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Working on f12 notebook
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@ -284,6 +284,9 @@
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"let mos_cabs = \n",
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" Util.list_range (mo_num+1) aux_num\n",
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" \n",
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"let mos_abs = \n",
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" Util.list_range 1 aux_num\n",
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" \n",
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"let mos_in = \n",
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" Util.list_range 1 mo_num\n",
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"\n",
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@ -653,17 +656,18 @@
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" [ List.map (fun hole -> \n",
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" List.map (fun particle ->\n",
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" Determinant.single_excitation Spin.Alfa hole particle ki\n",
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" ) mos_cabs\n",
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" ) mos_abs\n",
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" ) mos_a\n",
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" ;\n",
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" List.map (fun hole -> \n",
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" List.map (fun particle ->\n",
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" Determinant.single_excitation Spin.Beta hole particle ki\n",
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" ) mos_cabs\n",
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" ) mos_abs\n",
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" ) mos_b \n",
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" ]\n",
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" |> List.concat\n",
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" |> List.concat\n",
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" |> List.filter (fun x -> Determinant.is_none x = false)\n",
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" |> List.map (fun x -> Determinant.set_phase Phase.Pos x)\n",
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" in\n",
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" \n",
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@ -677,9 +681,9 @@
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" if hole' > hole && particle' < particle then\n",
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" Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Alfa hole' particle' ki)\n",
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" else None\n",
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" ) mos_cabs\n",
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" ) mos_abs\n",
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" ) mos_a \n",
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" ) mos_cabs\n",
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" ) mos_abs\n",
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" ) mos_a\n",
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" ; \n",
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" List.map (fun hole -> (* Beta-Beta *)\n",
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@ -689,9 +693,9 @@
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" if hole' > hole && particle' < particle then\n",
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" Some (Determinant.double_excitation Spin.Beta hole particle Spin.Beta hole' particle' ki)\n",
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" else None\n",
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" ) mos_cabs\n",
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" ) mos_abs\n",
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" ) mos_b \n",
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" ) mos_cabs\n",
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" ) mos_abs\n",
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" ) mos_b\n",
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" ;\n",
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" List.map (fun hole -> (* Alpha-Beta *)\n",
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@ -699,9 +703,9 @@
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" List.map (fun hole' -> \n",
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" List.map (fun particle' ->\n",
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" Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Beta hole' particle' ki)\n",
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" ) mos_cabs\n",
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" ) mos_abs\n",
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" ) mos_b \n",
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" ) mos_cabs\n",
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" ) mos_abs\n",
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" ) mos_a\n",
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" ]\n",
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" |> List.concat\n",
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@ -760,10 +764,10 @@
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" |> List.sort_uniq compare\n",
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" \n",
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" (* Filter out all determinants with incorrect numbers of electrons in the CABS *)\n",
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" |> List.filter good_cabs\n",
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" |> List.filter good_cabs \n",
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" \n",
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" (* Filter out all determinants with incorrect excitation numbers *)\n",
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" |> List.filter good_lr\n",
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" |> List.filter good_lr \n",
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" \n",
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" \n",
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"let compute_HaaF ki alphas kj =\n",
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@ -785,30 +789,48 @@
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" | 0 -> det_I\n",
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" | n -> Array.sub det_I 0 n\n",
