{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### Hydgrogen LDA with Plotted Potentials" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " iter Total Energy HOMO Eigenvalue Res \n", "\n", "----------------------------------------------------------- \n", "\n", " 1 -0.48889 -2.11156e-01 +1.00000e+00\n", " 2 -0.46283 -2.24647e-01 +5.63131e-02\n", " 3 -0.45241 -2.29956e-01 +2.30263e-02\n", " 4 -0.44831 -2.32059e-01 +9.15620e-03\n", " 5 -0.44670 -2.32896e-01 +3.60898e-03\n", " 6 -0.44607 -2.33231e-01 +1.41144e-03\n", " 7 -0.44582 -2.33365e-01 +5.50624e-04\n", " 8 -0.44573 -2.33419e-01 +2.13114e-04\n", " 9 -0.44569 -2.33441e-01 +8.16976e-05\n", " 10 -0.44567 -2.33450e-01 +3.09185e-05\n", " 11 -0.44567 -2.33453e-01 +1.14897e-05\n", " 12 -0.44567 -2.33455e-01 +4.15571e-06\n", " Total Energy: -0.4456678603283697\n" ] } ], "source": [ "import numpy as np\n", "from CADMium import Psgrid\n", "from CADMium import Kohnsham\n", "\n", "#Distance of the nucley from grid center\n", "a = 1.0\n", "\n", "#Nuclear charges on centers AB\n", "Za = 1\n", "Zb = 0\n", "\n", "#Set polaization. 1 Unpolarized, 2 Polarized\n", "pol = 1\n", "\n", "Nmo = [[1]]\n", "N = [[1]]\n", "\n", "optKS = {\n", " \"interaction_type\" : \"dft\",\n", " \"SYM\" : False,\n", " \"FRACTIONAL\" : True,\n", " }\n", "\n", "#Grid Options\n", "NP = 7 #Number of points per block\n", "NM = [4,4] #Number of blocks [angular, radial]\n", "L = np.arccosh(15./a) #Maximum radial coordinate value\n", "loc = np.array(range(-4,5)) #Non inclusive on upper bound\n", "\n", "#Create and initialize grid object\n", "grid = Psgrid(NP, NM, a, L, loc)\n", "grid.initialize()\n", "\n", "#Kohn Sham object\n", "KS = Kohnsham(grid, Za, Zb, pol, Nmo, N, optKS)\n", "KS.scf()\n", "\n", "print(f\" Total Energy: {KS.E.E}\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "#Visualize components\n", "import matplotlib.pyplot as plt\n", "\n", "vext,x,y = grid.plotter(KS.vext)\n", "vh,_,_ = grid.plotter(KS.V.vh)\n", "vxc,_,_ = grid.plotter(KS.V.vx + KS.V.vc)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(6,5))\n", "\n", "plt.xlim(-5,5)\n", "plt.ylim(-5,5)\n", "\n", "plt.title(\"$v_{xc}(r)$\")\n", "\n", "plt.contourf(x,y,vxc, \n", " levels=50,\n", " cmap=\"Greys\",\n", " antialiased = False,\n", " linestyles = \"dotted\",\n", " )\n", "\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(6,5))\n", "\n", "plt.xlim(-5,5)\n", "plt.ylim(-5,5)\n", "\n", "plt.title(\"$v_{xc}(r)$\")\n", "\n", "plt.contourf(x,y,vxc, \n", " levels=50,\n", " cmap=\"Greys\",\n", " antialiased = False,\n", " linestyles = \"dotted\",\n", " )\n", "\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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XHireOUxXiyXw1TlwEfTcI5Q5xdyVdXbl675Ef3Yhjz2fNlcRTyngOYi3C81+ugqRj0vPOUKZS8xTRSzldrf5MOuCoNgCFEtUfRYCuZRxKXfo0CEvEa8WlSxFxNuovwbX1+F6nmK/hy7EbCv2+5rDAp3Ud2vcZGZ35C7EnCvuIuIxjpXCgY/9cE+1IjR0cM/nBxZcYxcX5x2rTFUuljN3IUVeXlz58phNyGNGKksU8ZQCPvcS/q7j+/5cGgyLuo+gTyXCscosJS9P/YMYhWGyvvvhOop4KgGfW7xdCFl67+rSXQQ9N6F2Yc68fJ0oP76cMVOJeIzjpBDwmOIdGtuEOkFfUfcR9CExHzrmVGIee/DTlbkjlk29mKQk27M5JCw5iXgsF57ivjG+7cdq00d4fETdRdBjuPMlinnJqzeXLIU8luAsQcRTiffcs1naju8iMq6Diq6CPsadT+Xe5xj8LK58vVjkmYwhsKlFfGoBn1u4XfAZxPQR9LndeQwhjjn4Wdg8shPyGJFKahFP7cKnmGsce3DUV8hcRd0ldonlzlOK+ZQzWYorfzbbtm2Ldr/8HMlKyGO4yjlFfAoBz3UqYttxYk83HHLpQ4K+BDGPRXHvm0XWP/XWZG6nnUrEXVYh+qx+rNqbe0pivR+u/XF5nS7nqouhlaGxZjClbD9mjOY6T9tnPrdP/8o88Thk48hjxQ2hpBLxlKLk006MYzQJcXyuM1SG3HVKdz7GWeeUl881bbEwPVm8K3NHKqF1x7rw0Lqubfi258vYqYcx8m8XQc9NzKdcUORCCoEu0c60LCJaSRmJ5CbirtGCaxQzx421msd2vSiNOS9DdbsYillC/3ZSRzTgdnF2fe9TRCyulHhlPLM78rHRwxwi3kfo65ljIDS0jRCnNcWAZl/dvnpDg6B9pHTmuUYsS0TSWp+DWYU8dS6eSsS7XFyIY5wqQ/ctO6YdF2EZKjsmMukTwK56Y2KWPnKayTJE7OmIuU5FXEcWEa10ESr0SxDxsVFDvczU8YrPcV0ik77z11V3qF4bobNZUg7Ex/omtoQFY4Vwsr2NbeqphCH1fEU8JLcd48DHflhdz1mKxT9DZYZiE1933ufMoX0laGiMsqT557GdcXHl05DlbWznilSmEPEU8YuPgMdwj31tuN4jBYZFvUvQfTNwXzGH7qgllZiPZeqsvIhuXizynUjhtucU8RABn2J+eQhtxxsauIR2Ae4S5xB3nruYF1ee5tgVkrIZi0hBdhn5HJFKahHvynJDclzXTDlkiqLvwxWX/vS12Xf+usp39cOnfB8pLpBj/7anzsrLtEGQdL6k+yTtl3Rly/6flHTn6vE5Sa9o7N8u6U8k3VzbdpWkhyTdsXpcONSPRTryLmIPSMUScZ/+9IlZF66vLfaAV8iCoKFFQH0RSZuz63LnfW7eNzP3nc0yZ8RSmA5J24FrgTcAB4B9kvaY2T21Yn8OvMbMvinpAuAG4FW1/e8E7gVOajR/jZl90LUvox25pDMk/ZGkeyXdLemdoW3NMYDpu+BnrIj7uvDQmRn1urnOWgmZkRLDnceczdLFXAuJYrny2AuE1nTWzHnAfjO738wOAx8HLqoXMLPPmdk3V0+/AJxe7ZN0OvCjwIfHdiSGIz8KvMvMbpd0InCbpM80rkqjCf0Dz03Efdr1aWOordByrvS58BQzUnzdeSpnnsJ9b7prX9BA6k7gwdrzAzzTbTf5GeBTtee/BrwHOLGl7G5JbwVuZUtfv9lS5mlGO3Ize8TMbl/9/wm2vibs9G1nTOYYMxfPQcR9XWdfnfq+lO7ctf2+Ml0Ovc+dt5Hqwtr1txF7XGZs3alduStzuvJqZafPAzhF0q21x2XNZlsO1TolT9Jr2RLyX1g9fyPwdTO7raX4dcCLgXOAR4APDb2+qJc9SS8Cfgj4Ysx2Uy38cSWFYMRw4TFmtYSW91m92VXed1ZKm1v2ycJTOvMucp2uGJMFOWhfHjOzc3v2HwDOqD0/HXi4WUjS2WzFJxeY2V+tNr8aeNNqIPN44CRJHzWzt5jZo7W6NwI3N9tsEm3WiqTvBn4XuMLMDrbsv6y6sj3++OPP2JfCncSKVKYS8TbX6etQh/bV94916L7t9JXxceg+7jyVM28j9kD7mOPB8ld7LmRGzD7gLElnStoBXALsqReQ9ALgE8ClZvaVaruZvdfMTjezF63q/b9m9pZVndNqTVwM3DXUkShCLulYtkT8Y2b2ibYyZnaDmZ1rZud+z/d8j3PbsT8guYq4a90+IRzaN8UH1+V4MQYypxLzNqaKWKZeA9BGGfTsxsyOAruBW9iKlH/bzO6WdLmky1fFfhF4HvAbq6mEtzo0/QFJX5Z0J/Ba4OeHKoz+PiRJwEeAe83sV33rT+lWYhwrtYj7ZumuZceUcyFk6X1XLOI6kNkVtcSMWWINfqaISoba7Op7IR5mthfY29h2fe3/bwfePtDGZ4HP1p5f6tuPGI781cClwD/wmcDuQohbiTVfPLa7CxXxNpfq62jr+1K589hO3NWdd9Udqje2XEzmdOVzDHq6spB4JQtGO3Iz+0+0j94OMuVXx7GRytQi7uq2Ywx4hr4PLj/VBn5OvLm9bZuLc57Cmcd05ammKk7pylPc3jYW5X7kMxHTjftONQzFRcRdXeZQOz7b+vo3hq72ulZZwrBIV9uHtrlELWPjExfG/CiFK6lnsLi8/jWembIWzPbO5