{ "cells": [ { "cell_type": "markdown", "id": "1ae9ce3c", "metadata": {}, "source": [ "# Phonons and Born effective charges\n", "\n", "This lesson discusses how to compute phonon band structures, DOS\n", "and Born effective charges with Abinit and AbiPy.\n", "The discussion closely follows the [second lesson](https://docs.abinit.org/tutorial/rf2/index.html)\n", "on DFPT available on the Abinit web site.\n", "More specifically, we will discuss how to\n", "\n", " * Perform a convergence study for the phonon frequencies at $\\Gamma$ as function of `ecut`\n", " * Compute the full phonon band structure of `AlAs` with the inclusion of LO-TO splitting\n", " * Obtain thermodynamic properties within the harmonic approximation\n", "\n", "We assume that you have read the references mentioned in the\n", "[first Abinit lesson](https://docs.abinit.org/tutorial/rf1/index.html) on DFPT.\n", "You might find additional material, related to the present section, in the following references:\n", "\n", "* [Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.55.10355)\n", "* [Phonons and related crystal properties from density-functional perturbation theory](https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.73.515)\n", "\n", "If you are already familiar with python and AbiPy-Abinit are already installed and configured,\n", "you may want to use directly the command line interface.\n", "See the README.md file in the directory of this lesson explaining how to analyze the data from the shell\n", "using ipython and matplotlib.\n", "\n", "```{include} ../snippets/plotly_matplotlib_note.md\n", "```\n", "\n", "## Phonon frequencies at $\\Gamma$ as function of ecut\n", "\n", "Before starting, we need to import the python modules and the functions we will need in the notebook:" ] }, { "cell_type": "code", "execution_count": 1, "id": "76d1d536", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import warnings\n", "\n", "warnings.filterwarnings(\"ignore\") # to get rid of deprecation warnings\n", "\n", "from abipy import abilab\n", "abilab.enable_notebook() # This line tells AbiPy we are running inside a notebook\n", "import abipy.flowtk as flowtk\n", "\n", "# This line configures matplotlib to show figures embedded in the notebook.\n", "# Replace `inline` with `notebook` in classic notebook\n", "%matplotlib inline\n", "\n", "# Option available in jupyterlab. See https://github.com/matplotlib/jupyter-matplotlib\n", "#%matplotlib widget" ] }, { "cell_type": "markdown", "id": "3ee52c8a", "metadata": {}, "source": [ "and an useful function from the `lesson_dfpt` module that will be used to generate our DFPT flows:" ] }, { "cell_type": "code", "execution_count": 2, "id": "48882f10", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "

\n", "\n", "
def make_scf_input(ecut=2, ngkpt=(4, 4, 4)):\n",
       "    """\n",
       "    This function constructs an `AbinitInput` to perform a GS-SCF calculation in crystalline AlAs.\n",
       "\n",
       "    Args:\n",
       "        ecut: cutoff energy in Ha.\n",
       "        ngkpt: 3 integers specifying the k-mesh for the electrons.\n",
       "\n",
       "    Return:\n",
       "        `AbinitInput` object\n",
       "    """\n",
       "    # Initialize the AlAs structure from an internal database. Use the pseudos shipped with AbiPy.\n",
       "    gs_inp = abilab.AbinitInput(structure=abidata.structure_from_ucell("AlAs"),\n",
       "                                pseudos=abidata.pseudos("13al.981214.fhi", "33as.pspnc"))\n",
       "\n",
       "    # Set the value of the Abinit variables needed for GS runs.\n",
       "    gs_inp.set_vars(\n",
       "        nband=4,\n",
       "        ecut=ecut,\n",
       "        ngkpt=ngkpt,\n",
       "        nshiftk=4,\n",
       "        shiftk=[0.0, 0.0, 0.5,   # This gives the usual fcc Monkhorst-Pack grid\n",
       "                0.0, 0.5, 0.0,\n",
       "                0.5, 0.0, 0.0,\n",
       "                0.5, 0.5, 0.5],\n",
       "        ixc=1,\n",
       "        nstep=25,\n",
       "        diemac=9.0,\n",
       "        tolvrs=1.0e-10,\n",
       "        #iomode=3,\n",
       "    )\n",
       "\n",
       "    return gs_inp\n",
       "
\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from lesson_dfpt import make_scf_input\n", "abilab.print_source(make_scf_input)" ] }, { "cell_type": "markdown", "id": "faff8ae4", "metadata": {}, "source": [ "The function makes some assumptions for important parameters such as the crystalline structure and the pseudos.\n", "This is done on purpose to keep the code as simple as possible.\n", "It should not be so difficult to generalize the implementation to take into account other cases.\n", "Let's start to play with our new function:" ] }, { "cell_type": "code", "execution_count": 3, "id": "fe69a285", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "##############################################
#### SECTION: basic
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nband 4
ecut 2
ngkpt 4 4 4
nshiftk 4
shiftk
0.0 0.0 0.5
0.0 0.5 0.0
0.5 0.0 0.0
0.5 0.5 0.5
ixc 1
nstep 25
tolvrs 1e-10
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#### SECTION: files
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indata_prefix indata/in
tmpdata_prefix tmpdata/tmp
outdata_prefix outdata/out
pp_dirpath /usr/share/miniconda/envs/abipy/lib/python3.12/site-packages/abipy/data/pseudos
pseudos 13al.981214.fhi 33as.pspnc
##############################################
#### SECTION: gstate
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diemac 9.0
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#### STRUCTURE
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natom 2
ntypat 2
typat 1 2
znucl 13 33
xred
0.0000000000 0.0000000000 0.0000000000
0.2500000000 0.2500000000 0.2500000000
acell 1.0 1.0 1.0
rprim
0.0000000000 5.3050000000 5.3050000000
5.3050000000 0.0000000000 5.3050000000
5.3050000000 5.3050000000 0.0000000000\n", "
" ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "scf_input = make_scf_input()\n", "scf_input" ] }, { "cell_type": "code", "execution_count": 4, "id": "c2aaa621", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Full Formula (Al1 As1)\n", "Reduced Formula: AlAs\n", "abc : 3.970101 3.970101 3.970101\n", "angles: 60.000000 60.000000 60.000000\n", "pbc : True True True\n", "Sites (2)\n", " # SP a b c\n", "--- ---- ---- ---- ----\n", " 0 Al 0 0 0\n", " 1 As 0.25 0.25 0.25\n" ] } ], "source": [ "print(scf_input.structure)" ] }, { "cell_type": "code", "execution_count": 5, "id": "f26ee8b5", "metadata": {}, "outputs": [ { "ename": "AttributeError", "evalue": "'Arrow3D' object has no attribute 'do_3d_projection'", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", "File \u001b[0;32m/usr/share/miniconda/envs/abipy/lib/python3.12/site-packages/IPython/core/formatters.py:343\u001b[0m, in \u001b[0;36mBaseFormatter.__call__\u001b[0;34m(self, obj)\u001b[0m\n\u001b[1;32m 341\u001b[0m \u001b[38;5;28;01mpass\u001b[39;00m\n\u001b[1;32m 342\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m--> 343\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mprinter\u001b[49m\u001b[43m(\u001b[49m\u001b[43mobj\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 344\u001b[0m \u001b[38;5;66;03m# Finally look for special method names\u001b[39;00m\n\u001b[1;32m 345\u001b[0m method \u001b[38;5;241m=\u001b[39m get_real_method(obj, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mprint_method)\n", "File \u001b[0;32m/usr/share/miniconda/envs/abipy/lib/python3.12/site-packages/IPython/core/pylabtools.py:170\u001b[0m, in \u001b[0;36mprint_figure\u001b[0;34m(fig, fmt, bbox_inches, base64, **kwargs)\u001b[0m\n\u001b[1;32m 167\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_bases\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m FigureCanvasBase\n\u001b[1;32m 168\u001b[0m FigureCanvasBase(fig)\n\u001b[0;32m--> 170\u001b[0m \u001b[43mfig\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcanvas\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mprint_figure\u001b[49m\u001b[43m(\u001b[49m\u001b[43mbytes_io\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkw\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 171\u001b[0m data \u001b[38;5;241m=\u001b[39m bytes_io\u001b[38;5;241m.\u001b[39mgetvalue()\n\u001b[1;32m 172\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m fmt \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124msvg\u001b[39m\u001b[38;5;124m'\u001b[39m:\n", "File \u001b[0;32m/usr/share/miniconda/envs/abipy/lib/python3.12/site-packages/matplotlib/backend_bases.py:2175\u001b[0m, in \u001b[0;36mFigureCanvasBase.print_figure\u001b[0;34m(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)\u001b[0m\n\u001b[1;32m 2172\u001b[0m \u001b[38;5;66;03m# we do this instead of `self.figure.draw_without_rendering`\u001b[39;00m\n\u001b[1;32m 2173\u001b[0m \u001b[38;5;66;03m# so that we can inject the orientation\u001b[39;00m\n\u001b[1;32m 2174\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(renderer, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m_draw_disabled\u001b[39m\u001b[38;5;124m\"\u001b[39m, nullcontext)():\n\u001b[0;32m-> 2175\u001b[0m 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artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m 70\u001b[0m renderer\u001b[38;5;241m.\u001b[39mstart_filter()\n\u001b[0;32m---> 72\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43martist\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 73\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m 74\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n", "File \u001b[0;32m/usr/share/miniconda/envs/abipy/lib/python3.12/site-packages/matplotlib/figure.py:3162\u001b[0m, in \u001b[0;36mFigure.draw\u001b[0;34m(self, renderer)\u001b[0m\n\u001b[1;32m 3159\u001b[0m \u001b[38;5;66;03m# ValueError can occur when resizing a window.\u001b[39;00m\n\u001b[1;32m 3161\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpatch\u001b[38;5;241m.\u001b[39mdraw(renderer)\n\u001b[0;32m-> 3162\u001b[0m \u001b[43mmimage\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_draw_list_compositing_images\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m 3163\u001b[0m \u001b[43m \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43martists\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msuppressComposite\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 3165\u001b[0m renderer\u001b[38;5;241m.\u001b[39mclose_group(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mfigure\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m 3166\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n", "File \u001b[0;32m/usr/share/miniconda/envs/abipy/lib/python3.12/site-packages/matplotlib/image.py:132\u001b[0m, in \u001b[0;36m_draw_list_compositing_images\u001b[0;34m(renderer, parent, artists, suppress_composite)\u001b[0m\n\u001b[1;32m 130\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m not_composite \u001b[38;5;129;01mor\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m has_images:\n\u001b[1;32m 131\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m a \u001b[38;5;129;01min\u001b[39;00m artists:\n\u001b[0;32m--> 132\u001b[0m \u001b[43ma\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 133\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 134\u001b[0m \u001b[38;5;66;03m# Composite any adjacent images together\u001b[39;00m\n\u001b[1;32m 135\u001b[0m image_group \u001b[38;5;241m=\u001b[39m []\n", "File \u001b[0;32m/usr/share/miniconda/envs/abipy/lib/python3.12/site-packages/matplotlib/artist.py:72\u001b[0m, in \u001b[0;36mallow_rasterization..draw_wrapper\u001b[0;34m(artist, renderer)\u001b[0m\n\u001b[1;32m 69\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m 70\u001b[0m renderer\u001b[38;5;241m.\u001b[39mstart_filter()\n\u001b[0;32m---> 72\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mdraw\u001b[49m\u001b[43m(\u001b[49m\u001b[43martist\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrenderer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 73\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m 74\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n", "File \u001b[0;32m/usr/share/miniconda/envs/abipy/lib/python3.12/site-packages/mpl_toolkits/mplot3d/axes3d.py:441\u001b[0m, in \u001b[0;36mAxes3D.draw\u001b[0;34m(self, renderer)\u001b[0m\n\u001b[1;32m 437\u001b[0m zorder_offset \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mmax\u001b[39m(axis\u001b[38;5;241m.\u001b[39mget_zorder()\n\u001b[1;32m 438\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m axis \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_axis_map\u001b[38;5;241m.\u001b[39mvalues()) \u001b[38;5;241m+\u001b[39m \u001b[38;5;241m1\u001b[39m\n\u001b[1;32m 439\u001b[0m collection_zorder \u001b[38;5;241m=\u001b[39m patch_zorder \u001b[38;5;241m=\u001b[39m zorder_offset\n\u001b[0;32m--> 441\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m artist \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28;43msorted\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mcollections_and_patches\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 442\u001b[0m \u001b[43m \u001b[49m\u001b[43mkey\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mlambda\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43martist\u001b[49m\u001b[43m:\u001b[49m\u001b[43m \u001b[49m\u001b[43martist\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdo_3d_projection\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 443\u001b[0m \u001b[43m \u001b[49m\u001b[43mreverse\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m)\u001b[49m:\n\u001b[1;32m 444\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(artist, mcoll\u001b[38;5;241m.