Data
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{
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"cells": [
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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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"# Jastrow factors"
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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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"## H2O"
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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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"onedet = \"Jastrows/H2O/H2O-cc-pcvTz.wfj-1det_J2.ud_exp.dat\"\n",
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"os = 1.-7.92535494e-01\n",
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"\n",
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"multidet = \"Jastrows/H2O/H2O-cc-pcvTz-multidet.wfj_J2.ud_exp.dat\"\n",
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"ms = 1.-8.59001137e-01\n",
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"\n",
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"onedet_H = \"Jastrows/H2O/H2O-cc-pcvTz.wfj-1det_J1.H_exp.dat\"\n",
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"ohs = 1.-1.03221118e+00\n",
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"onedet_O = \"Jastrows/H2O/H2O-cc-pcvTz.wfj-1det_J1.O_exp.dat\"\n",
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"oos = 1.-1.43887500e+00\n",
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"\n",
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"#onedet = \"Jastrows/N2H4/N2H4-tr6.wfj_J2.ud_exp.dat\"\n",
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"#os = 1.-8.03464242e-01\n"
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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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"set yrange [1:1.4]\n",
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"set xrange [0:3]\n",
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"set grid\n",
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"set xlabel \"r_{12} (a.u.)\"\n",
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"set format y \"%.2f\"\n",
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"set format x \"%.1f\"\n",
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"set key bottom right\n",
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"\n",
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"plot onedet u 1:($2+os) w l title \"HF\"\\\n",
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", multidet u 1:($2+ms) w l title \"FCI\"\n",
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"\n",
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"set yrange [0:1]\n",
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"plot onedet_O u 1:($2+oos) w l title \"O\"\\\n",
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", onedet_H u 1:($2+ohs) w l title \"H\"\n"
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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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"f1(x) = exp(a_1 * x/(1. + b_1*x))\n",
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"f2(x) = exp(a_2 * x/(1. + b_2*x))\n",
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"f3(x) = exp(a_3 * x**2+b_3)\n",
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"f4(x) = exp(a_4 * x**2+b_4)\n",
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"a_1 = 0.5\n",
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"a_2 = 0.5\n",
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"a_3 = 0.5\n",
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"a_4 = 0.5\n",
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"b_1 = 1.\n",
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"b_2 = 1.\n",
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"b_3 = 1.\n",
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"b_4 = 1.\n",
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"\n",
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"fit f1(x) onedet u 1:($2+os) via b_1\n",
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"fit f2(x) multidet u 1:($2+ms) via b_2\n",
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"fit [0:1] f3(x) onedet_O u 1:($2+oos) via a_3, b_3\n",
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"fit [0:1] f4(x) onedet_H u 1:($2+ohs) via a_4, b_4\n"
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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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"set xrange [0:3]\n",
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"set yrange [1.:1.3]\n",
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"set grid\n",
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"set xlabel \"r_{12} (a.u.)\"\n",
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"set format y \"%.2f\"\n",
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"set format x \"%.1f\"\n",
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"set key bottom right\n",
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"\n",
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"plot onedet u 1:($2+os) w l title \"HF\"\\\n",
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", multidet u 1:($2+ms) w l title \"FCI\"\\\n",
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", f1(x) title \"exp(- 0.5 r_{12} / (1. + 1.93 r_{12}))\"\\\n",
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", f2(x) title \"exp(- 0.5 r_{12} / (1. + 3.99 r_{12}))\"\n"
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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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"set xrange [0:1]\n",
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"set yrange [0.6:1.]\n",
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"set grid\n",
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"set xlabel \"r_{12} (a.u.)\"\n",
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"set format y \"%.2f\"\n",
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"set format x \"%.1f\"\n",
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"set key bottom right\n",
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"\n",
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"plot onedet_O u 1:($2+oos) w l title \"O\"\\\n",
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", onedet_H u 1:($2+ohs) w l title \"H\"\\\n",
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", f3(x) title \"exp(- 0.5 r_{12} / (1. + 1.93 r_{12}))\"\\\n",
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", f4(x) title \"exp(- 0.5 r_{12} / (1. + 3.99 r_{12}))\"\n"
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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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"#set term pdf font \"Times,15pt\"\n",
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"#set output \"jastrow_h2o.pdf\""
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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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"## Range-separated Coulomb operator"
