{ "cells": [ { "cell_type": "markdown", "source": [ "# Tutorial" ], "metadata": {} }, { "cell_type": "markdown", "source": [ "DFTK is a Julia package for playing with plane-wave\n", "density-functional theory algorithms. In its basic formulation it\n", "solves periodic Kohn-Sham equations.\n", "\n", "This document provides an overview of the structure of the code\n", "and how to access basic information about calculations.\n", "Basic familiarity with the concepts of plane-wave density functional theory\n", "is assumed throughout. Feel free to take a look at the\n", "[Periodic problems](https://docs.dftk.org/stable/guide/periodic_problems/)\n", "or the\n", "[density-functional theory](https://docs.dftk.org/stable/guide/density_functional_theory/)\n", "chapters for some introductory material on the topic.\n", "\n", "!!! note \"Convergence parameters in the documentation\"\n", " We use rough parameters in order to be able\n", " to automatically generate this documentation very quickly.\n", " Therefore results are far from converged.\n", " Tighter thresholds and larger grids should be used for more realistic results.\n", "\n", "For our discussion we will use the classic example of\n", "computing the LDA ground state of the\n", "[silicon crystal](https://www.materialsproject.org/materials/mp-149).\n", "Performing such a calculation roughly proceeds in three steps." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "3×3 Matrix{Unitful.Quantity{Float64, 𝐋, Unitful.FreeUnits{(Å,), 𝐋, nothing}}}:\n 0.0 Å 2.7155 Å 2.7155 Å\n 2.7155 Å 0.0 Å 2.7155 Å\n 2.7155 Å 2.7155 Å 0.0 Å" }, "metadata": {}, "execution_count": 1 } ], "cell_type": "code", "source": [ "using DFTK\n", "using Plots\n", "using Unitful\n", "using UnitfulAtomic\n", "\n", "# 1. Define lattice and atomic positions\n", "a = 5.431u\"angstrom\" # Silicon lattice constant\n", "lattice = a / 2 * [[0 1 1.]; # Silicon lattice vectors\n", " [1 0 1.]; # specified column by column\n", " [1 1 0.]]" ], "metadata": {}, "execution_count": 1 }, { "cell_type": "markdown", "source": [ "By default, all numbers passed as arguments are assumed to be in atomic\n", "units. Quantities such as temperature, energy cutoffs, lattice vectors, and\n", "the k-point grid spacing can optionally be annotated with Unitful units,\n", "which are automatically converted to the atomic units used internally. For\n", "more details, see the [Unitful package\n", "documentation](https://painterqubits.github.io/Unitful.jl/stable/) and the\n", "[UnitfulAtomic.jl package](https://github.com/sostock/UnitfulAtomic.jl)." ], "metadata": {} }, { "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n Energy Eₙ-Eₙ₋₁ ρout-ρin α Diag\n", "--- --------------- --------- -------- ---- ----\n", " 1 -7.905213105183 NaN 1.95e-01 0.80 4.0\n", " 2 -7.909825278275 -4.61e-03 2.99e-02 0.80 1.0\n", " 3 -7.910051937518 -2.27e-04 3.03e-03 0.80 3.0\n", " 4 -7.910052832848 -8.95e-07 4.72e-04 0.80 2.5\n", " 5 -7.910052852330 -1.95e-08 4.01e-05 0.80 2.0\n", " 6 -7.910052854035 -1.70e-09 4.54e-06 0.80 3.1\n" ] } ], "cell_type": "code", "source": [ "# Load HGH pseudopotential for Silicon\n", "Si = ElementPsp(:Si, psp=load_psp(\"hgh/lda/Si-q4\"))\n", "\n", "# Specify type and positions of atoms\n", "atoms = [Si => [ones(3)/8, -ones(3)/8]]\n", "\n", "# 2. Select model and basis\n", "model = model_LDA(lattice, atoms)\n", "kgrid = [4, 4, 4] # k-point grid (Regular Monkhorst-Pack grid)\n", "Ecut = 7 # kinetic energy cutoff\n", "# Ecut = 190.5u\"eV\" # Could also use eV or other energy-compatible units\n", "basis = PlaneWaveBasis(model; Ecut, kgrid)\n", "# Note the implicit passing of keyword arguments here:\n", "# this is equivalent to PlaneWaveBasis(model; Ecut=Ecut, kgrid=kgrid)\n", "\n", "# 3. Run the SCF procedure to obtain the ground state\n", "scfres = self_consistent_field(basis, tol=1e-8);" ], "metadata": {}, "execution_count": 2 }, { "cell_type": "markdown", "source": [ "That's it! Now you can get various quantities from the result of the SCF.