Huckel.ipynb

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      "/home/romuald/ENSEIGNEMENT/0-JupyterNotebooks/pyPhysChem\n"
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      "text/markdown": [
       "**Start at:** Wednesday 05 April 2023, 12:30:16  \n",
       "**Hostname:** insa-12842 (Linux)"
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      "text/markdown": [
       "<p style=\"text-align: center\"><img width=\"800px\" src=\"./config/svg/pyPhysChemBanner.svg\" style=\"margin-left:auto; margin-right:auto\"/></p>"
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   "source": [
    "import os\n",
    "import sys\n",
    "\n",
    "print(os.getcwd())\n",
    "cwd0 = './config/'\n",
    "sys.path.append(cwd0)\n",
    "\n",
    "import visualID_Eng as vID\n",
    "from visualID_Eng import color\n",
    "vID.init(cwd0)\n",
    "import tools4pyPhysChem as t4pPC"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1f28f04-e5bf-45f6-b0a5-3ec11c1b11af",
   "metadata": {},
   "source": [
    "# The Hückel method"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65a806c4-a869-4a73-b162-278f9f0854c9",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Ethylene"
   ]
  },
  {
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   "execution_count": 2,
   "id": "91f8ab2d-4d3c-4d3e-a549-2d038a8dc2e7",
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     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}a & b\\\\b & a\\end{matrix}\\right]$"
      ],
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       "<IPython.core.display.Math object>"
      ]
     },
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   "source": [
    "import sympy as sym\n",
    "from tools4pyPhysChem import PrintLatexStyleSymPyEquation as ple\n",
    "a = sym.Symbol('a')\n",
    "b = sym.Symbol('b', negative=True)\n",
    "H = sym.Matrix([[a, b],\n",
    "                [b, a]\n",
    "               ])\n",
    "ple(H)"
   ]
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   "cell_type": "code",
   "execution_count": 3,
   "id": "fa8db71f-6401-4979-adb1-21000050db8d",
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    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[ \\left( a - b, \\  1, \\  \\left[ \\left[\\begin{matrix}-1\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( a + b, \\  1, \\  \\left[ \\left[\\begin{matrix}1\\\\1\\end{matrix}\\right]\\right]\\right)\\right]$"
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     "text": [
      "a - b\n",
      "a + b\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[ a - b, \\  a + b\\right]$"
      ],
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     "data": {
      "text/latex": [
       "$\\displaystyle \\left[ \\left[\\begin{matrix}- \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2}\\end{matrix}\\right]\\right]$"
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   "source": [
    "MO = H.eigenvects()\n",
    "# list of tuples\n",
    "ple(MO)\n",
    "\n",
    "eps = list()\n",
    "phi = list()\n",
    "for mo in MO:\n",
    "    print(mo[0])\n",
    "    eps.extend(mo[0] for i in range(mo[1]))\n",
    "    for eigvc in mo[2]:\n",
    "        phi.append(eigvc.normalized())\n",
    "ple(eps)\n",
    "ple(phi)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "029fdfcd-37d5-4fe2-9fdd-b9ec210e5fec",
   "metadata": {},
   "source": [
    "## Formaldehyde"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7e8c9f22-8a6f-4a84-9041-38b3b86a85de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}a & b\\\\b & a + b\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
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   "source": [
    "import sympy as sym\n",
    "from tools4pyPhysChem import PrintLatexStyleSymPyEquation as ple\n",
    "a = sym.Symbol('a')\n",
    "b = sym.Symbol('b', negative=True)\n",
    "H = sym.Matrix([[a, b],\n",
    "                [b, a+b],\n",
    "               ])\n",
    "ple(H)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 5,
   "id": "1a6578fe-2e06-4e69-94cb-1ea133a1cc9a",
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    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[ \\left( a + \\frac{b}{2} + \\frac{\\sqrt{5} b}{2}, \\  1, \\  \\left[ \\left[\\begin{matrix}\\frac{- a - b}{b} + \\frac{a + \\frac{b}{2} + \\frac{\\sqrt{5} b}{2}}{b}\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( a - \\frac{\\sqrt{5} b}{2} + \\frac{b}{2}, \\  1, \\  \\left[ \\left[\\begin{matrix}\\frac{- a - b}{b} + \\frac{a - \\frac{\\sqrt{5} b}{2} + \\frac{b}{2}}{b}\\\\1\\end{matrix}\\right]\\right]\\right)\\right]$"
      ],
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       "<IPython.core.display.Math object>"
      ]
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     "text": [
      "a + b/2 + sqrt(5)*b/2\n",