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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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"w(x) = 1./x\n",
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"w_lr(mu,x) = erf(mu*x)/x\n",
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"w_sr(mu,x) = w(x) - w_lr(mu,x)"
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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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"set xrange [0:4]\n",
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"set yrange [0:3]\n",
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"set key top right\n",
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"plot w(x) title '1/r_{12}',\\\n",
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" w_lr(0.5,x) title '{/Symbol m}=0.5' ls 2,\\\n",
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" w_sr(0.5,x) notitle ls 2, \\\n",
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" w_lr(1.0,x) title '{/Symbol m}=1.0' ls 4,\\\n",
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" w_sr(1.0,x) notitle ls 4"
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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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"## DMC Energies"
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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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"### Single-determinant"
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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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"data = \"Jastrows/data_dmc\"\n",
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"set key top right\n",
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"set xrange [0:7.5]\n",
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"set xlabel \"{/Symbol m} (a.u.)\"\n",
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"set ylabel \"Energy (a.u.)\"\n",
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"set format y \"%.4f\"\n",
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"set yrange [-76.4115:-76.4095]\n",
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"plot data index 0 u 1:5:6 w errorlines title \"1 det / cc-pVDZ\"\n",
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"set yrange [-76.4215:-76.4195]\n",
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"plot data index 1 u 1:5:6 w errorlines title \"1 det / cc-pVTZ\"\n",
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"set yrange [-76.4232:-76.4212]\n",
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"plot data index 2 u 1:5:6 w errorlines title \"1 det / cc-pVQZ\""
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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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"### Multi-determinant"
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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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"data = \"Jastrows/data_dmc\"\n",
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"set key top right\n",
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"set xrange [0:7.5]\n",
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"set xlabel \"{/Symbol m} (a.u.)\"\n",
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"set ylabel \"Energy (a.u.)\"\n",
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"set format y \"%.3f\"\n",
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"set yrange [-76.44:-76.405]\n",
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"plot data index 0 u 1:7:8 w errorlines title \"CIPSI / cc-pVDZ\", \\\n",
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"data index 1 u 1:7:8 w errorlines title \"CIPSI / cc-pVTZ\", \\\n",
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"data index 2 u 1:7:8 w errorlines title \"CIPSI / cc-pVQZ\""
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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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"## Fit $\\mu$"
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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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"-----\n",
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"$\\Psi(r_1,\\dots,r_N)$ is a CI trial wave function:\n",
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"$$\n",
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"|\\Psi \\rangle = \\sum_{I \\in \\mathcal{B}} c_I |I\\rangle\n",
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"$$\n",
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"When running a FN-DMC calculation, the fixed-node wave function can be written as $\\Phi(r_1,\\dots,r_N) = \\Psi(r_1,\\dots,r_N)\\times w(r_1,\\dots,r_N)$, where $w$ is a positive function, such that\n",
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"$$\n",
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"E = \\min_w \\frac{ \\langle w \\Psi | H | \\Psi \\rangle } {\\langle w \\Psi | \\Psi \\rangle}\n",
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"$$"
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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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"We want to find the change in the potential that would model the effect of the FN-DMC. This corresponds to removing some short-range potential:\n",
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"\n",
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"$$\n",
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"\\frac{ \\langle w \\Psi | V_{ee} | w \\Psi \\rangle } {\\langle w \\Psi | w \\Psi \\rangle} = \n",
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"\\frac{ \\langle \\Psi | V_{ee} - \\delta V_{ee} | \\Psi \\rangle } {\\langle \\Psi | \\Psi \\rangle} \n",
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"$$\n",
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"where\n",
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"\n",
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"$$\n",
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"V_{ee} = \\frac{1}{r_{12}} \n",
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"$$\n",
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"and\n",
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"$$\n",
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"\\delta V_{ee} = \n",
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"\\alpha \\left( \\frac{1}{r_{12}} - \\frac{\\text{erf}( \\mu r_{12})}{r_{12}} \\right).\n",
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"$$\n",
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"\n",
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"\n",
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"$$\n",
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"\\frac{ \\langle w \\Psi | V_{ee} | w \\Psi \\rangle } {\\langle w \\Psi | w \\Psi \\rangle} = \n",
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"\\frac{ \\langle \\Psi | V_{ee} | \\Psi \\rangle } {\\langle \\Psi | \\Psi \\rangle} -\n",
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"\\alpha \\frac{ \\langle \\Psi | V_{ee} | \\Psi \\rangle } {\\langle \\Psi | \\Psi \\rangle} +\n",
