a\" else \"m\";\n",
+    "      \n",
+    "      let string_h = \n",
+    "          Printf.sprintf \"h_two %s %s %s %s %s %s *.  \" \n",
+    "            exc0.(i).(spin s )\n",
+    "            exc0.(j).(spin s')\n",
+    "            exc0.(k).(spin s )\n",
+    "            exc0.(l).(spin s')\n",
+    "            (if s  = s0 then \"s \" else \"s'\")\n",
+    "            (if s' = s0 then \"s \" else \"s'\")\n",
+    "            (*\n",
+    "            (if exc0.(i).(spin s ) = \"i\" || exc0.(k).(spin s ) = \"k\" then \"s  \" else \n",
+    "             if exc0.(i).(spin s ) = \"j\" || exc0.(k).(spin s ) = \"l\" then \"s' \" else \"s''\")\n",
+    "            (if exc0.(j).(spin s') = \"i\" || exc0.(l).(spin s') = \"k\" then \"s  \" else \n",
+    "             if exc0.(j).(spin s') = \"j\" || exc0.(l).(spin s') = \"l\" then \"s' \" else \"s''\")\n",
+    "             *)\n",
+    "      in \n",
+    "      \n",
+    "      let i, j, k, l, s, s', p2 =\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",
+    "      let string_f = \n",
+    "          Printf.sprintf \"f_two %s %s %s %s %s %s\" \n",
+    "            exc0.(i).(spin s )\n",
+    "            exc0.(j).(spin s')\n",
+    "            exc0.(k).(spin s )\n",
+    "            exc0.(l).(spin s')\n",
+    "            (*\n",
+    "            (if exc0.(i).(spin s ) = \"i\" || exc0.(k).(spin s ) = \"k\" then \"s  \" else \n",
+    "             if exc0.(i).(spin s ) = \"j\" || exc0.(k).(spin s ) = \"l\" then \"s' \" else \n",
+    "             if exc0.(i).(spin s ) = \"n\" || exc0.(k).(spin s ) = \"n\" then \"s''\" else\n",
+    "             if s  = s0 then \"s\" else \"s'\")\n",
+    "            (if exc0.(j).(spin s') = \"i\" || exc0.(l).(spin s') = \"k\" then \"s  \" else \n",
+    "             if exc0.(j).(spin s') = \"j\" || exc0.(l).(spin s') = \"l\" then \"s' \" else \n",
+    "             if exc0.(j).(spin s') = \"n\" || exc0.(l).(spin s') = \"n\" then \"s''\" else\n",
+    "             if s' = s0 then \"s\" else \"s'\")\n",
+    "             *)\n",
+    "            (if s  = s0 then \"s \" else \"s'\")\n",
+    "            (if s' = s0 then \"s \" else \"s'\")\n",
+    "      in\n",
+    "      \n",
+    "    Format.printf \"|I> -> |a> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det ki alpha) string_h ;\n",
+    "    Format.printf \"|a> -> |J> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det alpha kj) string_f ;\n",
+    "    \n",
+    "    let sign = \n",
+    "        if Phase.add p1 p2 = phase then \"+. \" else \"-. \"\n",
+    "    in\n",
+    "sign ^ string_h ^ string_f\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=4 and l=5 in\n",
+    "           let i=1 and j=2 in\n",
+    "           let n=2 and a=7 in\n",
+    "           let s   = Spin.Alfa\n",
+    "           and s'  = Spin.Alfa\n",
+    "           and s'' = Spin.Beta\n",
+    "           in\n",
+    "           (* \n",
+    "           h_two j n l a s' s'' *. f_two a i n k s s''\n",
+    "           *)\n",
+    "           h_two i n k a s s'' *. f_two j a l n s s''\n",
+    "        in\n",
+    "\n",
+    "        match phase with\n",
+    "        | Phase.Pos -> result\n",
+    "        | Phase.Neg -> -. result\n",
+    "        *)\n",
+    "\n",
+    "in\n",
+    "integral_value ki kj\n",
+    "(*\n",
+    "let a = (compute_HaaF ki [alpha] kj)\n",
+    "and b = (integral_value ki kj)\n",
+    "in\n",
+    "if kk = 31 then\n",
+    "    Format.printf \"%6d %e %e@.@.\" (kk) a b\n",
+    "    *)\n",
