{ "cells": [ { "cell_type": "markdown", "source": [ "# Temperature and metallic systems\n", "\n", "In this example we consider the modeling of a magnesium lattice\n", "as a simple example for a metallic system.\n", "For our treatment we will use the PBE exchange-correlation functional.\n", "First we import required packages and setup the lattice.\n", "Again notice that DFTK uses the convention that lattice vectors are\n", "specified column by column." ], "metadata": {} }, { "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "┌ Warning: Package DFTK does not have Plots in its dependencies:\n", "│ - If you have DFTK checked out for development and have\n", "│ added Plots as a dependency but haven't updated your primary\n", "│ environment's manifest file, try `Pkg.resolve()`.\n", "│ - Otherwise you may need to report an issue with DFTK\n", "│ Loading Plots into DFTK from project dependency, future warnings for DFTK are suppressed.\n", "└ @ nothing nothing:910\n" ] } ], "cell_type": "code", "source": [ "using DFTK\n", "using Plots\n", "\n", "a = 3.01794 # bohr\n", "b = 5.22722 # bohr\n", "c = 9.77362 # bohr\n", "lattice = [[-a -a 0]; [-b b 0]; [0 0 -c]]\n", "Mg = ElementPsp(:Mg, psp=load_psp(\"hgh/pbe/Mg-q2\"))\n", "atoms = [Mg => [[2/3, 1/3, 1/4], [1/3, 2/3, 3/4]]];" ], "metadata": {}, "execution_count": 1 }, { "cell_type": "markdown", "source": [ "Next we build the PBE model and discretize it.\n", "Since magnesium is a metal we apply a small smearing\n", "temperature to ease convergence using the Fermi-Dirac\n", "smearing scheme. Note that both the `Ecut` is too small\n", "as well as the minimal ``k``-point spacing\n", "`kspacing` far too large to give a converged result.\n", "These have been selected to obtain a fast execution time.\n", "By default `PlaneWaveBasis` chooses a `kspacing`\n", "of `2π * 0.022` inverse Bohrs, which is much more reasonable." ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "kspacing = 0.5 # Minimal spacing of k-points,\n", "# in units of wavevectors (inverse Bohrs)\n", "Ecut = 5 # kinetic energy cutoff in Hartree\n", "temperature = 0.01 # Smearing temperature in Hartree\n", "\n", "model = model_DFT(lattice, atoms, [:gga_x_pbe, :gga_c_pbe];\n", " temperature=temperature,\n", " smearing=DFTK.Smearing.FermiDirac())\n", "kgrid = kgrid_size_from_minimal_spacing(lattice, kspacing)\n", "basis = PlaneWaveBasis(model, Ecut, kgrid=kgrid);" ], "metadata": {}, "execution_count": 