{ "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", "[Introductory resources](https://docs.dftk.org/stable/guide/introductory_resources/)\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": [], "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 log10(ΔE) log10(Δρ) Diag\n", "--- --------------- --------- --------- ----\n", " 1 -7.900389898870 -0.70 4.5\n", " 2 -7.904997932892 -2.34 -1.52 1.0\n", " 3 -7.905177165441 -3.75 -2.53 1.2\n", " 4 -7.905210622309 -4.48 -2.84 2.6\n", " 5 -7.905211106724 -6.31 -2.97 1.0\n", " 6 -7.905211520049 -6.38 -4.70 1.0\n", " 7 -7.905211531184 -7.95 -4.65 3.0\n", " 8 -7.905211531389 -9.69 -5.24 1.0\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, Si]\n", "positions = [ones(3)/8, -ones(3)/8]\n", "\n", "# 2. Select model and basis\n", "model = model_LDA(lattice, atoms, positions)\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-5);" ], "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 3.1020965 \n AtomicLocal -2.1987849\n AtomicNonlocal 1.7296095 \n Ewald -8.3979253\n PspCorrection -0.2946254\n Hartree 0.5530393 \n Xc -2.3986213\n\n total -7.905211531389" }, "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": "7×8 Matrix{Float64}:\n -0.176942 -0.14744 -0.0911692 … -0.101219 -0.0239771 -0.018408\n 0.261073 0.116914 0.00482505 0.0611643 -0.0239771 -0.018408\n 0.261073 0.23299 0.216733 0.121636 0.155532 0.117747\n 0.261073 0.23299 0.216733 0.212134 0.155532 0.117747\n 0.354532 0.335109 0.317102 0.350436 0.285692 0.417258\n 0.354532 0.389829 0.384601 … 0.436925 0.285692 0.417416\n 0.354532 0.389829 0.384601 0.449236 0.627541 0.443806" }, "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 irreducible k-points). There are 7 eigenvalues per\n", "k-point because there are 4 occupied states in the system (4 valence\n", "electrons per silicon atom, two atoms per unit cell, and paired\n", "spins), and the eigensolver gives itself some breathing room by\n", "computing some extra states (see the `bands` argument to\n", "`self_consistent_field` as well as the `AdaptiveBands` documentation).\n", "There are only 8 k-points (instead of 4x4x4) because symmetry has been used to reduce the\n", "amount of computations to just the irreducible k-points (see\n", "[Crystal symmetries](https://docs.dftk.org/stable/developer/symmetries/)\n", "for details).\n", "\n", "We can check the occupations ..." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "7×8 Matrix{Float64}:\n 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\n 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\n 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\n 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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/AxUDKwcxb+LCMdSGZSns7D5Md1tz3wtiIDSr9yOZD84Zyhr4zgcSng0ZbIyaDDbjAgFeTA9g9BT2/om3g6ili5V03w124UAe7gUxEJpVb0cyxZf5PzyJG92qvAE2XDC8Y94FArwgAO9FKN7EhWPoNm+eZl8PUbhY8vDR0q94QrNiEPN5Nptbg4ND6B/vphke7skEOUq8O2g0rjvpbgtfX8ZIiP5xqpieLqZz+vITkjAQmpu3DXmmN7PqLLYC6C95NXTbZXZJmJRnB1tYHaVYnsrW4sIx9Lc3TxtWDmKslfx8OgZCHrwZqthzg82qwE4hAgBYksI+15fxFP/52u0X4UaiPch/M/F2EAEA/HqT5tfCrEDe4hEGQh44WcCrwYqlKdgKIMiuoL/dZBcGy6g7aPRuBPN/53HhGAKWwuIzhg8iGSV/4QgDIT/m9WeSNfSkBjuFcvfGafb1EIWjBd/5MLtejuRBP+YDPIlb9r67yloo4H5fPoMRBkJ+WClgaTiz6DS2ArKWrKHny+iLPC0Q4N2ycMWXF9mbuHBMxhpZWJ7Kro5U8LtOTKY1UAie6sUU18HvudgKyNei04YV4eZ4ALcwednA7D7MSjyJW8Y+yWT7OZFRXjyvl8ZAyBsFgVURzOunDCyGQln6KYctbYAZ/C0QEII3QhT7c9hMXDgmS9U6+OC84Z0I/qsA/zmQswf8GDsV7LiGd8Syw1JYcoZ9P1LB85AQ3xwt4PWBisVnsArI0Zrzhnu7MSEu/NcBDIQ8Wx2pePsM24BzhTKz7TJrbwGTevDfBPBuTj8mpYQmFmGnUF6K6+GjTHZpuCBikCAyIWfDPUlfJ9h8Ee+IZaSRhXekfr52+1kpYDkuHJOfFamGJ3ox/vaCuBfEQMi/1ZGKVWcNWh3f+UDm8t8MdqALGaoWRBMgBI8HMWUN8OtN7BTKxXUt3X6VfYOP87VbhYGQf8Eu5J5uzLp07BTKglYH/5duWCWABQLCoSDwXgSz6DQuHJOLt8+wC4IVHoI5TQlroyC8M4j5MMNQVMd3PhD3PjhnmNCd6e+M3cFbTPZlHFTw7VW8HZS+c2U0Pp+d119A0UdAWZEzP3syM4h5Lw2nSSSuoBY+zWKXCWOBgNCsjlQsTcGFY9L3erJhWbjCXsV3PprBCikUi0MV311lr1bh2JCUrTxreLo342OH3cFWDPMkwc7k0yzsFErZkQJ6pQqe7i2s0COs3MiZmxXM7a9YjqdsSNflSvrDdfaNEKEsEBCg/0Qxq88ZqnDhmERRgEWnDe9HMhYCizwCy468vTKAOZzPni3FTqE0vX2GfTVY4crHA7jFoo8TGd+D+b/zODwqTT9cZ/UsTPMXXNwRXIbkzE4Fb4cq3j6DrYAEnSmhiRoqqAUCwrRqEPNpFluIC8ckx0BhWQr7Pt/na7cKq6WwzO7DXK6Eny9VlZeX850XZBoGg6GwsPDNU/plYYwNTw/gFpFutmRWELPyTENhYSHfeUEmo9FoPjlf190WxnYTYBwErJfComIgJGXjA29ud7axmDI6ZvPGNXznCHVJdnb2PQ/NqLbxrCkv/jJhL4A33zkSgfvYtLEzn9np4e1Oq078sd/FxYXvHKHO0+v190x9NKNQW6opWrV8KcBDfOeoFdgjFJba2toj+7/XLzpe/HLCvpNZV69e5TtHqEteXfZ+7tQPK57bq5/41ntrN/KdHXF4c9kK9rnvS5/bdzn0mfUff853dlCXHDhwIJX4FT//C/vGkY/XreY7O63DQCgser2eqKyAMAAAVnb19fV85wh1SX1DI1jaAQC1sK2pw//NdmloaAALWwBgLezqsNBErqGhwWBhCwCgtDAYBLoqHodGhcXBweG+4VH7v3iojNqEekO/fv34zhHqklWLXh4388nGnkNcbiYt3red7+yIw/tvL3xi/kNlXhHOeckvH9zHd3ZQl0ycOLH7B5suf5PvUnH5lRef5Ts7rSOUcrVYv7S0NDs7OyAgwNPTs9UEjY2NqampDg4OLZr7a9euFRYW+vv7N/9Fg8GQmppqaWkZHBxMSJvTrfPmzQsKCpo7d257cqjVau3t7dv315jVxYsXJ/5cu+uJ0HA3wU0sC7bQBOu+PSWhdRcWTY6ws7PjOy+iUVJSsnBfpnvv8DXDsNA6QJjV85tLjV8dPLttSrfu3bvznZfWcdUj/OGHH5577rmwsLC0tLR33333ueeea5Hgxo0bo0eP9vT0LCoqGjhw4M6dO5VKpcFgeOyxx86cOTNgwIDk5OSXXnpp6dKlAFBSUhIbG2tpaVlbW+vp6fnLL79YWwvmuFYO9O7de0KpIa6ACjAQog5hKSTXOG4Yh1GwY9zc3B4dNWhFBm66lIKjRYoHYyO7dxfuTBwnOdPpdPPmzdu2bduhQ4f++OOPhQsXVlZWtkjzzjvvjBkz5sSJE+fPn8/MzNy/fz8AxMfHJyQkXLhw4aeffoqLi1u+fLlxF8HatWt79ep15syZc+fO1dbWbtu2jYtsC0qsF4nPF+h4Omq/tFLqYUXUVnhIQodFubGZ5bSike98oC6Ly6exXoK+p+ckEJ44cYJl2YkTJwJAeHh4QEDAr7/+2iLNrl27nn76aQCwsbF59NFHd+3aBQCEEGtraysrKwBwcXFRKBQsywLAzp07n3zySQBQqVQzZ840Jpa2WG/mRBHVYSgUubgCOtpb0E2AYFkwMNiDHC/Eewhxy6mm1XraT9iPW+FkaPTmzZt+fn5NM3k9e/bMyclpnqCysrKqqsrPz8/40s/P7/DhwwAwevToqVOnTp48OSwsLCEhYdOmTa6urpTSvLy85olv3rzZ1kfX1NRcvHjx0KFDxpdKpXLkyJF3mFMULBdL6GlPzpTQaA/xZR41ic9nnxHY+cIiEuvFxBew9/ng6awidjifjvZmBN6KcRIIa2trLSwsml4a5/ZaJACApjRWVlY1NTUAoNVqs7OzHR0dbWxslErl+fPnKaV6vb6xsfH2xK3Ky8u7du1aZmam8aW1tXXv3r3bmj2uqakRcowc7q78/U99sI2e74zcQuCFJih6Fo4XWnwc0YCF1gk1NTVDnBULziir++N5a+0lwG/awRxVjDtbXc3byZFWVlZK5V0iHSeB0NPTs7S0tOllaWmpl5dX8wQeHh4KhaKsrMx4ZkRJSYkxwRdffNHY2Ggc+XzllVe6d+8+ffr0ESNGuLq6lpWVGX+3KXGrevXqNWnSpHauGqWUCnkJw70+dGOGYbmdFd8ZuYXAC01QkjTU38Hg62qr1bJYaB1FKR3hYXPjiK5eaecmrEogXAKsnidK9CujLOyE/egxTgZtwsPDr1y5UlxcDAANDQ2nTp2KiopqnkChUISHhx87dsz48vjx48YE1dXVzs7OxjctLS1tbW2rq6sBICoq6vjx4y0SS95IL5KsofV4BLdoxefjBGGXKBkYqiZHC3GqXKwuV1JKIdBB6LWAkx5hjx49HnrooZkzZ7788svbtm0LDw8PDw8HgK+++urrr78+cuQIALzyyiuvvPKKg4PDn3/++ccff6xduxYApkyZsnr16rVr14aFhf34448Gg2Ho0KEAsGDBgkcffbRbt25VVVXffPNNUlISF9kWGnsV9HMmyRo6UtgLrlBb4gvYl/vj/FaXxHoz8fn0QT++84E6RSyLxbiaxv/yyy+HDx++ZcsWf3//vXv3Gt/s27fvAw88YPz5scce27hx486dO7OzsxMSEowbLUNCQo4dO3b9+vVPPvnE3t4+KSnJ0dERAMaOHfu///3v559/Tk5OPnDggHzOW4n1IvEFeDssSo0sJGvoME8RtAJCFutF4vJx4ahYxefTWDEEQg5PluGFNE6WafJHHl111nD0PgGdhCf8QhOIIwX0jdOGk5OVgIXWKcZCYymov9WlP6TylPIRGiYjqG8aBfD6Vpc8Rekr7AlCwEO3BW6YmpwtpTXCWjeK2iW+gBX4JmJRYAgMUzN4uIQYZZRTOxURfhQEDIQCZ6OEMFeSWCSpXrtMxOXTWG+sXyYQ603iC7AKiI+IFothRRW60d541pr41OrhbCkdqhZHKyBwo71JPE4TilB8gdBPVmuCgVDoYr2YOLwdFpsTRTTMldgKaG5XxPo7E62O3qjGWiAmLIWjBaxYVrxjIBS6aDXBo4dFJz6fFcugkPARgFFeTALeDopKWilVWxNvG3HUAgyEQmfBQJQ7Hj0sMnEFNNYLK5fJxOLoqNjEFYhj44QR1lURiPVmcDehiGh1kFlOB+Np6aaDuwlFJz5fTKumMRCKAC4WEJcjBTTKnVjhkTKm08uRUIArVVgLxEHPQmIRHSmeQRHRZFTOIt3INS0tqec7H6h94gtY3DhhcrFeeDsoGqdLqJ89EdFR6VhdRQCPHhYXEW2fEhHcTSgioqsCGAjFwXj0MN+5QHdX1gBXq2iEm5haAVEY400O57NYB0QhvoAV12IxMeVVznCxgFgkFLDDPIkKK5ap+dgROyXJqsBaIHRiPG4e