+    ")\n",
+    "|> Array.to_list\n",
+    "|> List.sort_uniq compare\n",
+    "\n",
+    "let _ = compute_HaaF ki (generate_alphas ki kj 1 1 2 2) kj\n",
+    "\n",
+    "let _ = integral_value ki kj\n",
+    "\n",
+    "*)"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
-    "scrolled": true
+    "scrolled": false
    },
    "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",
+    "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_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",
+    "   let mos_virt, mos_virt' =\n",
+    "      match s with\n",
+    "      | Spin.Alfa -> mos_virt_a, mos_virt_b\n",
+    "      | Spin.Beta -> mos_virt_b, mos_virt_a\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",
+    "   let result = \n",
+    "       let s' = Spin.other s in\n",
+    "        sum mos_cabs (fun a -> \n",
+    "        sum mos_j    (fun n -> \n",
+    "        sum mos_virt (fun m -> \n",
+    "             h_two n i a m s  s  *.  f_two m a k n s  s \n",
+    "        ))) +.\n",
+    "        sum mos_cabs (fun a' -> \n",
+    "        sum mos_j'   (fun n' -> \n",
+    "        sum mos_virt (fun m -> \n",
+    "             h_two i n' m a' s  s' *.  f_two m a' k n' s  s'\n",
+    "        ))) +.\n",
+    "        sum mos_cabs  (fun a -> \n",
+    "        sum mos_j'    (fun n' -> \n",
+    "        sum mos_virt' (fun m' -> \n",
+    "             h_two i n' a m' s  s' *.  f_two a m' k n' s  s'\n",
+    "        ))) -. \n",
+    "        sum mos_cabs (fun a -> \n",
+    "        sum mos_j    (fun n -> \n",
+    "        sum mos_j    (fun l -> if l <=n then 0. else\n",
+    "             h_two n l a k s  s  *.  f_two i a l n s  s \n",
+    "        ))) -.  \n",
+    "        sum mos_cabs (fun a' -> \n",
+    "        sum mos_j'   (fun n' -> \n",
+    "        sum mos_j    (fun l -> \n",
+    "             h_two l n' k a' s s'  *.  f_two i a' l n' s s'\n",
+    "        ))) \n",
+    "    in\n",
+    "    match phase with\n",
+    "    | Phase.Pos -> result\n",
+    "    | Phase.Neg -> -. result\n",
+    "     \n",
+    "let _ = check 10 integral_value 1 1 2 2\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [],
+   "source": [
     "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",
+    "      h_two j i a m Spin.Alfa Spin.Alfa *.\n",
     "      f_two m a k j Spin.Alfa Spin.Alfa \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 m a Spin.Alfa Spin.Beta *.\n",
+    "      f_two m a k j Spin.Alfa Spin.Beta \n",
+    "    )\n",
+    "  )\n",
+    "\n",
+    "let m_1122_v3 =\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",
+    "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 j l a k Spin.Alfa Spin.Alfa *.\n",
+    "      f_two i a l 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",
@@ -2057,22 +2332,6 @@
     "    )\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",
@@ -2097,13 +2356,13 @@
     "     Array.to_list mos_virt_b |> Util.list_some\n",
     "   in\n",
     "\n",
-    "    let mos_virt, mos_virt' =\n",
+    "   let mos_virt, mos_virt' =\n",
     "      match s with\n",
     "      | Spin.Alfa -> mos_virt_a, mos_virt_b\n",
     "      | Spin.Beta -> mos_virt_b, mos_virt_a\n",
-    "    in\n",
+    "   in\n",
     "    \n",
-    "    let mos_j, mos_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",
@@ -2117,8 +2376,8 @@
     "      match s with\n",
     "      | Spin.Alfa -> alfa, beta\n",
     "      | Spin.Beta -> beta, alfa\n",
-    "    in\n",
-    "\n",
+    "   in\n",
+    "   \n",