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" in\n",
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" Printf.printf \"Checking...\\n%!\";\n",
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" let result =\n",
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" Printf.printf \"Checking ... \\n%!\";\n",
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" let percent = ref 0 in\n",
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" Array.mapi (fun i ki -> \n",
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" let p = (10 * (i+1))/(Array.length det_list) in\n",
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" if p <> !percent then\n",
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" ( percent := p ; Printf.printf \" - %3d %%\\n%!\" (p*10) );\n",
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" Array.mapi (fun j kj -> \n",
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" if i > j then 0. else\n",
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" if Determinant.degree ki kj <> exc then 0. else\n",
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" if i > j then (0,0,0.,0.) else\n",
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" if Determinant.degree ki kj <> exc then (0,0,0.,0.) else\n",
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" let alphas = generate_alphas ki kj exc cabs lexc rexc in\n",
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" let det_value =\n",
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" compute_HaaF ki alphas kj\n",
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" in\n",
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" integral_value ki kj -. det_value \n",
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" let int_value = \n",
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" integral_value ki kj\n",
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" in\n",
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" (i,j,det_value,int_value)\n",
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" ) det_list\n",
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" ) det_list\n",
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" |> Array.to_list\n",
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" |> Array.concat\n",
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" in\n",
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" let error = \n",
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" Array.fold_left (fun accu x -> accu +. x *. x) 0. result\n",
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" /. (float_of_int @@ Array.length result)\n",
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" let i,j,d,v = \n",
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" let rec aux k imax jmax emax dmax vmax = \n",
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" if k = -1 then\n",
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" imax, jmax, dmax, vmax\n",
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" else\n",
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" let i, j, d, v = result.(k) in\n",
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" let e = abs_float (d -. v) in\n",
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" if e > emax then\n",
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" aux (k-1) i j e d v\n",
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" else\n",
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" aux (k-1) imax jmax emax dmax vmax\n",
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" in\n",
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" aux (n-1) 0 0 0. 0. 0.\n",
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" in\n",
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" let error = abs_float (d -. v) in\n",
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" if error < epsilon_float then\n",
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" Printf.printf \"OK: %e\\n%!\" error\n",
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" else\n",
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" Printf.printf \"Failed: %e\\n%!\" error\n",
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" Printf.printf \"Failed: (%d, %d) | %e %e | %e\\n%!\" i j d v error\n",
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"\n",
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" "
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]
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@ -817,7 +839,198 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# 0 2 22"
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"******"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# 1. 0 1 11"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"png_image \"0_1_11.png\""
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"$i,j$ : orbital indices of MOs occupied in $|I\\rangle$.\n",
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"\n",
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"\\begin{align}\n",
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"\\sum_{a} \\left( \n",
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" \\sum_{i} \\sum_{j}\n",
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" \\left(h_{ia} + \\langle i j || a j \\rangle \\right) \n",
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" \\left(f_{ai} + \\left[ a j || i j \\right] \\right) + \n",
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" \\sum_{i} \\sum_{\\bar{j}}\n",
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" \\left(h_{ia} + \\langle i \\bar{j} | a \\bar{j} \\rangle \\right) \n",
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" \\left(f_{ai} + \\left[ a \\bar{j} | i \\bar{j} \\right] \\right) \n",
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" \\right) + \\\\\n",
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"\\sum_{\\bar{a}} \\left(\n",
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" \\sum_{\\bar{i}} \\sum_{\\bar{j}}\n",
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" \\left(h_{\\bar{i}\\bar{a}} + \\langle \\bar{i} \\bar{j} || \\bar{a} \\bar{j} \\rangle \\right) \n",
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" \\left(f_{\\bar{a}\\bar{i}} + \\left[ \\bar{a} \\bar{j} || \\bar{i} \\bar{j} \\right] \\right) + \n",
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" \\sum_{\\bar{i}} \\sum_{j}\n",
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" \\left(h_{\\bar{i}\\bar{a}} + \\langle \\bar{i} j | \\bar{a} j \\rangle \\right)\n",
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" \\left(f_{\\bar{a}\\bar{i}} + \\left[ \\bar{a} j | \\bar{i} j \\right] \\right) \n",
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" \\right) \n",
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"\\end{align}"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"let integral_value ki kj = \n",
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" (* Alpha-Beta *)\n",
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" let s, s' = Spin.(Alfa, Beta) in \n",
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" List.fold_left (fun accu j -> accu +. \n",
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" List.fold_left (fun accu i -> accu +. \n",
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" List.fold_left (fun accu a ->\n",
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" accu +.( (h_one i a s +. h_two i j a j s s') *. \n",
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" (f_one a i s +. f_two a j i j s s') )\n",
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" +.( (h_one j a s' +. h_two i j i a s s') *. \n",
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" (f_one a j s' +. f_two i a i j s s') )\n",
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" ) 0. mos_cabs\n",
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" ) 0. (mos_a ki)\n",
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" ) 0. (mos_b ki)\n",
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" +.\n",
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" (* Alpha-Alpha / Beta-Beta *)\n",
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" List.fold_left (fun accu (mos,s) -> \n",
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" let s' = s in accu +. \n",
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" List.fold_left (fun accu j -> accu +. \n",
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" List.fold_left (fun accu i -> accu +. \n",
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" List.fold_left (fun accu a -> \n",
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" accu +.( (h_one i a s +. h_two i j a j s s') *. \n",
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" (f_one a i s +. f_two a j i j s s') )\n",
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" ) 0. mos_cabs\n",
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" ) 0. mos\n",
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" ) 0. mos\n",
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" ) 0. [ (mos_a ki,Spin.Alfa) ; (mos_b ki,Spin.Beta)]\n",
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" \n",
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"let _ =\n",
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" check 0 integral_value 0 1 1 1\n",
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" "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# 2. 0 1 22"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"png_image \"0_1_22.png\""
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"$i,j$ : orbital indices of MOs occupied in $|I\\rangle$.\n",
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"\n",
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"$k$ : orbital indices of MOs unoccupied in $|I\\rangle$.\n",
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"\n",
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"\\begin{align}\n",
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"\\sum_{a} \\sum_{k} \\sum_{i} \\sum_{j<i}\n",
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" \\langle i j || a k \\rangle \n",
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" \\left[ a k || i j \\right] + \n",
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"\\sum_{a} \\sum_{\\bar{k}} \\sum_{i} \\sum_{\\bar{j}}\n",
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" \\langle i \\bar{j} | a \\bar{k} \\rangle \n",
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" \\left[ a \\bar{k} | i \\bar{j} \\right] + \\\\\n",
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"\\sum_{\\bar{a}} \\sum_{k} \\sum_{\\bar{i}} \\sum_{j}\n",
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" \\langle \\bar{i} j | \\bar{a} k \\rangle \n",
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" \\left[ \\bar{a} k | \\bar{i} j \\right] + \n",
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"\\sum_{\\bar{a}} \\sum_{\\bar{k}} \\sum_{\\bar{i}} \\sum_{\\bar{j}<\\bar{i}}\n",
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" \\langle \\bar{i} \\bar{j} || \\bar{a} \\bar{k} \\rangle \n",
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" \\left[ \\bar{a} \\bar{k} || \\bar{i} \\bar{j} \\right] \n",
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"\\end{align}"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"let integral_value ki kj = \n",
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" (* mos unoccupied in both I and J *)\n",
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" let mos_virt_a, mos_virt_b = \n",
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" Array.init mo_num (fun i -> Some (i+1)) , \n",
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" Array.init mo_num (fun i -> Some (i+1)) \n",
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" in\n",
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" List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n",
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" List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n",
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" List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n",
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" List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n",
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" \n",
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" let mos_virt_a, mos_virt_b = \n",
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" Array.to_list mos_virt_a |> Util.list_some,\n",
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" Array.to_list mos_virt_b |> Util.list_some\n",
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" in\n",
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" \n",
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" (* Alpha-Beta *)\n",
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" let s, s' = Spin.(Alfa, Beta) in\n",
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" List.fold_left (fun accu j -> accu +. \n",
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" List.fold_left (fun accu i -> accu +. \n",
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" List.fold_left (fun accu k -> accu +. \n",
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" List.fold_left (fun accu a ->\n",