66s4hLkSTT0txCd1C148nqzGmVhvvB0UgaQi2s+ZOFnwnY+OwBorDnj0sFjE5YvmWCnRwfUyoiDG4+YxEIoGLhYQPk0dFNTRUFeRtQJiMdqbOVLA4jyhwInxuHmRZVfOcDeh8B3OZ0d6MgqMg9zwsgF3a3KuDGuBcNXqIU2Ex81jIBQNPHpY+OJFdayUGOHtoMAdL6KhIjxuHgOhaODRw8Inuu1TohPrRfC4QSET6XHzGAjFBI8eFrKbNbRKR/s7i68VEJFYb+ZYIdVjKBSqeHEeNy++HMsZ7iYUsrh8GuvFYBjklKsl+NmRlBKsBUIk3uPmMRCKCR49LGTx+ThBaA6x3gQfVS1MRwroYA9RHjePgVBksFMoWAkFuIPQHGK9CG6oFSbRnazWRJSZljPcTShMV6qojoVejhgIOTfSizmpoQ0GvvOBbhMn2kERDIQiM8abxOHRw8ITn0/HiLMJEB1HC+jjRE4VYyUQlrIGuCba4+YxEIoMHj0sTLiD0JxG46GjwiPq4+bFmWt5w1ZAaChAfL74zlcUr1gvBncTCo2oj5sXa77lDHcTCk1WBbVREj97DIRmMtyTpJTQWj3f+UDNxOXT0aK9F8RAKD6xXkwCHj0sJOJdIyBSNkoIcSGJRVgHhMJ43HyIaI+bx0AoPl424IFHDwtJPD56yexGe+NZawIi9uPmMRCKEh49LBwshaOF7CgMhOYV681gFRAOsS8Ww0AoSnj0sHCcK6NuVqSbrYhbATGK8SAXymmVju98IAAQ/3HzGAhFyXj0sA5DoQCIvQkQKUsFRLqT44XYKeSfBI6bx0AoSsajh1Px6GEBiC/AjRP8iPVi8Kw1IZDAcfMYCMUKjx4WAgOFE0V0pDjPVxQ7rAICIYHj5rECixUePSwEZ4qpjy1xt+I7H7I02J1craKlDXznQ/YkcNw8BkKxwqOHhSBO5IvlRE3JQLQHOYqrxngljePmMRCKlfHo4WQ8ephXeLIav2K9GXwYC7/iJHHcPAZCEcPdhPxqZCFZQ0fgBCF/sArwTuw7CI2wDosYHj3Mr2QN7e1EnCz4zoeMhbmS/FpaVMd3PuSKAiRIYlAEA6GI4dHD/IrDHYR8UxAY7skk4O0gTyRz3DxXgbChoeHll18OCAiIiIj46aefWk2zbdu2kJCQoKCgJUuWsCwLALm5uffc6tdffwWAkydPNn/z1KlTHGVbXGyUEOqKRw/zJr6AjcVxUb7FeuHoKG8kcy+o5Oi6q1atSk1NTUhISE9Pf+yxx86dO9ezZ8/mCU6dOjV//vz9+/d7eXlNnTrVy8vrxRdfdHFxeeONN4wJcnNzn3nmmc2bNwNAcXFxQUHBhg0bjP/k7+/PUbZFx3jW2thuCr4zIjv1BkgpoTFqKbQCohbrTT7Kwh4hP+Lz6UM9pVAFOLmfpZRu3rx5xYoVPXr0mDhx4sSJE7/66qsWaT7//PPHH3982LBhAQEBb7311meffQYANjY2Y/+Wm5s7evRoPz8/Y97gppcAACAASURBVHonJ6emf3Jzc+Mi22IU683gQ3p5cbyQhrgQexXf+ZC9YBdS1Uhza7AWmJvxuPmRnhgI21BSUlJUVDRo0CDjy/Dw8MzMzBZpMjIywsPDmxJkZWUZR0eNKKVff/31008/3fROdnb2kCFDJkyY8NVXX1GKX/q/xHiQDDx6mA/xBaw0BoXEjgCM8MRNFDyQ0nHznAyNlpSUEELs7e2NL52cnDQaTYs0paWlDg4Oxp8dHR11Ol1lZaWzs7Pxnfj4+NLS0qlTpxpfBgYGfvLJJ4GBgdnZ2a+++mplZeX8+fNb/ei0tLQvvvhi6dKlxpcWFhZnz55t+qAWampqCBH9/2K4i+rg9dpx3mYaHZJGoXXdoZuqZSGG6up2FTsWWie0v9BiXBV/3CAPeOKyMbN+0w5cVwx3J9XV9eb5uE6zsrJSKu8S6TgJhM7OzpTS6upqYwSqqqpydXW9PY1WqzX+rNVqFQpF83C1ZcuWmTNnWltbG1/27du3b9++ABAWFlZfX79hw4a2AuHAgQMnTZo0e/Zs48sWl22BUmpnZ9fJP1IwxnZnT5YrH+plpmlCaRRaF1XrILNKF+tjad2+CoSF1gntL7QJPen6bIOdHZ50Z9ZvWmKZ/okgRhrFzsnQqLu7u4ODQ3Z2tvFlVlbW7ctbAgICmifo2bOnQvFXU15ZWblnz57m46LNOTk51dW1uW+IYRgbGxvnv90hCkrGaDx62OyOFtIod9LOKIi41tuRGChc02ItMB89C8cL6SiprJrm5M9QKBQzZsxYs2aNXq+/fPnynj17Hn/8cQAoKiqaM2eOMYw98cQT27ZtKygoaGho2LBhgzGB0bfffhsYGBgWFtb0zrFjx0pKSgDgxo0b77///vjx47nItkhF4dHDZhefjxsnhGWUF8FVY+aUUkJ97YibFHqDANztI1y1alV1dbWbm9uQIUOWLVsWEhICAFqtdt++fTqdDgDGjRv35JNP9unTR61We3h4LFy4sOl34+Pj582b1/xqBw8e9Pf3t7W1DQsLCw8Pf++99zjKthgpGYhR49HDZoVnbQsN7iY0s7gCiewgNCKcrsBsaGiwtLS8QwKWZfV6vYVFu06pqq+vt7K6yx3IvHnzgoKC5s6d254LarXaphU9orbmPHuzhm6KNsc0oWQKrdMqGsHne13JLJVFu28jsdA6oUOFdl1Lh/6kz/uXSjptc6eY7Zt272/6uf2Z+30kMi7C7Z9x5ygIAAzDtDMKAsBdo6BsxXrjuJD5JBSwQ9Wk/VEQmUFPe2KpIBcrsBaYg/G4+eGe0qkD0vlL5CzMlRTU0kI8etgs4vNprDdWHMEZjdOE5nJScsfNY32WAuPRw0dwmtAsJHO+osTEehPcVm8e8ZKrAhgIJQIXC5iHpg5ya2iYq6RaAWkY7U3i81kWKwH3pHfcvKT+GDnD3YTmEV/AjvBiFBgHhcfbhrhakfRyrAXcqtVDSgkdJokjRptgIJSIAS6kqpHmVGMrwK34fCqBx5BKFT6w3gwSi2ioK7GV1mkSGAglwnj0cAJ2CjkWL63tUxIT64XThJyLL5DCI+lbwEAoHbhYgGv5tbS0ng5wllorIBmx3szRAtaAlYBLcVJcNS21v0fORuNuQo4dzqejvRkG46BQuVtBDzuSWoK1gCtaHWSU0yHuUqsDGAilw3j08NUqbAW4Ep+PJ6sJXSzuJuTS0UIaKcXj5jEQSgrOkXAqvgBXyghdrDeJxw21nJHqcfMS/JPkLBZXzXHmmpY2GGgfJwyEgjbKi0kqoo0YCrkh1cViGAglZYw3OZyPW4o5EZdPR0tujYD0OFlAkCM5pcFKYHoVjXC1ikZKboIQMBBKjK8dsVGSbDx6mAO4g1AsRuPyaW7E57MxaqKSYtCQ4t8kb7hYgCNHCqU5KCQ9sV5MfD6OjZpefAGV5AQhYCCUHtxNyIXsCqog0NMeA6EIDPckp0tonZ7vfEhOnHRXTWMglJox3kwCHj1sanH5dKxEmwDpsVPBQBeShNOEJqWpgzzpHjePgVBqvGzADY8eNrX4AsneC0tSrBduojCx+AJ2pHSPm8dAKEF4xIxpUYAjBewoXCkjHrHeDFYB05