\u001b[39mCollection):\n\u001b[1;32m 445\u001b[0m artist\u001b[38;5;241m.\u001b[39mzorder \u001b[38;5;241m=\u001b[39m collection_zorder\n", "File \u001b[0;32m/usr/share/miniconda/envs/abipy/lib/python3.12/site-packages/mpl_toolkits/mplot3d/axes3d.py:442\u001b[0m, in \u001b[0;36mAxes3D.draw..\u001b[0;34m(artist)\u001b[0m\n\u001b[1;32m 437\u001b[0m zorder_offset \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mmax\u001b[39m(axis\u001b[38;5;241m.\u001b[39mget_zorder()\n\u001b[1;32m 438\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m axis \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_axis_map\u001b[38;5;241m.\u001b[39mvalues()) \u001b[38;5;241m+\u001b[39m \u001b[38;5;241m1\u001b[39m\n\u001b[1;32m 439\u001b[0m collection_zorder \u001b[38;5;241m=\u001b[39m patch_zorder \u001b[38;5;241m=\u001b[39m zorder_offset\n\u001b[1;32m 441\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m artist \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28msorted\u001b[39m(collections_and_patches,\n\u001b[0;32m--> 442\u001b[0m key\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mlambda\u001b[39;00m artist: \u001b[43martist\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdo_3d_projection\u001b[49m(),\n\u001b[1;32m 443\u001b[0m reverse\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m):\n\u001b[1;32m 444\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(artist, mcoll\u001b[38;5;241m.\u001b[39mCollection):\n\u001b[1;32m 445\u001b[0m artist\u001b[38;5;241m.\u001b[39mzorder \u001b[38;5;241m=\u001b[39m collection_zorder\n", "\u001b[0;31mAttributeError\u001b[0m: 'Arrow3D' object has no attribute 'do_3d_projection'" ] }, { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "scf_input.structure.plot();" ] }, { "cell_type": "markdown", "id": "2d477bcf", "metadata": {}, "source": [ "We are using the same pseudopotentials than the official tutorial.\n", "Note that the xc functional is LDA in both pseudos but with a different parametrization.\n", "This is the reason why we are specifying {{ixc}} in the input file.\n", "This is not needed if you are using pseudos generated with the same {{ixc}}." ] }, { "cell_type": "code", "execution_count": 6, "id": "15ae5b31", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " summary: Aluminum, fhi98PP : Hamann-type, LDA CA PerdewWang, l=2 local\n", " number of valence electrons: 3.0\n", " maximum angular momentum: d\n", " angular momentum for local part: d\n", " XC correlation: PW\n", " supports spin-orbit: False\n", " radius for non-linear core correction: 0.0\n", " hint for low accuracy: ecut: 0.0, pawecutdg: 0.0\n", " hint for normal accuracy: ecut: 0.0, pawecutdg: 0.0\n", " hint for high accuracy: ecut: 0.0, pawecutdg: 0.0 \n", "\n", "\n", " summary: Troullier-Martins psp for element As Thu Oct 27 17:37:14 EDT 1994\n", " number of valence electrons: 5.0\n", " maximum angular momentum: p\n", " angular momentum for local part: p\n", " XC correlation: LDA_XC_TETER93\n", " supports spin-orbit: False\n", " radius for non-linear core correction: 2.0573171556401\n", " hint for low accuracy: ecut: 0.0, pawecutdg: 0.0\n", " hint for normal accuracy: ecut: 0.0, pawecutdg: 0.0\n", " hint for high accuracy: ecut: 0.0, pawecutdg: 0.0 \n", "\n" ] } ], "source": [ "for pseudo in scf_input.pseudos:\n", " print(pseudo, \"\\n\")" ] }, { "cell_type": "markdown", "id": "c98d5729", "metadata": {}, "source": [ "As you can see, we essentially have a standard input to perform a GS calculation.\n", "This object will represent the **building block** for our DFPT calculation with AbiPy.\n", "\n", "It this is not your first time you use the DFPT part of Abinit, you already know that phonon calculations\n", "require an initial GS run to produce the `WFK` file\n", "followed by a DFPT run that reads the `WFK` file and solves the Sternheimer equations for $N_{\\text{irred}}(q)$\n", "atomic perturbations where $N_{\\text{irred}}$ is the number of independent atomic displacements\n", "(assuming $q$ belongs to the k-mesh).\n", "\n", "If you try to do a convergence study wrt {{ecut}} **without multi-datasets**, you will likely start\n", "from an initial GS input file with a given value of `ecut`, use it as a template to\n", "generate the DFPT input files, create symbolic\n", "links to the `WFK` file produced in the first GS step and then instruct Abinit to read this file with {{irdwfk}}.\n", "Once you have a set of input files that work for a particular {{ecut}}, one can simply replicate the set of\n", "directories and files and use a script to change the value of {{ecut}} in the input files.\n", "Then, of course, one has to run the calculations manually, collect the results and produce nice plots to understand\n", "what is happening.\n", "\n", "This approach is obviously boring and error-prone if you are a human being but it is easy to implement in an algorithm\n", "and machines do not complain if they have a lot of repetitive work to do!\n", "There are also several **technical advantages** in using this **task-based approach vs multi-datasets**\n", "but we discuss this point in more details afterwards.\n", "\n", "If the machine could speak, it will tell you: give me an object that represents an input for GS calculations,\n", "give me the list of **q**-points you want to compute as well as the parameters that must be changed in the initial input\n", "and I will generate a `Flow` for DFPT calculations.\n", "This logic appears so frequently that we decided to encapsulate it in the `flowtk.phonon_conv_flow` factory function:" ] }, { "cell_type": "code", "execution_count": 7, "id": "c1e6aee2", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "

\n", "\n", "
def build_flow_alas_ecut_conv(options):\n",
       "    """\n",
       "    Build and return Flow for convergence study of phonon frequencies at Gamma as function of ecut.\n",
       "    """\n",
       "    scf_input = make_scf_input()\n",
       "    return flowtk.phonon_conv_flow("flow_alas_ecut_conv", scf_input, qpoints=(0, 0, 0),\n",
       "                                   params=["ecut", [4, 6, 8]])\n",
       "