     "    let result = \n",
     "        sum mos_j    (fun j -> \n",
     "        sum mos_virt (fun m -> \n",
@@ -2126,18 +2385,18 @@
     "        )) +.\n",
     "        sum mos_j'   (fun j -> \n",
     "        sum mos_virt (fun m -> \n",
-    "          m_1122_v.{i,j,k,m}\n",
+    "          m_1122_v2.{i,j,k,m}\n",
     "        ))   +.\n",
     "        sum mos_j'    (fun j -> \n",
     "        sum mos_virt' (fun m -> \n",
-    "          m_1122_v2.{i,j,k,m}\n",
+    "          m_1122_v3.{i,j,k,m}\n",
     "        ))   -.\n",
     "        sum mos_j    (fun j -> \n",
-    "        sum mos_j    (fun l -> if l = i then 0. else\n",
+    "        sum mos_j    (fun l -> if l <= j then 0. else\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",
+    "        sum mos_j    (fun l -> \n",
     "          m_1122_o.{i,j,k,l}\n",
     "        )) \n",
     "    in\n",
@@ -2146,7 +2405,7 @@
     "    | Phase.Neg -> -. result\n",
     "     \n",
     "\n",
-    "let _ = check 0 integral_value 1 1 2 2\n",
+    "let _ = check 100 integral_value 1 1 2 2\n",
     "\n",
     "\n"
    ]
@@ -2231,14 +2490,14 @@
     "    | Phase.Neg -> -. result\n",
     "     \n",
     "\n",
-    "let _ = check 0 integral_value 1 2 2 2"
+    "let _ = check 100 integral_value 1 2 2 2"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
-    "scrolled": true
+    "scrolled": false
    },
    "outputs": [],
    "source": [
@@ -2297,7 +2556,7 @@
     "    | Phase.Neg -> -. result\n",
     "     \n",
     "\n",
-    "let _ = check 0 integral_value 1 2 2 2\n",
+    "let _ = check 100 integral_value 1 2 2 2\n",
     "\n",
     "\n"
    ]
@@ -2392,7 +2651,7 @@
     "        | Phase.Neg -> -. result\n",
     "\n",
     "\n",
-    "let _ = check 0 integral_value 2 1 1 2"
+    "let _ = check 100 integral_value 2 1 1 2"
    ]
   },
   {
@@ -2423,7 +2682,7 @@
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
-    "scrolled": true
+    "scrolled": false
    },
    "outputs": [],
    "source": [
@@ -2506,7 +2765,7 @@
     "    | Phase.Neg -> -. result\n",
     "     \n",
     "\n",
-    "let _ = check 0 integral_value 2 1 1 2\n",
+    "let _ = check 100 integral_value 2 1 1 2\n",
     "\n",
     "\n"
    ]
@@ -2600,14 +2859,14 @@
     "        | Phase.Neg -> -. result\n",
     "\n",
     "\n",
-    "let _ = check 0 integral_value 2 1 2 1"
+    "let _ = check 100 integral_value 2 1 2 1"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
-    "scrolled": true
+    "scrolled": false
    },
    "outputs": [],
    "source": [
@@ -2690,7 +2949,7 @@
     "    | Phase.Neg -> -. result\n",
     "     \n",
     "\n",
-    "let _ = check 0 integral_value 2 1 2 1\n",
+    "let _ = check 100 integral_value 2 1 2 1\n",
     "\n",
     "\n"
    ]
@@ -2699,7 +2958,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# *11. 2 1 22*"
+    "# 11. 2 1 22"
    ]
   },
   {
@@ -2768,41 +3027,67 @@
     "   \n",
     "    let result = \n",
     "        \n",
-    "        let mos, mos_virt =\n",
+    "        let mos_virt, mos_virt' =\n",
     "          match s with\n",
-    "          | Spin.Alfa -> mos_a ki, mos_virt_a\n",
-    "          | Spin.Beta -> mos_b ki, mos_virt_b\n",
+    "          | Spin.Alfa -> mos_virt_a, mos_virt_b\n",
+    "          | Spin.Beta -> mos_virt_b, mos_virt_a\n",
     "        in\n",
     "        \n",
-    "        let mos', mos_virt' =\n",
-    "          match s' with\n",
-    "          | Spin.Alfa -> mos_a ki, mos_virt_a\n",
-    "          | Spin.Beta -> mos_b ki, mos_virt_b\n",