L2YjEMhBKEuwlN63wZdbYk3W0l2wpIz1A1SS+jWh3f+ZCQOInuIDTCQChBo72ZY4V49LDJSO953JJnpYBBbuREEdYB08ivpeUNtL90j5vHQChBrpbQw46k4NHDJoInq4lRrDduojCZQ3k01kvKx81jIJQmfEKpqRgoHCtkR0p0+5SEjcYNtaYj+cViWL2lCVfNmUpqCe1uS9TWfOcDdVCUB7lUScsb+M6HJCRIeoIQMBBK1SgvJrGINhj4zof4xUl6sZyEWTAwxIMcLcTbwa66WkUbDLS3o5RrAQZCaXK0gN6O5HQxDg11VXwBK+1BIQmL9WbwlKWuiy+gY6R+3LzE/zw5i/UmcdgKdI2OhaQiOtITq4ko4Uy5ScjhedRYwyULjx7uumQNDXIkzpZ85wN1yiA3crOGFtXxnQ+RS5DBqmkMhJI13JOk4NHDXSPVx5DKhILAMDWD04RdkVVBVYz0j5vHQChZdioIdiGJePRwF8Tns1J97oxM4ClLXRSXT8fI4F4QK7mUjfYmODraafUGOFNCh3pKvxWQMHw8ZxdJfgehEQZCKYv1wlVznZdYRINdiIOK73ygLghxJWUNNK8Ga0FnUICjBazkJwgBA6G0xeDRw10QL48mQNoIwAi8Heys82XUxZJ0k8Fx8xgIpcxKARFu5HghtgKdEZdPY6W+fUoOYr1wmrCT4mRz3DzWc4mL9WbwrLVOqNFDehmN8ZBFKyBto73JYQyEnSKHHYRGGAglzjLjwKfzpz/xwnyNRsN3XkRj+67dQyY+bL/vzYbqCr7zgrrKpjJH88Wcofc/dvzECb7zIhqXLl2aMuOZAysedy5M4zsv5nCXQFhTU3Pp0qXKykrz5AaZVlZW1n/+s1p734r/McMmz3iG7+yIQ3Jy8pzVn1+Ifa/QZcBjz87hOzuoq+59aEZdyAOJkW8+NHtBYWEh39kRAZZlxz4wfX+Px3VjF8x6+lmtVst3jjjXZiD8+uuve/XqZWdn17t3bycnJx8fnw0bNlCKIwxikpqaqh0wBTwC2bApN/IK+M6OOCQlny4PeRTce7JDZlzIusR3dlCXNDQ0VDRQ6DsGvPs1BsWmp6fznSMRKCoqarT3gsAY6BGi9428ePEi3zninLLVd9esWfP6668PHjx4zZo1arW6tLT0l19+WbBgQU5Ozrp168ycRdRpkZGRDu8/WRI4guRnBPr24Ds74jB8aLTzltfKfMNUV46HDezPd3ZQl1haWrrZKIvP/UQd1JaXDoeEvMp3jkTA09PTqqYIMg6CpY3qxpk+fdbynSPu0ds0NDQ4ODg899xzLd5/5513FAqFRqO5/VeEY+7cuZs2bWpn4qqqKk4zIwRx8QmDpz7hPe3NsrIyk1xQDoW2+n+/Oo2ctXDxCq1Wa5ILyqHQTM5UhZafn//US6+oRj79R2KKSS4oZKYqtOvXr1vdM2fSzNkZGRkmuaDAtdIjLC4urqqqmjOn5ezIiy++uGTJkhs3bri7u7cnvu7atSs1NbVv374zZsxQKlv5oJSUlH379tnZ2T3xxBNqtRoAsrOzjx492jzNI4884uTkBACZmZm7du1SqVQzZ8708fFpf6SXudhRIw8OHen9nc7WEXeGtxcdMO6p1feuGaLgOyPIBLy8vLZ8uLbwd30NboZpN72Lr/tTG36e3vqQofS08s2ws7MjhJSWlrZ4v6SkRKFQ+Pr6tue6CxcuXLVqlVqt/uyzz5544onbE8TFxY0ZM8bS0vLKlSsRERHl5eXGj0j5265du1599VVjBE1NTY2OjmZZtri4eNCgQbm5uR3+Q2XMXgUB9iStFOd32ytJQ6PVslg1Lh/RHkxSEVaB9kosojGyqgKt9hPHjh07YMCAK1euNL2Tl5c3cuTIefPmtaebWVJSYm1tbfz1srIya2vry5cv3/4R69atM/587733rl27tkWC2bNnP/XUU8afp0+f/uabbxp/njFjRtPPt8Oh0Va9cFy/Id1gkktJvtBYSt2/abxZzZrwmpIvNC6YttAO5bHDftKZ8ILCZKpCe950LYYotD5W8NVXXzU2Nvbq1Ss8PHzixIlRUVE9e/ZMSUnJz89/5G9xcXFtBdeTJ0927949ICAAAJydnSMjI+Pj45snYFn2yJEj48aNM74cN25cQkJC8wR1dXU7d+585pm/VvzHx8ePHz++KXGLq6G7ilaTJHwMRftcqaTWStJdBsdKycoQD5JWShvxbIn2SZJZj7D1IeDu3bunpKR88803CQkJubm5LMsGBwcDwPXr15vSVFVVtXXRgoICDw+Pppdqtbqg4Ja1+yUlJTqdrimNWq3Oz89vnmDnzp0eHh4xMTEAoNfrNRpN08Tk7Ymby8nJOX369Llz54wvra2tly9fbmtr22ri+vp6lUoWM2fhjrCoUFFfb4JTRyVfaEfyyGA3Ul9fb8JrSr7QuGDaQlMA+NsxyfkNkW5SviM0SaFpdXBVq+ht22DSSsAblUqlUNxlvr/NuVA7O7sXXnjhhRde6MQHK5VKlv3n1stgMLRYLGN82ZRGr9e3+M/bsmXLM888QwgBAIZhFArFHRI3Z2tr6+PjM2jQoKYPsra2bqsUFArFXQtIGno5AUuhsEHRzaarl5J8oZ0qgWgPMO3fKPlC44LJCy1GDadKyRC1CS8pOCYptJQiCHMBa5VEvrHGOHJnnCwK8vLyysvLa3qZn59///33N0/g7OxsZWWVn59v7BTm5+d7eXk1/evly5eTkpK2b99ufMkwjLEX2L9//9sTt+Dq6hoUFNTO+K1SqeRznz7Yw3CqlDzi2NWFc5IvtOQS/ex+CpXKlONCki80Lpi80IZ6sj/lUJVU2vdWmaTQTpWxMZ4SL6gWOFlPPGzYsMrKyjNnzgBATk5OWlqacTqwsLDQOGhJCJk0adLu3bsBgGXZvXv33nfffU2/vmXLlgkTJjSPdvfdd9+PP/5o/PnHH39snhi1U7QHThPeXZUOrmnpQBcZzY7IR7QHPomlXZKK2GiZHTfPSY/Q1tZ2+fLlU6ZMmTJlyu+//z5//nxjVNuzZ89nn32WlpYGAIsXLx4zZszNmzdzcnIMBsP06dONv6vX67dt2/bJJ580v+Brr70WExNTUVGh1WqvXr36v//9j4tsS1uMmixMxqUCd5GsoYPciAXuN5OiAAfCUnqzhvbAlVBtowDJxfTrkfKqA1ztl5w/f/6oUaPOnj37+OOPDxkyxPjm1KlTBw8ebPw5NDQ0MzPz4MGD9vb248ePt7S0NL7f0NCwdevWUaNGNb+av79/Zmbm77//bmFhMX78+LYWv6A7iHAjGeW0Vg82ctkj2xmJRVRu98KyMsSDSSyij/rjf3GbMsupqyVRW/OdD/PisFEMDQ0NDQ1t/o6Xl1fzAU+1Wj1z5swWv2Vrazt27Njbr+bi4tLUa0SdYK2E/s4kpYQO98RWoE1JGvbFvvK6F5YV4z6iR/35zoeAyW4rPQDg8whlJQZ3E94RBThVTKPVWCkkK8aDJOL5MneUpJHjoAjWeRmJ9iB4ytQdZJRTNyvibsV3PhBnItxJZjmt1fOdDwFL0mCPEEnaUDVJ1OB6mTYlFdEY+d0Ly4qVAga4kJQSvB1sXXkDFNTS