mirror of https://gitlab.com/scemama/QCaml.git
Working on F12 notebook
This commit is contained in:
parent
2e6ccb1770
commit
56b6bb41a6
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@ -864,6 +864,8 @@
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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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"$\\sum_i \\sum_a \\hat{T}_{i}^{a} \\hat{T}_{a}^{i}$\n",
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"\n",
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"\\begin{align}\n",
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"\\sum_{a} \\sum_{i}\n",
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" \\left( h_{ia} +\n",
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@ -943,6 +945,9 @@
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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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"$\\sum_i \\sum_a \\sum_j \\sum_k \\hat{T}_{ij}^{ak} \\hat{T}_{ak}^{ij}$\n",
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"\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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@ -1047,6 +1052,8 @@
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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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"$\\sum_i \\sum_a \\sum_j \\sum_b \\hat{T}_{ij}^{ab} \\hat{T}_{ab}^{ij}$\n",
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"\n",
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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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@ -1099,7 +1106,7 @@
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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 100 integral_value 0 2 2 2\n",
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" check 0 integral_value 0 2 2 2\n",
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" "
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]
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},
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@ -1127,12 +1134,14 @@
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"\n",
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"$j$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n",
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"\n",
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"$\\sum_a \\hat{T}_{i}^{a} \\hat{T}_{a}^{k}$\n",
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"\n",
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"\\begin{align}\n",
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" \\sum_{a} \n",
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" \\left( h_{ia} +\\sum_{j} \\langle i j || a j \\rangle +\n",
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" \\sum_{\\bar{j}} \\langle i \\bar{j} | a \\bar{j} \\rangle \\right)\n",
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" \\left( f_{ak} +\\sum_{j} \\left[ a j || k j \\right] + \n",
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" \\sum_{\\bar{j}} \\left[ a \\bar{j} | k \\bar{j} \\right]\\right) \n",
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" \\sum_{\\bar{j}} \\left[ a \\bar{j} | k \\bar{j} \\right]\\right) \\\\\n",
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"\\end{align}"
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]
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},
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@ -1177,33 +1186,14 @@
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" | Phase.Neg -> -. result\n",
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" \n",
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"\n",
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"let _ = check 50 integral_value 1 1 1 1"
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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 ki = det_I.(0)\n",
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"let kj = det_I.(0)\n",
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"\n",
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"\n",
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"let _ =\n",
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" let alphas =\n",
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" generate_alphas ki kj 0 1 2 2\n",
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" in\n",
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" compute_HaaF ki alphas kj\n",
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"\n",
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"let _ = integral_value ki kj"
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"let _ = check 0 integral_value 1 1 1 1"
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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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"# 5. *1 1 12*"
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"# 5. 1 1 12"
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]
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},
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{
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@ -1219,7 +1209,22 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# 6. *1 1 21*"
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"$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n",
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"\n",
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"$\\sum_{j} \\sum_a \\hat{T}_{j}^{a} \\hat{T}_{ai}^{jk}$\n",
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"\n",
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"$j$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n",
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"\n",
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"\\begin{align}\n",
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" \\sum_{a} \\sum_{j} \n",
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" \\left( h_{ja} +\\sum_{m} \\langle j m || a m \\rangle +\n",
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" \\sum_{\\bar{m}} \\langle j \\bar{m} | a \\bar{m} \\rangle \\right)\n",
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" \\left[ a i || j k \\right] + \\\\\n",
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" \\sum_{\\bar{a}} \\sum_{\\bar{j}} \n",
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" \\left( h_{\\bar{j}\\bar{a}} +\\sum_{m} \\langle \\bar{j} m | \\bar{a} m \\rangle +\n",
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" \\sum_{\\bar{m}} \\langle \\bar{j} \\bar{m} || \\bar{a} \\bar{m} \\rangle \\right)\n",
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" \\left[ \\bar{a} i | \\bar{j} k \\right] \n",
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"\\end{align}"
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]
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},
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{
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@ -1227,10 +1232,184 @@
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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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" let i, k, s, phase =\n",
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" match Excitation.of_det ki kj with\n",
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" | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
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" hole, particle, spin, phase\n",
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" | _ -> assert false\n",
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" in\n",
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"\n",
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" let mos_j, mos_j' =\n",
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" let alfa = \n",
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" let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
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" let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
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" Bitstring.to_list (Bitstring.logand i j)\n",
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" in\n",
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" let beta = \n",
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" let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
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" let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
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" Bitstring.to_list (Bitstring.logand i j)\n",
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" in\n",
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" match s with\n",
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" | Spin.Alfa -> alfa, beta\n",
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" | Spin.Beta -> beta, alfa\n",
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" in\n",
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" \n",
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" let mos_i, mos_i' =\n",
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" match s with\n",
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" | Spin.Alfa -> mos_a ki, mos_b ki\n",
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" | Spin.Beta -> mos_b ki, mos_a ki\n",
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" in\n",
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"\n",
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" let result = \n",
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" let s' = Spin.other s in\n",
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" List.fold_left (fun accu a -> accu +.\n",
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" List.fold_left (fun accu j -> accu +.\n",
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" (h_one j a s +. \n",
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" (List.fold_left (fun accu m -> accu +. h_two j m a m s s ) 0. mos_i ) +.\n",
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" (List.fold_left (fun accu m -> accu +. h_two j m a m s s') 0. mos_i') ) *.\n",
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" (f_two a i j k s s )\n",
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" ) 0. mos_j\n",
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" +.\n",
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" List.fold_left (fun accu j -> accu +.\n",
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" (h_one j a s +. \n",
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" (List.fold_left (fun accu m -> accu +. h_two j m a m s' s ) 0. mos_i ) +.\n",
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" (List.fold_left (fun accu m -> accu +. h_two j m a m s' s') 0. mos_i') ) *.\n",
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" (f_two a i j k s' s )\n",
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" ) 0. mos_j'\n",
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" ) 0. mos_cabs\n",
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" in\n",
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" match phase with\n",
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" | Phase.Pos -> result\n",
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" | Phase.Neg -> -. result\n",
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" \n",
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"\n",
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"let _ = check 0 integral_value 1 1 1 2"
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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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"# 6. *1 1 21*"
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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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"scrolled": false
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},
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"outputs": [],
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"source": [
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"png_image \"1_1_21.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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"$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n",
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"\n",
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"$\\sum_{j} \\sum_a \\hat{T}_{ij}^{ka} \\hat{T}_{a}^{j}$\n",
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"\n",
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"$j$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n",
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"\n",
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"\\begin{align}\n",
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" \\sum_{a} \\sum_{j} \n",
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" \\langle i j || k a \\rangle \n",
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" \\left( f_{aj} +\\sum_{m} \\left[ m a || m j \\right] +\n",
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" \\sum_{\\bar{m}} \\left[ \\bar{m} a | \\bar{m} j \\right] \\right) + \\\\\n",
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" \\sum_{\\bar{a}} \\sum_{\\bar{j}} \n",
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" \\langle i \\bar{j} | k \\bar{a} \\rangle\n",
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" \\left( f_{\\bar{a}\\bar{j}} +\\sum_{m} \\left[ m \\bar{a} | m \\bar{j} \\right] +\n",
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" \\sum_{\\bar{m}} \\left[ \\bar{m} \\bar{a} || \\bar{m} \\bar{j} \\right] \\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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" let i, k, s, phase =\n",
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" match Excitation.of_det ki kj with\n",
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" | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n",
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" hole, particle, spin, phase\n",
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" | _ -> assert false\n",
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" in\n",
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"\n",
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" let mos_j, mos_j' =\n",
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" let alfa = \n",
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" let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n",
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" let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n",
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" Bitstring.to_list (Bitstring.logand i j)\n",
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" in\n",
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" let beta = \n",
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" let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n",
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" let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n",
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" Bitstring.to_list (Bitstring.logand i j)\n",
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" in\n",
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" match s with\n",
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" | Spin.Alfa -> alfa, beta\n",
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" | Spin.Beta -> beta, alfa\n",
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" in\n",
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" \n",
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" let mos_i, mos_i' =\n",
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" match s with\n",
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" | Spin.Alfa -> mos_a kj, mos_b kj\n",
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" | Spin.Beta -> mos_b kj, mos_a kj\n",
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" in\n",
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"\n",
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" let result = \n",
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" let s' = Spin.other s in\n",
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" List.fold_left (fun accu a -> accu +.\n",
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" List.fold_left (fun accu j -> accu +.\n",
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" (h_two i j k a s s ) *.\n",
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" (f_one a j s +. \n",
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" (List.fold_left (fun accu m -> accu +. h_two m a m j s s) 0. mos_i ) +.\n",
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" (List.fold_left (fun accu m -> accu +. h_two m a m j s' s) 0. mos_i') ) \n",
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" ) 0. mos_i\n",
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" +.\n",
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" List.fold_left (fun accu j -> accu +.\n",
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" (h_two i j k a s s') *.\n",
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" (f_one a j s' +. \n",
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" (List.fold_left (fun accu m -> accu +. h_two m a m j s s') 0. mos_i ) +.\n",
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" (List.fold_left (fun accu m -> accu +. h_two m a m j s' s') 0. mos_i') ) \n",
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" ) 0. mos_i'\n",
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" ) 0. mos_cabs\n",
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" in\n",
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" match phase with\n",
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" | Phase.Pos -> result\n",
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" | Phase.Neg -> -. result\n",
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" \n",
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"\n",
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"let _ = check 11 integral_value 1 1 2 1"
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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 ki = det_I.(0)\n",
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"let kj = det_I.(10)\n",
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"\n",
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"\n",
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"let _ =\n",
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" let alphas =\n",
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" generate_alphas ki kj 1 1 2 1\n",
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" in\n",
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" compute_HaaF ki alphas kj\n",
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"\n",
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"let _ = integral_value ki kj"
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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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@ -1525,7 +1704,7 @@
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"metadata": {
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"celltoolbar": "Raw Cell Format",
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"kernelspec": {
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"display_name": "OCaml default",
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"display_name": "OCaml 4.07.1",
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"language": "OCaml",
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"name": "ocaml-jupyter"
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},
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