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"\\alpha \\frac{ \\langle \\Psi | V_{ee}^{lr} | \\Psi \\rangle } {\\langle \\Psi | \\Psi \\rangle} \n",
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"$$\n",
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"\n",
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"$$\n",
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"\\frac{\\langle \\Psi | w^2 V_{ee} | \\Psi \\rangle}\n",
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"{\\langle w \\Psi | w \\Psi \\rangle}\n",
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"=\n",
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"(1-\\alpha) \\langle \\Psi | V_{ee} | \\Psi \\rangle +\n",
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"\\alpha \\langle \\Psi | V_{ee}^{lr} | \\Psi \\rangle \n",
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"$$\n"
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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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"$$\n",
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"w^2 = \\left[ (1-\\alpha) + \\alpha\\, \\text{erf}(\\mu\\, r_{12}) \\right]\\langle w \\Psi | w \\Psi \\rangle\n",
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"$$"
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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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"To find the parameter $\\mu$, we minimize\n",
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"$$\n",
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"\\int \\left|a\\, \\text{erf}(\\mu\\,r_{12}) + b - w(r_{12})^2 \\right|^2 \\text{d}r_{12}\n",
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"$$"
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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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"set yrange [1:1.3]\n",
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"set xrange [0:3]\n",
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"set grid\n",
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"set xlabel \"r_{12} (a.u.)\"\n",
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"set format y \"%.2f\"\n",
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"set format x \"%.1f\"\n",
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"set key bottom right\n",
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"\n",
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"f(x) = (a * (erf(mu*x)) +b)\n",
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"mu = 2.\n",
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"b=1.\n",
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"a = 1.\n",
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"fit f(x) multidet u 1:( ($2+ms)**2 ) via a, b, mu\n"
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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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"plot f(x), multidet u 1:( ($2+ms)**2) title \"{/Symbol m}=3.05\" w l"
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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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"set yrange [1:1.7]\n",
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"set xrange [0:2.5]\n",
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"set grid\n",
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"set xlabel \"r_{12} (a.u.)\"\n",
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"set format y \"%.2f\"\n",
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"set format x \"%.1f\"\n",
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"set key bottom right\n",
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"\n",
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"f(x) = (a * (erf(mu*x)) +b)\n",
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"mu = 2.\n",
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"b=1.\n",
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"a = 1.\n",
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"fit f(x) onedet u 1:( ($2+os)**2) via a, b, mu\n"
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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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"plot f(x), onedet u 1:( ($2+os)**2 ) title \"{/Symbol m}=0.94\" w l"
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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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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "gnuplot",
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"language": "gnuplot",
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"name": "gnuplot"
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},
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"language_info": {
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"codemirror_mode": "Octave",
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"file_extension": ".gp",
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"help_links": [
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{
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"text": "MetaKernel Magics",
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"url": "https://metakernel.readthedocs.io/en/latest/source/README.html"
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}
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],
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"mimetype": "text/x-gnuplot",
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"name": "gnuplot"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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@ -0,0 +1,34 @@
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onedet = "~/Anouar/Jastrows/H2O/H2O-cc-pcvTz.wfj-1det_J2.ud_exp.dat"
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multidet = "~/Anouar/Jastrows/H2O/H2O-cc-pcvTz-multidet.wfj_J2.ud_exp.dat"
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#f1(x) = exp(a_1 * x/(1. + b_1*x))
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#f2(x) = exp(a_2 * x/(1. + b_2*x))
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#a_1 = 0.5
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#a_2 = 0.5
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#b_1 = 1.
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#b_2 = 1.
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#fit f1(x) onedet u 1:($2-7.92535494e-01+1.) via b_1
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#fit f2(x) multidet u 1:($2-8.59001137e-01+1.) via b_2
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set xrange [0:3]
|
||||
set yrange [1:1.25]
|
||||
set grid
|
||||
set xlabel "r_{12} (a.u.)"
|
||||
set format y "%.2f"
|
||||
set format x "%.1f"
|
||||
set key bottom right
|
||||
|
||||
plot onedet u 1:($2-7.92535494e-01+1.) w l title "HF / cc-pVTZ"\
|
||||
, multidet u 1:($2-8.59001137e-01+1.) w l title "CIPSI / cc-pVTZ"\
|
||||
#, f1(x) title "exp(- 0.5 r_{12} / (1. + 1.93 r_{12}))"\
|
||||
#, f2(x) title "exp(- 0.5 r_{12} / (1. + 3.99 r_{12}))"
|
||||
|
||||
|
||||
set term pdf font "Times,16pt" linewidth 2.