\n", "For instance, the different components of the energy:" ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Energy breakdown (in Ha):\n Kinetic 3.0795155 \n AtomicLocal -2.1806376\n AtomicNonlocal 1.7339393 \n Ewald -8.3979253\n PspCorrection -0.2946254\n Hartree 0.5417570 \n Xc -2.3920764\n\n total -7.910052854035" }, "metadata": {}, "execution_count": 3 } ], "cell_type": "code", "source": [ "scfres.energies" ], "metadata": {}, "execution_count": 3 }, { "cell_type": "markdown", "source": [ "Eigenvalues:" ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "7×10 Matrix{Float64}:\n -0.170182 -0.131801 -0.0883282 … -0.0562607 -0.11494 -0.0700168\n 0.201343 0.0909036 0.0122924 0.0111144 0.0420613 0.0176495\n 0.249295 0.174773 0.176137 0.132964 0.220114 0.11233\n 0.249295 0.231428 0.20237 0.161043 0.220114 0.190456\n 0.350986 0.360027 0.340134 0.291807 0.320727 0.327376\n 0.36997 0.395897 0.389483 … 0.331814 0.38819 0.460232\n 0.36997 0.401676 0.412474 0.565533 0.38819 0.462717" }, "metadata": {}, "execution_count": 4 } ], "cell_type": "code", "source": [ "hcat(scfres.eigenvalues...)" ], "metadata": {}, "execution_count": 4 }, { "cell_type": "markdown", "source": [ "`eigenvalues` is an array (indexed by k-points) of arrays (indexed by\n", "eigenvalue number). The \"splatting\" operation `...` calls `hcat`\n", "with all the inner arrays as arguments, which collects them into a\n", "matrix.\n", "\n", "The resulting matrix is 7 (number of computed eigenvalues) by 8\n", "(number of k-points). There are 7 eigenvalues per k-point because\n", "there are 4 occupied states in the system (4 valence electrons per\n", "silicon atom, two atoms per unit cell, and paired spins), and the\n", "eigensolver gives itself some breathing room by computing some extra\n", "states (see `n_ep_extra` argument to `self_consistent_field`).\n", "\n", "We can check the occupations ..." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "7×10 Matrix{Float64}:\n 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0\n 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0\n 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0\n 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0\n 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0" }, "metadata": {}, "execution_count": 5 } ], "cell_type": "code", "source": [ "hcat(scfres.occupation...)" ], "metadata": {}, "execution_count": 5 }, { "cell_type": "markdown", "source": [ "... and density, where we use that the density objects in DFTK are\n", "indexed as ρ[iσ, ix, iy, iz], i.e. first in the spin component and then\n", "in the 3-dimensional real-space grid." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=1}", "image/png": 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Ua2HFJfbTcAWDk4N/Z6mE90OYhZhKgQAA4PUE7YchCnsTA70dBkJDWNVTcSSDXsTEYdnbkMT2cSSR8k6ZaMp0X6ZGCz/jlkyyt/c+W1ILr/oZLjxhIDQEKyV8gFe7spdbBZtuaT+SzSkTrcUQ2BCqWHaBrcbRExmr0sBbF9lPwxWG3GkC+6SBvOzDsAA/4BlsMrbionamP9OpHd4ONmmgKwm2J5swlULGPrqu7e9i6FETDIQGwhD4oq9i+QW2VM13VRAfrhbQo5ns8iBMmXiC9aHMhhvanEq+64H48KCMfnWHXWvwjSYwEBpOiAMZ1p6suYbjPnL0RqL2wxBFO0yZeJKOVuQVX2Ylnm4tS0vOsUu6KdwtDD1qgoHQoNb2VmxLYVNLcK5QRu7fvz9rzdYCVebLvtjdWuTdYMXBxDvvbPwmNzeX77ogw4nJpjeK6KKuPHQT7JkG5WwGy4IUS87j1a6MDBn/4h6VddXX0+V7zEQrWSmhZsuUz++bTnhpFt91QQaiZmFBgnZjGGPCx+wBBkJDWxDI3C2B3zLwplAuzKxtje7Fd/Zw4bsiYuJmZw13zzq5uvFdEWQgn99mPa1gTAd+QpL8DsbmmzEDn/dVzDmrHexmxMu1DzKwFz49dPv61R9e7s13RcTkWvyJgV9fe3FUCN8VQYaQVwVrrmnjxvAWj7gKv6mpqf3797e1te3Vq9fly5cfL1BTUzNjxgwHBwdPT8+vvvqq7vlvvvnG19fXwcGhd+/eMTExuie1Wu3ixYudnJzc3d3XrVvHUZ0NZog7CbAlm27hGnFZOJXLTIjoxjA4+tIKxsbGz4R1O6niux7IIFZc1L7iy/hZ8zZ5wFXnfPHFF6OiolQq1fTp0ydMmKDVNpwV+/jjj+/cuXP37t1Dhw698847ly5dAoDr168vWLBgz549+fn58+bNe+6552pqagBg69atJ06cuHHjxpkzZzZv3nz06FGOqm0wG8OY9Um43b70VWvh4iPa1xEvelptgJM2Bo8wk4HL+fT3TPbtHnyOj3ESCK9du5aSkrJixQoTE5M5c+awLHv8+PEGZbZt27ZixQpbW9ugoKAXXnhh+/btAPDw4cMOHTqEhIQAwPPPP19aWvro0SMA+OabbxYvXuzs7NypU6cZM2Zs27aNi2obUkcrMsOPWXERvx8l7mwu7WZHrIzwC73VutnSwhqaWYFNJ2UU4PUE7dreCmtjPqvBSSBMTU319fU1NTUFAEJIt27dUlJS6heorq5OT0/v3r277mH37t11BYYMGWJkZLR+/fq4uLhFixZNmDChffv2AJCSkvJ4YbH7V7DidA6NU2E/l7LYbDbKDVeLtgUBGODKnMzBDiJl36ayGham8n0YCyeTk4WFhZaWlnUPra2tCwoKGhQAACsrq7oC+fn5AGBhYTF16tTNmzcfOXIkPT19w4YNAFBbW1teXl5XuF27drrCjaqurl6wYMGCBQt0DydNmtTM7WNFRQUhfH5JvduVWZBgdHporYjOIuC90cQlOkP5fpAWG60NKioqIuyNjqWT8S4avusiGuL6pJVryDuXjHdHqCsrODymztzc/Ikz9JwEQjs7u7KysrqHJSUlDg4O9QvY29sTQkpLS21sbACguLjY0dERAPbu3btjx47k5GRzc/O0tLRu3bp17drVz8/P0tKytLS07tV0hRtlamr62WefzZ8/vyX1pJTWD9iGN70r7ErT/JRt/poB91l/Srw3moiUqSG5VD3I00RdqcVGay1K6Uhv00/uaC0tTfmui2iIq3u+f1470gMGdDDnuyLcDI36+vrevXu3uroaACilN2/e9PX1rV/AxMTEw8Pj5s2buoc3b9708fEBgFu3bvXs2dPc3BwAvLy83Nzcbt++rXvBxwtLAAH4NFzx7iVtcS3fVUEcOJXDhjoRU0ySaStfa8IQuIs7MUnRvVK68y77YYggugcngbBHjx6+vr7r1q1Tq9Vbt26llA4dOhQATpw4sWLFCl2ZV199de3atSUlJTdv3tyzZ8/06dMBoE+fPidOnLh16xYA/PrrrxkZGcHBwbrCGzduzM/Pf/jw4datW3WFpSHYnoz1ZN7HnRWlKDabRrmJ5l5fmAa6klicJpSiBYnat3soXPm/GwTgLqF+9+7dr7766n/+859OnTrt37/fyMgIAAoLC+/fv68rsGzZsvT0dG9vb0tLyw8//LB3794A8Oyzzy5btmzs2LFFRUUdOnT44YcfvLy8AGDWrFmpqaldunQxMjJasGDBqFGjOKo2Lz7qrQj4r3q6L9PNTjSD+6glYrPp1v4YCJ9KlBs5kkFn+fNdD6RXh9LZtDJ4PUAovYNQKqmrrQULFvj4+LRwjrCsrKxuDQ6/Nt9iD6SzMaNEsNGPcBpN4PKqwG+fOv+fSgXBRmsLXaNlV9Kg/ZrcKUoRLSjjkSg+abUsdPtZsylcMaK9UP5ThRKQZW5uAJNfDfvTMK1QOk7msJGuDG60/ZTczImdCblRJKnrdZnbkMQG2hLhREHAQCgQCgJf9FUsOsdW4kJxqYjNplGuAurq4jXYjcRmYyCUiKwK+skN7TqDH73bPGHVRs4iXEioI/nkBt4USkRMNh3sjoFQD6LcSEwW9guJWHaBnRfA+PC3rWijMBAKyCdhzGe3tOnlePEren+U0zI1DbQVVm8XqUFuTHwuVWMoFL+EXBqnosuDBJEyUR8GQgHxsCCvByiWX8AeL3ox2TTKDZd36Ie9CXhbkUv5eIEobiyFN85p14cyFsJbFIiBUFiWdWcuPKKnMHFK5GKz6WDcYlR/BrsRPIlC7LamsCYKmNRRiEFHiHWSMzMjWN+Hmbbx56937NJocOWMWJ3MobjXth5FuTGx2ThSIlbl5eVrN3319vcnP+8r0GXUGAgFxzEjPidm1/xvz/ywZy/fdUFtkVxMlQx0tBJmlxelSBdyKZ9W4ZWhOL2zet07J7Mrf3rbsTqH77o0DgOh4Dg5OVmUZtKcOx7t3fmuC2qLGEyc0DdLJXS3I2dzcXRUlLw7eMCDi+2gWrAbggtv1lL2/P39k+KOB+4p7xPhxXddUFvEZtMJ3hgI9SzKjZzMYYe4C27BIXqiIS/McFUPSH7VXbCBEO8IhaiDi0OIb3s8s1eMWApnVOxAvCPUtyg3JgbT6sUpOos+E9JZsFEQMBAK1lB3JhqTiEXoagF1MiVu5hgI9ayvM7lTRPHAMjGKzmKHCntzCQyEAjXUnUTjenERisUNZbhhzECoE4lT4dWhyNSycFZFBwn7PDJBV07OQhxITiXNqeS7HqiVYrJZTJzgCI6OilFCLvW3IXYmfNejWRgIBUpBYKAbcwJzp0SlloXEXDrABbsVJ6Jw920REv64KGAgFLKh7iQ6E7u9mJzPo77WxFbYF7/iFeJAsiqoqorveqDWiM6iQ92FHmiEXj85G+5OorNYjIQiEpPN4gQhdxQE+rswp3CYRDyKaiClmIY5Cb1TYCAULi8rYqEkNwsxFIpGbDaNEvaiALGLciOxuBOveJzIZvu7EBPBJ39ipxU0XDsqIpUauFpA+zkL/eJX1PCQXnERxbgoYCAUuKHuBLMJxSJORUMciACPmJGSAFtSoaZpZRgLxeFEFh3aXgSXhhgIBS3KjUnIpTVavuuBWiA2m8VxUa4RgEFuDI6OisK9UlqjhS42GAjR07Exhi62JCEPu70I4F7bhoFJFGIRnUWHuhNRdAkMhEI31J1EZ+LoqNAV18LdEtpH8KvjJGCoOzmBq6nFQBcI+a5Fi2AgFLqh7gyulxG+k9lsPxdijP2Je56WxNyIJBdjpxA0LYXTOaKZLBBHLeUs3IncK6X51XzXAzUrBhMnDCjKjeBeawJ38RH1sCCu5nzXo2Ww6wqdkoEIF3IyB0dHBS0WJwgNCKcJhU9E46KAgVAUcHRU4HIqIa+K9rAXTbcXu8FuzKkcVot9QsCis9ih7UUTX0RTUTkb6k6O46ajAhaTzQ50YxiMg4bibAZu5uRqAXYKgSpTw7UCGiGezSUwEIpAFxvCUrhbgt1eoHBc1PBwixkhO5XD9nEk5uLZXAIDoTgMxr3WBOxkDh7Ga2hRbiQWd98WKrHsrFZHTHWVM9x0VLDul9JaLfhZYyA0qIGuuOmScIlrpQxgIBSLYe7MyRxWjVfAwhOTTQfjkfQGZ20M/jbk/CO8OhScrAqaXy2ytWMYCMXBwRS8rcilfOz2ghObTaMwEPJhMI6OCtLxLDpYbGvHMBCKBo6OChAFOJXDDsJAyIcoNwbXywiQ6MZFAQOhiAx1Z/BIJqG5WUjbGRNPS5F1e2no50yuFdByNd/1QPVQgJhsVnSTBRgIRaO/C7leQEtq+a4HqgdPnOCRuRH0dCDxuXhTKCDXCqitMfGyElmnwEAoGqYKCHUip3GvNSHBCUJ+RbkxOE0oKGIcFwUMhOKCe60JipZCfC47CPfa5s9g3H1bYKKzWAyEiFu4XkZQLj6iHSyIoynf9ZCxUEdyH89mEYxqLZzPowNcxRdWxFdjOethT4pqaVoZxkJBiM3GDWV4ZsRAP2dyRoWjo4IQp6Ld7Yi1Md/1aD0MhGJCdJMiORgIBSE2WzTnjkoYJlEIR3QWK66d1eqIstJyhqOjAlGthQuPaH8XvCPkGR7SKxwiXSkDABxuD3758uUjR444ODi8+OKLNjY2jxfIzc3dvXt3ZWXlc88916VLFwAoKSn58ccf65eJiIgICAhIT08/duxY3ZMjR4708PDgruZCNtydLL+gZalCXBs3SE9CLu1qS9op+a6H7AXZkYJqmlVB3S2wS/ApvxrSymhvR1H+L3B1R3jkyJGhQ4cCwOnTp8PDw6uqqhoUyM/P79mz561bt6qrq8PDwy9cuAAA1dXVl/8nISFh1qxZOTk5AJCUlLRy5cq6H5WUlHBUbeFztyAOpuQansTGt9hsFicIhYAhMMCVOYnzBXw7nsUOdGWU4hxk5OqOcPXq1WvXrp05cyalNDQ09Mcff3z55ZfrF9i6dWtwcPA333wDAMbGxmvXrt2/f7+zs/OWLVt0BX788cfTp08PGjRI97BTp051P5I53ehoTwf8FuZTbDb9d28F37VAAH8eyUSndua7HvIm3nFR4OiOsKKi4ty5c6NGjQIAQsiIESNiYmIalImJiRk5cqTu36NGjXq8wPbt21955RWG+bOGhYWFX3/99b59+woKCrios4gMdSe41xq/ytRws4iGiXMUSHpwmlAIYsQcCDm5I9SNZzo5Oekeuri4JCQkPF7G2dlZ929nZ+fS0tLy8nJLS0vdM5mZmSdPnvz66691D01MTDp27Hjz5s3k5OQ5c+YcO3YsJCSk0bfWaDQHDhxIT0/XPQwKCpo4cWJT9ayurlYqxTfJE2YLUx4pCsureTkAWqSNpl/RmaSXPSGa6mpNi8pjo7VByxvN0wS0rOLWo+pOVlxXSuj4+qQllwABhYdJTbXwcjqNjY3rbqiawslXqe5dKf3zGk2r1SoUDQeRGIZh2T9va3T/qF9m27ZtUVFRnp6euofDhg0bNmyY7t9Lly596623oqOjm3p3c3NzOzs73b+trKwef+s6CoWimZ8Klo0CutvBuQLFUDce3l2kjaZfZ/JgkCu0vB2w0dqgVY02yBVO5yl8G1mTJy98fdJO5sIQt1b0CEMi5Mn3qZwEQldXV0JITk6Ol5cXAOTk5Li6ujYo4+bmprtxBIDs7GxbW1szMzPdQ0rprl271qxZ0+iLDx48eN++fU29tZGR0bBhw+bPn9+SeiqVSpFepw9rz55U0VGePHzsxNtoenRSpfk6QqFUtnQgCButDVrVaEPas79l0LmBQvwiNiS+PmmxKs0/OzNKkS6V4WiO0MzMbNCgQQcOHAAAjUZz+PBh3XyhblGoVqsFgJEjRx48eFB313jw4MG6+UIAiImJKS4uHjt2bN0zGs1fI1AnTpzw8/PjotoigtmEPCqogfRyGoKLlYRkiBuJzWZZ7BN80LAQr6Ki3nSXq1mmlStXjjW++48AACAASURBVBs37u7du8nJyRYWFuPGjQOAhw8f9urVq6ioyMbG5pVXXvnqq6/Gjh3r7