/s6yqwUYCGWkmy2xZMjVKmwFWodnbcsBjo7eQaKGRrkThfwqAQZCeYlWk0ScJmxDIvYIZQDP3b0DGe4gNMJAKC84TdiW0gYorKP95DcoJDdD1eREEYt1oFWJRTJdLCbHv1nOcOFoW5KKZDooJDfeNsRagRMErTBQSCmhg93lWAcwEMpLmCu5UkWrTPAUCqlJ0rAyXCwnTzFqnCZsxblS2sOOOFvynQ8+YCCUFxUDYa7kdDG2Ai0lFtFoD6wOsoDn7rZKnhsnjLDmy040rpq7jZ6FlBIaJctBIRmKUeNMeSvkuZXeCAOh7ESrSRLuJrzVuTLqK9dBIRkKdSVXtbSyke98CIycD9rFQCg7MR7MSQ3FZXPNyXlQSIZUDITjBMGtiuqgqpH2dpJpLcBAKDse1uBiSbIrsRX4R5KM74XlCTfUtnCiiB3i0Y5HuUsUBkI5wsM1WkjEM2VkJtqDJBXhBME/kuS6g9BIvn+5nEXjYoFmCmpB20h7OWIglJGhaia5GCcI/pEo79kBDIRyhNvqm0ssYqPV8h0Ukic3K3C1JFkVWAsAABoMcK6URrrJtxJgIJSjAc4kv5aW1POdD2FI0uAOQjnCbfVNUktpbydip+I7H/zB+i9HCgKR7uQUrpoDALk+khvhtvom+AAyDIQyFe2BuwkBABoMcL6MRsh4UEi2cIKgCT6ADAOhTEV7MDguBAApJbSPvAeFZGuAMynACQIAkPeZMkYYCGUqWk1OF1O97PuEuJVethgCUe4kWfYTBDeqqZ6lPe1lXQswEMqUkwX0sCXp5XJvBfBeWM5wNyEAJBbRoTLeQWgk979fznDVHACcxEAoY9FqnCDACUIADIRyFi37xQJ/aiml4CfvQSE5G+JBzpTIfYIgUfZLRgEDoZzFeMj9fBk8WU3mnCzAx46cL5NvLajTw8VKGi77VdMYCOWrtxOp0tGCWr7zwR88axvFyPv07eRiGuxMrBR854NvGAjliwAMdicnZbybUObnKyL4a72MfAMhrpo2wkAoa9FqRrbThDV6uFhBw12xFZA1mW+rx0ERIwyEshYt4+cxnS6mIa7EUvaDQjLXy5FodTS/Vo61gAKc1LBDMBBiIJS5wR4krZQ2GPjOBx9wsRwCAAIwxIOclGWn8HIltVWRbrZYCzAQyputEno5krOlcmwFkjQsLhlFABDtwchzmjARx0X/hoFQ7uQ5R0IBTmroYHdsBRBEy3XhKB6r1AQDodzJc9XcpUpqh4NCCAAAotzJOVlOEOCS0SYYCOUuWk1OyC8Q4gQhamKrhN5OJFVmEwRVOvhTSwe6YC0AwECI/O0JBZpTLa9WAM9XRM3J8JSlkxo6yI2oMAIAAAZCBABD5PdsQnwkN2pOhufuJhaxOEHYBAMhMj6tXkatQJUOblTjoBD6hww31CYV4aDIPzAQItk9jympiEa4ESV+99HfetoTQuCGbCYIWAqniukQD6wDf8GCQBDhRrIraa2e73yYC+4gRLcb7C6j28GMcuphTdyt+M6HYHAYCA0GQ0ZGRkFBwR3S5OTkZGdnU9ry+1dQUJCenl5dXW18qdPpypvR6XRcZVqWLBUwwJmcLpZLK5BYRKPxXhjdSlbThHjcfAtcNQfXr1/v27fvjBkzQkNDX3rppdsT6PX6Rx99NCYm5sEHHxw0aFBJSYnx/erq6qlTp/bv33/WrFk+Pj7GOHrgwAEPD4+AvyUkJHCUbdmSz7b6vweFsBVAt4iR0zQhnrXdAleBcPHixePGjUtLS8vMzPzxxx+PHj3aIsHu3bvT09MvXryYmZkZGBi4evVq4/tz584lhBQUFKSlpeXm5rq6uhrfHzx4cNnf7rnnHo6yLVvyWS9zoZx6WhM3HBRCtxrkRrIraLU8BptwK30LnARCnU63e/fu2bNnA4Crq+tDDz20Y8eOFmm2b98+Y8YMW1tbAJg9e/b27dsBoKqq6ttvv12zZo1Op2toaLCxsbGwsGj6leLi4sbGRi4yjGLUJLGIlUMkTCzCJgC1wlIBA13ImRLpV4KSeiiqo32dsBb8g5NAWFhY2NDQEBAQYHzp7+9/48aNFmlu3Ljh7+/flCA/P7+xsfHq1auWlpbvvfdeeHi4t7f37NmzDYa/Dj46c+ZMWFiYo6Pjww8/XF5e3tZH19fX37x5M+VvaWlpt09Aott52xBbJblSKf2ywvMVUVtkMkGQpGGHeBAFVoJmlFxctKamBgAsLS2NL21sbLRa7e1prKz+Gp+ytramlNbW1paVlVVXV/v4+Fy6dKm8vDwqKmrr1q1PP/300KFDNRqNg4NDaWnpgw8++MYbb3z++eetfvT169ezs7MPHjzYdOVdu3Y5ODi0mrhpMQ4CgEhXi7icRk+/uxy5KPZCO1FoOSegUas1a3sn9kLjhfkLLdSe+e5P5Uv+Ih52ak+hHbmpDHcErbbODPkRAisrK5VKdec0nARCtVoNAOXl5W5ubgBQWlrq6el5e5qmjl1ZWZmVlZWjo6Mx2eOPPw4Azs7OU6ZMOX78+NNPP+3i4mJM6erq+uqrry5YsKCtj+7bt+/kyZPnzp3bzqza29t37G+TruHe7Nly5XP2d39SrXgLraQeyhp1Ed3sGLPfDou30Hhk5kIb7Ufnp+jt7O1F3Vm6a6GdqdC/FaoQ+V9pYpwMjTo7O/v7+yclJRlfJiUlDRo0qEWa8PDwpgSJiYnh4eGEkICAAGdn5+YB0tHRscUvFhQUODk5cZFtmYuRwcNoEovYwe7E/FEQiYK3DbG3IJclPUGgZ+FsCT6ArCVOeoQAMG/evNdee83a2vrChQsnTpz48ssvAeDKlStjxoxJT093cHB44YUXIiMjY2Ji1Gr1ihUr1q1bBwBWVlZz5syZP3/++++/f/Xq1R9++MG43HTjxo2Ojo4+Pj5ZWVnLli17//33Ocq2nIW6kBtaWtkIjhZ3TyxSSRoarcYdhKhNxrPWejlKNk6klVFfeyLhOt45HAZClUq1bt06Z2fnuLg4Dw8PALCzs5s4caJxuLZ3794///zzf//737q6utWrVz/yyCPGX1y+fPmmTZvee+89Nze3gwcPhoaGAoCfn9+uXbuKioq8vLy2bt06adIkjrItZ0oGwtxIcjG9t5tkW4HEIro4DAMhapNxH9GTvfjOB2fwAWStIhJbVDlv3rygoKB2zhFqtVqcuWnurdMGSwVZFn6nUCHeQtOx4PKNLne6yvy3w+ItNB7xUmgpJfTJI4b0h7jqIXDtroU2Pd4wvjt5IghvB2+BxYH+Ea0mSRqW71xwJa2U+uOgELqjEBdyo5qWN/CdD87gA8hahYEQ/SPagzmpoVLdV4+naaC7UjIwyI2clui2+vxaWqOngdKdAe00DIToH25WoLYmmRXSbAVwKz1qD+MpS3znghOJRTRGjYumW4GBEN1Cwk8oxcPVUHtEezBJEq0CeC/YFgyE6BZSfRhNfi2t1dMAB2wF0F1Eq0lyMTVIsBIYH0CGVaAVGAjRLWI8iCRvh0/goBBqH1dLUFuTzHKp1YIGA6SX0QjcSt8aDIToFv2dSVEdLa7nOx+mhg9gQ+0nyVOWzpTQvk7EVqwbQ7iFgRDdgiEQ5U6SJdcK4CO5UftFS3FcBFdN3wEGQtSS9HYTNhggo5xGuGErgNpFks9jwkGRO8BAiFqK9mAktnD0dDHt60RscFAItU8/J1JcL7UJgiQNG409wjZgIEQtRatJSgnVS6hPiINCqEOMEwQnJTQucl1LCRBfO6wFrcNAiFpyUIGvHTlXJp1OIW6fQh0lsd2EuIn2zjAQolbEqCW1rT6piMVAiDokWloLR/Fe8M4wEKJWGB9Gw3cuTOOaljKE+OCgEOqIIR4kpYTqpDI4ij3CO8NAiFohpVVziUV0KDYBqIMcVNDTXiITBDV6uFRJw1yxFrQJAyFqRZAjqdHRvBoptAJJGoqL5VAnxEjl3N1kDQ11JZYKvvMhYBgIUSsIwBAP5qQkOoX4SG7UOZI5dxdXTd8VBkLUOmm0AjV6uFJFw3ArPeo4yZy7i4vF7goDIWqdNJ7HdFJDQ12JBX7NUccFOpJaPc0V+QQBBUgupkM8sA7cCZYOat1gd5JeTusNfOeja5JwXBR1FgGIVot+guBiBXVQES8bvvMhbBgIUeusldDbkaSWiLsVwGOlUFdIYB9RIi4WawcMhKhNYn8YDQU4qcFBIdR5EpggwLO22wPbCNQmsT+MJruCOlsST2u+84FEK8qdXBD5BAFupW8PDISoTTFqcqJIxEdrJOK9MOoaayX0cSQpop0gqGiEmzU02BlrwV1gIERt8rUjSoZc14q1FcDzFVHXifrc3aQiGulOlNjM3w2WELoTUS8WwEEh1HWirgJJGharQHtgIER3It5pwopGyK2hA3BQCHVNjJokinaCIElDo3GxWDtgGaE7Ee/DaJKKaBQOCqEu87EjKnFOELAUThfTKHe8F7w7bCfQnYS7kkuVtFrHdz46DgeFkKmIdBNFejn1tiFuVnznQwwwEKI7sVTAQBdyWoSr5hKLcFAImYZIz93FVdPthy0FugsxHj1soHCmhA7GVgCZgkh7hElFeKZMe2EgRHcRrSZJGpEtFkgvo942xMWS73wgSRjkRi5XiW+CAJ++1H4YCNFdDFUzSUVUXPfDuHECmZCKgRAXcqpYTJVAUwelDbSPI9aCdsFAiO5CbQ0OFuRSpZhaAdxKj0wrRmzThEkadogHYbAStA8GQnR3opsjwUEhZFrRHiRJVLsJcQdhh2BJobsT16o5TR2UNdDeOCiETCdGzSRqKCuaSoBLRjsGAyG6uxhR9QgTNWw0Dgohk1Jbg7N4Jgh0LJwtpVEYCNsNAyG6uxBXklNNyxv4zkf7JOEOQsQBEZ2ydLaUBtgTBxXf+RAPbC/Q3SkIRLiRZJGsmsNHciMuiOjcXVw13VEYCFG7xKjFsVhAx0JaKY3E8xWRqYnoeUxJeC/YQVwFwqKiolmzZgUHBz/00EPXr1+/PQHLsqtWrQoNDR0xYsTPP//c9H5jY+O7774bGRkZFhb2+uuvN72/cePGQYMGRUdHf//99xzlGd1BtJoRxXqZ1BIa6ICDQsj0BrqQ3BpaJoYJgqQiGoMThB2h5Oi6M2fO9PX13bNnz5dffjl58uTz588Tcst/zEcfffT9999v3779+vXrM2bMSE5O7tOnDwA8++yzOTk569atc3JyunDhgjHx9u3b169f/8MP/e0dDgAAHIdJREFUP1RVVU2bNs3Pzy86OpqjnKNWDfEg/9JQg+BDYSJunEDcUBCIcCfJGjqhh6C/YHk1tIGlAQ6CzqTQcNIjvHjx4rFjx9avXx8YGLhq1SqNRnP06NEWaT7++OPly5cHBwdPnjz54Ycf3rx5MwCcP39+z549u3fvHj58eHBw8PTp042JP/roozfeeCMiImL06NH//ve/P/nkEy6yje7A1RK8bUlGudAjYRKuGkeciRHDcYMnimgMLhbrIE7K68KFC71797a3twcAhUIRHh6enp7ePEFjY+PFixcjIyONLyMjI40JTp06FRkZ+d13302aNOnf//73tWvXmi4YERFh/DkiIqLF1ZB5iGJbPW6lR9yJ9hDBBAFOEHYCJ0OjxcXFTk5OTS+dnZ2LioqaJygpKaGUOjo6Gl86OTlpNBoAuHnz5smTJ/v3779ixYq9e/cOGzYsOzvbysqqoqKiKbGzs7MxcavOnz//3XffrVu3zvhSqVQmJCQ0/W4LNTU1LQZs0R2EOyqO5TNTnYVbaDdroMFg4UHqq6v5zsqt8JvWCQIstIG25JRGVamtVggrX/+oqak5lm/xXpihulroPVezsbKyUirvEuk4CYSOjo41NTVNL7VarbOzc/MExjBZU1NjfL+6utr4g4ODg5WV1fr165VKZURExPbt2w8fPvzAAw/Y2Ng0XbApcav69es3atSoxx9/3PjSxsbG09OzrcSUUjs7u87/nTIT60M3XjTY2toKttDOa9hhnkL8P8VvWicIsNDsALrZ6v/U2Ya4CDQS1upodhUzrIelDVfLP6SJk6HRnj17Xrt2Ta/XG19eunSpZ8+ezRPY2Nio1epLly41JfDz8wMAf39/e3v7pujt5ORUXV1tvODly5dbJG6VUql0dXX1/9sdoiDqqH7OpLSBauoF2gQAnrWNuCfwCYKz5Ux/Z4JRsKM4CYSDBw92c3PbunUrAPz222+lpaUTJkwAgOTk5A8//NCYZsaMGZs2bWJZVqPRfPfddzNnzgSAiRMn1tfXHzp0CABSUlKysrJiYmIAYObMmR999JFOp6uqqtqyZYsxMTIzAjDYnZwuFW6kwfMVEdei1YLeVp9cwuAceSdwEggJIVu3bl25cqWPj89TTz31zTffWFlZAUBGRsbOnTuNaZYsWVJTU+Pp6dm7d++ZM2eOGTMGACwtLb/99tunn346MDDw/vvv//zzzwMCAgDg5ZdfdnFx8fb29vX1HTly5COPPMJFttFd+WszNn+5JS0tje+MtFRXV7dl27fnD2zvbyeGfV5ItAZYVvy+46u9e/eyrOAm4eLj43/49utAXQ7fGREfQjl75CrLsmVlZU5OTneYqCwvL7eysrK2tm7+psFgqKiocHV1bZG4srJSqVTa2tre4UPnzZsXFBQ0d+7c9uRQq9Ual7ai9vj94KFH5i+vipjlem775pWvPDD5fr5z9BeWZUOGjr7UbYzewA4sPpp67JDQFlngN60TBFhoVVVVwTGjbwb/y7YyJ9axYv/3X/Odo38se2/Npt9SKvxGuCZvPvnrrsDAQL5zJCYcjiUzDOPm5nbnNK0ue1EoFLdHQQBoa/EnMo+Pt26vengD9Agp7T1y05fLhRMIr169qrHwbBy/CAAKtqbfuHHjDrPICHVaYmJiRdC9dMzcaoDk9cP0ev1dlyOazbYduyvmxAOjLLNx3L577+I3FvKdIzHBfZeovQJ9u6lyUgCAuXEmwLc739n5h7u7O6u5Cro6aKhhi6+1eheFUNd169ZNlX8eWD1UFVlQAUVBAFB7uEPuBQCwyT3j7yOg6ikKAvqPRAK3fNHCtJnPnF/zWaW9z/Jfv+I7O/9wcnK656lX966NdbNiVq98W2jjaUgygoOD5z04+tP1Q0sNlnPf28B3dm7xwdp1Y6c/76IrHT9m5GOP4iqKjuFwjpAXOEfINa1WO/uMTbgreW2gUIYT6g0QuFP/yziFYHd34TetE4RcaLuvs++fY09PVQrnC/fMUYOPHXklqEawhSZkQmnLkIgsDWP+L92g1fGdj799nMnGeBDBRkEkPQ/2ZPQs/HZTKL2IG9X0pxx2Xn9szzsJCw51WF8nMsab+SRLEMvH6w2w7gK7OAy/ych8CMDScGZpilAex7IilZ3TT+FsyXc+RAubD9QZy8OZdcLoFH6UyQ5Vk4HYHUTm9YAfo2fhVwF0Cq9WYXewq7DsUGf0ciRjvJmPM3nuFNbpYf0F9u1Q/BojczN2CpcJoFP4bho7tz92B7sEWxDUScvDmfUXeO4UfpSF3UHEmwf8GAOFX3L4DIXYHTQJLD7USUGOZGw35iP+OoW1elh73rAYu4OIJwRgaRizLJXPTuGqNHZef4WTBX85kARsRFDnLQtjNvDXKfw4ix3pxQRjdxDxZ6ofwwBvncKrVfTnHHYudge7DEsQdZ6xU/hfPjqFNXpYe96As4OIXwTgbf46he+cZV/G7qApYDuCumRZGLORj07hx5nsKG/sDiL+TfFlGICfc8x9O3i1iv5yk30Ju4OmgIWIuiTIkdxj9k5hjR7WpRveCsFvL+IfAVgcxixLYc3cKVx5lp0/ALuDpoFNCeqqZeHmnin8KJONxe4gEowpvoySgZ9umO928EoV/fUmO6cfNuCmgeWIuirQgYzrxnyYYaZWoEYP69MNb+HsIBKSxaHM8lTzdQpXpmJ30JSwNUEmsDSc2ZhhqDJLp/C/Gexob2aAM3YHkYBM9mWUDOw3S6fwShX9PQ8Xi5oSFiUygUAHMr67OTqFNXrYcMGAJ4siAVocyqwwS6dwZSr7cn+Fg4r7T5INbFCQaSwJYzZcMFQ0cvspH2awo72Zvk7YHUSCY+wU7uO4U3i5kv6B3UFTw9JEphHoQCb1YP7LZaewRg8bLxiWYHcQCdWSMM47hSvPsi8PUNhjd9CksE1BJrMkjNmYwWGn8MMMdkw3pg92B5FQ3e/DWHDZKbxcSQ/msS/hYlFTwwJFJhPAZafQ2B3Ek0WRwC0JUyw5w3LUK1xxlp2P3UEOYLOCTIm7TuGmDHYsdgeR4N3nQ2yUnHQKL1fSQ3m4d5ATWKbIlAIcyH0+pl8+Wq2DTbhYFInE0nDF0hTTdwqXp2J3kCvYsiATWxzKbDJ1p3BTBntPN6a3I3YHkQhM6kFslLDXpJ3Cy5X0cD52B7mCxYpMLMCB3O/DbDJdp7BaBx9mGN7G7iASj2Wm7hQuT2UXYHeQM9i4INN7O5T5MMNQ3mCaq23MYO/tjt1BJCYTexA7Fez50zS3g5cq6eF89kXsDnIGSxaZXoADmWyiTmG1Dv6bgSeLIvFZFqZYlmqaTuHyVPaVYOwOcgjbF8SJpeHMR5km6BRuuMCOw+4gEqEJPYidCn7scqcwq4Iezmdf6IttNYewcBEnfO3I/T7MxgxDVy5SpYNNGYY3sTuIxGlZmGJ5lzuFK8+yC7E7yDFsYhBXloYzH2eyXekUbrzATuyB3UEkVhN6EGdL2N2FTmFWBY3D7iD3sHwRV3ztyGTfzncKq3TwIc4OIpF7O1SxogudwhWp7GsDFXbYHeQYtjKIQ0vCOt8p3HiBneTD9MLuIBKz8d073ynMrKDxBezzfbCV5hwWMeKQrx2Z4stsuNDhTqGxO/hmCH4/kegtDlUs79SeQuwOmg02NIhbi8OYT7LYsg52CjdcYO/D7iCShHHdiYsV/HC9Y53CzAp6BLuD5oKljLjla0em+jEbO9IprGyE/2YYFmF3EEnFkrAOzxRid9CcsK1BnFsc2rFO4YYL7P3YHUQScm834moFu9rdKcwop8cKcbGo+WBBI8752JEH/No7U1jZCB9lYncQSc2SMMXKdncKV6SyC4MVNkqO84T+hs0NMoe3290pXH/BMNmXCcLuIJKWe7oRVyvYee3uncKMcnq8iH0eu4NmhGWNzMHHjjzox6y/W6ewshE+yWJx7yCSpCVhipVn794pXJ7KvjYQu4NmxWFhnzt37vfff3dycpo+fbq9vf3tCUpKSnbs2FFXVzdlypSgoCDjm7///ntVVZXxZ3d391GjRgFAfn7+iRMnmn5x2LBhXl5e3OUcceHtUCZsj/7l/go3qzbTrL9guN+H8bfH7iCSoHu6EXcr2HGNnR7Q5q1eRjlNLKJbRyrMmTHE1a33gQMHYmNjq6qqfvvtt5iYmPr6+hYJysrKwsPDk5OTNRpNZGRkSkqK8f0FCxZ88sknu3bt2rVrV0JCgvHNlJSUF198cdffCgsLOco24o6PHZnW804zhdgdRJK3JEyxPJU1tN0pXJbKLhzIYHfQzLgq71WrVr333nvPP/88y7KRkZG7du2aNWtW8wSbN28eMGDAtm3bAMDGxmb16tW7du0y/tM777wzdOjQFhfs3bv3zp07OcotMo+3jJ3CAQr31jqF69INk7E7iCRtbDfiaQ072+gUZpTTpCK6DbuDZsfJ3Xdtbe2JEycmTZoEAAzDTJw48eDBgy3SHDp0aOLEicafJ02a9McffzT9U1xc3NatW8+dO9c8fUVFxZYtW/bu3VtZWclFnpEZ+NiRR/xb31OI3UEkE0vDFcva6BQuS2Vfw+4gHzgp8vz8fABQq9XGl56enklJSben8fT0NP7s5eVVVVVVXV1tZ2fn5+d35cqVy5cvL1iw4Mknn1y3bh0AqFQqT0/P5OTk7Ozs559//sCBA6Ghoa1+dF5eXkZGRk5OjvGlSqV6/fXXra2tW03c0NBgYWHR5T9XXrpYaAv7QdRP5IVeBjfLW1qC/5wj9/cAb4vGBhM9115Q8JvWCVIttGGu4GlF/nex4bGet7yfUQGJhczmIWxXqoBUC60rlEqlQnGXTjYngZAQAgCU/tXSsSx7ez4IIc0TAADDMADw66+/Gt+8evXqgAEDnnjiiZCQkPHjx48fP974/vz58994443ff/+91Y9WKpU2NjbOzs5NL5VKpfHKt2MYpq1/Qm3pYqH52MG0nvDfbFgZ9s8QaEUjbL4EJyYBw0hzXBS/aZ0g4UJbHAJzTpJHeoKy2d/3zjlYOADsLLr0J0u40DrNGI/ujJNA6O3tTQgpLCz09fUFgMLCwqbOX/M0TWteCgsLnZycbGxsmicICAgICAjIzs4OCQlp/v64ceP27NnT1ker1eqgoKC5c+e2J58qlUqlwiOMOqbrhfZ2OA39Uf/KQFXTTOGm84YH/CDIWbJTI/hN6wQJF9q9PtAtXf/jTWZG4F9B60I5PVVi+G60UtW1JlnChcYpTu4drK2tR4wYsX//fgAwGAy//PKLsT/X0NCQnp5u7P+NHz/emAAA9u/fb0xg/CejnJyca9euBQYGtng/Pj6+aa8FEqMetuRRf2Z9+l8zhRWN8FkWi0fJIFlZFq5YcZbV/92wLU1h/7+9e42J4lzjAP7iriBKVtyFshcuSzwtp1qrKMVWT+naw1pAlOBCseFIuQioKC3VxnjsMbTVpBC0tWnVkp7YixZSi0qhAgtKAbUgakutaECBgLsFKReBBRZ2Z86HSfYYwGt0Z9j5/z4N5tH882SZx533nZlt86c4YnWQJU+q8Tt37tRoNE1NTVevXhUKhatXryaENDU1Pf/88z09Pc7OzvHx8QcOHNBoNDKZ7LvvvisvLyeEXLp0KTExccmSJRRF5eXlxcTELFq0iBASHx8/MDDg6el59erV8+fPFxcXP6HYYB3bF0xZcMyUNk/gOo3suWxerZzijc2iwCfLZHby6SS3ifrX36b80UPX3KKPqGz2igj3/X+h7rFrbGwsKSlxcXEJCwtjtqsMDAxUVFS89tprQqGQENLX13f8+PHBwcHQ0FAPDw9CyMjIyJkzZ65duyYUChcuXOjn58f8U21tbVVVVZ2dnTKZTK1WW5YAx0tNTX3wS6P9/f0T3ukP9/C4mpZyzjyDNq7z7PtHhaQmTGjbgxCftEdg8007007HV5rKlnSm/iH5p8fUzXMfw0URm2/aE/IEByErMAiftMfVtP8eLUzassNBLBM5CFqrjtv2Vjd80h6BzTets7PT6x8r7ZxcjF26c8e/8vedf/+/cz8237QnBAszwI5du3ZR754e2lTQp1h07O67nwBsVca+/cOqzYMbjpvjv3r3P7vYjsNrGITADrPZTIT2hBDKfvrwsC3ePAhwT8PGEWI/gxBCHGYM2+T9s5MHdikBO/6dlrJzXzAt/btL97UIDXY/Ae9sTUk8EbzaeL1kSkttxsG9bMfhNQxCYMf6hNhVwcv1ev38+fNx5xPwkFKpbLh45vLly08/vVssFrMdh9cwCIE1crlcLpeznQKANdOnT1+8eDHbKYDfa4RarfbOW/XhQeAmzkeApj0ss9k8/kn9cG/Dw8PMDdnwsHg9CFNSUm7dusV2iklm7dq1RizsPwyDwRAbG8t2iknmzz//TE1NZTvFJNPQ0LBjxw62U0xKvB6EAAAAGIQAAMBrGIQAAMBrtrZr9Pr161qt1vJei3vr7e2Nioqy7Yd7PXajo6MhISF459mDoyjKaDSq1Wq2g0wmRqOxq6sLTXsoAwMDLS0taNoY4eHhGzduvHeNrT1rtLa29ubNmw/4tL3m5mZvb+/718Ed0LRHgKY9LJqmW1pa0LSHQlFUW1sb8xZYsPD29p49e/a9a2xtEAIAADwUXOACAABewyAEAABewyAEAABewyAEAABeE6Snp7OdwRq6u7tPnDjR0NDg5eU14f0SJpNJq9WePXtWLBbPnDnT+gk5yGAwFBQU1NXVKRQKR0fH8QXXr18vLS29du3arFmz8F5sRktLS35+fkdHh7e39z1uMqmvr6+vr1cqlVaMxl1NTU35+fmdnZ3e3t52dnYT1ly6dKm4uFin07m5uU2bNs3KCTmosbGxoKCgu7tbqVRO2DSdTldUVFRfXy8Wi/HreR80DzQ1Nbm5uUVFRYWEhPj4+HR3d48pMJvNy5cvf+GFFxISEsRi8enTp1nJySk9PT0+Pj5BQUFr1qyRSqU3btwYU/D555/LZLLIyMjVq1eLRKKCggJWcnKKVqsVi8UJCQl+fn7BwcEURU1YptfrXV1dJRKJleNx008//SSRSNatW+fr6xsWFja+gKKopKQkDw+PtWvXrly5Misry/ohuSYvL08ikSQmJs6bN++NN94YX1BcXOzs7JyQkBAXF+fs7Ixz2r3xYhBu2LAhKSmJOQ4KCsrIyBhTUFRUpFQqBwcHaZrev3//0qVLrR2RezIzM9VqNXMq37BhQ3Jy8piC1tZWo9HIHGdlZfn6+lo7IvcsXrz44MGDNE0PDg56enqWlpZOWBYeHr5161YMQsaCBQsOHTpE03R/f79MJqusrBxTcPjw4dmzZ/f09LAQjpMoivLx8cnNzaVpure3VyKRXLhwYUxNaGhoeno6c7x9+3aNRmPtlJMKL9YICwoKIiIimGONRlNYWDimoLCwcMWKFczVv4iIiLNnz3Z3d1s7JccUFhZqNBrmkktERMT4pnl4eFguMstkMryS4tatWzU1NRqNhhDi6OgYEhIyvmmEkJycHAcHh1WrVlk9IBe1tbXV1dUxTXNycgoKChrftJycnPXr13d1dZ0+fbqrq4uNmNzS2NjY1NQUFhZGCJk5c6ZarR7fNIlEYjAYmOPBwUEXFxdrp5xUbO0Ra+NRFNXe3q5QKJgfFQqFTqcbU6PT6fz9/ZljV1dXe3t7nU7H83dG63S6O5vW3t5uNpsFAsH4yuHh4czMzHXr1lk3IOfo9XoHBwfLGUehUNTV1Y2p+euvvz744IOff/65oaHB6gG5SK/Xi0QiywqWQqFobm4eU3Pjxg2DwXD06FF3d/eKiorc3NzAwECrJ+UQvV7v4uJiWSid8JyWkZERHR0dHBxsNpvt7OyOHDli9ZiTie1/I6QoiqIoy2KyQCAwmUxjasxm8537Gias4Zs7eyIQCGiaNpvNE5bFxMQolUq8Pe5BPkWbNm3atm2bm5ubdaNxF3Oatvw4YdOGh4cFAkF1dXVeXt6HH3741ltvWTcj5zxI006ePKnT6V5//fU1a9Y0NzeXlJRYN+MkY/vfCIVCoaura2dn57PPPksI6ejokMv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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: 7%|█▏ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 71%|███████████▍ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 100%|████████████████| Time: 0:00:01\u001b[K\n" ] }, { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=44}", "image/png": 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"output_type": "execute_result", "data": { "text/plain": "2-element Vector{StaticArraysCore.SVector{3, Float64}}:\n [-8.07703158014576e-16, -1.997111975669032e-16, 5.041803165151351e-16]\n [4.1960487441262853e-16, -5.372225803253413e-16, -6.326561455332186e-16]" }, "metadata": {}, "execution_count": 8 } ], "cell_type": "code", "source": [ "compute_forces_cart(scfres)" ], "metadata": {}, "execution_count": 8 }, { "cell_type": "markdown", "source": [ "As expected, they are numerically zero in this highly symmetric configuration." ], "metadata": {} } ], "nbformat_minor": 3, "metadata": { "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.8.4" }, "kernelspec": { "name": "julia-1.8", "display_name": "Julia 1.8.4", "language": "julia" } }, "nbformat": 4 }