DCQ00aoyw4R41Dh9xFwn/PsGyEM/SgEuC2d99k2JMyhYt72GsYIfk5Z+ZIp8Yob2d00C+KO/k8Rqbj010X4h0TcN0vuGziNkZm71K/64fp6Q87B0EU09FuQa0wWaxZLqqx8ypkiRXjnIcv7kfeRysmPnZLW11YM9x46oNdVto8uYRqKEJrHcZ150izb5qqHyoQ487b+h7h38ItYcnTlU+fWc+Tk60x2oddcbtyVsW7Qt3zMGRl1Qs5BX502EevKxl0E3VXgx4h5aHwSI2IJKT9GrGMI55Jz8nUf7MwyWulibjeem4j7rHw8dOjQMx5DPPXUU894DDHUflckkuKcjCnfxtiIxbXNQiGUrC6vubjxWIObPuVjCxYMv1YXgXYte9xxx3Ueu+7W25y2r5NO7cxjf+2P6cpT1KuI9bpznoa4rizGkU/pxlO36yPaTSfr4mK7XLGvy67XcS3XVratP0Ovq7l/7IXOF5f25nDlcw96lsHMPMnKkfuSqxvvK+8r4j7H7RLvLmI58qYbr5et72v7hXofd9yWo7sOaIbk5U3GON6pXHlhM8lGyOdYpuziUKYS8THtuAq4j3D70CXc9X19gt4U6OZgaJ8I9+2bImJpK5N6BkuqAVGYPl6ZinUf7MznTHsylRvvY8zXe1cR93XhvgIeQ9zrIt1sr9rXJeiu7jyVmPsypStPQW6zV0pOHofFZOSxieHG++gTYNf8vK+NZu7clk/3bfPJyYfoa6+5vfm8+TpifaPpaqPJ2EHsrjIxsvLQb6JlRszmkYUjjxWr5OTGu/a5ipFrlNIm1E1SOnLXfLzpyJvP6+68LWrpcuZ1+ly6q7sfarfZ1lyk7MO6xivrzCIdeewZCS5lQl3dnCI+hSPva69rW9fzPnc+9pw2CXXwPu21GYiYy/ZDSTVTqzAfa3+5nMKNd7UV4tK76vdl4WNceSpH7uPGn3rqqc7svCvv7nPfdfry8q5ybWVTu/IcXL4PxW3nxezvROpYpUlqN+5SboyI94m2q4DHnL0yNLjZtq1NwIeiFh8xd40GYg+0uc5giSXaKWevTMkUA56SFnM+QlhctOIj7jHcuM/gl8vX/676sUW8a5CxTcSrxTi+jzZcIpa+wc9m1FLhG7O4XCyb+A58xo49Yg96jqHEL8ticUI+htAZCDHKutZ3EXFfYWwKq4sgu9DXzlA+PvQaKlzEPKTfbW22PV9XpnqdZSXoNMwq5FPHKr71UrpxH1EKcbN9At7kyJH2+5MPPZq4CLqrgLuIeds2329CQ8T4G4kx6Ol6/BTHKOTP2jrykNu0+sxy8HX3obm4q+j1xSxtAtsnyK50tdEl6F3PXf7fRqyL55TfwoZYkvjGdNub8k0oFbMPdvow5o885h+K63TDIVxnqECY8IV+o3DB5Xc5m0vthwY7+/7vMvg5hpDBUpe2YjHH4OUUg5BTse5L9Gdz5EuLVVzKhX7FH8rFU4n4mJy8r27TpTfL+b6e6v+xI5aQ97jt2C7tpIxXQikueDySzpd0n6T9kq5s2f+Tku5cPT4n6RW1fTdJ+rqkuxp1rpL0kKQ7Vo8Lh/qxltFK6lglBm0f4hgi3hTNLlH1EbGh8l1l2o7t81raopUhQYz1Xi1J5HLPydd1wFPSduBa4AJgF/BmSbsaxf4ceI2ZnQ1cDdxQ2/d/AOd3NH+NmZ2zeuwd6stihDzHWCW2G68YmvvdJ+L1dl2do+sUQ5cpiF2C3tYHHwFv2zbkrmNm5b5/f2P+5nIQ34IT5wH7zex+MzsMfBy4qF7AzD5nZt9cPf0CcHpt3x8D34jRkeyEfI5YJdX8YJ+v9H25eIiI1xkS5TH0iX6drqhl6LWNjVhSESte8SFHgd/wAc+dwIO15wdW27r4GeBTjm3vXsUxN0k6eahwdkI+lrEflia+U9iGyrQJ7lCk0tzX/H+XiPcJeF//XNz50GtrO1aX+IW4cdfM2Xc6Yowpiz7kKM7rSDXY6fMATpF0a+1xWbPZlkNZx/Ffy5aQ/4JDd68DXgycAzwCfGiowiyzVsxaX2snucQqdXxy2ViRStu2PhHv6m+T0EE/ePbsleZMlWpbfVk98KwZBG0zVYa2VbTNrvCZceE6I8R35siUsz5CZ7UM9XGdZq4E8JiZnduz/wBwRu356cDDzUKSzgY+DFxgZn81dFAze7RW90bg5qE6i3XkU8QqY+dYDx0b/H/dJ6aIx4xWhrZ3nfeuzNxlW4gr98VnEDymuy5OfRHsA86SdKakHcAlwJ56AUkvAD4BXGpmX3FpVNJptacXA3d1la1YrJBPTYxYpa9cXybcdX+UtvaGRDxWNt7Wny5B7+pL23bXaKmJ67ee2AuEfJkjJy8XhTSY2VFgN3ALcC/w22Z2t6TLJV2+KvaLwPOA31hNJby1qi/pt4DPAz8g6YCkn1nt+oCkL0u6E3gt8PNDfVnUgqAhYufjXYyNVSr6+jt25saQqKZiKFppxix9C3v64pS2hUJtx6uIFRGERhhTt5kb63rb29XUwL2NbdfX/v924O0ddd/csf1S335k5chjC43vV9+pY5UKFxfaFqm4iriPA/cd4Oxrp+v50LeJPuft68rHlIvR1gJnYnizrvPEl8T6XSI9iPnB9/1q7+LGhyKVvm0u+4bKNl11G31Osuk0XZx5RdONt7nyir5frQ8dzAtdsr9Ed70JA5rlfuQzk1u+N+TafR3Y0I2h6mVcvjG4ZNJD9Xxwmc7Y9Tw0/um70PW14zM1NAd8+5Oq/5vwrWLpZC/kS8BVIPrKuYhT2/G6hNFlrnhf2T73smPHjs5ph13HG8JlANj33MQo18ZYwZxqLKewOSxSyHNzTm2EDnJW+LrOWHPB20S6vn0oSnGZmRJzULZvKmLFEhxl6m9PS/jMFMJZpJC3EXNa11QffB+n6eLqm2X7tjcFeUikYzAk4D7fWHzO2RBjp5Yu4UKxFMq5DCMbIZ/aMYz9Cu6aj/sIcKhIhebiY+n74V8f+ly5y7loMkZ0U1zQizjNT+AS/cWQjZDHJsWquxht+HxzaBvkDKXPjQ/hm5c3j9e1PdYqTJd4ZUpKjFGYmrUV8tyJ5TR9V072Uc/Bm5n4UPTiI+Zj+gh+31wq5rpLYqEwBVkL+RKczViBSJn9ttElxl2ZuY+gu4q5z+waCBNul/bHsIS/zdwoC4fSkbWQt7EpHyCXWCVGNt4m0l2i7ePQxzCHU87VnS/l772I9LysxcrOXGesxPwQhvbLNRuvC3Sd5qBPtXKxfk+V5jHaFgGluE1sH32rFXNYydi3GnUMS1xZOgXbtm1b6/OyOEc+JT53x5tqelrMi0NTvKt/q1H7E044gR07dnDCCSc8va1L8H2JPdMm5oBnV39yde0xWOfXtgkUIZ+QSmRCst6xtGXgzX/r4n3iiSdy3HHHPf2oopQ2Me9qOyZdYwmpz+WUAreUGKWQH2sRrSyVuQfxmiJePa8LeNW/6sZVzT60RSlVm2P6WMUfJSooFIaJ4sglnS/pPkn7JV0Zo81NpCnsY5bd99EcwKz+rcT7pJNO4qSTTnrG86Y7rwt/s81cSemuSzRRmJPRjlzSduBa4A1s/YbdPkl7zOyesW0XpqE+8FcX7fpg3OOPPw6ERxlzDHgWCptCjGjlPGC/md0PIOnjwEVAEfKMaYplPUo57rjjOPHEEznhhBMA+Ou//utn7INnz4Yp+W4hZ6ol+utKjGhlJ/Bg7fmB1bbCAqmceBWfPOc5z+GEE07gxBNPfHo/LCNKcaFEIoV1IIaQq2WbPauQdJmkWyXdevDgwQiHLUzBkSNHnn4UCoU8iSHkB4Azas9PBx5uFjKzG8zsXDM796STTopw2EJM6gOthw4d4vDhwzz55JM8+eSTHD58mEOHDvHUU089/ViXKGWdv24XNocYGfk+4CxJZwIPAZcAPxGh3UJC2gYVm9MMq8HOSsSrMm1tDbEuUUyhkCOjhdzMjkraDdwCbAduMrO7R/esMBn12OTgwYNPD3w2xfvgwYPJ3XgR/EIKJCW5JUIuRJlHbmZ7zewlZvZiM/ulGG1uEs0ZIb4Dir7i1/ejFPX45ODBg0+Ld/VvxZEjR57x026xxT1F5JEyRikRzWYytIZG0kslfV7SU5Le3dj385LulnSXpN+SdPxq+1WSHpJ0x+px4VA/yhL9GWgKdggxnGtdhCtXXol5Jdz1/1fCXYm4S9tjKQ69kCu1NTQXALuAN0va1Sj2DeDngA826u5cbT/XzF7GVppxSa3INWZ2zuqxd6gvRcgdiSEoMb7ahfaj7Y6EzX+r2SmVYD/xxBM88cQTzxDwuoh3ufExK0276PrWEuOi2MeUTrtctBbH02tozOwwUK2heRoz+7qZ7QPapn0dA3yXpGOA59AyScSVIuQN6h/crg9x2/a+D3yuX7vbBLku2M1HV50h2gQqlWilvFjm+j7GYJ1fW0KC19CY2UNsufSvAo8Aj5vZp2tFdku6U9JNkk4eam8thHzshzeVqMRsd+iD5vKrPX2/1tPMu7sezTpd7YUw1fnKQbRSDbwVV99OdT9ynwdwSrX2ZfW4rNGs0xqaNlbifBFwJvDfASdIestq93XAi4Fz2BL5Dw21t7i7H677cvBqtkj1b9/rjXUu6lMRu36IwiU+ifW+zCG0OYh7G0sR5mOOWZyUuPCYmZ3bs99pDU0Hrwf+3Mz+EkDSJ4D/EfiomT1aFZJ0I3DzUGNZO/Il/BH7xixNQjLeMeel7wea28S6ub2tXB9DsYrLrxaNycGX8G1rU1hDsX96DY2kHWwNVu5xrPtV4IclPUeSgNcB9wJIOq1W7mLgrqHG1u7M5s7xxx/PoUOHWu/vPcSxxx77rKXyfT+71lZmiFBX3XVcV3zKhgx0jr3gFgpNutbQSLp8tf96SacCtwInAd+WdAWwy8y+KOk/ALcDR4E/AW5YNf0BSeewFdM8ALxjqC/ZCHnsyKQpes3220QxZR9DjtcXr/j2pV4+5q1i+2Kfoe1tZcaIay4LPopb3xxWUwP3NrZdX/v/19iKXNrq/nPgn7dsv9S3H1lHK3MRc+bKmKl1rsed6wcexoj40PYxscqYgc56X1wvKkPlivMvpCYbRz6WKrIIZY5BVJ94xad/LhFL05V3DXL6MmY1qovg+Qi7a19cjlvEeBpSnWdJa/1NaZGOPLc3xNWdV9tcIgAXwepz4j7ut2uQs21b39RDl4HLoX7Xt7mIdVWm75zGzsdT/P2lGk8YU6ewHLIX8nX4AwyJV/raqYtQSKxSmyfrVa+iLa93FfEu+oR17KBmbuSS5RfWh+yFPDeGMlSXfB2+82H2cZ1dx+nqX2qX51Kv75tCqBv3/bZSkSIfdzluKL5tpTI9S7g4bjobJeTNP3TXQbGYGaqP82wTqjaxGXLDoU69mZt3rH7rba/ruevrcBFt31jFZ/9QmXUY