2 }, { "cell_type": "markdown", "source": [ "Finally we run the SCF. Two magnesium atoms in\n", "our pseudopotential model result in four valence electrons being explicitly\n", "treated. Nevertheless this SCF will solve for eight bands by default\n", "in order to capture partial occupations beyond the Fermi level due to\n", "the employed smearing scheme." ], "metadata": {} }, { "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n Free energy Eₙ-Eₙ₋₁ ρout-ρin Diag\n", "--- --------------- --------- -------- ----\n", " 1 -1.761856955924 NaN 5.05e-02 4.7 \n", " 2 -1.762191494485 -3.35e-04 9.85e-03 1.0 \n", " 3 -1.762240119040 -4.86e-05 6.64e-04 3.0 \n", " 4 -1.762241611055 -1.49e-06 9.61e-05 3.3 \n", " 5 -1.762241620394 -9.34e-09 9.87e-06 2.3 \n" ] } ], "cell_type": "code", "source": [ "scfres = self_consistent_field(basis);" ], "metadata": {}, "execution_count": 3 }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "9-element Array{Float64,1}:\n 1.999999999907795\n 1.9999975862913428\n 0.004016904710677525\n 3.000549966653429e-15\n 1.111554993638759e-18\n 1.1114840616587883e-18\n 7.977938940318961e-19\n 7.9772485775433185e-19\n 3.2497156903340497e-22" }, "metadata": {}, "execution_count": 4 } ], "cell_type": "code", "source": [ "scfres.occupation[1]" ], "metadata": {}, "execution_count": 4 }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Energy breakdown:\n Kinetic 0.7180648 \n AtomicLocal 0.3145387 \n AtomicNonlocal 0.3265759 \n Ewald -2.1544222\n PspCorrection -0.1026056\n Hartree 0.0055003 \n Xc -0.8610489\n Entropy -0.0088446\n\n total -1.762241620394\n" }, "metadata": {}, "execution_count": 5 } ], "cell_type": "code", "source": [ "scfres.energies" ], "metadata": {}, "execution_count": 5 }, { "cell_type": "markdown", "source": [ "The fact that magnesium is a metal is confirmed\n", "by plotting the density of states around the Fermi level." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=2}", "image/png": 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wCIlIUwR2jYoNQp9do9x3mzwYhESkIQK7RsVWcuwapQAYhESkIQLXEcoyWYZdo+TBICQiDRE4RighCPv3uLIiJA8GIRFpiEI7y/i8LccIyYNBSEQaImRnGbkqQnaNkgeDkIg0JOjx9GDXKMmNQUhEGqLQgnp/XaMMQgKDkIg0xWfp5oUVIcmLQUhEGqLc8gkGIfnDICQiDRGys4xcXaM8fYI8GIREpCFCJsvExcHhgMsl7rasCMkfBiERaYiQrlGDQfTh8j4LTQYheTAIiUhDhHSNQnyvJjfdpgAYhESkIXa7oCAUezavvwX1DEICg5CINEVI1yjEZxi7RikABiERaYXLBYcDsbHBnym2V9Nf16jdLuImFKkYhESkFZ4OTIMh+DNl6RrlGCF5MAiJSCsE9otCfK+mvy3WWBESGIREpB0Cp4xC0qxRjhGSPwxCItIKIavpPSSMETIIyR8GIRFphfCuUc4aJRkxCIlIK4QcPeEhNgh9Lk9kEJIHg5CItEJURSgqw9g1SgEwCIlIKxSqCO12mM0w9vu0i4kBgM5Owe2jCMUgJCKtED5rVNRkmQD5yqKQwCAkIu0QPmtUVNcog5ACYxASkVYo1DUaoNBkEBIYhESkHcKDUGzXqL9Ck0FIYBASkXYotLMMu0YpMAYhEWkFxwhJFQxCItIKux1xcYKeGR+P9naht2UQUmAMQiLSClFdo8IDLMA6fQYhgUFIRNqh3IJ6f4Umg5DAICQi7RB1+oQsFWFcHIOQGIREpBkKVYQcI6TAGIREpBUKbbHGBfUUGIOQiLRCueUTnCxDATAIiUgr2DVKqmAQEpFWKBeEnDVKATAIiUgrhAdhXBw6OuB2C71tgFmjHR1Cm0eRikFIRFohPAgNBsTGCi3m2DVKgTEIifTq6FGhJZFeCA9CAAkJQntHA9xWVBcrRSoGIZEulZZi+nTcdZfa7ZCVqCAUnmGsCCkwBiGRLr3xBi6/HG+/jaoqtZsiH1FBKHwpIdcRUmAMQiJd2roV11yDRYvwwQdqN0U+YitC4WOEXEdIATAIiXRpzx5ceCHmzcMnn6jdFPmwa5RUwSAk0p+qKphMyMjA7Nn4z3/Ubo1MXC50diI2VujzGYQkFwYhkf4cO4aRIwFg6FDY7SgrU7tBchBVDoJjhCQfBiGR/hw/3hWEAL7zHezZo2prZCI2CEVVhBwjpAAYhET6U1qKoqKur6dMwZdfqtkYuUgIQi6oJ1kwCIn059w55Od3fR0xQSj8DCYPUV2jPJiXAmAQEulPRQXy8rq+njIFe/eq2hqZ2O3iglCunWUYhMQgJNKf3hVhfj4MBpw7p2qD5KBKRciuUQKDkEiPeleEACZNwr596rVGJgpVhG437HYew0SBMAiJdKazE/X1yMjouTJ5ciQMEyq0fKKjA2YzjH4+6hiEBAYhke7U1yMtrc8ne2TMl1Fo+USAflEAMTEA4HCIeF+KPAxCIp2pqelTDgKYOhVffKFSa+QT4Bx5nwTOcwmarywKiUFIpDM1NcjK6nNl0CAYDCgtValBMgmw7N0nWSpCABYL7HYR70uRh0FIpDP9K0IA06Zh9241WiMf5bpGWRFSYAxCIp2pq/MRhNOnY+dONVojnwBzO30SGIRBC00eUk8MQiKd8VkRzpyJ7dvVaI18FKoIOUZIQTEIiXSmoQEDB3pfnDYNhw+jvV2NBslElVmjYBASg5BId+rrfQRhfDwmTsSOHWo0SCYKrSNkEFJQDEIinWlsRGqqj+tz5uDTT8PeGvmIDUKBO8uwa5SCYhAS6UxDA9LSfFy/5BJs3hz21shHQteokK5gIUHIyTJRjkFIpDP+gnDGDHzzDRoawt4gmai1fIIHUBCDkEhnfI4RAoiNxUUXYcuWsDdIJsoFYUJCoCewa5QYhEQ609SEAQN8P7RgATZtCm9r5KPQGKGQipBdo1GOQUikJw4H7HYkJfl+dN48HQ8Tig1CsxluNzo7gzxNyKxRBmGUYxAS6UlTE1JSYDD4fnTMGFitOHVKxA03b9bKTptiN92GsPkyQnaWYddolGMQEulJgH5RAAYDZs/GZ58Jvdv27bjsMnz/+7I0LVRiK0II69XkOkIKikFIpCeBgxBAcbGIIHztNfz3f2PrVpw9G3rTQiX2hHoIGyYMGoQcIyQGIZGeNDcjJSXQE2bMELH79oYNWLoUl1+O998PvWmhYkVIaukJwk2bNn3aa1+Kffv2rVy58tVXX23X9faFRJElaEU4ZgwqK1FfH/xW1dVob8fw4Zg/XxNTbNQKQlaE1BWEn3zyyZVXXvnII494vv3nP/85f/785ubm//u//5s1a1Zn0IlZRBQWQYPQZMLkyYIOrN+/HxMmAEBxMbZtg9stTwslkxaEQf+jzoqQgjICaGtru+eee372s591X3300UefeeaZxx57bP369e3t7evXr1evhUTUI2jXKIBJk7BvX/BbHTyI8eMBIC8PSUk4flyG5oWCFSGpxQjgwQcfXL58eVFRkedSbW3tvn37lixZAsBkMl166aWb9LtGlyiyBK0IITgIT57E8OFdX194ofrn+koIQlkmy7AipJidO3d++eWXzz333CuvvOK5VFFRYTabB367iVNOTs62bdv8vd5ms61evfrDDz/sfXHmzJkLFy5UrtFe7HZ7bGxs2N6OtKmzs9PhcBiNmp7/5Xa7nU6nPYSFew0NMWlpbrvdGeA5o0cbnnzSbLd3BL7V8ePmhQuddrsLwJQpph07DNdfr+YgiM0WZzCI+7uxWMxNTV1/hG5eHwjt7bEmk8Nu99vzGxNjbGsz2e0O8U0m7XI4HE6n02AwxMbGGvwtvP1WzIoVK/72t7+ZTKbuSwaDwd1ruMDlcgW4i8FgiI+PT+q70YXFYgnn55HRaNT4xx+FgfFbajckEIPBYDAYQmlkS4uhqAiB7zB6NE6dMjidRrM50K1KSgzDhnU15oIL8Ne/9vnbq6rCv/9tvPZal/8byMnlgsMBi8UY7COrj/h42GzefxlevwZWKxITjUaj3yCMjzfY7SH9UEiDjEaj2+0W+GONKSsru/feewGUlZVVVFQsWLDgzTff7OzsrK2tzczMBFBZWZmbm+vv9XFxcbfccktxcbFcrZfAbDabA/+Lpyjg+e+a9n8TjEZjKI1sa0NaGsxmU4DnmM0YNAinT5vHjPH7HJcL585hxIgYT1umTcPx47DbzZ7/07rduOIKnD4Ni8V01VWSGyuC1Yq4OMTGivubSUqC3e79t+H1gWCzITk5JsBfeXIybDYd/OaQWML/rRnXrVv3wAMPPPDAAwsXLiwsLLz//vvT09OnTp3qmSDjcDg2bNiwaNEihRtMRII0NyM5OfjTRo/G118HekJVFdLS0N2DGBeHiROxe3fXtx98AKMRK1fijTdCa65gEgYIId8YISfLRLmYefPmeb46efLkl19+6fn20Ucfvfnmm7/++uuvvvoqPT198eLFqjaSiLq0tAgKwpEjg8wCLS1FYWGfK8XF2LoVc+cCwJ/+hJ/8BAsX4v77Q2irGJKDMOjyifZ2zhqlIHr6T5csWfLss896vv7ud7+7bdu2wsLCO+64Y8uWLTExMSo1j4j6EBiEI0YED8KCgj5XFizAxo0AUF6O7dtxzTXIyYHZjNLSEJormLQgDLqO0O0WtOk2gzDK9SRcfn5+fn5+97fnnXfeeeedp0aTiMgv4UH4+uuBnnDunHdFeOGFKC3F8eN44w1cdx0SEwFg0iR89ZX3M5UguSI8dy7IbePiEHjCBIOQWOoR6YnAIBw2DCUlgZ5QVuZdEZrNuP12/PjH2LevZ7Bw5EicOCG1rWIoNEYYtF9UyE0o4nHGMJGetLQE31kGQH4+6uoCrROvqED/yeC//CXGjsXq1Rg6tOtKURFOn5bYVFEUGiO0WpGQEOQmAg/4pQjGICTSDafTsyou+DONRhQW4swZv08oK0NenvdFiwX/+7/ovV4ibEEYdG6nT0F7NdvaggchuLlM1GMQEulGaysSE/0eT+9l6NBAvaOVlcjJCX6TIUPEnXcvmd0u+nh6AAkJaGsL9ASB+Spk9ilFMAYhkW4IHCD0CFzMVVT4qAj7KyxEWZnQdwyFil2j4HyZqMcgJNKN1lb03c0wkEGD/K58sFphtyM1NfhN0tLQ3o4Q9kYVSrnJMgKDkBVhNGMQEulGa6uIinDQIJw96/shgf2iAAwGZGWhslLom0qmUEUoZNYoWBFGPQYhkW60tIirCP0Foc8po/7k5oYjCKVNlgk6RtjeLmhuUXw8J8tENQYhkW6I7Rr1N2u0qgpZWULvk5MTpopQwmSZxMTgY4ScLENBMQiJdENUEObno6oKTl8HFwrvGkUYg1BCRZiYGLwi5GQZCopBSKQbosYIzWakp6OiwsdDVVUigjAjAzU1Qp8smbQxQosFDofvsPfgGCEJwSAk0g1RFSGAwkLfW3GKqgjT01FbK+JNpZEWhAjWq8mKkIRgEBLphsDDCLsVFvpeQSEqCDMyUFcn4k2lsVoVCcK2NkGTZThGGOUYhES6IfBjvZu/IKyqQna20JtovCIMPEwocNZo0NmnFNkYhES6IWqMEEBBgQxdoxkZYQpCCZNlIF9FyK7RaMYgpAixd6+hsVHYLpy6JXaM0F8QiqoIw9M1GkpF2Nrq91GBm26zazTKMQgpQjz0kHHWrDi3W+12KEmWIGxuhtksovzSftdo4MkyHCOkoBiEFAnKy3HggMHpxMGDajdFSZ7TJ4TzOUZYUSGiXxRASgqsVsWP6wtl1miA4T1OliEhGIQUCb76CpMnu+fMcW7dqnZTlCS2IszNRU2Nd4ZVVorYXw2AwYABA9DYKOIlEkieNRq4IhTeNcrJMtGMQUiR4NAhjB3rPv989+HDajdFSW1t4oIwJgaZmd5r6kVtNOqRloaGBnEvEUv1WaOsCKMZg5AiweHDGDsWw4a5jh9XuylKEts1CqCgwLt3VGzXKMIVhNJmjSYlBZkswyCkoBiEFAnOnMGQIe4RI9zHjin7RtXVkPAWDQ146CEZ3l1s1yh8bS4jtmsUmq8IOWuUQsQgpEhQWoqCAhQUuOvqlD1PZ/VqzJ0rehbl/fdj5UocORLqu4vtGoWv+TLl5aKDMDVV8TFCyUGYlMSuUQoVg5B0z+1GeTny891GI/LyUFam4Hv9+c9ISsInn4h71UcfYfFifPBBSG/tcsFmE1Tf9Nb/VMKyMuTni7tJGCpCaecRImDXqNsNq5UVIQXHICTdq65GSkrXaXb5+QoGYX09Ghpw++3Yvl3Eq8rK0NGBq6/Gvn0hvXtbG+LjYRC5Z8Dgwd6nEmozCJXoGm1vR1wcjAI+5BiEUY5BSLrn6Rf18LeXiiwOHMD48Zg2TVyk7d+PSZMwaRK++iqkd5cwQAhfx/NKCMIBA9DUJPqthXO7Q+oa9ReEwv/Ggh7wS5GNQUi6V13dc966ohXh4cMYNw7Dh+PECRGvKinB0KEYMQKnT4f07hIGCAEMHtyna7ShAWaz6PsoHYQdHTCbBZVu/QUYIxQVhAFm3FDEYxCS7vUOQkXHCM+cQVER8vLQ3Czic9MThBYLUlPhckl/dwlrJwCkp8Ph6Imxc+dEl4NQPgglDxBCporQYoHTqfjuOaRZDELSvd5BmJ2Nqiql3qi0FIWFMBgwZAhKSoS+yhOEAAYPDnSWelDSKkIAQ4f2tPb0aRQVib5DGIJQWr8oAhZzojqTAy/Mp8jGICTd6x2EWVmorlbqjTxBCKCoyHsqZgBnz3Zlz6BBIQWhtIoQwLBhOHmy62ttBqHk1fQI2DUq6r8ODMJoxiAk3QtnRThoEADk5aG8XOirysuRlwcAhYUhdY2GUhF2B+GpUxgyRPQdtFwRytI1Cg4TRjcGIeleTQ0yM7u+Vq4idLlQUdEVacKDsLMTDQ1dOZ2To8IYIYARI9C989ypUxFYEba0+H6IXaMkEIOQdK+2ticIMzLQ2KjIrIe6OqSkwGwGxARhZSWysrrmQ2ZnhxqE0vsuZfcAACAASURBVCrCMWN6NrX55huMHi36DlqeLJOcjNZW+DyHsqUFyclC78MgjGYMQtK9hgakpXV9bTIhLU2Rg2R7153Cg7D3DtchBqHA/aP7GzsWR47A7UZHB86cwYgRou+QnIy2tpAaH5jkRYQATCbExfleBSjqbyzw5t0U2RiEpHv19Rg4sOfbjAzU1cn/Lr1HInNzvc828qf3mUehB6G0ijAtDUlJOH0ax49j8GDExoq+g9GIxES/PZChC2WMEEBysu+2iepMZkUYzRiEpG9OJ1pakJracyUjQ5GKsKoK2dldX2dmCh2J9JrIo8oYIYALL8SOHdi9G1OmSLxDSgqamyW+NqhQxggBpKT4DkJRXaOBN++myBajdgOIQtLQgJQUGI09GaNQEHot0qipEfqq3uOXqlSEAC66CFu3oqMDxcUS76BoECpUETY3IyVF6E1YEUYzVoSkb/X1SE/vcyU9Xakxwu4gtFgQGyto/kjvkUWzGQYD7HaJDQilIrzmGrz3Hj78EJdeKvEO/qouWYRYESYn+w5pUUHIMcJoxoqQ9M1rgBCKVYR1dRgzpudbzzqNAQOCvKqmBpMn93xrNEo/LjGUijA/H088gdbWnt3JxfIXNrIIZdYo/FeELS0igtDfTSgaMAhJ3+rre6aMemRkKHIAhVfiZmaipib4DMzeFSFCC8JQKkIAK1ZIfy2U7xpVIgibm0WMESYnex/TQdGDXaOkb42N3kGoUNdoXV2fPliBK/d7d6gCIXWNSl4+IYuIHyNkRRjNGISkb42NfaaMAkhPR329/G9UV9enIkxPF7RIo7YWGRk934ZYEUruGg2domOEIVaE/kKaQUgCMQhJ33qvpvcYOFCpIOwdaQJXK3oFocGg1yBUeowwIUH6y/1tfCN2sgyDMGoxCEnfmpq8Z6wMHKjIgnqvwUghFaHVCre7z0d8KBVhe3skd42GUhH6DEK3G62tIsYIFf0DksYxCEnfwtM16nDAZutTXggJQq9hRQBGozrLJ0KnaM+hEkHY1ob4eJhMQm/CrtFoxiAkfevfNZqWhsZGmTfG9JSDBkPPFSFTcmprvYNQ8mQZtxtWa8QGYXt7SEGYmorGRu+LDQ3e/0MKzLN5N0UnBiHpW/+KMCYGiYkyd3P5rDvDWRG2t8Ni6TrFQhVanizjsyLs/yMLjBVhNGMQkr71HyOEAsOE/d9FSBD23/VGckWo7toJKDxZJpTTJ+AnCH3+YgSg6B+QNI5BSPrmLwgbGuR8l/4dsEJGIr1WXCCEIFR3gBDaHiP02TUqtiL0JLHkqUykawxC0jefn3eyr6Dwt0jD53mw3bxWXCCErlF1105A+TFC2ZdP9N97T9p9KBowCEnffK4VS0uTuSLsX3fGxiIuLsj0iv4hrd+uUY0fw9TaCqezz0WxXaPwU1lSNGAQko51dMDl8vEZGoaKUMi79C9KPPNOrVbRDQhlx21ZaLlr1GRCcrJ3hontGgUrwijGICQda2ryvXVIWpomgrD/GCGAuDgpZUdLi8pBmJCAjg50dipy8xCXT8DXkK3PH1lgrAijFoOQdMxf95fsk2V8dsAGDcKGBtmCUPWuUYNBwRP7Quwaha+fhdh1hGBFGMUYhKRj/oJQ9jFCGStCgSf6elF9sgwU243T7VYkCL12eRWCFWHUYhCSjjU3+w1CebtG/U3JCVoR9o9PnVaEUGxNvc2GuLg+u/ZI0D8I++9mEBQrwqjFICQd8zdGKHvXqLTVij67RqVVhKpPloFi82VCHyCEnyBkRUgCMQhJxwJUhGEIwsAVoc0Gl8vH8rjYWCmftqovqIdiQRjiGUwe/fcS6r/Ra1ACz5ikyMMgJB1TfYwwwLv4HCAEEBfHMcI+QlxN75GZiZqanm87O9HcLHpBPYMwajEISccCdI3KO0YooSL02S8KPU+WUa5rNPQgzM5GVVXPt57TQsTuUc4gjFoMQtKxlhbfJ68mJqKjAx0d8rxLZyfsdh89k4ErQn/r2KRVhBE8WSbE1fQeWVmoru75VsKUUTAIoxiDkHTM3xihwSDnxAdP3dl/WmPgutPfXpdms14rQi13jWZn9wnCigrk5Ym+iZAzJikiMQhJx5qbfVeEkLV3VNoiDX8LulkRepFl1mhWVp+u0cpKZGeLvomQE0UoIjEIScf8RRRknS8jbZGG7GOE/iI/bLQ8azQtDe3tPRuaV1YiN1f0TTzNaG8PtTGkOwxC0jF/EQW5g9Bn3CYnw273OxLpma/RHyfLeJGlIjQYkJuL8vKubysqpAQhgJwcVFaG2hjSHQYh6ZjPDV88ZNxcJsC7BOiA9TdGyCD0IktFCKCwEOfOdX1dUYGcHCk3yc1lEEYjBiHpWOCIUroiRMC49dc1Km2MUPXTJ6Dt5RMACgtRWtr19ZkzKCyUcpOcHFRUyNAY0hcGIelY4IowDEEooSI0m9HSEuRoey8uF+x2edIiFFruGkXfIDx9GkOGSLlJ/4rw7bdx/vk4fTrE1pGmMQhJx8IThNLqTn9BaDTCYhF3nlFrKxISQt2WOnTKBaEsE2ILC3H2LADY7airQ36+lJt4VYStrfjZzzBpEh55RIYWkmYxCEmvrFaYTIiN9f1o2IJQbEUI8accaGGAEJrvGh01CkePAkBpqbGgQPS2Mh75+T0DjQDeew8XXIAnn8QHH8DhkKGRpE0MQtKrAPkEWSfLyNs1CmDAADQ3i2hAZAdhW5s8QTh6NL75BgCOHjWOGiXxJkOGoKSk59t163DDDcjLQ34+Dh6UoZGkTQxC0qvAQSjjZJkAqxX7H3rg4XSipcXvCekpKaIrQtUXEULJnWVk6RotKEBTE5qbcfCgccIEiTcZOhSnTnV9bbXi3//GokUAMHUqvvhChkaSNjEISa+CVoRKL6iH/90pGxowYIDf3jmddo3GxsJkgs0m823lqggNBkyejF27cOCASXIQ5uejtrZrYf7WrZg0qet/M1OmYO9eGRpJ2sQgJL0KWhEqvcUa/G/K5e8MJo+UFF12jUKZ3lG5xggBzJ6Njz7Ctm2mWbMk3sFkwpAhOHYMADZswKWXdl0/77yufleKSAxC0istV4R1dYFOhRVbEWphEaGHQkEo1zaq112Hl17ChAkuaavpPaZM6eoFff99LF7cdXHkyK50pIgUo3YDiCQKHISepWmyVBuBZ436DML6+iBBKKoi9HfaVPgpEYRydY0CGDMGa9dixgwrIP0/DlOn4vPPMX48zGaMG9d1MT8fzc1BfuVIvxiEpFdBP5U882VC/5ANMGtUWkUotmtUU0EoquVCyFgRArj2WrS0iNmtoJ/vfhdPPYWGBixb1nPRYMCwYSgpwcSJobaQNIhdo6RXQYNQrt7RlpZAXaP+xggDB6EeZ41C8xWhLEaMwIIF2L8fP/pRn+uDBnUt2KfIw4qQ9EpIRRj6fJm2NpjNMJt9P5qUBKfTxxnrso8RSjhvXQlKHEko42QZubz2Gmw2WCx9Lg4ezCCMWKwISa/CUxEGfZeMDB/HmtfWBoouXY8RarxrVC5eKQhWhBGNQUh6FZ6KMMDaCQ+fQVhTg8xMvy8R2zWqqSCUtyJ0OOBy+d0nT1MYhBGMQUh6FTSi/M1kESXA2gmPjAzU1HhfrK4OFIQSukYjNQjb2rSyMiSo/HyUlandCFIGg5D0KmhEydI1GmDKqEdmpu+uUQahEG1tWuwX9SkvD+XlajeClMEgJL0KT9do0CD01zUaeIxQp0Eo+2SZ1ladBaGogyRJL2JsNtumTZu+/PJLAHPnzp317d5EW7Zs2bhxY3p6+vLlywcG2C2KSCUBVjV4+FvtLoqEyTJOJ5qbkZbm9yU63WsU4ldABqWjijA+HgkJQbZKIJ0yrl69+re//a3RaDQajVdfffWzzz4L4K9//euNN96Ym5t74MCBmTNn2j170BJpiUYmy2Rno7q6zxXPRqMmk9+XeGYkCt+9Omjkh43ss0Z1NEYI9o5GrpgVK1b87Gc/83wzcuTIhx9++J577nn88cd/97vfLV261O12T548+e9///v3v/99dRtK5CXoGKG/1e7yvkt2Nqqq+lypqkJ2dpDbeorC/nP0fWpu1lDXqLxBqKOuUQC5uaisxPjxareD5GaM77USuKOjIykpqaam5uuvv16wYAEAg8Ewf/78zz77TL0WEvngKacCB4ksXaNBxwizs1FZ2edKRQWCbvosPFFcLrS3a6VsiuZZo/D1nx6KDD07yzQ0NDzyyCOPPfZYZWVlbGxs6reHimZlZX399df+Xm+1Wn/729++/vrrvS/OmzfvyiuvVKjF/dlsNrO/nT8oQtXUGJKTY222nk77zs5Oh8NhMBi6ryQmor7eYgvtAL2GBvOIES6bzenvCamphqqqPi0pKzNlZBhtNkf/J7vdbqfTabPZUlJiq6s7CwtdQRvQ3IzEREtHh9zHAEpisRiamvr8YUPU2GiyWHz/XUmm3AdCRkbMuXOw2TqVuDnJy+FwOJ1OALGxsUZ/R4N+qysI29vbr7zyyiVLltx8881HjhxxOp1ut9vzmdLZ2Rngt8pkMo0aNWrEiBG9Lw4aNCicyWQ2mxmE0aatDampht4/d8+va+8rAwd61mub4+Kkv1FLi3HgQIPZ7PcfUkEBqqr6tKSmxpCXZ/D5O2kwGIxGo9lsTk01tLXFmM3B5yBarUhJgUZ+w9PS0NLi+48mjdVqSEmR84ZQ8gMhN9dQXW0wmw3Bn0oa4Pm31vs/x/7EAGhvb1+8ePGoUaNeeOEFALm5uU6ns6qqKicnB0BZWVleXp6/18fGxl5xxRXFxcXyNV40k8lkCjAzgSJRWxtSUtD75+52u10ul9dvQloaGhtN/n9/g2tpQWqqIcDvV3IyjEa0t5u6h/Fqa5GdDX+/kwaDwWQypaWhuTnQbbu1tSE52e/dwiwtDc3NcjbGakViosx/OuU+EHJzcfCgVn4WFJjL5QKE/rCMdrv9mmuuGTx48B//+EdPcqalpV100UXvvPMOAKvV+q9//euyyy5TtMVEYgWdzOkR+nyZoGOE6LfnSHk5cnODvET4CgrtLCIEEBsLkwlWq2w31NcYYU4OxwgjU8xzzz23cePG4uLihQsXAjAYDJs2bfrNb35z1VVX7d2799ChQ6NGjZo/f77a7STqI+hkTo/Qd1kTHoSjR3d9e+4cCgqCvCQ1FY2NghqgtcNgPdN8vE7bkKy1FaHU62GWmckgjEwxt9xyy7x587yuFhcX79+//7PPPvv+978/Z86coCONRGEmJJ8gx8TRhoZAS+M9vCpCIUEovCLUWhB6Jo4GXR8ikHaOWhQiK8t7zShFhpjc3NxcX/04BQUFXDtImiUwHjIyQg1CIT2TvYPQ7UZ5OfLzg7xkwACUlAhtgKaCUOwZUoFpZ9McITIzUVcHlwssDSIMf56kSwIrwvR0HxuBCtfRAYcj+IrvggKcO9f1dV0dEhKC9xwK7xoV2AkcNmLPkAqspUVPQWg2IzlZhl0aSGsYhKRL4akIBcZtURFOner6+vRpDBoU/CXCu0YFtiFsZK8IddQ1CvaORigGIelSeCpCge8ydGhPP2dJCYYNC/4SXU+WidqKEEBmpo/jJ0nvGISkS0LmsCBcFeGQIThzBi4XAJw4IXMQNjbi212eNEHe7UY1tThECFaEEYlBSLoksE4KT0VosSA9HaWlAFBSgqFDg79E+KHBWqsIU1PlrAj1NVkGrAgjFIOQdElgneTz1FzhBNadAMaNw6FDAHDwIMaODf58UZNlNFURynsSk+4qQgZhRGIQki4JnywThooQwPnnY/9+OJ04cgTnnx/8+SkpaG+H0+9W3j20cwaTh9hThQNwu3W2swwYhBGKQUi6JDCi0tLQ1gaH1LMNhAfhpEn48kt88w1ycgTllsGA5GRBiaLBWaNyBaHViri4QCcYaxCDMCIxCEmXBMaDwRDS5jLCJ6pccgm2bME//wnh2xEKHCbUYBDK1TWquymjYBBGKAYh6Y/DgY4OoZ+hGRnSP7mEB2F2NqZMwZNPYulSoTcXOEyowVmjclWEWpsHJASDMCLFBH8KkcY0NoookkL55BIVQq+/jg0bMHu20OenpgavCAVubRNOwqf5BKW13eOEyMwMadSZtIkVIemP8MmcCG2+jKggzM3FsmUibj5wYPAgFPUnDQ8Zg1Bru8cJ4VmZ6lkzShGDQUj6I2rYLJSKUNHxOSFjhFobIISsk2V0t3YCgNmMxETZ/itAGsEgJP0RVSeFEoT19Rg4UOJrgxo4MPj2zYo2QJqkJNhs0ifi9qbBmBeCvaORh0FI+iOqxzKUIFS0Z1JIRai1mTIADAbZikI9TpYB58tEIgYh6Y+oSiKUzSEVzaG0tOAVoTZrJrmCUI9do2AQRiIGIemPqA5DyUHocMBuV3Chm04ny0C++TI6rQhDWZBD2sQgJP0RNdtQ8v/fPYs0DAYprxVCp12jkC8I9bh8AqwIIxGDkPSnsVFEnSS5IlS6GhOy5Y0GJ8sg6itCBmHkYRCS/oiKh/R0tLSgs1P0uygdhOnpeg1C4WdIBSZqYwTtYBBGHgYh6Y+oiDIakZ4u5ZOLQeiPXEGozalAQTEIIw+DkPRHbERJ6x1VOggTE+F2o7090HPq6zU6WUauilCDI6BBMQgjD4OQ9EdsnZSdjaoq0e9SV6d4NRa0KGRFqEEMwsjDICT9CVsQZmSIfpUoQYOwrg7p6cq2QQIhCz+E0ObikKA8Qeh2q90Okg+DkHTG5UJLi7hKQptdoxAQhNqMCllmjXqOp9fjgvr4eMTGynYoI2kBg5B0pqkJSUnijjXPyUFlpeg3CkO3ZOCTMTzDh5o6g8lDlq7R5mYkJOjsePpu7B2NMAxC0hkJ+SQtCMMwRhj487S2VvG+WWmEbBcelE4HCD1C2bePNIhBSDojYdhMsxVh4CCsqYnkINTplFEPVoQRhkFIOhPOIFR6oopOK8K0NDQ3w+kM6SbaXBkiECvCCMMgJJ2prQ1TEIahIAtaEWZlKdsAaYxGpKSEOl8mDP/PUA6DMMIwCElnJPRYenZZE3WWbGcnWloUL1kCB6E21054CNkWJzBdd41KW5BDmsUgJJ2REA8GA7KyxBWF9fVITYVR4X8fWVm67BqFsB3DA9PmXgECsSKMMAxC0hlpdVJuLsrLRTw/PCGUnR3o87S6GtnZirdBmvT0UOfLaHOJpECsCCMMg5B0RtqGL3l5qKgQ8fzwBGHgPtuqKk0HYegVoX6DkBVhhGEQks7U1CAzU/SrtFkRGgzIzPRbW2g5CANvBSBEQ4OOu0ZZEUYYBiHpjLTJnNqsCAFkZ/sdvNR4EIa4kE7XY4QSpl+RljEISWekVYR5eSgrE/H86uowLV3IydFlRZiZGWpFKGEZjHYYjcjMZO9o5GAQkp643RLHCPPztRuEPkvV5mbExCAhIRxtkCD0ilDLc2KFkLY4lbSJQUh60tCAxETExop+YUEBzp0T8fywVWP+ErqsDHl54WiANKGPEdbWSqnstYNBGEkYhKQnkj89xVaE0jpgJfDXsPJyTQdhiJtttrfD7dZuvSsEgzCSMAhJTyQvrUtNRWcnWltFvFF4ukYDBGF+fjgaIE1WVkgVod77RcEgjCwMQtKTUHosRfWOhm0xu067RtPS0NaGjg6JL5c20KspYhfkkJYxCElPQgnCwkKcPSvomQ4HmprC9EntL57LyjRdERoMIc2X0ewJU8KJXZBDWsYgJD2prEROjsTXFhaitFTQM6uqkJWl+EajHhkZsNnQ0uJ9/cwZDBoUjgZIFsqi8lB+jhrBijCSMAhJT0KpCAcNEhqEFRVh/ZgePBhnznhfPH0aRUXha4MEoQRh2IZglZOXxyCMHAxC0pMQu0aFV4ThDMKiIpw+7X3xzBkMHhy+NkgQShCGbVKucnJyUF0Nl0vtdpAcGISkJxUVyM2V+FqfhZe/d1E3CBsaYDBo/bi+AJvDBRUBFWFsLFJTublMhGAQkp6Esrpu8GAfhZfs7yLBsGE4frzPlZMnMXRo+BogTW6u9NkiERCEEL9LA2kWg5B0w+UKaVXDoEEoKxPUl3XuHAoKJL6LBCNHegfhsWMYMSJ8DZAmlGmT1dW6nywDBmEEYRCSblRVYeBAmM0SXx4Xh4EDBU1wCHMQjhiBY8f6XDl2DKNGha8B0oQybVLjqyQFYhBGDAYh6UYoA4QeQ4agpCT408K8hm/oUJSXw2bruaKXilBaEDqdqKtj1yhpCIOQdCP0Qm3YMEFBGOaK0GzGyJE4fLjnyoEDGD8+fA2QJjcXlZVwu0W/sLoaAwciJkaBNoWX8C0aSOMYhKQbpaUoLAzpDkOH4uTJIM9paUFHR7jPjJ0wAfv3d31ts+HUKYwZE9YGSBAfj8REKTuOVlREQr8oxMxDJo1jEJJuhB6EQipCVRbwTZqEL77o+vrgQYwcKeWoqfArKBC6NLO38vJQu7g1gkEYMRiEpBuyBKHX/Mz+VAnCmTOxbVvX19u2YebMcDdAmsJCKYNkpaVh7XlWTl4eamul7zxO2sEgJN0IffvNkSO952f2p8reZpMm4ezZrj2st27FrFnhboA0wjfr6S30/9BohMmEvDwOE0YCBiHpRugRlZ6OmJggG4OpEoQxMfjud/GPf6C5GZ99hgULwt0AaaTNFikt1fp+4sINHSpo+hVpnP5nblF0sNlQVyfDqoZRo3DsWKBV+SdOYPr0UN9Fgltvxb334tw5LFqk9c3VuhUVYd8+0a+KmIoQguchk8axIiR9OHMGhYUyHI00ZgyOHAn0hBMnMHx4qO8iwcKFmD4df/sbnnxShXeXZsgQnDol+lXaP2FKOFaEkYEVIelDSQmGDJHhPoGD0O1GSYk6QQjg1VfhcoXpHERZFBWJDkKHAxUVEVUR7t6tdiMoZPr5N0fR7fhxeTZbCRyEpaVIS0NiogxvJI2OUhBAVhasVh+nCgdw9ixyc6Xvk6c1I0fi6FG1G0Eh09U/O4oU9fXYvl3cWW5y7To2fjwOHPD76JE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