Oz8yy+/nDp1qu53t23bNnXqVBMTk7pnpk+fXlRU5OnpeefOnRs3btTPKZSnPo4ko4KqqsDFjO+qyE9MFjvAlTESca+XIHcLYmdCbhbR7nZ4gWJoiXm0cztxb7rLVSCMjIy8fPlyTExMVFTUM888Y2xsDAAdOnQ4fvy4bkWMtbX1pUuXDh8+XFlZ+cEHH9QfO507d26De76PP/747Nmz+fn5Q4YMiYqKateuHUfVFgsFgQGuTEwWO6Uzfh8bWiyeQShIurWjGAgNT6QnTtTH4bpDb2/v1157rf4zFhYWuix7HUtLy8mTJz/+i/3792/wjIuLy4QJE7iopHjpRkenYO6UwcVk03kBeP0hOFFuZNdddlFX/K8xtONZdI3Ic2rxQyNWukCIcyIGllFBS9W0K952CE+UGxOnomrMsDWs4lq4U0T7Oom7R2AgFKvO7YiJAu4UYyg0qJgsGuWG+7wKkb0JeFuRy/nYIwwqNpvt60xMxH1DiIFQzIa4k+hM7PYGhROEQoZbzBhedBYV6dFL9Yn+D5Az3GvN8E7m0Cg3DIQCFeXGxGZjjzAoUW8xWgcDoYgNcWPiVLRGy3c9ZCO5mDIEOrUTfbeXqkgXcvERrWrZvnfo6aWV0XJJTJljIBQxWxPwsyHnH+FYkIHEZNMheDsoYFZK6GZHEvKwRxjI8Sw6zF0KU+YYCMUNR0cNKTYbx0WFLsqN4OiowURn0aHtpdAjMBCK21B35jiulzEIlsIZFTsQV8oI22A3JhbXyxiElsLJbHaImHdWqyOFv0HO+jqT5GJaWMN3PWTgWgF1MiXuFhgIBa2vM7ldREtq+a6HDFzOp67mxNWc73roAwZCcTNmoJ8LOYljQdyLwXFRMTBmoI8TOaPCHsE5aawX1cFAKHpD3Rk8icIAYrNZDISiEIWjowYRncVKIINQRyJ/hpwNdSfHMBByTM1CQi4d4Ir9RQQGuxEMhFyr0MCVfNrfRSKXhtixRa+rLVGz8KAMez6HzudRX2tiZ/Lkkoh3IQ4ko4LmVvFdD0k7nUNDHIilVE6bxkAoBYPd8JxebuEEoYgoCPR3YU7l4DQhh6Q0LgoYCKUBD6znWmw2GyWJZeIyEeWKo6Pcis6iwySRQaiDfVsKhrozsdmsFjs+Nyo1cLWARkhlOkQOBrvj7tscyq6k2ZU02F46PQIDoRQ4m0F7C3IJ91rjRpyKBtsTCw4PsUZ6FmhLKtQ0DSfOuRGdRYe4MQrpxEEMhFKBo6PcwXFR0SEAA92YkznYIzghpQxCHezeEjHUncFNRzkSm00H40oZscEkCo5QgNhsdggGQiRAkS7kSgEtVfNdD8kproXUEtrHSVLdXg6i3EhMNouRUO9uFFILI+JtJakegYFQIsyNoLcDiVNhx9ezk9lsX2dijB1FbDpaEVMFSS7GHqFn0hsXBQyEUjK0PY6O6l9sNsUJQpGKwtFRDkRnsRgIkXANcyfReCSTvuEEoXhhINS7WhYSc+lAye01KLW/R86C7cmjappRgT1fb3KrILeK9pBQvpSsDHZjTuZgfq0+xalooC2xldxegxgIpYMhMMiNicEkCv05kcUOcGUYjIPi5GwGrmbkWgH2CL2R5LgoYCCUGMwm1K9Y3GJU5Aa74+ioPkVnUSltMVpHgn+SnA11Jydwybj+xObgBKG46ZIo+K6FRBTUwP1SGirFVCIMhJLiaUmsjUlSIYZCPbhfSmu01N9Ggt1ePga6Mgm5tEbLdz0k4UQWG+nCKKUYNKT4N8kbjo7qS2w2HYyJEyJnYwx+1uQCbsOrD5LMINTBfi41Q91JdCaOBekBjotKw2B3HB3Vj5hsDIRIJAa7MYl5tErDdz1EjgKcymYHYSAUvyg3BtfLPL3UEqphQaozBRgIpcZKCd3syNlc7PlP5WYhtVQST0tpdntZiXAm1wpoBV4aPp3jWXSYRG8HAQOhJA11J7jX2tMoLi5+b8MXXYsu8F0RpAfmRuCVdvTtjdtqamr4rouISXiCEDAQStJQdwbXyzyN15e9e/BueczHc0tLS/muC3pa169fv/fzpv+LTvr8q61810WsNCycyZHyqZyS/cPkLNSRPCyjeVV810O0vD09yP1EKyWYmpryXRf0tOzs7EwrH0HWDU8Pd77rIlbnH1FvK+Jkxnc9OIOBUIKMGIh0ZWJxpVxb/fP1N12n/vve1URjY2O+64KeloeHx43EU8YvbxkzdjzfdRErqe6sVgcDoTRhNuHTSMyjkcFdzMykewEsM+6Otn6dvXHT0TaT6s5qdaT8t8nZUHdyHANhWyXm0nAp7iMlZ+HOJDEPe0RblKnhRiHt5yzlHvGEQFhRUZGamlpSUmKY2iB98bMmRgyklGDPb4vEPBou6W4vQ+FOGAjbKDabDXciZkZ814NLTQbCnTt3+vr6Wlpa+vn52djYdOjQ4dNPP6UUP0miMdiNHMdzeluvTA33S2l3OwyEkhLmRBIxubZNorPo0PYSHzts/M9bv379K6+8Ymdnt379+l27dm3cuNHPz2/RokVLliwxcP1Qm+E0YdtceESDHYixxDu+7HRuR2pZmonHVrfecUlnEOo0crtbW1u7evXqWbNmffXVV3VPvvHGG6tXr161atWKFSscHR1b+OolJSXW1tbNFKisrFQqlUqlsiWvVl1dzTAMLuRroSHuzKx4tZpVSHK3eO7gBKFU9XFkzuXR573xP7cV0stpSa30B0ga+Y589OhRaWnpvHnzGjw/d+5crVabnp7ekte9ePGij4+Pj49P+/btT5w48XiB0tLS0aNHu7u7Ozg4rFq1Svfkrl277P4uIyMDAGpqaiZPnuzi4uLo6Lhw4UIcoW0JexPo1I6cx3mRVkrMYzEQShKul2mD6Cw6xI2RfH9oJBBaWloSQgoKCho8n5+fr1AoPD09n/iilNJp06a98cYbeXl5mzdvnjJlyuObG/373/8GgEePHt2+fXvLli2nT58GgH/84x/3/2f58uXe3t4eHh4AsHnz5oyMDJVK9fDhw99+++3nn39u218rN7jXWmtRgAuPpHn0KAp3IucwELaStHdWq9NIILS2th48ePD8+fPv379f92R2dvbMmTPnzZvXknHRixcvqlSqmTNnAsD48ePbtWt39OjRBmV27dq1aNEiIyMjd3f3KVOm7Nq1CwBMTExs/+enn36aPn26rvC33377+uuvm5qa2tnZvfbaa7rC6Ilwr7XWultCLZXEzVz6PV+GejuS6wV4SG8rsBROZrODZRAIG18Su2PHjsGDB/v6+gYFBbm4uOTn51+/ft3Y2NjR0XHSpEm6MrNnz46Kimr01+/fv9+5c+e6mT9/f//6MRUAKisrVSpVly5d6gp8//339QskJSXdvn37xRdf1D188OBB/cLNBEJKaUFBwYMHD3QPLS0tnZycmv7zJS7CmdwqokU1YGvCd1VEIjEPJwgly8IIfK3JtQK842+pqwXUwZR4WEi/uRoPhO3bt798+fJ333136tSpzMxMlmW7desGAA8fPqwr08x+xCUlJebm5nUPraysioqK6hcoLi4GgLoylpaWumfqfPPNN88995ytrS0A1NbWVlZWNlO4vtra2s8///zbb7/VPRw1atTatWubKlxeXt7UjySjt73y6MPaZ9z1NkAq7UY7k6nsaU3LyvR8Zo+0G40jXDRaLzvlqQx1gJlkz2TSb6MdfmA00AnKysS9bbG5ublCoWi+TJNJkpaWlnPmzJkzZ04b3tjR0bF+Dn5xcXGD2zIHBwdCSElJiS7UFRcX1x9xra2t3bNnz969e3UPjY2Nra2t6+Jug8INmJiYrFy5cv78+S2sqpWVVQtLitRITza+kL7g/4TPQatIuNEuFWnmdFNYWen/EljCjcYdvTdapDv76x/UykrKm+fpsdHO5GsWc9MdhIaTlfUBAQEpKSm6axOWZa9evdq1a9f6BYyNjX18fK5cuaJ7ePny5foF9u/fb2lpOWjQoLpnAgMDL1++3Ghh1Lyh7uT3m1l4EltLYCq95GFafcvlFpaef5jf30UW3YGTQNilS5c+ffq89dZbmZmZH3zwgY2NzcCBAwHg0KFDr732mq7MrFmzPvjgg9TU1OPHj+/bt6/ueQDYtm3b9OnTGeavus2ePXv9+vU3btxISEjYunWrbhkOaonEA7vSP33ZOyisrKyM77oIHabSSx6m1bdQamqqf+iA2o1jk87H810XQ+Bq/7g9e/YsWrRo4MCBAQEBhw4dIoQAgEKhMDH5c9nGwoULi4qKxo8fb2lpuX379sDAQN3zpaWlDMO89NJL9V9t6tSpOTk5L774orGx8fr16yMjIzmqtvTcTE6lAUPKbh0pLi7G0bnmncujYY6yuP6VM0yrb4nMzMwq+87U0unu/QcRERF8V4dzRGLJ6QsWLPDx8WnhHGFZWZnkY0NJScnUD76ucQk4/uZovbyghBvtmWOaV/2Y8V76vyWUcKNxh6NGW3OdLaimG0L1OWsuHPpqNEqpz+Kdwx2rPn1zRgt3/hI1HAaSOGtr64/eWZrmNZzviggdBTiPqfQygMdQtES1lqiCpq5fNlcOURAwEMpBVztSWE1zKvmuh7BhKr1MYFp9S1x4RLvaEXNJH71UHwZC6SMA4c4kIRf3WmsOptLLRF1aPd8VEbT4XNpfTkdyYiCUhQhnJh5XjTcLD52QD9x9+4niVWyEPBIndDAQykKEC4lTYc9vTmIeDcNAKA9hOE3YLC2Fc3m0r7OMooOM/lQ56+VAUkpomZrvegiVLpU+yB4DoSyEY1p9s5IKqas5cTTlux4GhIFQFkwU0NMez6BpEqbSywqm1TcvXkVlsqFMHez6chHhQuJUuF6mcThBKDe6tHq+ayFQcSoqqwlCwEAoHxHOTDxOEzbhHJ5KLzPhzjhA0qSzuTRCTktGAQOhfPRzIRfzaS3eEz4GU+llCNPqm3K/lBIC3jI4caI+DIRy0U4JnduRK/nY+RvCVHoZwrT6psTJb4IQMBDKSoQzwWzCx2EqvQxhWn1T4uU3LgoYCGUlwoXgNOHjcKWMPGFafaPi5bdSBjAQykqkCxOnYlns+3+HqfTyhGn1j3tUDblVtKut7LoDBkIZcTUHG2OSXIKd/y+YSi9bmFb/uDgV29eZKOTXGzAQykt/HB39O0ylly1Mq39cvIpGuMixM8jxb5YznCZsACcI5QzT6huQ26ETdTAQykuEM4nD4aB6MJVezjCtvr4KDdwppr0c5dgdMBDKi58NqdTQDBwOAgBMpZc9TKuvLzGX9rAnpgq+68EHDITyQgD6OTNncXQUADCVXvYwrb6++FxWnuOigIFQhjCtvg6m0sscptXXJ9uVMoCBUIbwkN46uFIGYVq9joaFi4/km1CLgVB2etqTtDJaWMN3PQQAU+kRptXrXCmgXlbEzoTvevAEA6HsGDHQ2xEXy2EqPQLAtPr/keFhvPVhIJQjPKQXMJUeAQCm1f9PnEqOe23Xwa8BOYpwZnC9DE4QIh1Mq6cACXlsP7wjRLIS7kyuFdBqea8ax1R6pINp9SnF1NyIeFjItztgIJQjCyPoYkMuPpJv58dUelQH0+rjVDLdWa0OBkKZknk2IabSozqYVh+fK8czCOvDQChTES4kXsbrZTCVHtXBtHp5HsZbHwZCmervwiTkUq1c+35iLmYQor/IOa0+pxJK1bSLjay7AwZCmXI0BWczcrNIpp0f7whRfXJOqz+jYvs5MzLvDBgI5Uu2h/RiKj1qQM5p9TguChgI5SzCRabrZTCVHjUg57R62R7GWx9+GchXhLNMd9/GVHr0OHmm1Zeq4V4pDXaQe3fAQChfndoRSuFhmew6P6bSo8fJM63+rIr2xtERDIQyJ8PRUUylR42SZ1p9fC4r572262AglLUIZ9mtl8FUetQoeabVy/kw3vqwCWRNhof0YuIEapQM0+prtHClABNqATAQylx3O5JTSR9V810PA8JUetQUuaXVX8qnftbESsl3PQQAA6GsKQiEOZGEXBnttYZ3hKgpckurl/lhvPVhIJS7CBdGPqOjmEqPmiG3tPo4FSvnw3jrM+LupY8cOXLkyBEbG5u5c+e2b9/+8QKpqalbt26trq6eOHFiZGRk/ed37txZWFjo6+s7Z84cMzOze/fu/fzzz3UFJk6c2LFjR+5qLisRzmT5RbncEWIqPWpGXVp9exmczEcBEvPo1v7YGQC4uyPcvXv3a6+9FhwcXFFRERYWVlpa2qBAZmZmWFiYmZlZly5dxo4dGxMTo3s+Li4uNDRUo9H06tUrLS2trKwMAO7cubN58+ai/1Gr1RxVW4ZCncitIlqh4bseBoGp9Kh58kmrv1lI7U2Jqznf9RAGru4I161b98knn7z44osAcP369R9++GHOnDn1C2zZsmXYsGEffPABANTU1Kxfv37w4MGU0lmzZn388cczZsxo8IJeXl5r167lqLZyZqqA7nbkfB6NcpN+hDiXx77qh5fAqEm6tPrnvfmuB/fwMN76OPlSKCsrS0pKioqK0j2MioqKj49vUCY+Pn7QoEENCmRkZKSkpERERHzyySebNm3KycmpK69Sqd57771NmzY9fPiQizrLmUwO6cVUevRE8kmrx8N46+PkjlAXwBwcHHQPHR0dT5482aCMSqVydHSsK1BRUVFaWpqWlmZiYjJ16tQpU6akpKR07979ypUrHh4e7dq1GzhwoLm5+ZUrV/71r38dOnSoLog2UFtbu23btlOnTukehoeHz507t6l6VlVVKRSKp/tbpaC3Lfkyhan0a1EusXgb7W4pWBgpbaCqstLQby3eRuMRL40WaAHXC5RFZZUm4vzvanmjxeUo3+qiNnxfMDxTU1OGecItHyeB0MTEBADUarWRkREA1NbWmpmZPV6mtrZW9+/a2lpCiLGxsZGRUVVV1bp164YMGQIAOTk5X3755UcffTRgwIABAwboCnfs2PG9996Li4tr9K0VCkXPnj1HjBihe+jh4WFqatpUPdVqdTM/lY9B7eHVBK2RsdKoBQME4m20q5k03InyUnnxNhqPeGk0UwBfaza5wkSkIwctbLT0cqqmbFcnWXwmnxgFgaNA6OLiolAoMjMzfXx8ACAzM9PNza1BGXd398zMTN2/MzIyHBwcTE1NdYtLdb8FAL6+vllZWQ1+sXfv3jt27GjqrRUKRXBw8KRJk1pST4ZhWtJGkmdvBh0s2aRi0qsFm9CLt9HO5WnDnfmpvHgbjUd8NVq4Mz2fT8LFufFYCxvtbB7b3wU/k3/hpCFMTExGjhy5e/duAKiqqjpw4MC4ceMAoLy8/Ndff9VoNAAwbty4ffv2abVaANizZ4+uQIcOHXr37q2722NZNj4+vlu3bgBQt+iUUvrf//43KCiIi2rLmRwO6cVUetQSckirj1dRzCCsj6tVox988MGIESOuXbt2//59f3//kSNHAkBGRsazzz5bVFRkY2MzderUHTt2hIeHOzk5Xb9+/cyZM7pf3LBhw8SJE48cOXL//n1jY2PdDN/MmTPv3bvXoUOH5ORkrVZ7+PBhjqotWxEuZH8afaMr3/XgDKbSoxYKdyLvSD2zNj6XzvTH28G/cBUIg4ODk5OTz549a29vHxoaqrsH79Sp082bN9u1awcAZmZmZ86cOXv2bGVlZf/+/S0tLXW/GBkZefv27YSEBBcXl5CQEN0v7ty58+rVq7m5uW5ubsHBwUol7o6nZ5Eu5I1ELQWFVAMFptKjFpJ8Wn1hDWSU0+520vzr2obDnWVsbW2feeaZ+s8YGxsHBgb+9d5GRnVLYOqzt7cfM2ZM/WdMTU3Dw8M5qicCgPYWxMyI3C2hvtbS7B6YSo9aTpdW/7y3ND8w8So2zIm0ZGWcfGBjoD/1l/QhvXgqPWo5aZ9WH5+LZxA2hM2B/iThQ3oxlR61irTT6vHQicdhIER/kvAhvXgqPWoVCZ9WX6WBpELaxxH7wt9gIER/CrQlRTU0R4o7TWDiBGoVCZ9Wf/4R7WZHzDlcHCJKGAjRnwhAX2fmrBQP6cVT6VFrSTWbEMdFG4WBEP1FqqOjeEeIWivcWZqBEA/jbRQGQvQXSR5Dgan0qA0keVq9lsL5RzTcGb/2G8IWQX/p5UjultCSWr7roVeYSo/aQJdWn1UhqVh4vYC6mxNHWWy13Tr49YD+YsxATwepZVCdw3FR1CbSO60+DicIm4CBEP1NhDOJl9Z6mcRcTKVHbSG9aUI8jLcpGAjR30S4MFJKq8dUetRm0kurP5uLK2Uah4EQ/U1fZ3Ipn9ZK5Z4QU+lRm0ksrf5eKWUI8bLCvtAIDITob9opwacduZwvkQthTJxAbSaxtPo4FY3EcdEmYCBEDUnpkF5MpUdPQ0pp9XgYbzMwEKKGIiR0DAXeEaKnIaX1MvG5uGS0SRgIUUP9XZh4FcuKv/tjKj16SpJJq39UDY+qaaAt9oXGYSBEDbmYga0JuVMs+v6PqfToKUkmrf5MDtvXiTAYB5uAXxKoEdI4pBdT6dHTk0ZaPR7G2zxsGtQIaRzSi6n06OlJY5oQD51oHgZC1AgJHEOBqfRILySQVl+uhuQSGuKAfaFJGAhRI3ytSZWWZoh5agRT6ZFeSCCtPjGPBtsTUwXf9RAwDISoEQQgwlnce61h4gTSCwmk1cerWBwXbR4GQtQ4sY+OYio90hexp9XHqWgEnkHYLGwd1DixH9KLd4RIX0S9XkbNwqV8Go57yjQLAyFqXLA9SS+jhTV816NNMJUe6ZGo0+qv5NOOVsTGmO96CBsGQtQ4Iwb6OJEEcfZ/TKVHeiTqtPo43FmtBfCrAjUpwpkR6SG9mEqP9Eu8afXxKjyM98kwEKImRYj2GApMpUf6JdJpQgqQkMv2wwnCJ8FAiJoU7kSuF9IqDd/1aCVMpUd6J9K0+uRiaqkk7S2wLzwBBkLUJHMjCLAhF8V2SC+m0iO9E2lafRzurNYyGAhRc8R4SC8mTiC9E2laPR7G20IYCFFzIlyI6NbLYCo94oIY0+rxMN4WwkCImhPhzCTkUq2ouj/eESIuiG69TFYFLVNTPxvsC0+GgRA1x8EUXM3JjULR9H9MpUccCXci4sqg0O2shj2hJTAQoicQ1yG9FzGVHnGjcztSoxVTWn18LmYQthR+YaAnENchvTguirgjrrR6PIy35TAQoieIcCFnVKJZL4Op9Ig7IpomLKmF+2W0B84RtAwGQvQEHa2IgpAHZSLo/5hKjzglorT6s7m0jyPOEbQUthN6sn4iGR3FVHrEKRGl1eNhvK2CgRA9mVgO6U3MwwxCxCELI/ARSVp9XC4extsK2FLoycRySG9iLq6UQdwSxehojRauFeAcQStwGAirqqpSU1PLy8ubKkApvXfvXl5e3uM/Sk9Pf/DgAcv+bY3Gw4cPs7Oz9V9R9CTd7YiqkuZV8V2PJ8Elo4hrolgvc/ER9bcmVkq+6yEeXAXC6OhoT0/PSZMmeXp6/vjjj48XyM3NDQkJGT16dLdu3WbOnEnpn5+te/fu9ezZs0+fPiNGjOjVq5fuydLS0sjIyMGDB/fq1WvixIlqtZqjaqNGMQTCnclZYe+1hqn0yABEkVaPh/G2FieBUKvVzpgx47PPPrt27dovv/wye/bsioqKBmVWr17t7++fkpKSkpISHR39+++/A4BGo3n22WfHjx+fm5ubmpoaHR2tK7xx40Zzc/N79+7dv38/NTV19+7dXFQbNSPCmRHy6GhVVdUL85ZZHf4XW1vNd12QlLWrfpS3feEbq9bVXbsLULyKxVT6VuEkECYmJlZUVEycOBEAIiMj3dzcfvvttwZldu/ePWfOHACwsbF54YUX9uzZAwAxMTHl5eVvv/12ZWUlANjb29cVnjlzJsMwZmZmL7/8sq4wMqT+wl4vc+DAgWNZkF+h/vXXX/muC5Kyjf/3dY1Tl23HLl69epXvujSOpZCYR/vhSpnW4KSx0tPTvb29FQqF7mHnzp3T0tLqFygrKyssLOzcuXNdgfT0dABITk5u37798OHDAwICnJycdu7cqSuQkZHxeOFGsSybkZFx+X8ePnyo579Nrvo4kjvFtFyoY9JBPXvTOycdM+JDQkL4rguSshFRA2wu7tQUqzp16sR3XRp3s4g6mhJnM77rISpGXLxoWVmZmdlf/w/m5uZlZWUNCgCAqalpXYHS0lIAKCgoOHfu3O+//z58+PALFy4MGDAgIiLC09Ozurr68cKN0mg0e/bsOXHihO7hkCFD3nvvvaYKV1RUEIIDCC3V1Vp56o/KXhZCbLToKvdhn5/ZG6FmGKaZ9Vl8wU9aGwiz0UJ6Bt8/f6LvcfOEAk1/hRA/aSdyjMLsSXk5zhH8ydzcnGGecMvHSSB0dnYuKiqqe1hYWOjs7Fy/gKOjI8MwRUVFtra2ugIuLi66X/Tw8Bg+fDgA9OnTJzAwMCEhoXPnzra2tnUvWFe4UcbGxsuWLZs/f35L6kkptbS0bP3fJ1MD3bWXS5QDnLRCazQthS/uanZEKtq1E+hlMH7S2kDIjbY0iP0slRnZkZPvz6dBKb1YbDy8PbG0NOW7LmLCydBoUFBQSkpKcXExAGg0mkuXLgUHB9cvoFQqu3bteu7cOd3Dc+fO6QqEhISUl5drtX/u3FBcXGxlZQUAPXr0qCucmJjY4NWQYUS4MMI8pPfnh6ydCfTDk7iRoUzzYW4VwVVBZtafxb22W4+TK5qOHTsOGzZs5syZS5cu3bFjR6dOnfr27QsAe/bs2bt378GDBwFg/vz57777rru7e1pa2sGDB3Uzz2FhYX5+fosXL54+ffr+/ftramqGDBkCAAsWLJg9e3ZAQEBJScn27dtjY2O5qDZqXj9n8kIsVQsvFH6cxK7siUsDkOEoGZgfyGxIYn8YpOC7Ln/zRwVRZ1xaRgAAGGBJREFUs7RTOwyErcPVrf133323cuXKN99808/P79ChQ7onXV1d627mXnvtNbVa/f7779vY2Bw+fLhjx4665w8ePLhq1aqFCxf6+fnFx8fr7gjHjh1bVla2fv16Y2PjPXv29OzZk6Nqo2bYGIOXFblRzAyw5rsq9ZzIohUaGO2BgRAZ1OwujPde9f1SRlBRJyGf6e+CfaHViJCzYdpgwYIFPj4+LZwjLCsr0wVa1ELzErQeJrVvhQhoKm7o75qpnZmXfATd+fGT1gbCb7QVF7XlatjcV0A3hdNPVvdwMl4QKOjuIEDYXqgVellVHPz9RElJCd8V+dP1QppcDC90wo8x4sEbXRW777OPBLM8U6VSnYg5GWYn1CQnAcNvENQKny2YfP5cYsSIsXxX5E9rr7OLujJ46BrihbMZPO/NfHFbEMcyaTSa4MjhmeeObH5/Gd91ER/8CkGtoKAsMTEvrBbEgpkHZTQmi53hj59hxJul3Zgv77AVGr7rAQAA5WqWMTHXaoRRG1HBLxHUCicO7H13iDfM3VcpgL62IYmd1YXBLfYRj3ysSaQLsy2F/0vD3BqFcuHBjc/32P75J3zXRXwwEKJWsLGxWTL12YhODv+5wXPPz6uCvQ/YeQECWqeA5Gl5ELMhieU9reiti+z8/p4vPz+mbhMu1HIYCFGrre3NfHpTm1PJZx0+u6V9oRPjIqDlq0imejkQH2v48QGfkfBqAY3JZpd2x+vCNsJAiFrN24q84susvMLbGoEKDWxNYRd1xU8vEoTlQYqPk1geE9GWntd+GKLAaYI2w68S1BbvBCsOpbM3Cvnp+1vusFFuTGchJTIjORvmTpQM/J7BT3f4JY3Nr4aXffHLvO2w7VBb2BjDv4IVb5zj4aZQzcKmW+yb3fCjiwTkzW7Muuv8dIe3LrLrQxUKvCx8Cvhtgtpotj+jqoRjmYa+Cv7hHutvDT0dsN8jAZnYkcmuhIRcQ3eH/7vNdm4Hw9yxOzwVDISojYwYWNObWXROqzHgKgEKsOEGuzwIFwUgYVEQWNSVWZ9k0CUzxbWw5rp2XR/sDk8LAyFqu2c9GXcL2JFquM7/azprpoAoN7z+RYIz3Y85/4i9XWy4m8IPr2rHezFdbbE7PC0MhOiprO+jeO+yttRQuxt+nMQuD8IPLRIiUwXM7aL4xFA3hQ/L6K677MqeeDuoB/idgp5KD3syrD2zPskQywTiVTSnEsZ74YcWCdS8AOZAOptRYYibwmUX2MXdFJhKqxf4nYKe1ke9mC9vs3+Uc9751yVplwcxuDoOCZatCbzkw3x2k/ObwnN59HweXYjHLekJtiN6Wu4WZE4A8+5lbjv/nWJ66RH9Z2f8xCJBW9yN2ZHKFtdy+BYUYOl57ZrejDlXB6vLDn6tID1Y3l1xIoteyufwpnDtdXZhV4UZ9nwkbO0tyDMdmC/vcHhduPc+W6nBYzj1CZsS6YGlElb1ZJae52qmMLOCHvmDnd0FP65IBN4KYj67qa3i5oSWWhbevcx+Gq5gcI5Af/CbBenHdD+msAYOpnNyIfzJDXa6H2NjzMVrI6Rn/jaktyOz6x4nfWHjDba7HYl0wTCoTxgIkX4oCHwaplhynq3Vd/cvrIFdd9n5uC4Aicc7PZiPr7Nafc8VPKqGT25o1/bGvqBn2KBIb6LciE872KLv2ZEvbrPjvRgPC7wERqIR6kRczWF/mp77wqor2imdGV9r7At6hoEQ6dN/whSrr2kLa/T2gtVa+PKOdjFusY3EZnkQ89E1fZ7NlFJC9z1g/xWMGfT6h98vSJ+62JBxnsyaa3pbNbMthQ1zYgJs8BIYicwzHRgNC7HZeguFS89rV/RQ2Jvo6/XQXzAQIj37MESx8y57r1QP/V9LYeNN9s3u+ClF4kMAlnbX29lMp3Lo7SKYiwunuYHNivTMyQze6Kp455IeZkd+esC2t4BwJ7