\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from lesson_dfpt import build_flow_alas_ecut_conv\n", "abilab.print_source(build_flow_alas_ecut_conv)" ] }, { "cell_type": "markdown", "id": "80e898df", "metadata": {}, "source": [ "Let's call the function to build our flow:" ] }, { "cell_type": "code", "execution_count": 8, "id": "f5b8537a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Number of works: 6, total number of tasks: 9\n", "Number of tasks with a given class:\n", "\n", "Task Class Number\n", "------------ --------\n", "ScfTask 3\n", "PhononTask 6" ] } ], "source": [ "flow = build_flow_alas_ecut_conv(options=None)\n", "\n", "flow.show_info()" ] }, { "cell_type": "markdown", "id": "808e8491", "metadata": {}, "source": [ "and call the `get_graphviz` method to visualize the connection among the `Tasks`:" ] }, { "cell_type": "code", "execution_count": 9, "id": "097a4fe9", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "flow\n", "\n", "Flow, node_id=60, workdir=flow_alas_ecut_conv\n", "\n", "clusterw0\n", "\n", "Work (w0)\n", "\n", "\n", "clusterw1\n", "\n", "PhononWork (w1)\n", "\n", "\n", "clusterw2\n", "\n", "Work (w2)\n", "\n", "\n", "clusterw3\n", "\n", "PhononWork (w3)\n", "\n", "\n", "clusterw4\n", "\n", "Work (w4)\n", "\n", "\n", "clusterw5\n", "\n", "PhononWork (w5)\n", "\n", "\n", "\n", "w0_t0\n", "\n", "w0_t0\n", "ScfTask\n", "\n", "\n", "\n", "w1_t0\n", "\n", "w1_t0\n", "PhononTask\n", "\n", "\n", "\n", "w0_t0->w1_t0\n", "\n", "\n", "WFK\n", "\n", "\n", "\n", "w1_t1\n", "\n", "w1_t1\n", "PhononTask\n", "\n", "\n", "\n", "w0_t0->w1_t1\n", "\n", "\n", "WFK\n", "\n", "\n", "\n", "w2_t0\n", "\n", "w2_t0\n", "ScfTask\n", "\n", "\n", "\n", "w3_t0\n", "\n", "w3_t0\n", "PhononTask\n", "\n", "\n", "\n", "w2_t0->w3_t0\n", "\n", "\n", "WFK\n", "\n", "\n", "\n", "w3_t1\n", "\n", "w3_t1\n", "PhononTask\n", "\n", "\n", "\n", "w2_t0->w3_t1\n", "\n", "\n", "WFK\n", "\n", "\n", "\n", "w4_t0\n", "\n", "w4_t0\n", "ScfTask\n", "\n", "\n", "\n", "w5_t0\n", "\n", "w5_t0\n", "PhononTask\n", "\n", "\n", "\n", "w4_t0->w5_t0\n", "\n", "\n", "WFK\n", "\n", "\n", "\n", "w5_t1\n", "\n", "w5_t1\n", "PhononTask\n", "\n", "\n", "\n", "w4_t0->w5_t1\n", "\n", "\n", "WFK\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "flow.get_graphviz()" ] }, { "cell_type": "code", "execution_count": 10, "id": "65d8ee79", "metadata": {}, "outputs": [], "source": [ "# matplotlib version based on networkx\n", "#flow.plot_networkx(with_edge_labels=True);" ] }, { "cell_type": "markdown", "id": "3b346e5c", "metadata": {}, "source": [ "The flow contains three independent groups of tasks, one group per each value of {{ecut}} specified in `params`." ] }, { "cell_type": "code", "execution_count": 11, "id": "40babc26", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "w0_t0 uses ecut: 4\n", "w1_t0 uses ecut: 4\n", "w1_t1 uses ecut: 4\n", "w2_t0 uses ecut: 6\n", "w3_t0 uses ecut: 6\n", "w3_t1 uses ecut: 6\n", "w4_t0 uses ecut: 8\n", "w5_t0 uses ecut: 8\n", "w5_t1 uses ecut: 8\n" ] } ], "source": [ "for work in flow:\n", " for task in work:\n", " print(task.pos_str, \"uses ecut:\", task.input[\"ecut\"])" ] }, { "cell_type": "code", "execution_count": 12, "id": "30fcb05a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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ecutclass
w0_t04ScfTask
w1_t04PhononTask
w1_t14PhononTask
w2_t06ScfTask
w3_t06PhononTask
w3_t16PhononTask
w4_t08ScfTask
w5_t08PhononTask
w5_t18PhononTask
\n", "
" ], "text/plain": [ " ecut class\n", "w0_t0 4 ScfTask\n", "w1_t0 4 PhononTask\n", "w1_t1 4 PhononTask\n", "w2_t0 6 ScfTask\n", "w3_t0 6 PhononTask\n", "w3_t1 6 PhononTask\n", "w4_t0 8 ScfTask\n", "w5_t0 8 PhononTask\n", "w5_t1 8 PhononTask" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "flow.get_vars_dataframe(\"ecut\")" ] }, { "cell_type": "markdown", "id": "592fcdd2", "metadata": {}, "source": [ "Each group represents a `Workflow` and consists of one `ScfTask`(red circle) that solves\n", "the `KS` equations self-consistently producing a `WFK` file that will be used\n", "by the two children (`PhononTasks` - blue circles)\n", "to compute the first-order change of the wavefunctions due to one of the *irreducible* atomic perturbations.\n", "\n", "Note that `phonon_conv_flow` invokes Abinit under the hood to get the list of irreducible perturbations\n", "and uses this information to build the flow.\n", "This explains why we have two `PhononTasks` per **q**-point instead of the total number of phonon modes that\n", "equals $3*N_{atom}=6$.\n", "\n", "Perhaps a table with the values of the input variables associated to the DFPT perturbation will help.\n", "`None` means that the variable is not defined in that particular input." ] }, { "cell_type": "code", "execution_count": 13, "id": "c931e3cd", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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rfphonrfatpolrfdirqptkptoptclass
w0_t0NoneNoneNoneNoneNoneScfTask
w1_t01[1, 1][1, 0, 0][0.0, 0.0, 0.0]2PhononTask
w1_t11[2, 2][1, 0, 0][0.0, 0.0, 0.0]2PhononTask
w2_t0NoneNoneNoneNoneNoneScfTask
w3_t01[1, 1][1, 0, 0][0.0, 0.0, 0.0]2PhononTask
w3_t11[2, 2][1, 0, 0][0.0, 0.0, 0.0]2PhononTask
w4_t0NoneNoneNoneNoneNoneScfTask
w5_t01[1, 1][1, 0, 0][0.0, 0.0, 0.0]2PhononTask
w5_t11[2, 2][1, 0, 0][0.0, 0.0, 0.0]2PhononTask
\n", "
" ], "text/plain": [ " rfphon rfatpol rfdir qpt kptopt class\n", "w0_t0 None None None None None ScfTask\n", "w1_t0 1 [1, 1] [1, 0, 0] [0.0, 0.0, 0.0] 2 PhononTask\n", "w1_t1 1 [2, 2] [1, 0, 0] [0.0, 0.0, 0.0] 2 PhononTask\n", "w2_t0 None None None None None ScfTask\n", "w3_t0 1 [1, 1] [1, 0, 0] [0.0, 0.0, 0.0] 2 PhononTask\n", "w3_t1 1 [2, 2] [1, 0, 0] [0.0, 0.0, 0.0] 2 PhononTask\n", "w4_t0 None None None None None ScfTask\n", "w5_t0 1 [1, 1] [1, 0, 0] [0.0, 0.0, 0.0] 2 PhononTask\n", "w5_t1 1 [2, 2] [1, 0, 0] [0.0, 0.0, 0.0] 2 PhononTask" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "flow.get_vars_dataframe(\"rfphon\", \"rfatpol\", \"rfdir\", \"qpt\", \"kptopt\")" ] }, { "cell_type": "markdown", "id": "efcef7f2", "metadata": {}, "source": [ "If the meaning of these variables is not clear, you can consult the [Abinit documentation](https://docs.abinit.org)\n", "e.g. the documentation of the {{rfatpol}} input variable or access the documentation directly from python with:" ] }, { "cell_type": "code", "execution_count": 14, "id": "1f8611e8", "metadata": {}, "outputs": [ { "data": { "text/html": [ "

Default value:

[1, 'natom']

Description

\n", "Control the range of atoms for which displacements will be considered in\n", "phonon calculations (atomic polarizations).\n", "These values are only relevant to phonon response function calculations.\n", "May take values from 1 to natom, with rfatpol(1)<=rfatpol(2).\n", "The atoms to be moved will be defined by the do-loop variable iatpol:\n", "\n", " - do iatpol=rfatpol(1),rfatpol(2)\n", "\n", "For the calculation of a full dynamical matrix, use rfatpol(1)=1 and\n", "rfatpol(2)=natom, together with rfdir 1 1 1, both being the default values.\n", "For selected\n", "elements of the dynamical matrix, use different values of rfatpol and/or\n", "rfdir. The name 'iatpol' is used for the part of the internal variable\n", "ipert when it runs from 1 to natom. The internal variable ipert can also\n", "assume values larger than natom, denoting perturbations of electric field\n", "or stress type (see [the DFPT help file](/guide/respfn)).\n", "\n", "As a side technical information, the value rfatpol(1)=-1 is admitted, and transformed\n", "immediately to rfatpol(1)=1, while rfatpol(2)=-1 is transformed to rfatpol(2)=natom,\n", "while the default input values are actually rfatpol=-1 .\n" ], "text/plain": [ "rfatpol " ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "abilab.docvar(\"rfatpol\")" ] }, { "cell_type": "markdown", "id": "8602f820", "metadata": {}, "source": [ "```{note}\n", "For your convenience the links to the doc of the different variables are listed below:\n", "\n", "- {{qpt}}\n", "- {{rfphon}}\n", "- {{rfatpol}}\n", "- {{rfdir}}\n", "- {{kptopt}}\n", "```\n", "\n", "Now we can generate the `flow_alas_ecut` directory with the input files by executing\n", "the `lesson_dfpt.py` script.\n", "Then use the `abirun.py` script to launch the entire calculation with:\n", "\n", " abirun.py flow_alas_ecut_conv scheduler\n", "\n", "You will see that all `PhononTasks` will be executed in parallel on your machine.\n", "\n", "```{warning}\n", "Please make sure that AbiPy is properly configured by running abicheck --with flow\n", "```\n", "\n", "If you prefer to skip this part, you may want to jump to the next section, that presents the post-processing of the results.\n", "Note that the output files are already available in the repository so it is also possible to try\n", "the AbiPy post-processing tools without having to run the flow." ] }, { "cell_type": "markdown", "id": "1616382e", "metadata": {}, "source": [ "## Convergence study at $\\Gamma$\n", "\n", "There are several output files located inside the `outdata` directories:" ] }, { "cell_type": "code", "execution_count": 15, "id": "c8f4afe5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "flow_alas_ecut_conv/w2/t0/outdata/out_DDB\r\n", "flow_alas_ecut_conv/w4/t0/outdata/out_DDB\r\n", "flow_alas_ecut_conv/w1/outdata/out_DDB\r\n", "flow_alas_ecut_conv/w3/outdata/out_DDB\r\n", "flow_alas_ecut_conv/w0/t0/outdata/out_DDB\r\n", "flow_alas_ecut_conv/w5/outdata/out_DDB\r\n" ] } ], "source": [ "!find flow_alas_ecut_conv/ -name \"*_DDB\"" ] }, { "cell_type": "markdown", "id": "689107d0", "metadata": {}, "source": [ "Remember that our goal is to analyze the convergence of the phonon frequencies at $\\Gamma$\n", "as function of {{ecut}}.\n", "So we are mainly interested in the DDB files located in the `outdata` directories\n", "of the `PhononWorks` (`w0/outdata`, `w1/outdata`, `w2/outdata`).\n", "These are indeed the DDB files with all the information needed to reconstruct the\n", "dynamical matrix at $\\Gamma$ and to compute the phonon frequencies (AbiPy calls `mrgddb`\n", "to merge the DDB files when all the perturbations in the `PhononWork` have been computed).\n", "\n", "The code below tells our robot that we would like to analyze all the DDB files\n", "located in the output directories of the works:" ] }, { "cell_type": "code", "execution_count": 16, "id": "bde1c327", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
    \n", "
  1. flow_alas_ecut_conv/w1/outdata/out_DDB
    2. \n", "
  2. flow_alas_ecut_conv/w3/outdata/out_DDB
    3. \n", "
  3. flow_alas_ecut_conv/w5/outdata/out_DDB
    4. \n", "
" ], "text/plain": [ "Label Relpath\n", "-------------------------------------- --------------------------------------\n", "flow_alas_ecut_conv/w1/outdata/out_DDB flow_alas_ecut_conv/w1/outdata/out_DDB\n", "flow_alas_ecut_conv/w3/outdata/out_DDB flow_alas_ecut_conv/w3/outdata/out_DDB\n", "flow_alas_ecut_conv/w5/outdata/out_DDB flow_alas_ecut_conv/w5/outdata/out_DDB" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "robot = abilab.DdbRobot.from_dir_glob(\"./flow_alas_ecut_conv/w*/outdata/\")\n", "robot" ] }, { "cell_type": "markdown", "id": "6d476ff8", "metadata": {}, "source": [ "For more examples on the use of DDB and robots, see the\n", "[DDB notebook](https://nbviewer.jupyter.org/github/abinit/abitutorials/blob/master/abitutorials/ddb.ipynb).\n", "Now we ask the robot to call `anaddb` to compute the phonon frequencies at $\\Gamma$ for all DDBs\n", "and return a pandas `DataFrame`:" ] }, { "cell_type": "code", "execution_count": 17, "id": "111b5b1f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Calculation completed.\n", "Anaddb results available in dir: /tmp/tmp0v7hudop\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Calculation completed.\n", "Anaddb results available in dir: /tmp/tmpuf71i84y\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Calculation completed.\n", "Anaddb results available in dir: /tmp/tmpokkuifqq\n" ] } ], "source": [ "data_gamma = robot.get_dataframe_at_qpoint((0, 0, 0))" ] }, { "cell_type": "markdown", "id": "c0362788", "metadata": {}, "source": [ "The `DataFrame` is a dict-like object whose keys are the name of the colums in the table" ] }, { "cell_type": "code", "execution_count": 18, "id": "291c10f1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Index(['mode0', 'mode1', 'mode2', 'mode3', 'mode4', 'mode5', 'nkpt', 'nsppol',\n", " 'ecut', 'tsmear', 'occopt', 'ixc', 'nband', 'usepaw', 'formula',\n", " 'natom', 'alpha', 'beta', 'gamma', 'a', 'b', 'c', 'volume',\n", " 'abispg_num', 'spglib_symb', 'spglib_num', 'spglib_lattice_type'],\n", " dtype='object')\n" ] } ], "source": [ "print(data_gamma.keys())" ] }, { "cell_type": "markdown", "id": "c3c0299d", "metadata": {}, "source": [ "where `mode-i` is the frequency in eV of the i-th phonon mode.\n", "\n", "We are mainly interested in the convergence of the phonon frequencies versus {{ecut}} so we filter these columns with:" ] }, { "cell_type": "code", "execution_count": 19, "id": "eddad54f", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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ecutmode0mode1mode2mode3mode4mode5
flow_alas_ecut_conv/w1/outdata/out_DDB4.00.00.00.00.0436410.0436410.043641
flow_alas_ecut_conv/w3/outdata/out_DDB6.00.00.00.00.0444850.0444850.044485
flow_alas_ecut_conv/w5/outdata/out_DDB8.00.00.00.00.0446250.0446250.044625
\n", "
" ], "text/plain": [ " ecut mode0 mode1 mode2 mode3 \\\n", "flow_alas_ecut_conv/w1/outdata/out_DDB 4.0 0.0 0.0 0.0 0.043641 \n", "flow_alas_ecut_conv/w3/outdata/out_DDB 6.0 0.0 0.0 0.0 0.044485 \n", "flow_alas_ecut_conv/w5/outdata/out_DDB 8.0 0.0 0.0 0.0 0.044625 \n", "\n", " mode4 mode5 \n", "flow_alas_ecut_conv/w1/outdata/out_DDB 0.043641 0.043641 \n", "flow_alas_ecut_conv/w3/outdata/out_DDB 0.044485 0.044485 \n", "flow_alas_ecut_conv/w5/outdata/out_DDB 0.044625 0.044625 " ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data_gamma = data_gamma[[\"ecut\"] + [k for k in data_gamma if k.startswith(\"mode\")]]\n", "data_gamma" ] }, { "cell_type": "markdown", "id": "55fe6139", "metadata": {}, "source": [ "and we get some statistics about our data with:" ] }, { "cell_type": "code", "execution_count": 20, "id": "2edb9754", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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ecutmode0mode1mode2mode3mode4mode5
count3.03.03.03.03.0000003.0000003.000000
mean6.00.00.00.00.0442500.0442500.044250
std2.00.00.00.00.0005330.0005330.000533
min4.00.00.00.00.0436410.0436410.043641
25%5.00.00.00.00.0440630.0440630.044063
50%6.00.00.00.00.0444850.0444850.044485
75%7.00.00.00.00.0445550.0445550.044555
max8.00.00.00.00.0446250.0446250.044625
\n", "
" ], "text/plain": [ " ecut mode0 mode1 mode2 mode3 mode4 mode5\n", "count 3.0 3.0 3.0 3.0 3.000000 3.000000 3.000000\n", "mean 6.0 0.0 0.0 0.0 0.044250 0.044250 0.044250\n", "std 2.0 0.0 0.0 0.0 0.000533 0.000533 0.000533\n", "min 4.0 0.0 0.0 0.0 0.043641 0.043641 0.043641\n", "25% 5.0 0.0 0.0 0.0 0.044063 0.044063 0.044063\n", "50% 6.0 0.0 0.0 0.0 0.044485 0.044485 0.044485\n", "75% 7.0 0.0 0.0 0.0 0.044555 0.044555 0.044555\n", "max 8.0 0.0 0.0 0.0 0.044625 0.044625 0.044625" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data_gamma.describe()" ] }, { "cell_type": "markdown", "id": "8f6c9186", "metadata": {}, "source": [ "Pandas tables are extremely powerful and the `describe` method already gives some useful info\n", "about the convergence of the phonon modes.\n", "Sometimes, however, we would like to visualize the data to have a better understanding of what's happening:" ] }, { "cell_type": "code", "execution_count": 21, "id": "c413e481", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data_gamma.plot(x=\"ecut\", y=\"mode3\", style=\"-o\");" ] }, { "cell_type": "markdown", "id": "9c4abaf7", "metadata": {}, "source": [ "Let's plot all the modes in different subplots with:" ] }, { "cell_type": "code", "execution_count": 22, "id": "673d93b6", "metadata": {}, "outputs": [ { "data": { "image/png": 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DYDBAqVTCaDT6nKR1retfC8sy0OlUrW5fz1Fcde1KhBBCRINlGfTu7v13ryPkPvWcV9nAQUPxlw+/8Cpf/+YuweO7f3M/7v7N/X6v33/AELzy+tuCsluGjfSql5Scgj8vfNXvtRiGwf0PPYr7H3rUUxYX1e2ayQ7HMWBZFlptNyiVrZ+LRPsYBYjjeBiNNW2+joxpWT/oguyhSOmlu3bFTo6VMNCEh8FoqgXXyhUVnZnY4wPEF+MPF6rwRuF/r1lPLD+DgPjew6aCGZ/DYUdV5VVERakgk/lfKd1hGAYSloGL4xHwWFonZbW7UFJ57b+pDHDN4VGXiwfHcTAYalBb6xI8p9GEQSJpWS9SyBIjjUbjWQrYmMFggFar9dGioZ3dbofNZhP0GhmNRjAM42mr0WgEE8EaX79Hjx5tuvdgjM0nx2tbtFKhfy+dKOY3SCUslAopamtYOHnxzW0Qe3yA+GLs30t3Xf0MAuJ7D5sKZnwcy4Bh3L0XrdlMsb2wLOOes9OJ7qktlHIJJBIWLlfz75dEwkIha9kqQMCdILXl73TIVqUlJSV5zfUxmUwoKyvzmhvUtB0AFBcXC8r1ej3i4+M93We+rs/zPIqLi/1ev6N05ZUKhIgB/QwSEnoMwyBSo/BbJ1Kj6NDkNGSJUUZGBr766isYjUZP2cGDB8GyLNLTm1+Sl5qaCrVajQMHDnjKHA4HDh06hIyMDMH1v//+e/z888+esuPHj6O6uhp33nlncINppWEpsZj10E3QhQu/KSLDFZj10E20hwoh7Yx+BgkJPZVShhid91CXRMIiRhcGlVLWofcTsqG07OxsbN++HbNmzUJubi5KSkqwevVqZGdnIy4uzlMvJycHly9f9izFVygUyM3NRV5eHiIjI9GvXz/s2rUL1dXVmD59uqfdvffeiy1btmD27NmYP38+amtrsXr1aowePTrkS/UbG5YSi1v6xuD8ZQMcPEO77hLSwehnkPjDi2QuT2enUsrQTSGFzeECD/ecIoVMElBPUbDeq5AlRlqtFtu2bcPy5csxa9YsqFQqZGVlYd68eYJ6HMfB5RJOopoxYwZ4nsfWrVs9R4IUFBR4dr0G3Fuav/POO1ixYgXmz58PqVSKsWPHYuHChR0SXyBYlsGA3pHQ6VSoqrKIcn8RQjoz+hkkTbGse04Lx7muUZMEC8MwUMqlkErZVv0M1r9X9e9dq++Dp3Q4IC4Xh8pKS9CvK5Wyov6lTPF1fWKPUezxAeKPMZjx8TyPsrJfIZcrERERHaQ7bLvWJg1dSWtjrK4uh91uRUxMT6+epshIVedflUYIIYR0VgzDQK2OgNFYAbNZBrlc2SlWp3Ec0+pDZLuKQGPkeR52uxVWqwUaTVSb3ydKjAghhBAfwsJUcDhsMJsNAKpDfTsAAJZlwXHi7jFqXYwMwsLUCAtr+wbMlBgRQgghPrj3xotCeHiE11zXUJBIGGi13WAw1Ii216i1MUokkjbPLapHiREhhBDiB8sG749uW0ilLJRKJWprxXkIMNA5YgzZPkaEEEIIIZ0NJUaEEEIIIXUoMSKEEEIIqUOJESGEEEJIHUqMCCGEEELqUGJECCGEEFKHEiNCCCGEkDohTYy++OIL3H///Rg8eDDuvfde7Nmzp0XtTCYTFi5ciOHDh+OWW27B008/jdLSUkGdvLw8pKSkeP3btWtXe4RCCCGEEBEI2QaP33zzDZ566ilkZWVh4cKF+Prrr/Hiiy9CpVJh3LhxftvOnTsXP/30E5YsWQKFQoH169djxowZ2LNnD6TShpCUSiW2bdsmaJuYmNgu8RBCCCGk6wtZYvTWW29hyJAhWLZsGQBg5MiRuHjxIjZu3Og3MTp16hSOHj2KgoICjBo1CgDQp08fjB8/HocOHcL48eM9dVmWxdChQ9s1DkIIIYSIR0iG0ux2O06cOOGVAI0fPx7nz5/HpUuXmm175MgRaDQapKene8qSkpIwYMAAHDlypN3umRBCCCHiF5IeowsXLsDhcCApKUlQnpycDADQ6/VISEjw2Vav16NPnz5gGEZQnpSUBL1eLyizWq0YOXIkjEYjevfujalTp+Lhhx9u8/1LpcHPJyUSVvBRbCi+rk/sMYo9PkD8MVJ8XV9niDEkiZHBYAAAaDQaQXn94/rnfTEajQgPD/cq12q1KCoq8jzu1asXFixYgIEDB8Jms+GTTz7Byy+/DJPJhOnTp7f63lmWgU6nanX7a9Fowtrt2p0Bxdf1iT1GsccHiD9Giq/rC2WMQUuMTCaT18owXzpq8vMDDzwgeDx69Gg4HA689dZbmDJlCmQyWauv7XIF/8RfhnHPieI4Djwf9MuHHMXX9Yk9RrHHB4g/Roqv62uvGFmW8Rppak7QEqODBw/ipZdeuma9/fv3Q6vVAnAnU40ZjUYA8Dzvi0ajwdWrV73KDQaD33YAkJmZic8//xwXLlzwDNsFimEYSCQt++K2BsuKt4sUoPjEQOwxij0+QPwxUnxdXyhjDFpiNGnSJEyaNKlFde12O2QyGfR6Pe644w5Pef0coaZzjxpLSkrC8ePHwfO8IPsrLi5Gv379Wnn3hBBCCCEhWpUml8sxYsQIfP7554Ly/fv3Izk5udmJ1wCQkZEBg8GA48ePe8qKi4tx9uxZZGRk+H3d/fv3Q6PRoFevXm0LgBBCCCGixPB8aEYqv/nmG0yZMgUPP/wwMjMzceLECbz55ptYt24dMjMzPfUGDhyIBx98ECtXrvSUTZ8+HefPn8dzzz0HhUKBdevWgWVZwQaPEyZMwIMPPoikpCRYrVZ88sknOHjwIBYuXIicnJwOj5cQQgghnV/IEiMA+Pvf/47169ejuLgY8fHxmDlzJrKysgR1UlJS8NBDD2HVqlWeMpPJhFdffRWHDx+G0+nEqFGj8NJLLyEuLs5TZ+7cuTh9+jTKy8vBMAz69euHyZMn4/777++w+AghhBDStYQ0MSKEEEII6UzEP7WdEEIIIaSFKDEihBBCCKkT0sTo/PnzePzxxzF06FCkp6dj9erVsNvt12zH8zzefvttjB49GkOGDMEjjzyC//73v4I6J06cQEpKite/efPmtVM0hBBCCOnqQnIkCODekDEnJwe9e/dGXl4eSkpKsGrVKlitVixatMhv2/z8fGzcuBELFixASkoKduzYgWnTpmHfvn1eO2u/+uqrgn2RdDpdu8RDCCGEkK4vZIlRYWEhLBYLNm3ahIiICACAy+XC0qVLkZubK1hh1pjNZsOWLVswbdo0TJ06FQAwbNgwjBs3DgUFBViyZImgft++fTF48OB2jIQQQgghYhGyxOjIkSNIS0vzJEWA+8iOxYsX49ixY5gwYYLPdidPnoTZbBbsdSSXyzF27FgcPny4vW8bPM+D49pnIR/LMu127c6A4uv6xB6j2OMDxB8jxdf1tUeMITkrLVB6vR4TJ04UlGk0GsTExHiOBmmuHeB9bEhycjK2bdsGq9UKpVLpKZ85cyaqq6sRExOD3/72t5gzZ47g+UBxHA+jsbbV7ZsjkbDQaMJgsVjb5ZDaUKP4uj6xxyj2+ADxx0jxdX3tFaNGE9bic05DlhgZjUZoNBqvcq1WC4PB4LedXC6HQqEQlGs0GvA8D4PBAKVSifDwcDzxxBO47bbboFAo8PXXX2Pr1q3Q6/XYsmVLq++bZRnodKpWt78WjSas3a7dGVB8XZ/YYxR7fID4Y6T4ur5QxhiyxKi9DRw4EAMHDvQ8TktLQ2xsLJYtW4bTp09jyJAhrbquu8eoJli36VGfJRuNtaL8nwDF1/WJPUaxxweIP0aKr+trrxjdPUYtW4gfssRIo9HAZDJ5lRsMBmi1Wr/t7HY7bDaboNfIaDSCYRi/bTMzM7Fs2TIUFRW1OjECAKez/b4hXS6uXa8fahRf1yf2GMUeHyD+GCm+ri+UMYZsH6OkpCSvuUQmkwllZWVe84eatgOA4uJiQbler0d8fHyb5g8RQggh5PoWssQoIyMDX331FYxGo6fs4MGDYFkW6enpzbZLTU2FWq3GgQMHPGUOhwOHDh1CRkaG39f87LPPAICW7xNCCCHEp5ANpWVnZ2P79u2YNWsWcnNzUVJSgtWrVyM7O1uwh1FOTg4uX77sWYqvUCiQm5uLvLw8REZGol+/fti1axeqq6sxffp0T7sFCxbghhtuwMCBAz2Tr9977z3cc889lBgRQghpMY7j4HI5Q30b4DgGVqsEdrsNLpc4l+y3NkaJRAqWDU5fT8gSI61Wi23btmH58uWYNWsWVCoVsrKyvI7scH9DugRlM2bMAM/z2Lp1KyorKzFgwAAUFBQIdr3u27cvPvnkE2zduhUOhwM9e/bEH//4R8ycObND4iOEENK18TwPo7EStbXmUN+KR3k5C44T9/yi1sYYFqaGRhPZ4v2KmsPwPC/OtLOduFwcKistQb+uVMpCp1Ohqsoiykl1FF/XJ/YYxR4fIP4Ygx2fwVCB2loz1God5HJFm//gBoNEwoi2t6heoDHyPA+73QazuQphYWpotVFedSIjVZ1/VRohhBDSWXGcy5MUqdXee+6FilTKijKpbaw1Mcrl7lXqZnMVwsN1bRpWC9nka0IIIaSzqp/CUf8Hl3R+9e9VW+eDUWJECCGENKMzDJ+RlgnWe0WJESGEEEJIHUqMCCGEEELqUGJECCGEdACe4+C8fA6On76G8/I58CJfdj916qN45ZUlAbfbvfsDPPvsXNx33z0YNepWfPnl34J/c37QqjRCCCGknTmKv4Htqx3gLVWeMkalg+L2xyDrc2sI76zzOXDgU/A8MHJkOg4e/KzDX58SI0IIIaQdOYq/gfXwJq9y3lLlLh/7FCVHjeTnvweOA65cuUyJESGEENLZ8TwPOO0tq8txsB3b4beO7asdkMQPAtOCvXd4SesOSn/llSX4/vuzePrpZ7Bp0zpcvHgRAwcOwosvLoFKpcLrr7+KEyeOIyIiArm5s3D33b/xtP3ooz3461934OrVK4iKisZ99z2AKVOmCfYKOnPmW6xb9zp+/lmPnj0T8OSTc3zeR1HRabz99ps4e7YIEokEaWmjMGfOM9DpIj11WDa0u3tTYkQIIYS0EM/zqPn4FXAlPwXvmpYqWLb9qUV1Jd37Iux3C1u1NL2ysgKbNq3HlCnTIJVKsX79G1i27CUoFEoMHZqK++9/EB9//BGWLXsZgwYNRvfuPbB7dyHWr38DWVmP4Pbb78CZM9/i3XfzYTab8dRTcwEAFRXlmD9/NpKTb8SyZa/CZDJhzZpVsFpr0bdvP8/rFxWdxuzZuRg5Mh1Ll74Kq7UW+flv4fnnn8GWLe8GHE97ocSIEEIICQCDrrm3kdFoRF7e20hKSgYAlJeXYd261/HYYzmYOvUJAED//oNw5MiXOHLkH5g48WG89947uPvu32Du3D8DAIYPHwmn04nCwr9g8uSp0Goj8MEHu8AwDN54YyPUajUAIDY2DnPmCJO9zZs3oX//AVi58nVPYpeUdCOmTHkEx48fRVraqI76UvgV0sTo/PnzWLFiBU6dOgWVSoUHHngAc+fOhVwu99uO53nk5+dj586dnkNkX3jhBQwdOlRQr6SkBCtWrMDRo0chk8kwduxYvPDCC543rrPgOQ6OX3+A+XItHHwYENO3RV2qhJDgoJ9B0lIMwyDs/oUtHkpzXvkB1oNrr1lPOW4+pD1SrllPqlS2+qy06OgYT1IEAImJNwAAbr11uKcsPDwcERE6lJaW4JdffkZ1dTXGjLlHcJ0xY8Zi+/Z3cfbsd0hLS8fZs0VITR0m+Ns6bNht0Gi0nsdWqxVnznyLWbPmCA6GT0zshdjYOJw7dxYjR6YDThtcDg48WITqKNeQJUYGgwE5OTno3bs38vLyUFJSglWrVsFqtWLRokV+2+bn52Pjxo1YsGABUlJSsGPHDkybNg379u1DYmIiAMDhcOCJJ9wZ8Jo1a2C1WvHaa6/hmWeewZYtW9o9vpZqvFKh/vxmWqlASMehn0ESKIZhAFnLjgqRJtwERqUTrEbzup4q0l2vBcm4u6eldQlD004BqdSdAoSHhwvKZTIZ7HYbTCYTAAjm/wBAZKT7sclkBOAeSktISPR6PZ1O5/ncZDLC5XJh48a12LjRO1EsufIruMpLAOdE/ewirroygOiCJ2SJUWFhISwWCzZt2oSIiAgA7rNpli5ditzcXMTFxflsZ7PZsGXLFkybNg1Tp04FAAwbNgzjxo1DQUEBlixZAgD4/PPP8eOPP2L//v1ISkoCAGg0GkyfPh2nT5/GkCFD2jvEa6KVCoSEFv0MkvbGsCwUtz/m8/usnuL2RztlD6VG4z48t6pKmNRVVroTlvBw9/NRUdGoqvJOYhq3U6vDwTAMJk9+HBkZowX1OHstNBInwDU544x3P+YdtjbFEaiQJUZHjhxBWlqaJykCgMzMTCxevBjHjh3DhAkTfLY7efIkzGYzMjMzPWVyuRxjx47F4cOHBddPSUnxJEUAkJ6ejoiICPzzn/8MeWLEcxxsXwVvpUJnx/MsOLsEvMMGXoQnQ4s9PkB8MQZ7tVBXILb3sKlgxsc7HeB5HjzHtXkjRukNqVDePQu2r3c22ccoEoqRv4f0htQWvQbDADzPADyHQEeZ6oelBK/TqMzr9XkgMSERERE6fPnlYWTccafnqS++OASZTIYB/QeA5zgM6D8QH+37vzAZjZ5eqf/8598wGg2er6FSocCgQYPxy8/FSHnij4KX4qp+9U6KGt+K1Qye5zvs3LqQJUZ6vR4TJ04UlGk0GsTExECv1/ttB0CQ8ABAcnIytm3bBqvVCqVSCb1e71WHYRj06dPH7/VbQipt+y9Jx68/+O1aBQJbqdAVVIf6BtpZdahvoANUh/oGOpjYfgYB8b+H1UG6jksVBX74Y+BYDhzb9j/IrCYayrFPgSu/AN5qAqMMBxvdCwzDgqv4peX31dobsJkBp0PwWpyxxP3RcBVcharRizjBW41gqi9hStZD2PjOVkQopRg5LBXf/fA/7PxgN7J+91uEOw3gKgzIuucO7N37ARbM+yMem/AgTGYL3i38ANrwcMBm9rzmnx57GPMWLcWiF+ZgzKh0hKvVKCuvwDffnkbm3XfhlpsGAQC+/+k8rpaWotroHqo7+8P3YLodhC4qFrfcMuyaoUokTJv+TocsMTIajZ5uusa0Wi0MBoPfdnK5HAqFcHxXo9GA53kYDAYolUoYjUavcdOWXP9aWJaBTqe6dsVrMF+u9cxnIIQQIn4Mw0IS0zvUtxGQib/NhFQiwQcff4qPDn6OKJ0OU7Mfxh8mPuSpExWpw2svv4iN72zF4tfXIr57HObOnI53duwSXOum/inIW7kc7xb+Fa/lvQmH04mYqCikDrkJPbt399Tbu/8ADn75T8/jv+77BNj3CW65ZRjeeiu/2XvlOAYsy0Kr7QalsnX7PQG0XD9gHMfDaKxp83UcfFiL6ql+uwCy+GuvVOjsJBIG4eFhMJlqW72iojMTe3yA+GJ0XP4Bls/euGY9sfwMAuJ7D5sKZnx2hx3WijJIdN0hkflfKd1RGIYBK2HBubiAV2y9tOx1r7JbR9+Ao/9vvFf57v8r3G16wh9mYMIfZvi9fmrGDXgvY5ygbNQ47ykxg6JvwBsjx3ge8w4bOMNVQZ0Xnn4KLzz9lKCMjegBRqaE088QqcvFg+M4GAw1qK0V9q1pNGGQSFrWixSyxEij0XhmvDdmMBig1Wp9tGhoZ7fbYbPZBL1GRqMRDMN42mo0GpjN3n0yBoMBPXr0aNO9+3tjWiymb4tWKjA9BsLFdP35DQzLgpUrwbEuuER4cKLY4wPEFyPTY+B19TMIiO89bCqY8XEM757Uw7Duf50AD3dyxINx35sYyJQAK/U7xwisFJC2bBUg4E6Q2vJ3OmTvdlJSktdcH5PJhLKyMq+5QU3bAUBxcbGgXK/XIz4+3tN95uv6PM+juLjY7/U7Sv1KBX8660oFQsSAfgYJCT2GYcCoI/3XUUd22MRrIISJUUZGBr766isY6yZXAcDBgwfBsizS09ObbZeamgq1Wo0DBw54yhwOBw4dOoSMjAzB9b///nv8/PPPnrLjx4+juroad955JzoDWZ9boRz7FBiVTlDOqCKhpGXChLQ7+hkkJPRYhQqMJtbdMyR4QgpGEwtW0fZ5vYEI2VBadnY2tm/fjlmzZiE3NxclJSVYvXo1srOzBXsY5eTk4PLly56l+AqFArm5ucjLy0NkZCT69euHXbt2obq6GtOnT/e0u/fee7FlyxbMnj0b8+fPR21tLVavXo3Ro0eHfKl+Y7I+t0J6QypQ9iO6MbWooV13CelQ9DNISOixChV4eTfAaQMLDhxYQKro0J6ieiFLjLRaLbZt24bly5dj1qxZUKlUyMrKwrx58wT1OI4TbB8OADNmzADP89i6davnSJCCggLPrteAe+fOd955BytWrMD8+fMhlUoxduxYLFy4sEPiCwTDspD2HAC1TgVHlSU4c5gIIS1GP4OkOaE6luJ65N5RXAmJlG3VPlTBeq8Ynt71gLhcHCorLUG/rlTKQqdToUqkv5Qpvq5P7DGKPT5A/DEGMz6Oc6G09BLUah3Uau+tZUJFKmVF+d411toYzWYjzOYqxMYmgm3S4xsZqer8q9IIIYSQzoplJQgLU8Nsdq9alMtDM6zTFMcxotxqobFAY+R5Hna7DWZzFcLC1F5JUaAoMSKEEEJ80Gjcq6Xqk6POgGVZcCLcaqGx1sYYFqb2vGdtQYkRIYQQ4oN7b7wohIfr4HL52Weng0gkDLTabjAYakTba9TaGCUSaZt7iupRYkQIIYT4wbIsWDb0u19LpSyUSiVqa12inWfUGWKk9aiEEEIIIXUoMSKEEEIIqUOJESGEEEJIHUqMCCGEEELqUGJECCGEEFKHEiNCCCGEkDqUGBFCCCGE1AlpYvTFF1/g/vvvx+DBg3Hvvfdiz549LWpnMpmwcOFCDB8+HLfccguefvpplJaWCurk5eUhJSXF69+uXbvaIxRCCCGEiEDINnj85ptv8NRTTyErKwsLFy7E119/jRdffBEqlQrjxo3z23bu3Ln46aefsGTJEigUCqxfvx4zZszAnj17IJU2hKRUKrFt2zZB28TExHaJhxBCCCFdX8gSo7feegtDhgzBsmXLAAAjR47ExYsXsXHjRr+J0alTp3D06FEUFBRg1KhRAIA+ffpg/PjxOHToEMaPH++py7Ishg4d2q5xEEIIIUQ8QjKUZrfbceLECa8EaPz48Th//jwuXbrUbNsjR45Ao9EgPT3dU5aUlIQBAwbgyJEj7XbPhBBCCBG/kPQYXbhwAQ6HA0lJSYLy5ORkAIBer0dCQoLPtnq9Hn369AHDMILypKQk6PV6QZnVasXIkSNhNBrRu3dvTJ06FQ8//HCb718qDX4+KZGwgo9iQ/F1fWKPUezxAeKPkeLr+jpDjCFJjAwGAwBAo9EIyusf1z/vi9FoRHh4uFe5VqtFUVGR53GvXr2wYMECDBw4EDabDZ988glefvllmEwmTJ8+vdX3zrIMdDpVq9tfi0YT1m7X7gwovq5P7DGKPT5A/DFSfF1fKGMMWmJkMpm8Vob50lGTnx944AHB49GjR8PhcOCtt97ClClTIJPJWnVdjuNhNNYE4xYFJBIWGk0YjMZauFziOzWZ4uv6xB6j2OMDxB8jxdf1tVeMGk1Yi3uhgpYYHTx4EC+99NI16+3fvx9arRaAO5lqzGg0AoDneV80Gg2uXr3qVW4wGPy2A4DMzEx8/vnnuHDhgmfYLlAsy7RrJqtSKdrt2p0Bxdf1iT1GsccHiD9Giq/rC3aMLMtcu1KdoCVGkyZNwqRJk1pU1263QyaTQa/X44477vCU188Rajr3qLGkpCQcP34cPM8L5hkVFxejX79+rbz7lmMYBhJJy7/AgRLz2DFA8YmB2GMUe3yA+GOk+Lq+UMYYkleWy+UYMWIEPv/8c0H5/v37kZyc3OzEawDIyMiAwWDA8ePHPWXFxcU4e/YsMjIy/L7u/v37odFo0KtXr7YFQAghhBBRYnie50Pxwt988w2mTJmChx9+GJmZmThx4gTefPNNrFu3DpmZmZ56AwcOxIMPPoiVK1d6yqZPn47z58/jueeeg0KhwLp168CyrGCDxwkTJuDBBx9EUlISrFYrPvnkExw8eBALFy5ETk5Oh8dLCCGEkM4vZIkRAPz973/H+vXrUVxcjPj4eMycORNZWVmCOikpKXjooYewatUqT5nJZMKrr76Kw4cPw+l0YtSoUXjppZcQFxfnqTN37lycPn0a5eXlYBgG/fr1w+TJk3H//fd3WHyEEEII6VpCmhgRQgghhHQm4p/BRQghhBDSQpQYEUIIIYTUocSIEEIIIaROSBOj8+fP4/HHH8fQoUORnp6O1atXw263X7Mdz/N4++23MXr0aAwZMgSPPPII/vvf/wrqnDhxAikpKV7/5s2b107REEIIIaSrC8lZaYB7p+qcnBz07t0beXl5KCkpwapVq2C1WrFo0SK/bfPz87Fx40YsWLAAKSkp2LFjB6ZNm4Z9+/Z5HTny6quvCjaM1Ol07RIPIYQQQrq+kCVGhYWFsFgs2LRpEyIiIgAALpcLS5cuRW5urmDpfWM2mw1btmzBtGnTMHXqVADAsGHDMG7cOBQUFGDJkiWC+n379sXgwYODdt88z4Pj2mchH8sy7XbtzoDi6/rEHqPY4wPEHyPF1/W1R4wsywhOy/AnZInRkSNHkJaW5kmKAPdZZosXL8axY8cwYcIEn+1OnjwJs9ks2ARSLpdj7NixOHz4cHvfNjiOR2WlJejXlUpZ6HQqGI01cDrFdzggxdf1iT1GsccHiD9Giq/ra68YIyNVLT7OK2SJkV6vx8SJEwVlGo0GMTExnjPTmmsHeJ+nlpycjG