+    "        let mos, mos' =\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",
-    "        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",
+    "\n",
+    "        if s = s' then            \n",
+    "            let s'' = Spin.other s' in\n",
+    "            sum mos_cabs (fun a -> \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",
-    "                 -.\n",
+    "                 h_two i n a k s  s  *.  f_two j a n l s  s \n",
+    "              +. h_two i n a l s  s  *.  f_two j a k n s  s \n",
+    "              -. h_two j n a k s  s  *.  f_two i a n l s  s   \n",
+    "              -. h_two j n a l s  s  *.  f_two i a k n s  s\n",
+    "              )\n",
+    "            +. sum mos_virt (fun m ->\n",
+    "                -. h_two i j a m s  s  *.  f_two m a k l s  s )\n",
+    "            +. sum mos' (fun n ->\n",
+    "                 h_two i n k a s  s'' *.  f_two j a l n s  s''\n",
+    "              +. h_two j n l a s  s'' *.  f_two i a k n s  s''\n",
+    "              -. h_two i n l a s  s'' *.  f_two j a k n s  s''\n",
+    "              -. h_two j n k a s  s'' *.  f_two i a l n s  s''\n",
+    "              )\n",
+    "            )\n",
+    "        else\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",
+    "            sum mos_virt  (fun m ->\n",
+    "                  h_two i j m a s  s' *.  f_two m a k l s  s' ) +.\n",
+    "            sum mos  (fun n ->\n",
+    "                  h_two n i a k s  s  *.  f_two a j n l s  s'\n",
+    "               +. h_two n j a l s  s' *.  f_two i a k n s  s \n",
+    "               -. h_two n j k a s  s' *.  f_two i a n l s  s'\n",
+    "               ) +.\n",
+    "            sum mos' (fun n -> if n >= j then 0. else \n",
+    "                  h_two i n k a s  s' *.  f_two j a l n s' s'\n",
+    "               +. h_two n j a l s' s' *.  f_two i a k n s  s' ) +. \n",
+    "            sum mos' (fun n -> if n <= j then 0. else \n",
+    "               -. h_two i n k a s  s' *.  f_two j a n l s' s' \n",
+    "               -. h_two j n a l s' s' *.  f_two i a k n s  s' ) +.\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",
+    "               -. h_two i n a l s  s' *.  f_two a j k n s  s'\n",
+    "               )\n",
+    "            )\n",
     "    in\n",
     "\n",
     "    match phase with\n",
@@ -2810,117 +3095,144 @@
     "        | Phase.Neg -> -. result\n",
     "\n",
     "\n",
-    "let _ = check 10 integral_value 2 1 2 2"
+    "let _ = check 300 integral_value 2 1 2 2"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "scrolled": false
+   },
    "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",
+    "let ki = det_I.(99)\n",
+    "let kj = det_I.(193)\n",
     "\n",
+    "let alpha_to_string alpha = \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",
+    "      let exc0 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in\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",
+    "            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",
+    "      in\n",
+    "      let spin = function\n",
+    "        | Spin.Alfa -> 0\n",
+    "        | _ -> 1\n",
+    "      in\n",
+    "        exc0.(i).(spin s ) <- \"i\" \n",
+    "      ; exc0.(j).(spin s') <- \"j\" \n",
+    "      ; exc0.(k).(spin s ) <- \"k\" \n",
+    "      ; exc0.(l).(spin s') <- \"l\" \n",
+    "      ;\n",
+    "      let s0, s0' = s, s' in\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",
+    "      let i, j, k, l, s, s', p1 =\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",