wdRKL0YicmtQQuP3V+LUth6Xntx30YExwW5QYGQqR/i7sy5/NovOpp+/+GG+zy7tj1kVgpGVioj7OZdt1ljRl4zhu/rrmCLYv0z8wIPuzFLL3wVKvHj2VSNQsjPPB2EInYTH/mZM5TzRRUaWDlFXZDKG6yyyEMhIgTUzszWhZ+etD2a+F117XLu+PuGUjcLIxgpj/znxtt7wgfJ7H9nElfZ+wKHMJAiDhBADaEKt66yFa3aa3AxUf0XilM6oifTyR68wMUex+wqqq2/G5uFXxxW/tRL+wI3ML2RVwZ4EqC7MjmW225Fl6XxC7tzijx44nEz8kMJndkPr/VlkvCty9qp/sxXlZ4O8gt/KZBHPoklNlwQ5tf3brful9Kz+Sw033xw4kk4s3uzNfJbJm6db+VVEiPZLArgnC9GOfwuwZxqFM7Mrkj8/6V1l0Lr0ti5wYwlkqOKoWQoXlbkSg3Zmty60ZH3jyvfS9YYY17zXMPAyHi1qqeip8esreLW7pqLrcKfn7IzgvAq2AkKSt6MBtvtmJL+t8y6B8VMMMfv6INAVsZccvWBJZ1V6y42NIvgI03tVM6M46mnFYKIUMLsiNdbGB3y85m0lJYfkG7IVSB0+SGgc2MODc/kLldRE9kPfmmsFQN21LYxV3xY4kkaHmQYl0S25J9uLcms46mMBqTaA0Fv3EQ54wZ+Kg38+YF7RO/Ar66ww5vj2vkkDQNdiPWxnD4jyfcFJap4cOr7PpQnB0wHAyEyBAmejOWSvi+2XGhGi18dotdgicuIela0o356PoTAuGaa9rh7UmIA14OGg5+6SAD2dBH8c4ltkLTZIHv77Hd7SDYHvs/kqznvJjCGjib2+TYSGYF/TqZfT8Ev5kNCpsbGUioE+nnTDY2sdcUBfgPbrGNpE5BYEk3Zl3TN4VvXWRfD2Q8LPBy0KAwECLDWdub2XRLm1PZyI8OpLEWShjgiv0fSdzLPszlfHqzqJGbwqsFNDabXdINLwcNDQMhMhwvK/KKL/Pe5Uby69cnsSuC8NOIpM9EAa8HMhsaO5tpYaJ2dS+FFW4lYXD41YMM6t1gxW8Z9Ebh3y6HT+fQwhoY64mfRiQL8wKYIxnsH+V/6wX709iSWnjJB3sBD4w4el1K6bZt2w4dOuTg4LB48eKuXbs+XiYxMfHzzz+vqqqaPHnypEmTdE+uWrUqJydH929fX98lS5YAQFJS0hdffFH3i/Pnz2/0BZHwWSlhRQ/mjXPamFF/ffbWJWnf7M7gkUtIJtop4WUf5tOb7H/C/hwFVbPw1kX2874KPHWQF1xdfXz55Zdr166dNWuWr6/vgAED8vPzGxS4d+/e8OHD+/XrN23atAULFvzyyy+653/66ScbG5uQkJCQkBBfX1/dk+np6TExMSH/Y21tzVG1kQHM9mdyq+Bo5p+XwzcK6bUCOqUzXggjGXmjK7PzLltQ8+fDL26zvu1gmDuGQX5wdUe4cePG9evXjx49evTo0WfOnPn2229193Z1vvzyywkTJsydOxcAVCrVxo0bx48fr/vRs88+269fvwYv6OLiMnPmTI5qiwzJiIE1vZnF57RDnjMyYmBdEruoq8IU1wcgOXG3IOM9mS9vs/8KZopqYO31v42RIAPj5DK8uLj43r17ERERuof9+vW7ePFigzKXLl2qKxAREXHp0qW6H23evHn27NlffvllbW1t3ZMZGRkzZ85cvnz54y+FRGdMB8bdAranshkV9GgGOxN3FkbysyyI+eyWtkIDH17VPufFBNri7SBvOLkGUalUhBA7OzvdQ3t7e5VK1aBMbm5u/QJVVVXFxcU2Njbjxo3z8vKilH7zzTd79+6NjY1VKBROTk4vvfRSp06dkpOTBw0a9N1339XdPjZQW1u7efPmuoHWyMjIBnei9ZWXlz/tnyo/+mq0lYFkwpGS/eq7/wzuzdRUl9U8+VfECz9pbSD5RnNjoLc1/PPLk6dNQy6OMykra+kJLc2QfKO1gbm5uULxhBEnTgKhhYUFpbSmpsbc3BwAqqqqLC0tH69cdfWfB7ZWVVURQnSFP/roI92TL7zwgqen59mzZyMjI0NDQ0NDQ3XPOzg4rF27tqlAaGRkNGzYsHHjxukeuri4WFlZNVPV5n+KGqWXRgtmKso+HnnMLahTzhmr/u89/QsKHH7S2kDyjVa4dcq5SnuHnJUdZyTq6zUl32hc4CQQuri4GBsbP3z4MDAwEADS0tI8PDwalPHw8EhLS9P9Oy0tTfcr9Qu0a9fO1dX18VtJf3//vLy8pt6aYRgfH58hQ4Y8/V+BOKXRaCyUjMbWTVtdwXddEOKHkbpSYR9klpPAd0XkjpO5GaVSOW7cuG3btgFAcXHx/v37ddkRxcXFW7Zs0c38TZo0affu3VVVVQCwfft2XYHS0tKioiLdi8TExDx48KBXr14A8Mcff1BKAaCmpmbbtm1hYWFcVBsZkrW19ekDu7+dErzxo1V81wUhfhzavX37aNezR3/huyJyx9U6pdWrVw8bNuzs2bOZmZmjRo0aOHAgAOTk5MyePfsf//iHsbHxpEmT9u3bFxgYaGNjo1aro6OjASAtLa1fv36dOnUCgPT09C+++KJjx44AsHLlyuPHj3t4eDx8+NDHx+enn37iqNrIkAICAgICAviuBUK8sbW1nTbtn3zXAnEWCH18fFJTU2/dumVjY+Pl5aV70s/Pr7CwUJcFqFQqDxw4cPfu3erq6sDAQIZhAKB79+45OTn3799XKBSdOnUyMzPT/eKOHTvS0tIKCgqcnZ3bt2/PUZ0RQgjJEIeZK0qlskePHvWfYRjG1ta2/jM+Pj4NfsvS0jIoKOjxV/Py8qoLqAghhJC+yDp/KyQkpJl1N6hRPj4+NTWSznXQt8rKSn9/f75rITLZ2dl1C8VRC926dWv48OF810KUZB0IS0tLWfYJp0WjBoqLi/mugshQSrHRWotl2dLSUr5rITJarbasrIzvWoiSrAMhQgghhIEQIYSQrEltm1dHR8etW7ceOnSoJYXVavXkyZOVSjwHsxVMTU1HjRqlW+WLWoJlWaVSOXToUL4rIia1tbXV1dXYaK1SWVmZl5eHjdbAV199pUvJawbRJapLhlqtPn36NN+1QAghJAihoaFP3HZOaoEQIYQQahUc4EIIISRrGAgRQgjJGgbC/2/vXkOa+sM4gP9sXpJk6aZtc14Jkiwhy+wi2Ywp3sXUNCTTvKdZlhBRL1YRpMzKKCsJpFKUzNA0L/OWiqVpFwMlNC+sNrbMe1On287/xYEh0/7//6ud087zefWbPC++PJydx3PZOQAAACgNBiEAAABKowkEAqIz6MPU1FRVVdXQ0JCjo6POiw9xKpVKJBJ1dXUxGAz8seBAoVDU1NT09/dzuVztA9BX+/btW1NT09evX62srOB1oLjx8fHq6mq5XO7s7PwvPzIZHBwcHByEx+fiRkdHq6urJyYmnJ2djYyM1q35+PFjQ0ODRCJhsVgbN27Uc0ISGh4erqmpmZqacnJyWrdpEomkvr5+cHCQwWDA1/M/YBQwOjrKYrGio6MDAwPxN2DoFKjVaj8/v7179yYmJjIYjNbWVkJyksr09LSLi4u/v39MTAybzR4ZGdEpuH//PofDiYqKOnr0KJ1Or6mpISQnqYhEIgaDkZiY6OHhERAQoNFo1i2TSqU2NjZMJlPP8cjp9evXTCYzKSnJ3d09LCxsbYFGo0lJSbG3tz9x4kRISIhQKNR/SLKprKxkMpnJyclubm7Hjx9fW9DQ0GBpaZmYmJiQkGBpaQn7tH9HiUGYnp6ekpKCr/39/XNzc3UK6uvrnZycFhYWMAwrLCz08vLSd0TyycvL8/X1xXfl6enpqampOgVisVipVOJroVDo7u6u74jks2/fvocPH2IYtrCw4ODg0NTUtG5ZeHh4Tk4ODELcrl27iouLMQybn5/ncDgdHR06BSUlJVu3bp2eniYgHClpNBoXF5fy8nIMw2ZmZphMZl9fn05NcHCwQCDA15cuXYqIiNB3yr8KJa4R1tTUREZG4uuIiIja2lqdgtra2qCgIPzsX2RkZFdX19TUlL5TkkxtbW1ERAR+yiUyMnJt0+zt7bUnmTkcDryS4ufPnz09PREREQghc3PzwMDAtU1DCJWVlZmZmYWGhuo9IBl9//69v78fb5qFhYW/v//appWVlaWlpU1OTra2tk5OThIRk1yGh4dHR0fDwsIQQps3b/b19V3bNCaTqVAo8PXCwoK1tbW+U/5VDO0Ra2tpNBqZTMblcvGPXC