6FxCHwv9ZDXYmXoK4lTHH5rv3aRv0LO50rOrreZ8cgj/geSxzs5nEVCbiIS68ZgX5i7WIeqLzRIW+pTBzgUxVfbo8xXcJV6p0ydUQ+I1NODp485DCRXxtkgl1I0v7QM7RQQ2N0sQ+yWzWCGP9QedS7zSJ9yuEUtze9vzaltsQWhrs29Qta/P4H8+fGcO9fUhlntvY46BzqWKf8GdxQp5KL65biiui4P6XHnbtvq+MWJebR87Z7yrjb4+dPXVV7xd3XiqDLjZ7pwDnYXNZhYh37pHjDtj/qhjfohdHJxrvfq2thksrhFLn0A23fCQoPs++tpqbuvqY9trGhMv9W3r2u8zGOzDEn6UYh0Gawtr6MhDvrrGvHd119dyV7FxdaUuYt7cVz1P4fZcopVQEY/lxn3jsSlErDjv75DyfFeDnWONSq5kJ+RTDPzEildiHt83Ymn+f0jMu0R2zB+tT7TiI+J12vbXz9VcdzUMiVVy/QGUMZRBzDzITsi78Pkjbn5gUsUrXdtjuvIhh9on5i6C3tw3xrG07Wv2w0XEY8zYae73HeRsMmWskqNgj6GIfXpmE/Lc/lhD4xWfrLyrXkX9AjRGzF0FPdZ70NZW13GH+j/0uocilVgX7SVlw33vY26fs0IasnTkuccrY7LWIVc+Rsy73Hl1jK6ZND4xy1B5l28CPiJexydSSenGY8Uqc4tsGehcH7IU8i7mjFdCXPmQgHfV6xLztm1NAe9z59VxukS9Wc9H5F0F3FfEh3Jxn7+JGLdRmKJ+G3OLfmrKRWMcJbyq0Vxav2NH97J23+X/XXXrx6hvr99fvW2ZfnNZf3Mf8Iwl/fDsuxY2Pzw+r8c3T+5z2z6u3HcRT1c/p3TjPsRsL7X4Lyn7Lkv0ExIr20sVrzSJ6cpdBKnNmbu68bbnQ8667taHHk262h5y4S4i7pOL+wp6kxRuPGWskrs4LUnsl8yiohVIH6/4OK6YH3oXMa/wFcfmtup4YwY9++q3HTNU0Idy8RBCB0dTf/2fUpRLlLFebPzlsi8+aaMvUumKSbr+P9Rek2Zk0henNJ93bav3fSwu0wZ9nrvk4mO+/TTxjU2mmDvuepzYFKFfFrM78qnjlblc+Zjc9vjjj++dzTIUr3Rt63LrrvS10bWt63m9fPP1xhLxJmOycd/2+toOZV2mHZaLxnjW3pG7/CjzFK68+bzr/3312wZAK9rcOTzbode31QkVc5c2Ql04xBvcbNZv4ismUw1yphDkGMK5tOxb0lpfMGZ35CGM/eNO7cpdM1jXwc++AdA+dz60bYwbH2rHNSfvi1J8RbxJX6QSKvgux6rIce64C7EEb2liH4Kk8yXdJ2m/pCtb9r9U0uclPSXp3Y19D0j6sqQ7JN1a236VpIdW2++QdOFQP7I4032O2Mctd5WdwpX3TV10zci7nHlzXyUQfe4c3PPxGG68ry2XbX2Dmq4iHhqpDAlX6imHIeTQh01H0nbgWuANwAFgn6Q9ZnZPrdg3gJ8Dfqyjmdea2WMt268xsw+69mWRjhzyc+VDbYYIUHNGSLNenzsf2pbCkfscv/4aQkS8Sd/5HTPAGZqN+wxyxo5VyvzxyTgP2G9m95vZYeDjwEX1Amb2dTPbB4QtOnFk7d6R2K68Lw8fmnHS56pdnXmznUo0+tw5tLvx5va2/WNxzcnBPQ9v7vNx1CHC3McYkcxh7nhuOXFu/fFkJ/Bg7fkB4FUe9Q34tCQD/q2Z3VDbt1vSW4FbgXeZ2Tf7GsrGkYeMwE/hyoeOOSQqPm7Qx1W2ufMhh17fPtaNu7bXtr3NhccScZ9cPGc3Hsocn4k2cnPt1WCnzwM4RdKttcdlzWZbDmUe3Xq1mb0SuAD4WUl/b7X9OuDFwDnAI8CHhhrK62xHIrUr73PaQ+WHyjadOdCbm9f3V68Rnu3QK5qOPKYb72uvTdzaRKMvSplbxKd04yUDz4LHzOzcnv0HgDNqz08HHnZt3MweXv37dUmfZCuq+WMze7QqI+lG4OahtrJx5EPk5MrbjusjFGMFqu3YQw69IqYbd2mzqx9t5yfWORo6VhOXv6G2MnO48bljldyc9szsA86SdKakHcAlwB6XipJOkHRi9X/gR4C7Vs9PqxW9uNreR1bviu/MkZC2UmTlXfjk677Pqw+0q0MHnvW6Y7vxtmPWcXW5Y0V8zKC0y35fpnLjS4tVFp6PY2ZHJe0GbgG2AzeZ2d2SLl/tv17SqWzl3CcB35Z0BbALOAX45Or3i48B/i8z+4NV0x+QdA5bMc0DwDuG+pKVkA/RJc5jLwBtghsjYhnqZ5tYA53RSptQuwo69Iv6GIZcaCwBdykzVaSSWzY+xNJFM1fMbC+wt7Ht+tr/v8ZW5NLkIPCKjjYv9e1HdkKeiyvvqh8zL6/2A97uvFmnT9CbZcFNdA4dOhR8rxCfmSRt5UOilJgD0T59he7zGdONz70kv8Qq+TLLO7P6OhGEryt3vTCERCddxwiNRXzFu+ubRLPtev1mG334iHhoDh3iulOJ+FSRSo4Dmeseq0ha6wtRlq8spivvos2Vh0Ysbbi6aJ+oxbVM1XbF0A9KNOnL9X3wvbdJiKi3HcdnINSn3a5yMe5w2HU8l31DlFhl/Vnkjy/7Op2u7SFT4rrKuX7oQzLaNmHq2tbV/7bZLl3U2+prt42+Y3W15bOt7Vh9ZUKEv61MV7kupnTjUwxyzuVm19lFxyTbszSFK/chJC9vK+NSr8uJu2yrb2/b1/Wh9z3XPhcFn32u20IHS0Nz8S5yd+M5Ur4hxGeUkEv6FeB/Ag4Dfwb8tJn9V9f6Y8Q6VlbuGrGM6VeImPfVAzdBr+/r2l8/fkx8Bbxre2oRdxWVGAOcc7jxKUWzuOf5GButfAZ4mZmdDXwFeO/4Ln2HqZYvx4xYfMq5RgU+zrUvBgmNS/pwjWFc9g1tcz0/U7x3XcRe5JPajW9KrFINdvo8lsSo3prZp2tPvwD8Y982pnTlvowZ/Ax15n11od2JN7cP7esqF5tYrhzCL44+dX1E3DdSWXc3XpiXmIOdbwM+FbE9YF5X7tPGWGfu4j676ne10dwXy4V34XKcoX1NfM7D3CIeEqmsixvPddrhpjB49iX9IXBqy673m9nvrcq8HzgKfKynncuAywCe//znP2Pf1K48Rl4e25n71q8IceIuH6aYLj7EmcM4F+5TP4Zgxo5UxtZdumAuLdqYm8GzZWav79sv6Z8AbwReZ2adt3Bc3Wv3BoCXvOQlPrd6DBb63MUcuoV4aAHRUDv1fV37+xgrBEP1fQW8q46PMI8tC9NFKkuaqVJEd37Gzlo5H/gF4DVm9uSYtlK48rHt1kkh5lVZaBd011Wb9Xba2mru7yvnS0x37iuquYj41JFKDDc+xyDnnN8S1v3Hl8e+U/8GOA74zGrZ/RfM7PLRvWphSJBDBNvHlUMcMYduIXZx5/V2+tpqq9dVLiUux4gh4L7tpBbxTSGFGy8O35+xs1a+P1ZHII1YD9WbWsz7junjzuttwbBLr4jhwvtwvTj0CWBIpu4zWDmFiBc37n/MQjhrdemLHbHEEnPodtW+7rytraH2utrpa8+3DVdChSiWKOcs4oVCKNkJ+VhXHjNigThiHloe+vPuPkGvEyLusXARrpizWvrqpB7Y7DtGjLpTuXFXSqySD1nexjaniAWmEXMIn5Uy5KibApDyHjauQpZiVktfvZginmImylgRj0mJVZbHYi9/oaI8pZhD9y1kfS4AQ/V8pxkOiULf+RnLGAHv60NM5x4q4rkv7sndjaek3I88EX0DeDB+2mAOYt7XXog7r+qB+2KfkMHNmKLjKh6hAt5XN6TOHCI+hRt3fR/mdOPrLLSpyfrMpczLpxZz8HfnbXVc6raVq8hl1opr2dDZLZsk4lNHF0Vw82PWd2TIlbsQa8GPT7shYt7XpstFAMIWAvWV76Nv1sxYxgr4UBsh8UsKEZ+CmJFKcePLZfazl2vEMrS/T8yhW1RDZqnU68KwS68Yc5GM7fJizC8faifUvacS8RwiFVeKkC6bRbx7c0UsQ/u7xBzGL+IZI+jNtipSxyptx3RhbHwwRvxTzE5xqTtVpBL7grzUKYfrPtg522921onxxzbmgzGmbp8QHHts/21jhxykywBg9XCharPvMaauz/vo2veU53CMiM89lXCOGSg+QrgpUw4lnS/pPkn7JV3Zsv+lkj4v6SlJ765tP0PSH0m6V9Ldkt5Z23eVpIck3bF6XDjUj2wuUakjlqE2UjlzCHfnVV2Ybq743IuDXPuQyoW7tJ06M48VqSxBTJfskiVtB64F3gAcAPZJ2mNm99SKfQP4OeDHGtWPAu8ys9slnQjcJukztbrXmNkHXfuShSN3JYbTSenMx7pzF3fpkzX7uPXY1I/v2g+fbyGhbcwt4rlFKsWNj+I8YL+Z3W9mh4GPAxfVC5jZ181sH3Cksf0RM7t99f8ngHuBnaEdyUrIp4hYhsq4fNBCoxZwmy89Nm7oajNEXEPbd8X1AuV6XvpYBxEvZMVO4MHa8wMEiLGkFwE/BHyxtnm3pDsl3STp5KE2svteEyNiSTnTxaWMS9QC4wc0c1v844rvRWhsey73TFmnuGQpbnzqWCXgeKdIurX2/IbVD+RUtN1rxOtHcyR9N/C7wBVmdnC1+Trg6lVbVwMfYuunNDvJTshdiCHmY/cPlanEYwpBb7ZXMcUsFVd8v23FihhSuvAp24B5ZqlsOI+Z2bk9+w8AZ9Senw487Nq4pGPZEvGPmdknqu1m9mitzI3AzUNtZRWtVMQY7HIpE+sDOCZqgTjZcF+7IbNKxhBjNovLMYZYJxGPzaa58UTsA86SdKakHcAlwB6Xitq6c+BHgHvN7Fcb+06rPb0YuGuovWzPZoxVnxDHmcOwIx7rzsHPobv0qe8Ybcz1i0K+mfoQY6MU1z5NKeI5r+DcVMzsqKTdwC3AduAmM7tb0uWr/ddLOhW4FTgJ+LakK4BdwNnApcCXJd2xavJ9ZrYX+ICkc9iKVh4A3jHUlyxvY+uKaxaeOkZxLRNT0Kvj1Rk7PXMqxx7yzcKFGAIeq0yuIu5DcePDrIR3b2Pb9bX/f42tyKXJf6I9Y8fMLvXtR5bRSkWsiMWl3FQfcHD/wYJUi2zmYMyMliGGpn7W+zBFmZjnf66VmWW64bLI9ja2PuWmdubQ735dyri6c/C/MVa9D01S/qhE33F98BGGnATctYxrOdfzsKRIxbcPsfosie3bt0dpK0cWcffDqcUcxmXiPmV8BB3CRL3ZpxzxdXWu32qKiPtT3PjymP8S7ciUYh67DAxfGHwFHcaL+pyECIDPb2hOLbwx20rBJrvxTWD2M+UzOyVXMQc3B+9SLkTQIX9RH+PcYgt4inIx25ozUilufJnMLuQQb6phxdRi7lsO3AUdxol6nVxvY9uG7y/