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Simplification integrales

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Anthony Scemama 2020-04-27 12:20:22 +02:00
parent f0b67e1122
commit 8b7f153ef6
1 changed files with 19 additions and 7 deletions
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26
HartreeFock.ipynb
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@ -767,22 +767,33 @@
"let i = 1;;\n",
"let j = 2;;\n",
"\n",
"let integral_general g =\n",
"Array.map (fun a ->\n",
" let v = \n",
" Array.map (fun b ->\n",
" let u = \n",
" Array.map (fun e ->\n",
" let t = Array.map (fun f ->\n",
" m_C.{f,j} *. ERI.get_phys ee_ints a b e f\n",
" (g a b e f i j) *. ERI.get_phys ee_ints a b e f\n",
" ) (Util.array_range 1 n_ao)\n",
" in m_C.{e,i} *. sum t\n",
" in sum t\n",
" ) (Util.array_range 1 n_ao)\n",
" in m_C.{b,j} *. sum u\n",
" in sum u\n",
" ) (Util.array_range 1 n_ao)\n",
" in m_C.{a,i} *. sum v\n",
" in sum v\n",
") (Util.array_range 1 n_ao)\n",
"|> sum\n",
"\n"
"\n",
"let func_a = \n",
" integral_general (fun a b e f i j ->\n",
" m_C.{a,i} *. m_C.{b,i} *. m_C.{e,i} *. m_C.{f,j}\n",
" )\n",
"\n",
"\n",
"let func_b = \n",
" integral_general (fun a b e f i j ->\n",
" m_C.{a,i} *. m_C.{b,i} *. m_C.{e,i} *. m_C.{f,j}\n",
" )\n"
]
},
{
@ -791,8 +802,9 @@
"source": [
"$\\langle \\phi_i \\phi_j | \\phi_i \\phi_j \\rangle =\n",
"\\sum_a c_{ai} \\langle \\chi_a \\phi_j | \\phi_i \\phi_j \\rangle =\n",
"\\sum_a \\sum_b c_{ai} c_{bj} \\langle \\chi_a \\chi_b | \\phi_i \\phi_j \\rangle$\n",
"$\\sum_a \\sum_b \\sum_e \\sum_f \\left(c_{ai} \\left(c_{bj} \\left(c_{ei} \\left(c_{fj} \\langle \\chi_a \\chi_b | \\chi_e \\chi_f \\rangle \\right)\\right)\\right)\\right) $"
"\\sum_a \\sum_b c_{ai} c_{bj} \\langle \\chi_a \\chi_b | \\phi_i \\phi_j \\rangle =$\n",
"$\\left(\\sum_a c_{ai} \\sum_b \\left(c_{bj} \\sum_e \\left(c_{ei} \\sum_f \\left(c_{fj} \\langle \\chi_a \\chi_b | \\chi_e \\chi_f \\rangle \\right)\\right)\\right)\\right) =$\n",
"$\\sum_a \\sum_b \\sum_e \\sum_f \\left( c_{ai} c_{bj} c_{ei} c_{fj} \\langle \\chi_a \\chi_b | \\chi_e \\chi_f \\rangle \\right) $"
]
},
{