|
||||
set output "jastrow_h2o.pdf"
|
||||
replot
|
||||
set term cairo
|
||||
|
||||
|
||||
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|
|
@ -0,0 +1,38 @@
|
|||
# mu ndet E(PBE) RS-CI DMC(1det) DMC(RS-CI)
|
||||
|
||||
# DZ
|
||||
0.5 2396 -76.33604445222997 -76.3441442508 -76.410018 0.000198 -76.411258 0.000383
|
||||
1.0 40963 -76.27348956941330 -76.3336831179 -76.410771 0.000218 -76.415616 0.000479
|
||||
1.5 138253 -76.20172972611051 -76.3147073528 -76.411030 0.000143 -76.418327 0.000311
|
||||
2.0 207380 -76.15446145849143 -76.3018300218 -76.410994 0.000168 -76.417751 0.000544
|
||||
2.5 311071 -76.12743299891538 -76.2963616190 -76.410997 0.000138 -76.418830 0.000320
|
||||
3.0 466607 -76.11231786534898 -76.2953530572 -76.410925 0.000175 -76.418333 0.000604
|
||||
4.0 466607 -76.09737987601412 -76.2973907108 -76.410767 0.000183 -76.417842 0.000485
|
||||
5.0 466607 -76.08892265698270 -76.299088319 -76.410719 0.000167 -76.417461 0.000481
|
||||
6.0 466607 -76.08222148947996 -76.2995315838 -76.410730 0.000172 -76.417162 0.000632
|
||||
7.0 466607 -76.07645402100390 -76.2992732268 -76.410741 0.000192 -76.417398 0.000384
|
||||
|
||||
|
||||
# TZ
|
||||
0.5 8090 -76.37411359270587 -76.3853803202 -76.420407 0.000116 -76.422574 0.000253
|
||||
1.0 466607 -76.30808407357975 -76.3810129344 -76.420450 0.000117 -76.427268 0.000494
|
||||
1.5 2000000 -76.23450972568928 -76.3699240165 -76.420484 0.000129 -76.430965 0.000937
|
||||
2.0 2000000 -76.18647332232358 -76.3659759776 -76.420322 0.000123 -76.430956 0.000704
|
||||
2.5 2000000 -76.15905488759424 -76.3681700530 -76.420125 0.000170 -76.432259 0.000539
|
||||
3.0 2000000 -76.14366220610044 -76.3730744570 -76.420003 0.000149 -76.432267 0.000611
|
||||
4.0 2000000 -76.12827446549065 -76.3829546254 -76.420138 0.000139 -76.430869 0.000996
|
||||
5.0 2000000 -76.11950514107885 -76.3892344149 -76.419934 0.000119 -76.431917 0.000943
|
||||
7.0 2000000 -76.10674756885926 -76.3942237680 -76.419851 0.000161 -76.430150 0.000752
|
||||
|
||||
|
||||
# QZ
|
||||
0.5 12136 -76.38318565911486 -76.3952959489 -76.422831 0.000207 -76.425846 0.000254
|
||||
1.0 2382775 -76.31599767191094 -76.3917462575 -76.422337 0.000151 -76.428929 0.000748
|
||||
1.5 2408343 -76.24211906926882 -76.3816852280 -76.422451 0.000188 -76.432489 0.000531
|
||||
2.0 3698407 -76.19399206529708 -76.3795304096 -76.422567 0.000139 -76.435818 0.000763
|
||||
2.5 3847936 -76.16655117814619 -76.3834274230 -76.422184 0.000103 -76.435031 0.000546
|
||||
3.0 2000000 -76.15117119770653 -76.3898019841 -76.421932 0.000201 -76.435098 0.000539
|
||||
4.0 2000000 -76.13583094033078 -76.4016324447 -76.422268 0.000097 -76.433833 0.000530
|
||||
5.0 2000000 -76.12708615152579 -76.4093388884 -76.421901 0.000154 -76.434136 0.000370
|
||||
7.0 3468702 -76.11433599757845 -76.4159382168 -76.421721 0.000183 -76.434913 0.000523
|
||||
|
||||
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|
|
@ -0,0 +1,22 @@
|
|||
w(x) = 1./x
|
||||
w_lr(mu,x) = erf(mu*x)/x
|
||||
w_sr(mu,x) = w(x) - w_lr(mu,x)
|
||||
|
||||
set grid
|
||||
set xlabel "r_{12} (a.u.)"
|
||||
set xrange [0:4]
|
||||
set yrange [0:3]
|
||||
set format y "%.1f"
|
||||
set format x "%.1f"
|
||||
|
||||
set key top right
|
||||
plot w(x) title '1/r_{12}',\
|
||||
w_lr(0.5,x) title '{/Symbol m}=0.5' ls 2,\
|
||||
w_sr(0.5,x) notitle ls 2, \
|
||||
w_lr(1.0,x) title '{/Symbol m}=1.0' ls 4,\
|
||||
w_sr(1.0,x) notitle ls 4
|
||||
|
||||
set term pdf font "Times,16pt" linewidth 2.
|
||||
set out "rs-coulomb.pdf"
|
||||
replot
|
||||
set term cairo
|
||||
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Loading…
Reference in New Issue