Y+whuzk58KZFK6raLG/cjm7MVMy+H+GIO8Vy3b9mmqPkKe4XLhz/mrwyFkIOAu5ZdgoinEsQc+uDDut+PfJGvLIWYQ5wBTp/2fNqsM8atDzH112Vf4a7wjTzmilyWIuI5iVxOfVkKWZ2x2Hk5+AllzKilKgtxnXyTlKKeilDxhnQC7lN2CSLug69wLs2NbwLZneWliDm4C6+vk/dpu06XQM4t8GOEu2JJAu5Tdm5xTiniIRThDyPLs7YEMQ9pE/zEv2LsIp42IY0t7jHEuknIjJG5Ixefsj6iuEQXnEs/NoFsz3QOYg7xY5GQGCWmqFekEN5Y5CTgqcrmIOKb5MbLYOeMzC3mPuWnEPR6vZC6uTJmrnZKAfctX0Q8vP3COLK/+2EqMYf4Gbdv2XpffPrTVjek/lzEWGST2rWnKpuDiKcmpC859X+JzHb2jjnmGI4ePepUNoWYQzqBHuu2QwW5TVByEPdYqyND28nBhUM6EfdlkyKVTWExZzAXMYdlxSdDQjP2t02nIEcB9y2fUsRLpFKY9az7uHLIQ8yr8pBe0Ot1Q+v7tJ8TU+bmIXWWKOK+TLE4rAh/HGY/izmJOfjPJkl5AYhdP3fGXlRyE3DIS8RTi2buolzuR54YXzH3wfVn0yqmEOfYWfgShT3mN4EpBDykzpJFfIpvBrkL/5LI5kymGvwMqRNy/5M554fnOshZkSK+yTl68RXBIuKFsWR1Nn3FHPxuzZo6aqnqjcnCYwnwHOKeOm9fQvSydBEvLJPs3uWUmXlI+ancebNuaH3XtpfEHAIeUi+1iPsSIuLFjS+TLM9ojmIO884LzykqmYK5Fg2F1AsR5BydeE4zZmKz7kv0t83dgViEuCHfOjt27Aj+eh7DVdYf60is1zfl+5SjiIcw1X3o101MJZ0v6T5J+yVd2bJfkv71av+dkl5Z2/dOSXdJulvSFbXtV0l6SNIdq8eFQ/3I9qyGzGRJnZtX5LrQZ0mufR0GQHMV8SnEcqp+5Sz8krYD1wJvAA4A+yTtMbN7asUuAM5aPV4FXAe8StLLgH8KnAccBv5A0u+b2f+3qneNmX3QtS9ZO/LQN3GqrHKscMQWs6Zrz8m5p+zXmDZDXfg6iXiO3xAWwnnAfjO738wOAx8HLmqUuQj4TdviC8BzJZ0G/CDwBTN70syOAv8RuDi0I9m/I9UfTYg793Xm4P8Dxbnn4C4iFeO4U1805hoADb3ob7qIr5sbX7ETeLD2/ABbrnuozE7gLuCXJD0P+BvgQuDWWrndkt662vYuM/tmX0eyv/thRWjUknK+eZ0Y0wfnWrmZk3PvY84B0KkEHPIV8VByEHFJbNvmHUCcIqkurjeY2Q31ZlvqWPPQbWXM7F5J/wr4DPDfgC8BlcBdB1y9autq4EPA2/o6GuVsSXo38CvA95rZYy51QoR5SjEHf3cOcQV9bDvrwNx3ToQi4mOOswBX3cdjZnZuz/4DwBm156cDD7uWMbOPAB8BkPTLq7KY2aNVYUk3AjcPdXR0Ri7pDLbC/q/61p3yjzY00xyTn8dykDlm3imJ+XrHtDPm/c9ZKKfqWygLEv99wFmSzpS0A7gE2NMoswd462r2yg8Dj5vZIwCSnr/69wXAPwR+a/X8tFr9i9mKYXqJccauAd4D/F5I5amcOYTHJqH1IL67Xof7rNTJbfZKxZQCDnmLeCgLEuQgzOyopN3ALcB24CYzu1vS5av91wN72cq/9wNPAj9da+J3Vxn5EeBnazn4BySdw1a08gDwjqG+jDrTkt4EPGRmXwrJvZ/uRKCYQ/pB0Ho9CItbKlJk4EsR9im+Tcwp4GPq5i7iU0YqSxN/M9vLlljXt11f+78BP9tR9+92bL/Utx+DZ03SHwKntux6P/A+4EdcDiTpMuAygFNPfXZzoS57qvnmMepWzLkMP5XQzxn7zC3gY+oXER9fr+Ag5Gb2+rbtkl4OnAlUbvx04HZJ55nZ11rauQG4AWDXrl3Nkd2tzgS67DFRC4QL+hgxr5h6YHNdcvaYr2MpLjy03tR9zPVY5X7kLZjZl4HnV88lPQCc6zprpbdTE+bmMG/cUmfdfzhiDCkuQEty4WPqTXms4qrnIduzPoeYw3xxS52l5N6pyVG8x7QxRuSmWuU85lhF/Ocj2hk0sxfFaqtiajGHOIIeWr+LTRL2VNHPnAIORcRj1ys8k+zP4pQzWuqMzcBju/Q66yTsqTP7uQUc5hG53OeKz3G8dWYRZ3LKGS11YohxSkGvWIKwTz3IGmu+9NJcOEwv4ksQ5MAl+osh/3dgxZgZLSH16sQU9LHtuDDVjbLGHD8VOQg4LCdKGUuJVPJgMTfNqpjLnUO8KYdTuPQh1mUaIsQVsDkFfEz9Ob45FBHPh9nO6BhRHCPmML87b7YVq71NIYXzjNFmEfF09Qr9zHpW5xDzqi7EEXSIL+qx2lwnUsUGSxZwWJaIF9Ix+zsyl5jHqF+RIiopwp42843VdhHxaerGoAx2JmZuMYdx7rwiZfa9CcKeerAuZvsxRGlpIj6GuUV83cnm7I4VcxgnxrHcOUwzmLlkYZ96dsU6CTgsc0pkIS1ZvTNjBXCsoMd05zDtYKbrh3sqwZ9jKlzKPsQSsblc+Nhjz1V3nW90FZOshLxi7DS/nOKWihymHNb7sa6keH1Ld+Fjj19EPH+yFHKII+YwPm4Z20aTXAR9nUh1ccrBhUMR8cIw2Qo5xFmAEyP7TinoFUXY3Un9rSJmFlxEPA8krfXFIa+z3UIsMYfxQpxC0CuKsPczRSRUBDxO/bHHXmfBTUX2Qg7xlsbHmpmSUtAryqrP6fL8nAQciogX/FmEkEO8bDmmCNf/aKcSdVhfYV/6L7wXES8iPheLEfKK3Nx5vT1IK+gVbR/2JYn7nDNn1lXAY/SjiPhyme3uh3P9LFudFOI7paDXGRKCqYU+t2mOuQo4LF/El0JZop/q4Bn88EPVD0gj6LHbDSU3YZ2CVOKUk4DD/CK+yW5c0vnArwPbgQ+b2b9s7Ndq/4XAk8BPmdntq33PBT4MvAww4G1m9nlJVwH/FPjLVTPvM7O9ff2Y/TKc033CU7np3ER93cldwCEPFx6jjQ0X8e3AtcAbgAPAPkl7zOyeWrELgLNWj1cB163+hS2B/wMz+8eSdgDPqdW7xsw+6NqX2YUc4ok5xIkQUsYjRdTjkzoWyE3AoYh4JpwH7Dez+wEkfRy4CKgL+UXAb5qZAV+Q9FxJpwF/Dfw94KcAzOwwEPyzXdmERrl9XYWtPqUUiar91MdZR6Y4b7Hbz0XEY7yuIuIA7AQerD0/sNrmUub72IpO/p2kP5H0YUkn1MrtlnSnpJsknTzUkVnU4+67735s165dfzHR4U4BHpvoWFOxjq8J1vN1reNrgmlf1wvHNnDbbbfdsm3btlM8qx0v6dba8xvM7Iba87bfrLTG864yxwCvBP6ZmX1R0q8DVwL/O1vxy9WrclcDHwLe1tfRWYTczL53qmNJutXMzp3qeFOwjq8J1vN1reNrguW9LjM7P0GzB4Azas9PBx52LGPAATP74mr7f2BLyDGzR6vCkm4Ebh7qSDbRSqFQKCyMfcBZks5cDVZeAuxplNkDvFVb/DDwuJk9YmZfAx6U9AOrcq9jla2vMvSKi4G7hjpSgtlCoVAIwMyOStoN3MLW9MObzOxuSZev9l8P7GVr6uF+tqYf/nStiX8GfGx1Ebi/tu8Dks5hy7U/ALxjqC/aGkxdXyRd1si1Fs86viZYz9e1jq8J1vd1LZW1F/JCoVBYd0pGXigUCgtnY4Rc0rslmSTfKUhZIulXJP3paq7pJ1fLfReJpPMl3Sdpv6Qr5+5PDCSdIemPJN0r6W5J75y7T7GQtH0193lwNkVhGjZCyCWdwdYy2q/O3ZeIfAZ4mZmdDXwFeO/M/Qmitsz5AmAX8GZJu+btVRSOAu8ysx8Efhj42TV5XQDvBO6duxOF77ARQg5cA7yHZ0/WXyxm9mkzq9b4f4Gt+alL5OllzqtlytUy50WzmmJ2++r/T7AlfM1Vf4tD0unAj7J1s6dCJqy9kEt6E/CQmX1p7r4k5G3Ap+buRCAuy5wXjaQXAT8EfHGg6BL4NbZM0bdn7kehxlrMI5f0h8CpLbveD7wP+JFpexSHvtdlZr+3KvN+tr7Gf2zKvkXEZZnzYpH03cDvAleY2cG5+zMGSW8Evm5mt0n6+zN3p1BjLYTczF7ftl3Sy4EzgS9t3RaY04HbJZ23WlmVNV2vq0LSPwHeCLzOljuP1GWZ8yKRdCxbIv4xM/vE3P2JwKuBN0m6EDgeOEnSR83sLTP3a+PZqHnkkh4AzjWzxd/EaHVD+18FXmNmfzlUPlckHcPWYO3rgIfYWvb8E2Z296wdG8nqBwX+T+AbZnbFzN2JzsqRv9vM3jhzVwpsQEa+xvwb4ETgM5LukHT93B0KYTVgWy1zvhf47aWL+IpXA5cC/2D1/tyxcrKFQnQ2ypEXCoXCOlIceaFQKCycIuSFQqGwcIqQFwqFwsIpQl4oFAoLpwh5oVAoLJwi5IVCobBwipAXCoXCwilCXigUCgvn/wezkwSv0UU93wAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(6,5))\n", "\n", "plt.xlim(-5,5)\n", "plt.ylim(-5,5)\n", "\n", "plt.title(\"$v_{hxc}(r)$\")\n", "\n", "plt.contourf(x,y,vxc + vh, \n", " levels=50,\n", " cmap=\"Greys\",\n", " antialiased = False,\n", " linestyles = \"dotted\",\n", " )\n", "\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "#Extract components along the z axis\n", "x, v_hartree = grid.axis_plot(KS.V.vh)\n", "_, v_xc = grid.axis_plot(KS.V.vx + KS.V.vc)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(dpi=200)\n", "\n", "plt.title(\"Hartree, Exchange, and Correlation Potentials\") \n", "\n", "plt.plot(x, v_hartree, label=\"vh\")\n", "plt.plot(x, v_xc, label=\"vxc\")\n", "plt.plot(x, v_hartree + v_xc, label=\"Self-Interaction Error\")\n", "\n", "\n", "plt.legend()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }