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Last active December 19, 2023 09:52
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GTO.ipynb
{
"cells": [
{
"cell_type": "markdown",
"id": "f7319733",
"metadata": {},
"source": [
"# ガウス型軌道の形と軌道指数の関係\n",
"\n",
"量子化学で用いられる1sガウス型軌道の形と軌道指数の関係を可視化します. [A.ザボ, N.S.オストランド著, 大野公男, 阪井健男, 望月祐志訳『新しい量子化学 上　電子構造の理論入門』(東京大学出版会, 1987)](http://www.utp.or.jp/book/b302128.html)の第3章より\n",
"\n",
"$$\n",
"\\phi_\\mathrm{1s}^{\\mathrm{GF}}\\left(\\alpha, \\boldsymbol{r}-\\boldsymbol{R}_A\\right)\n",
"= \\left(\\frac{2 \\alpha}{\\pi}\\right)^{3 / 4} \\mathrm{e}^{-\\alpha\\left|\\boldsymbol{r}-\\boldsymbol{R}_A\\right|^2} \\tag{3.203}\n",
"$$\n",
"\n",
"の$\\alpha$を変えていきましょう. 原点を中心として次のように関数を実装できます."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "0a2f7db5",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"φ (generic function with 1 method)"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"φ(r;α=1.0) = (2*α/π)^(3/4) * exp(-α*r^2)"
]
},
{
"cell_type": "markdown",
"id": "172bfc1e",
"metadata": {},
"source": [
"数値積分で規格化条件$\\int 4\\pi r^2 |\\phi(r)|^2 \\mathrm{d}r=1$を確認しておきましょう. 積分には[QuadGK.jl](https://juliamath.github.io/QuadGK.jl/stable/)を用います. `using Pkg; Pkg.add(\"QuadGK\") `でインストールした後に, 次のように積分を計算できます."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "573f995c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"α = 1.0,\t∫4πr²|φ(r)|²dr = 1.0000000000000138\n",
"α = 2.0,\t∫4πr²|φ(r)|²dr = 1.0000000000000002\n",
"α = 3.0,\t∫4πr²|φ(r)|²dr = 0.9999999999999999\n",
"α = 10.0,\t∫4πr²|φ(r)|²dr = 0.9999999999996987\n"
]
}
],
"source": [
"using QuadGK\n",
"println(\"α = 1.0,\\t∫4πr²|φ(r)|²dr = \", quadgk(r -> 4π*r^2*φ(r;α=1.0)^2, 0, Inf)[1])\n",
"println(\"α = 2.0,\\t∫4πr²|φ(r)|²dr = \", quadgk(r -> 4π*r^2*φ(r;α=2.0)^2, 0, Inf)[1])\n",
"println(\"α = 3.0,\\t∫4πr²|φ(r)|²dr = \", quadgk(r -> 4π*r^2*φ(r;α=3.0)^2, 0, Inf)[1])\n",
"println(\"α = 10.0,\\t∫4πr²|φ(r)|²dr = \", quadgk(r -> 4π*r^2*φ(r;α=10.0)^2, 0, Inf)[1])"
]
},
{
"cell_type": "markdown",
"id": "885ff39c",
"metadata": {},
"source": [
"正しく規格化されていますね. 次に, 可視化に使用するため[Plots.jl](https://docs.juliaplots.org/)をインストールしておきましょう. `using Pkg; Pkg.add(\"Plots\") `でインストールできます. これを使って軌道を可視化できます."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "cc42bdf0",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Plots\n",
"plot(xlabel=\"\\$r\\$\", ylabel=\"\\$\\\\phi(r)\\$\", xlim=(0,3))\n",
"plot!(r -> φ(r,α=1.0), label=\"\\$\\\\alpha=1.0\\$\")\n",
"plot!(r -> φ(r,α=2.0), label=\"\\$\\\\alpha=2.0\\$\")\n",
"plot!(r -> φ(r,α=3.0), label=\"\\$\\\\alpha=3.0\\$\")\n",
"plot!(r -> φ(r,α=10.0), label=\"\\$\\\\alpha=10.0\\$\")"
]
},
{
"cell_type": "markdown",
"id": "5164ecc0",
"metadata": {},
"source": [
"このように, 軌道指数$\\alpha$が大きいほどガウス型軌道は縮んでいる. 逆に, 軌道指数が小さいほど軌道指数は拡がっていることが確認できました."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.9.2",
"language": "julia",
"name": "julia-1.9"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.9.2"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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