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" accu +. h_two i j a k s s' *. f_two a k i j s s'\n",
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" ) 0. mos_cabs\n",
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" ) 0. mos_virt_b\n",
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" ) 0. (mos_a ki)\n",
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" ) 0. (mos_b ki)\n",
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" +.\n",
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" List.fold_left (fun accu j -> accu +. \n",
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" List.fold_left (fun accu i -> accu +. \n",
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" List.fold_left (fun accu k -> accu +. \n",
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" List.fold_left (fun accu a ->\n",
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" accu +. h_two i j a k s s' *. f_two a k i j s s'\n",
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" ) 0. mos_cabs\n",
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" ) 0. mos_virt_a\n",
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" ) 0. (mos_b ki)\n",
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" ) 0. (mos_a ki)\n",
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" +.\n",
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" (* Alpha-Alpha / Beta-Beta *)\n",
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" List.fold_left (fun accu (mos_virt,mos,s) -> \n",
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" let s' = s in accu +.\n",
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" List.fold_left (fun accu j -> accu +. \n",
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" List.fold_left (fun accu i -> accu +. \n",
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" if i < j then accu else\n",
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" List.fold_left (fun accu k -> accu +. \n",
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" List.fold_left (fun accu a -> \n",
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" accu +. h_two i j a k s s' *. f_two a k i j s s'\n",
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" ) 0. mos_cabs\n",
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" ) 0. mos_virt\n",
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" ) 0. mos\n",
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" ) 0. mos\n",
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" ) 0. [ (mos_virt_a,mos_a ki,Spin.Alfa) ; (mos_virt_b,mos_b ki,Spin.Beta)]\n",
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" \n",
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"let _ =\n",
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" check 0 integral_value 0 1 2 2\n",
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" "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# 3. 0 2 22"
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]
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},
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{
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@ -835,13 +1048,22 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"$i,j$ : orbital indices of MOs occupied in $|I\\rangle$.\n",
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"$i,j$ : orbital indices of MOs occupied in $|I\\rangle$.\n",
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"\n",
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"$$\n",
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"\\sum_{j} \\sum_{i<j} \\sum_{b}\\sum_{a<b}\n",
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" \\langle i j || a b \\rangle \n",
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" \\left[ ab || ij \\right]\n",
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"$$"
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"\\begin{align}\n",
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"\\sum_{a} \\sum_{b>a} \\sum_{i} \\sum_{j<i}\n",
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" \\langle i j || a b \\rangle \n",
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" \\left[ a b || i j \\right] + \n",
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"\\sum_{a} \\sum_{\\bar{b}} \\sum_{i} \\sum_{\\bar{j}}\n",
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" \\langle i \\bar{j} | a \\bar{b} \\rangle \n",
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" \\left[ a \\bar{b} | i \\bar{j} \\right] + \\\\\n",
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"\\sum_{\\bar{a}} \\sum_{b} \\sum_{\\bar{i}} \\sum_{j}\n",
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" \\langle \\bar{i} j | \\bar{a} b \\rangle \n",
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" \\left[ \\bar{a} b | \\bar{i} j \\right] + \n",
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"\\sum_{\\bar{a}} \\sum_{\\bar{b}>\\bar{a}} \\sum_{\\bar{i}} \\sum_{\\bar{j}<\\bar{i}}\n",
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" \\langle \\bar{i} \\bar{j} || \\bar{a} \\bar{b} \\rangle \n",
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" \\left[ \\bar{a} \\bar{b} || \\bar{i} \\bar{j} \\right] \n",
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"\\end{align}"
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]
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},
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{
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@ -880,7 +1102,7 @@
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" ) 0. [ (mos_a ki,Spin.Alfa) ; (mos_b ki,Spin.Beta)]\n",
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" \n",
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"let _ =\n",
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" check 10 integral_value 0 2 2 2\n",
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" check 100 integral_value 0 2 2 2\n",
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" "
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]
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},
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@ -888,7 +1110,156 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# 1 2 22"
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"# 4. *1 1 11*"
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]
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},
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{
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"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"
|
||||
},
|
||||
|
||||
Loading…
Reference in New Issue
Block a user