5XIpHo1EgkEk9PT3xtY2NjamoqkUgYDIZeg5KMRCJZ3TSZTKZWq2k02trKpaWlvLy8pKQk/QYkHalUamZmpt3jcLnc/v5+nZpfv35du3btzZs3Q0NDeg9IRlKplE6na69gcbncsbExnZqRkRGFQlFRUWFnZ9fe3l5eXs7n8/WelESkUqm1tbX2Qum6+7Tc3NzY2NiAgAC1Wm1kZFRaWqr3mH8Twz8i1Gg0Go1GezGZRqOpVCqdGrVavfq+hnVrqGZ1T2g0GoZharV63bK4uDgnJ6esrCz9BiSd/7MVZWZmXrx4kcVi6TcaeeG7ae3HdZu2tLREo9G6u7srKyuvX79+9uxZ/WYknf/TtLq6OolEcuzYsZiYmLGxscbGRv1m/MsY/hGhsbGxjY3NxMTE9u3bEUJyudzW1lanhsPhaN/QOzc3t7i4uLaGalb3RC6XW1tbr73bVqPRJCQkzM7Ovnr1at2DRUphs9mLi4u/f/+2sLBACMnlcg6Hs7pALBZXV1fT6fR3797JZDKFQpGamioQCHTKKIXNZs/NzSmVSjMzM7Re0xBCtra23t7e+K6fx+NlZmaqVCpjY8Pfd/0Jm82emprSnqGRy+XakzdaV65cKSoqCgoKQghZWVnl5OTExsYSkPUvYfhHhAghHx8fkUiEr0UiEY/Hw9eTk5P4UQ6Px8Pva0AINTY2urq6wv/sPB5P27TGxkZt02ZmZpaXlxFCGIadPn16fHz85cuX+F6M4mxtbbdt24Y3TaPRNDc3+/j4IIRUKhV+ZYvBYDx9+tTX15fP5+/Zs8fExITP52/atIng3IRycnJydHRsampCCKnV6paWFm3TtNfpjxw5Mjw8jK+Hh4fZbDaVpyBCyMXFhcFg4G8XWFlZaWtrw5u2srIyPT2N19BoNPx7ihBSKpXwf+p/IPhmHb3o6+uj0+kCgeD8+fNMJlMsFmMYhm8lvb29GIYplUpXV9fo6GihUMhisUpLS4mOTDyxWMxkMrOzswUCAZ1OxxuFYZidnd3z588xDLtz546RkVFsbGxKSkpKSkpGRgaheUnhyZMnbDZbKBRGRUXt3LlzeXkZw7Du7m6EkM5PKTo6OuCuUVxRURGXy83Pzw8PD3d3d1epVBiGtbe3m5iY4AVSqdTW1vbChQu3b9+2s7N79OgRoXlJoaCgwNHR8datW8HBwQcOHMC3rvr6ejqdjhfcuHGDy+UKhcK8vDw2m52fn09oXrKjytsnBgYGKioqTE1NY2NjHR0dEUIYhj1+/Dg8PBy/u2FmZqa4uHhyctLPz8/b25vovKQgFotLSkqWl5ejoqJ27NiB/7GsrGz//v3Ozs69vb2fPn3SFhsbG586dYqgpCTS1tbW3Ny8ZcuW+Ph4/MkMExMTVVVVycnJq8tkMplIJIqLiyMoJrk0Nze3tbWxWKyEhAT8xhmZTFZXV6fdoqRS6bNnz5RKJZ/PP3jwIKFhyaKhoaGjo4PL5cbHx+PnFX78+NHS0nLy5Em8oK2trbOz08jIiMfjHTp0iNCwZEeVQQgAAACsixLXCAEAAIA/gUEIAACA0mAQAgAAoDQYhAAAACgNBiEAAABKg0EIAACA0mAQAgAAoDQYhAAAACgNBiEAAABKg0EIAACA0mAQAmA4UlNTHRwcxsfH8Y/Ly8ve3t6enp6Li4uE5gKA1OBZowAYjvn5eQ8PD0tLy87OTlNT0+zs7AcPHrx9+3b37t1ERwOAvGAQAmBQPnz44OXllZWVdfjw4ZCQkIKCgjNnzhAdCgBSg0EIgKG5e/fuuXPnLCws+Hx+ZWUl/m53AMCfwCAEwNDMzs46ODj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axis\n", "x = [r[1] for r in rvecs] # only keep the x coordinate\n", "plot(x, scfres.ρ[1, :, 1, 1], label=\"\", xlabel=\"x\", ylabel=\"ρ\", marker=2)" ], "metadata": {}, "execution_count": 6 }, { "cell_type": "markdown", "source": [ "We can also perform various postprocessing steps:\n", "for instance compute a band structure" ], "metadata": {} }, { "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing bands along kpath:\n", " Γ -> X -> U and K -> Γ -> L -> W -> X\n", "\rDiagonalising Hamiltonian kblocks: 9%|█▌ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 22%|███▌ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 38%|██████ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 50%|████████ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 62%|██████████ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 78%|████████████▌ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 91%|██████████████▌ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 100%|████████████████| Time: 0:00:00\u001b[K\n" ] }, { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=126}", "image/png": 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"execution_count": 7 }, { "cell_type": "markdown", "source": [ "or get the cartesian forces (in Hartree / Bohr)" ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "2-element Vector{StaticArrays.SVector{3, Float64}}:\n [0.00044877908158149965, 0.00044878576936763426, 0.00044878069296800077]\n [-0.0004487857693680684, -0.0004487790815807546, -0.00044878069296811157]" }, "metadata": {}, "execution_count": 8 } ], "cell_type": "code", "source": [ "compute_forces_cart(scfres)[1] # Select silicon forces" ], "metadata": {}, "execution_count": 8 }, { "cell_type": "markdown", "source": [ "The `[1]` extracts the forces for the first kind of atoms,\n", "i.e. `Si` (silicon) in the setup of the `atoms` list of step 1 above.\n", "As expected, they are almost zero in this highly symmetric configuration." ], "metadata": {} }, { "cell_type": "markdown", "source": [ "## Where to go from here\n", "Take a look at the\n", "[example index](https://docs.dftk.org/stable/#example-index-1)\n", "to continue exploring DFTK." ], "metadata": {} } ], "nbformat_minor": 3, "metadata": { "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.7.1" }, "kernelspec": { "name": "julia-1.7", "display_name": "Julia 1.7.1", "language": "julia" } }, "nbformat": 4 }