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@pjknowles
Created June 16, 2023 09:24
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "1a33424a",
"metadata": {
"ExecuteTime": {
"end_time": "2023-06-15T22:23:22.694108Z",
"start_time": "2023-06-15T22:23:22.680788Z"
}
},
"outputs": [],
"source": [
"from sage.symbolic.integration.integral import definite_integral"
]
},
{
"cell_type": "markdown",
"id": "fd0330d7",
"metadata": {},
"source": [
"Make various densities with <1/r>=Z"
]
},
{
"cell_type": "code",
"execution_count": 244,
"outputs": [],
"source": [
"def normalised_gaussian(alpha):\n",
" return (2*alpha/pi)^(3/4)*exp(-alpha*r^2)\n",
"sto_scale=1/(.95909793)^2\n",
"sto_scale2=1/sqrt(2)\n",
"densities = {'exponential': pi ^ (-1) * (Z ^ 3 * exp(-2 * Z * r)),\n",
" # 'gaussian': pi ^ (-3 / 2) * ((Z ^ 2 * pi / 4)) ^ (3 / 2) * exp(-(Z ^ 2 * pi / 4) * r ^ 2),\n",
" 'STO-1G' : normalised_gaussian(Z^2*pi/8)^2,\n",
" # 'STO-2G' : (.678914*normalised_gaussian(Z*.151623*sto_scale)+.430129*normalised_gaussian(Z*.851819*sto_scale))^2,\n",
" 'STO-2G' : (.678914*normalised_gaussian(Z*.2331359749*sto_scale2)+.430129*normalised_gaussian(Z*1.309756366*sto_scale2))^2,\n",
" 'STO-3G' : (.15432897*normalised_gaussian(Z*3.4252409*sto_scale2)+.53532814*normalised_gaussian(Z*.62391373*sto_scale2)+.44463454*normalised_gaussian(Z*.1688554*sto_scale2))^2,\n",
" }"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T09:20:15.597199Z",
"start_time": "2023-06-16T09:20:15.587690Z"
}
}
},
{
"cell_type": "code",
"execution_count": 246,
"outputs": [
{
"data": {
"text/plain": "[[1,\n 1,\n 0.500000864255864*2^(1/4)*pi^(3/2)*(sqrt(2)*Z/pi)^(3/2)/Z^(3/2),\n 0.5000001098261299*pi^(3/2)*sqrt(sqrt(2)*Z)*(sqrt(2)*Z/pi)^(3/2)/Z^2],\n [3/2,\n 4/pi,\n 1.519385349211248*pi*(sqrt(2)*Z/pi)^(3/2)/Z,\n 1.516501435370285*pi*(sqrt(2)*Z/pi)^(3/2)/Z],\n [1,\n 1,\n 0.7452721612769007*sqrt(2)*pi*(sqrt(2)*Z/pi)^(3/2)/Z^2,\n 0.7686661654474823*sqrt(2)*pi*(sqrt(2)*Z/pi)^(3/2)/Z^2]]"
},
"execution_count": 246,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"[[definite_integral(4 * pi * r ^ 2 * r ^ power * d, r, 0, Infinity).simplify_full()*Z^power for d in densities.values()] for power in\n",
" [0, 1, -1]]"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T09:20:17.422583Z",
"start_time": "2023-06-16T09:20:16.943411Z"
}
}
},
{
"cell_type": "code",
"execution_count": 247,
"outputs": [
{
"data": {
"text/plain": "[[1.0, 1.0, 1.0000017285117282, 1.0000002196522597],\n [1.5, 1.2732395447351628, 1.4416687835206818, 1.4389323818823234],\n [1.0, 1.0, 1.0000632246093846, 1.0314550898405679]]"
},
"execution_count": 247,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"[[float((definite_integral(4 * pi * r ^ 2 * r ^ power * d, r, 0, Infinity).simplify_full()*Z^power).subs(Z=1)) for d in densities.values()] for power in\n",
" [0, 1, -1]]"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T09:20:18.929043Z",
"start_time": "2023-06-16T09:20:18.375065Z"
}
}
},
{
"cell_type": "code",
"execution_count": 248,
"outputs": [
{
"data": {
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\n",
"text/plain": "Graphics object consisting of 4 graphics primitives"
},
"execution_count": 248,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot([d.subs(Z=1) for d in densities.values()],(r,0,5),legend_label=list(densities.keys()))\n"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T09:22:59.821098Z",
"start_time": "2023-06-16T09:22:59.712072Z"