+    "      if exc0.(i).(spin s ) =  \"-\" then exc0.(i).(spin s ) <- \"n\";\n",
+    "      if exc0.(j).(spin s') =  \"-\" then exc0.(j).(spin s') <- \"n\";\n",
+    "      if exc0.(k).(spin s ) =  \"-\" then exc0.(k).(spin s ) <- if k > mo_num then \"a\" else \"m\";\n",
+    "      if exc0.(l).(spin s') =  \"-\" then exc0.(l).(spin s') <- if l > mo_num then \"a\" else \"m\";\n",
+    "      \n",
+    "      let string_h = \n",
+    "          Printf.sprintf \"h_two %s %s %s %s %s %s *.  \" \n",
+    "            exc0.(i).(spin s )\n",
+    "            exc0.(j).(spin s')\n",
+    "            exc0.(k).(spin s )\n",
+    "            exc0.(l).(spin s')\n",
+    "            (if s  = s0 then \"s \" else \"s'\")\n",
+    "            (if s' = s0 then \"s \" else \"s'\")\n",
+    "      in \n",
+    "      \n",
+    "      let i, j, k, l, s, s', p2 =\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",
+    "      let string_f = \n",
+    "          Printf.sprintf \"f_two %s %s %s %s %s %s\" \n",
+    "            exc0.(i).(spin s )\n",
+    "            exc0.(j).(spin s')\n",
+    "            exc0.(k).(spin s )\n",
+    "            exc0.(l).(spin s')\n",
+    "            (if s  = s0 then \"s \" else \"s'\")\n",
+    "            (if s' = s0 then \"s \" else \"s'\")\n",
+    "      in\n",
     "(*\n",
-    "if a <> b then\n",
-    "*)\n",
-    "Format.printf \"%6d %e %e@.\" (kk) a b\n",
-    ")\n",
-    "\n"
+    "        Format.printf \"|I> -> |a> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det ki alpha) string_h ;\n",
+    "        Format.printf \"|a> -> |J> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det alpha kj) string_f ;\n",
+    "        *)\n",
+    "\n",
+    "    \n",
+    "        let sign = \n",
+    "            if Phase.add p1 p2 = phase then \"+.\" else \"-.\"\n",
+    "        in\n",
+    "        sign ^ string_h ^ string_f\n",
+    "    \n",
+    "\n",
+    "let alpha_debug alpha = \n",
+    "   \n",
+    "      let i, j, k, l, s, s', p1 =\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",
+    "      Printf.printf \"%d %d %d %d \" i j k l;\n",
+    "      \n",
+    "      let i, j, k, l, s, s', p2 =\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",
+    "        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",
+    "      Printf.printf \"%d %d %d %d \\n%!\" i j k l\n",
+    "\n",
+    "      \n",
+    "let strings = \n",
+    "    Format.printf \"|I> -> |J> : %a |\\n@.\" Excitation.pp (Excitation.of_det ki kj) ;\n",
+    "    generate_alphas ki kj 2 1 2 2\n",
+    "    |> Array.of_list\n",
+    "    |> Array.mapi (fun kk alpha -> alpha_to_string alpha)\n",
+    "    |> Array.to_list\n",
+    "    |> List.sort_uniq compare\n",
+    "    |> Array.of_list\n",
+    "\n",
+    "let _ = Array.iteri (fun i x -> Printf.printf \"%d %s \\n%!\" i x) strings\n",
+    "\n",
+    "let _ =\n",
+    "  let v =\n",
+    "    let alphas =\n",
+    "      generate_alphas ki kj 2 1 2 2\n",
+    "      (*\n",
+    "      |> List.filter (fun alpha ->\n",
+    "        let x =  alpha_to_string alpha in\n",
+    "           x = strings.(6)\n",
+    "        )\n",
+    "        *)\n",
+    "    in\n",
+    "    (*\n",
+    "    List.iter alpha_debug alphas ;\n",
+    "    Printf.printf \"\\n%!\";\n",
+    "    *)\n",
+    "    compute_HaaF ki alphas kj \n",
+    "  in\n",
+    "  let x = (integral_value ki kj) in\n",
+    "  Printf.printf \"%20.8e %20.8e %20.8e\\n%!\" x v (v-. x)\n"
    ]
   },
   {