      "a - sqrt(5)*b/2 + b/2\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[ a + \\frac{b}{2} + \\frac{\\sqrt{5} b}{2}, \\  a - \\frac{\\sqrt{5} b}{2} + \\frac{b}{2}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
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     "data": {
      "text/latex": [
       "$\\displaystyle \\left[ \\left[\\begin{matrix}\\frac{\\frac{- a - b}{b} + \\frac{a + \\frac{b}{2} + \\frac{\\sqrt{5} b}{2}}{b}}{\\sqrt{\\left|{\\frac{a + b}{b} - \\frac{a + \\frac{b}{2} + \\frac{\\sqrt{5} b}{2}}{b}}\\right|^{2} + 1}}\\\\\\frac{1}{\\sqrt{\\left|{\\frac{a + b}{b} - \\frac{a + \\frac{b}{2} + \\frac{\\sqrt{5} b}{2}}{b}}\\right|^{2} + 1}}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\frac{- a - b}{b} + \\frac{a - \\frac{\\sqrt{5} b}{2} + \\frac{b}{2}}{b}}{\\sqrt{\\left|{\\frac{a + b}{b} - \\frac{a - \\frac{\\sqrt{5} b}{2} + \\frac{b}{2}}{b}}\\right|^{2} + 1}}\\\\\\frac{1}{\\sqrt{\\left|{\\frac{a + b}{b} - \\frac{a - \\frac{\\sqrt{5} b}{2} + \\frac{b}{2}}{b}}\\right|^{2} + 1}}\\end{matrix}\\right]\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
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   "source": [
    "MO = H.eigenvects()\n",
    "# list of tuples\n",
    "ple(MO)\n",
    "\n",
    "eps = list()\n",
    "phi = list()\n",
    "for mo in MO:\n",
    "    print(mo[0])\n",
    "    eps.extend(mo[0] for i in range(mo[1]))\n",
    "    for eigvc in mo[2]:\n",
    "        phi.append(eigvc.normalized())\n",
    "ple(eps)\n",
    "ple(phi)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc1843ce-b1ca-4040-9a45-ad242b36a407",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Cyclobutadiene"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f62c919f-9f0b-4b26-b737-8aa82a4d7380",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}a & b & 0 & b\\\\b & a & b & 0\\\\0 & b & a & b\\\\b & 0 & b & a\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
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   ],
   "source": [
    "import sympy as sym\n",
    "from tools4pyPhysChem import PrintLatexStyleSymPyEquation as ple\n",
    "a = sym.Symbol('a')\n",
    "b = sym.Symbol('b', negative=True)\n",
    "H = sym.Matrix([[a, b, 0, b],\n",
    "                [b, a, b, 0],\n",
    "                [0, b, a, b],\n",
    "                [b, 0, b, a],\n",
    "               ])\n",
    "ple(H)"
   ]
  },
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   "execution_count": 7,
   "id": "4c2bc581-fc2a-4f98-8542-4ee69a11c0e9",
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     "data": {
      "text/latex": [
       "$\\displaystyle \\left[ \\left( a, \\  2, \\  \\left[ \\left[\\begin{matrix}-1\\\\0\\\\1\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\-1\\\\0\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( a - 2 b, \\  1, \\  \\left[ \\left[\\begin{matrix}-1\\\\1\\\\-1\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( a + 2 b, \\  1, \\  \\left[ \\left[\\begin{matrix}1\\\\1\\\\1\\\\1\\end{matrix}\\right]\\right]\\right)\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a\n",
      "a - 2*b\n",
      "a + 2*b\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[ a, \\  a, \\  a - 2 b, \\  a + 2 b\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
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     "data": {
      "text/latex": [
       "$\\displaystyle \\left[ \\left[\\begin{matrix}- \\frac{\\sqrt{2}}{2}\\\\0\\\\\\frac{\\sqrt{2}}{2}\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\- \\frac{\\sqrt{2}}{2}\\\\0\\\\\\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}- \\frac{1}{2}\\\\\\frac{1}{2}\\\\- \\frac{1}{2}\\\\\\frac{1}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{1}{2}\\\\\\frac{1}{2}\\\\\\frac{1}{2}\\\\\\frac{1}{2}\\end{matrix}\\right]\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
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   "source": [
    "MO = H.eigenvects()\n",
    "# list of tuples\n",
    "ple(MO)\n",
    "\n",
    "eps = list()\n",
    "phi = list()\n",
    "for mo in MO:\n",
    "    print(mo[0])\n",
    "    eps.extend(mo[0] for i in range(mo[1]))\n",
    "    for eigvc in mo[2]:\n",
    "        phi.append(eigvc.normalized())\n",
    "ple(eps)\n",
    "ple(phi)"
   ]
  },
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   "execution_count": 8,
   "id": "d00285a4-2212-4c00-ba16-6802399663a2",
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    {
     "data": {
      "text/markdown": [
       "**End at:** Monday 21 November 2022, 16:43:08  \n",
       "**Duration:** 00:00:07 776ms"
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       "<p style=\"text-align: center\"><img width=\"800px\" src=\"./config/svg/logoEnd.svg\" style=\"margin-left:auto; margin-right:auto\"/></p>"
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    "vID.end(cwd0)"
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