}
}
},
{
"cell_type": "code",
"execution_count": 249,
"outputs": [
{
"data": {
"text/plain": "{'exponential': Z^5*e^(-2*Z*r)/pi,\n 'STO-1G': 1/128*pi^2*Z^7*r^2*e^(-1/4*pi*Z^2*r^2),\n 'STO-2G': (-0.0531044639216583*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.116567987450000*sqrt(2)*Z*r^2) - 0.689734787859862*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.654878183000000*sqrt(2)*Z*r^2))^2,\n 'STO-3G': (-0.0197767246004288*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.0844277000000000*sqrt(2)*Z*r^2) - 0.234470399380275*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.311956865000000*sqrt(2)*Z*r^2) - 1.33093522612882*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-1.71262045000000*sqrt(2)*Z*r^2))^2}"
},
"execution_count": 249,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tau = { k: diff(sqrt(rho),r)^2 for k,rho in densities.items()}\n",
"tau"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T09:23:00.293690Z",
"start_time": "2023-06-16T09:23:00.283213Z"
}
}
},
{
"cell_type": "code",
"execution_count": 250,
"outputs": [
{
"data": {
"text/plain": "{'exponential': 3/10*6^(2/3)*pi^(2/3)*e^(-4/3*Z*r),\n 'STO-1G': 6/5*6^(2/3)*e^(-1/6*pi*Z^2*r^2)/(pi^(2/3)*Z^2*r^2),\n 'STO-2G': 3/10*6^(2/3)*pi^(4/3)*((0.227783223693540*(sqrt(2)*Z/pi)^(3/4)*e^(-0.116567987450000*sqrt(2)*Z*r^2) + 0.526613044811009*(sqrt(2)*Z/pi)^(3/4)*e^(-0.654878183000000*sqrt(2)*Z*r^2))^2)^(5/3)/(-0.0531044639216583*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.116567987450000*sqrt(2)*Z*r^2) - 0.689734787859862*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.654878183000000*sqrt(2)*Z*r^2))^2,\n 'STO-3G': 3/10*6^(2/3)*pi^(4/3)*((0.117122251348958*(sqrt(2)*Z/pi)^(3/4)*e^(-0.0844277000000000*sqrt(2)*Z*r^2) + 0.375805801517262*(sqrt(2)*Z/pi)^(3/4)*e^(-0.311956865000000*sqrt(2)*Z*r^2) + 0.388566896456486*(sqrt(2)*Z/pi)^(3/4)*e^(-1.71262045000000*sqrt(2)*Z*r^2))^2)^(5/3)/(-0.0197767246004288*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.0844277000000000*sqrt(2)*Z*r^2) - 0.234470399380275*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.311956865000000*sqrt(2)*Z*r^2) - 1.33093522612882*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-1.71262045000000*sqrt(2)*Z*r^2))^2}"
},
"execution_count": 250,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"t = { k: (3 / 10) * (6 * pi ^ 2) ^ (2 / 3) * densities[k] ^ (5 / 3) / tau[k] for k in densities.keys()}\n",
"t"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T09:23:11.838813Z",
"start_time": "2023-06-16T09:23:11.833756Z"
}
}
},
{
"cell_type": "code",
"execution_count": 251,
"outputs": [
{
"data": {
"text/plain": "{'exponential': (3*6^(2/3)*pi^(2/3)*e^(-4/3*Z*r) - 10)/(3*6^(2/3)*pi^(2/3)*e^(-4/3*Z*r) + 10),\n 'STO-1G': (6*6^(2/3)*e^(-1/6*pi*Z^2*r^2)/(pi^(2/3)*Z^2*r^2) - 5)/(6*6^(2/3)*e^(-1/6*pi*Z^2*r^2)/(pi^(2/3)*Z^2*r^2) + 5),\n 'STO-2G': (3*6^(2/3)*pi^(4/3)*((0.227783223693540*(sqrt(2)*Z/pi)^(3/4)*e^(-0.116567987450000*sqrt(2)*Z*r^2) + 0.526613044811009*(sqrt(2)*Z/pi)^(3/4)*e^(-0.654878183000000*sqrt(2)*Z*r^2))^2)^(5/3)/(-0.0531044639216583*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.116567987450000*sqrt(2)*Z*r^2) - 0.689734787859862*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.654878183000000*sqrt(2)*Z*r^2))^2 - 10)/(3*6^(2/3)*pi^(4/3)*((0.227783223693540*(sqrt(2)*Z/pi)^(3/4)*e^(-0.116567987450000*sqrt(2)*Z*r^2) + 0.526613044811009*(sqrt(2)*Z/pi)^(3/4)*e^(-0.654878183000000*sqrt(2)*Z*r^2))^2)^(5/3)/(-0.0531044639216583*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.116567987450000*sqrt(2)*Z*r^2) - 0.689734787859862*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.654878183000000*sqrt(2)*Z*r^2))^2 + 10),\n 'STO-3G': (3*6^(2/3)*pi^(4/3)*((0.117122251348958*(sqrt(2)*Z/pi)^(3/4)*e^(-0.0844277000000000*sqrt(2)*Z*r^2) + 0.375805801517262*(sqrt(2)*Z/pi)^(3/4)*e^(-0.311956865000000*sqrt(2)*Z*r^2) + 0.388566896456486*(sqrt(2)*Z/pi)^(3/4)*e^(-1.71262045000000*sqrt(2)*Z*r^2))^2)^(5/3)/(-0.0197767246004288*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.0844277000000000*sqrt(2)*Z*r^2) - 0.234470399380275*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.311956865000000*sqrt(2)*Z*r^2) - 1.33093522612882*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-1.71262045000000*sqrt(2)*Z*r^2))^2 - 10)/(3*6^(2/3)*pi^(4/3)*((0.117122251348958*(sqrt(2)*Z/pi)^(3/4)*e^(-0.0844277000000000*sqrt(2)*Z*r^2) + 0.375805801517262*(sqrt(2)*Z/pi)^(3/4)*e^(-0.311956865000000*sqrt(2)*Z*r^2) + 0.388566896456486*(sqrt(2)*Z/pi)^(3/4)*e^(-1.71262045000000*sqrt(2)*Z*r^2))^2)^(5/3)/(-0.0197767246004288*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.0844277000000000*sqrt(2)*Z*r^2) - 0.234470399380275*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-0.311956865000000*sqrt(2)*Z*r^2) - 1.33093522612882*sqrt(2)*Z*r*(sqrt(2)*Z/pi)^(3/4)*e^(-1.71262045000000*sqrt(2)*Z*r^2))^2 + 10)}"
},
"execution_count": 251,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"w = { k: (tt-1)/(tt+1) for k,tt in t.items()}\n",
"w"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T09:23:13.208339Z",
"start_time": "2023-06-16T09:23:13.203233Z"
}
}
},
{
"cell_type": "code",
"execution_count": 252,
"outputs": [
{
"data": {
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\n",
"text/plain": "Graphics object consisting of 4 graphics primitives"
},
"execution_count": 252,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot([ww.subs(Z=1) for ww in w.values()],(r,0,3),legend_label=list(w.keys()))"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T09:23:13.788133Z",
"start_time": "2023-06-16T09:23:13.665023Z"
}
}
},
{
"cell_type": "code",
"execution_count": 253,
"outputs": [],
"source": [
"def ff(w):\n",
" return .5877943 - .1371776 * w + .2682367 * w ^ 2 - 2.515898 * w ^ 3 - 2.978892 * w ^ 4 + 8.710679 * w ^ 5 + 16.88195 * w ^ 6 - 4.489724 * w ^ 7 - 32.99983 * w ^ 8 - 14.49050 * w ^ 9 + 20.43747 * w ^ 10 + 12.56504 * w ^ 11"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T09:23:19.319502Z",
"start_time": "2023-06-16T09:23:19.310792Z"
}
}
},
{
"cell_type": "code",
"execution_count": 254,
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": "Graphics object consisting of 4 graphics primitives"
},
"execution_count": 254,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot([ff(ww.subs(Z=1)) for ww in w.values()],(r,0,5),legend_label=list(w.keys()))"
],
"metadata": {
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T09:23:22.731396Z",
"start_time": "2023-06-16T09:23:22.472357Z"
}
}
},
{
"cell_type": "code",
"execution_count": null,
"outputs": [],
"source": [],
"metadata": {
"collapsed": false
}
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath 10.0",
"language": "sage",
"name": "sagemath-10.0"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.1"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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