3btsFqtUKpVHrKZ86cierqasTExOC3v/0t5syZI3i+NaTS4E/Nqj8XRqxn4FB8XZ/YYxR7fID4Y6T4ur7OEGPIEiOj0QiNRuNVrtVqYTAY/LaTy+VQKIQn72o0GvA8D4PBAKVSifDwcDzxxBO47bbboFAo8PXXX2Pr1q3Q6/XYsmVLq++bZRnodKpWt78WjSas3a7dGVB8XZ/YYxR7fID4Y6T4ur5QxhiyxKi9DRw4EAMHDvQ8TktLQ2xsLJYtW4bTp09jyJAhrboux/EwGmuCdZseEgkLjSYMRmMtXC7xdZFSfF2f2GMUe3yA+GOk+Lq+9opRowlrcS9UyBIjjUYDk8nkVW4wGKDVav22s9vtsNlsgl4jo9EIhmH8ts3MzMSyZctQVFTU6sQIQLuO7bpcnGjHjgGKTwzEHqPY4wPEHyPF1/WFMsaQDeIlJSV5zSUymUwoKyvzmj/UtB0AFBcXC8r1ej3i4+PbPH+IEEIIIdevkPUYZWRkYPPmzYK5RgcPHgTLskhPT2+2XWpqKtRqNQ4cOID+/fsDABwOBw4dOoSMjAy/r/nZZ58BQFCX7xNCCBE3juPgcjlDfRvgOAZWqwR2uw0ulziX7Lc2RolECpYNTl9PyBKj7OxsbN++HbNmzUJubi5KSkqwevVqZGdnC/YwysnJweXLlz1L8RUKBXJzc5GXl4fIyEj069cPu3btQnV1NaZPn+5pt2DBAtxwww0YOHCgZ/L1e++9h3vuuYcSI0IIIdfE8zyMxkrU1ppDfSse5eUsOE7cw2itjTEsTA2NJrLF+xU1J2SJkVarxbZt27B8+XLMmjULKpUKWVlZXkd2uDN1l6BsxowZ4HkeW7duRWVlJQYMGICCggLBrtd9+/bFJ598gq1bt8LhcKBnz5744x//iJkzZ3ZIfIQQQrq2+qRIrdZBLle0+Q9uMEgkjGh7i+oFGiPP87DbbTCbqwAAWm1Um16f4Xle3F/hIHO5uHbd4LGqyiLKSXUUX9cn9hjFHh8g/hiDGR/HuVBaeglqtQ5qtffWMqEilbKifO8aa22MZrMRZnMVYmMTvYbV3Bs8tmyoTby7RBFCCCGtVD9SIZcrrlGTdBb171Vb54NRYkQIIYQ0ozMMn5GWCdZ7RYkRIYQQQkgdSowIIYQQQuqI9kgQQgghhITO1KmPom/ffnjxxSUtblNeXo4PP9yJEye+xq+/XoJarcbNN9+CP/7xKXTv3qP9brYRSowIIYSQDsDxHH6qLobRZoRGocGNEX3AMjRw09gPP5zDP//5BcaPvx+DBg1GdXU1tm17BzNm5OD99/8KnU7X7vdAiREhhBDSzv5begYf/vgxqm0GT1mEQotJfe/H0FjadLjekCFDUVj4f9F4ps/gwUMwceJ9OHjwM/z+939o93ugVJUQQghpR/8tPYP8ou2CpAgAqm0G5Bdtx39Lz7T7PbzyyhJMnvww/v3vE8jJycaYMel46qmZuHLlMoxGA15++Xn85jd34uGHH8Df/35I0Pajj/bg97+fgLvuSkNW1u/w3nvveO1MfebMt5g27Q8YM+Z2TJ78MI4fP+bzPoqKTuPpp/+Ie+4ZhXvvvRNLlryIqqpKz/Ph4eGQSoV9NrGxcYiI0KG8vCxIXw3/qMeIEEIICQDP87BzjhbV5XgOH/xvn986H/74MVIi+7ZoWE0iaf2+SpWVFdi0aT2mTJkGqVSK9evfwLJlL0GhUGLo0FTcf/+D+Pjjj7Bs2csYNGgwunfvgd27C7F+/RvIynoEt99+B86c+RbvvpsPs9mMp56aCwCoqCjH/PmzkZx8I5YtexUmkwlr1qyC1VqLvn37eV6/qOg0Zs/OxciR6Vi69FVYrbXIz38Lzz//DLZsebfZ+75w4RdUVVWid+8+rY49EJQYEUIIIS3E8zzWnnwTesMvQbtmtc2ABUcWtahuckRvzLvlT63as8doNCIv720kJSUDAMrLy7Bu3et47LEcTJ36BACgf/9BOHLkSxw58g9MnPgw3nvvHdx9928wd+6fAQDDh4+E0+lEYeFfMHnyVGi1Efjgg11gGAZvvLERarUagLuXZ86cPwlef/PmTejffwBWrnzdc/9JSTdiypRHcPz4UaSljfK6Z57nsX79G4iOjsE999wbcMytQUNphBBCSEC65qaP0dExnqQIABITbwAA3HrrcE9ZeHg4IiJ0KC0twS+//Izq6mqMGXOP4DpjxoyFw+HA2bPfAQDOni1CauowT1IEAMOG3QaNRut5bLVacebMt7jrrnvgcrngdDrhdDqRmNgLsbFxOHfurM973rr1bfznP//CSy8tRVhYWNu/CC0Q0h6j8+fPY8WKFTh16hRUKhUeeOABzJ07F3K53G87nueRn5+PnTt3eg6RfeGFFzB06FBBvZKSEqxYsQJHjx6FTCbD2LFj8cILLwjevM6A4zn8UKmH02iH1ClHn/DetFKBkA5EP4OkpRiGwfzUP7V4KO2naj3e/HbrNes9efM03BiRdM163eSKVh8i2/RvX/1cnvDwcEG5TCaD3W6DyWQCAOh0kYLnIyPdj00mIwD3UFpCQiKaaryCzGQywuVyYePGtdi4ca1X3dLSEvA8DxtnB1wcABaff/oZ3n03H88//7IgeWtvIUuMDAYDcnJy0Lt3b+Tl5aGkpASrVq2C1WrFokX+uxTz8/OxceNGLFiwACkpKdixYwemTZuGffv2ITHR/eY4HA488YS7a3DNmjWwWq147bXX8Mwzz2DLli3tHl9L0UoFQkKLfgZJoBiGgULi/z/w9QZE9kOEQus18boxnUKLAZH9WpSMu4egOubsd43GfXhuVVWVoLyy0j1ZOjzc/XxUVLRgAnW9xu3U6nAwDIPJkx9HRsZor7pylQKXLVfh5Nxn1P37q6+xcc1qTHl8Ou6774GgxNNSIfsvUWFhISwWCzZt2oQ77rgDWVlZ+POf/4zCwkKUlJQ0285ms2HLli2YNm0apk6dirS0NKxduxYREREoKCjw1Pv888/x448/YsOGDRgzZgzGjx+PV155Bf/4xz9w+vTpjgjxmjrDSgVCrmf0M0jaG8uwmNT3fr91svre3yl7KHv1ugERETp8+eXfBOVffHEYMpkMAwcOAgAMGDAIJ0/+B2az2VPnP//5N4zGhp+rsLAw3HTTYPzySzH69x8o+NcruTckWoUnKTp7+gz+z2trcNe43+DeSb9DjaOmA6JtELIeoyNHjiAtLQ0RERGesszMTCxevBjHjh3DhAkTfLY7efIkzGYzMjMzPWVyuRxjx47F4cOHBddPSUlBUlJD12R6ejoiIiLwz3/+E0OGDAl+UAHgeA4f/vix3zqBrFTo7FxgYHVKYXPa4GxlN3BnJvb4APHFGOzVQl2B2N7DpoIZn9NlB8/z4HgOHM9du4EfQ2IGYfpNf8CeHz/x6pmc2Pd3GBIzqEWvwTAAxzPgwYEPMDy+rkHj1+HRUNb09XkADMsgJ2caNmxYgwidDiNH3o6z3xVh5873kTUpG+EaDTieQ9akbOzd+yGeWTAbjz2WA5PJiHe35kOr1Xq+hgDwxz89jXlzn8TLi57H3XePRXi4BmWlpThy/B+4Y+wYDBwyGL9euIh1y19FXHwPjBozGj9+/wP0DIuYsCjodJHo2TMhsMBbIWSJkV6vx8SJEwVlGo0GMTEx0Ov1ftsBECQ8AJCcnIxt27bBarVCqVRCr9d71WEYBn369PF7/ZaQStv+S/KHSr3frlUgsJUKhJDgo5/B61ekTIvshN/CbmEBSdt/50cpI/HETZNxyXQZZocFapkKCeHxYBkWF02Xg3DH/lmcNXBwTsFrldaUAwBKLOVQNSp3ck6Y7RZcNF3G8HvvwONOCw7s/Rh79+5GhE6Hhx59BPc9MrHhWgpgwdKX8P7md7Do5ecR26M7/vDH6fjg/b/A4qzx1IvoHY2XV6/Enh27sHLlUjidTkRGRWPQ0CGIi3cf9/HTD/9DjaUGNZYLWLrgeUEMmZn3teh4EYmEadPf6ZAlRkaj0TN+2ZhWq4XB0HzCYDQaIZfLoVAI93LQaDTgeR4GgwFKpRJGo9FrQllLrn8tLMtAp1O1un09p9He5msQQgjpOliGRS9N+/d4+PLH+XO8ygYOGYwd+z/yKt/wXr7g8T2/HYd7fjvO7/X73zQIKzetE5TdMvxWr3pJ/W7En5e+3Ox17hx7N+4ce7dXeZwqCmqF/7+9HMeAZVlotd2gVCr91vWH9jEKEMfxMBrbPt4pdbZs4t7sW6ajr+7aKxU6O4mERbgmDCZjLVyutnVLd0Zijw8QX4w/VumRd6rgmvXE8jMIiO89bCqY8TkcdlRVlCFKHQuZrGW/r9sbAwashAXn4jzDYF2d1Wn39Fz5x8Lp9P+eulw8OI6DwVCD2lqX4DmNJgySFvb8hSwx0mg0nqWAjRkMBmi1Wh8tGtrZ7XbYbDZBr5HRaATDMJ62Go1GMBGs8fV79GjbCb3XenNaok947xatVOgX0ResCLabkjIslFIFahknAPH9QhZ7fID4YuwX0fe6+hkExPceNhXM+DjwYNypCJhO9P6zDAOu7s7EQClRQMpKPBOvfZGyEijYlienLhffpr/TIXu3k5KSvOb6mEwmlJWVec0NatoOAIqLiwXler0e8fHxnu4zX9fneR7FxcV+r99RuvJKBULEgH4GCQk9hmGgUzTfGQK4/4PSmp2+WytkP/EZGRn46quvYDQaPWUHDx4Ey7JIT09vtl1qairUajUOHDjgKXM4HDh06BAyMjIE1//+++/x888/e8qOHz+O6upq3HnnncENppWGxg7GjJsmI6LJN4VOocWMmybTHiqEtDP6GSQk9LrJuiEmLBJSViIol7ISxIRFopusW4feT8iG0rKzs7F9+3bMmjULubm5KCkpwerVq5GdnY24uDhPvZycHFy+fNmzFF+hUCA3Nxd5eXmIjIxEv379sGvXLlRXV2P69Omedvfeey+2bNmC2bNnY/78+aitrcXq1asxevTokC/Vb2xo7GAMiRmEYtPPcEpp111COhr9DBJ/+EDXxZNW6SbrhjBpmHvna7h3vlaw8oB6ioL1XoUsMdJqtdi2bRuWL1+OWbNmQaVSISsrC/PmzRPU4zgOLpdw7HHGjBngeR5bt271HAlSUFDg2fUacG9p/s4772DFihWYP38+pFIpxo4di4ULF3ZIfIFgGRYpkTdCp1OhqsoSlDlMhJCWo59B0pRE4u69sNttkMtbf6I9aTmGYdxzjqTXnmjti91uAwBIJG1LbRie0uGAuFwcKistQb+uVMqK+pcyxdf1iT1GsccHiD/GYMdnMFSgttYMtVoHuVzRofNcmiORMK0+K62rCDRGnudht9tgNlchLEwNrTbKq05kpKrzr0ojhBBCOjONxn1YqtlcdY2aHYdlWXCc+JLaxlobY1iY2vOetQUlRoQQQogP7i1gohAeroPL5Qz17UAiYaDVdoPBUCPaXqPWxiiRSMGywZkXSIkRIYQQ4gfLsmAD2EenvUilLJRKJWprXaIcCgU6R4y07IIQQgghpA4lRoQQQgghdSgxIoQQQgipQ4kRIYQQQkgdSowIIYQQQupQYkQIIYQQUocSI0IIIYSQOpQYEUIIIYTUCWli9MUXX+D+++/H4MGDce+992LPnj0tamcymbBw4UIMHz4ct9xyC55++mmUlpYK6uTl5SElJcXr365du9ojFEIIIYSIQMh2vv7mm2/w1FNPISsrCwsXLsTXX3+NF198ESqVCuPGjfPbdu7cufjpp5+wZMkSKBQKrF+/HjNmzMCePXsglTaEpFQqsW3bNkHbxMTEdomHEEIIIV1fyBKjt956C0OGDMGyZcsAACNHjsTFixexceNGv4nRqVOncPToURQUFGDUqFEAgD59+mD8+PE4dOgQxo8f76nLsiyGDh3arnEQQgghRDxCMpRmt9tx4sQJrwRo/PjxOH/+PC5dutRs2yNHjkCj0SA9Pd1TlpSUhAEDBuDIkSPtds+EEEIIEb+Q9BhduHABDocDSUlJgvLk5GQAgF6vR0JCgs+2er0effr0AcMwgvKkpCTo9XpBmdVqxciRI2E0GtG7d29MnToVDz/8cJvvXyoNfj4pkbCCj2JD8XV9Yo9R7PEB4o+R4uv6OkOMIUmMDAYDAECj0QjK6x/XP++L0WhEeHi4V7lWq0VRUZHnca9evbBgwQIMHDgQNpsNn3zyCV5++WWYTCZMnz691ffOsgx0OlWr21+LRhPWbtfuDCi+rk/sMYo9PkD8MVJ8XV8oYwxaYmQymbxWhvnSUZOfH3jgAcHj0aNHw+Fw4K233sKUKVMgk8lafW2Xi2vr7XlhGPecKI7jwPNBv3zIUXxdn9hjFHt8gPhjpPi6vvaKkWUZr5Gm5gQtMTp48CBeeumla9bbv38/tFotAHcy1ZjRaAQAz/O+aDQaXL161avcYDD4bQcAmZmZ+Pzzz3HhwgXPsF2gGIaBRNKyL25rsKx4u0gBik8MxB6j2OMDxB8jxdf1hTLGoCVGkyZNwqRJk1pU1263QyaTQa/X44477vCU188Rajr3qLGkpCQcP34cPM8Lsr/i4mL069evlXdPCCGEEBKiVWlyuRwjRozA559/Lijfv38/kpOTm514DQAZGRkwGAw4fvy4p6y4uBhnz55FRkaG39fdv38/NBoNevXq1bYACCGEECJKDM+HZqTym2++wZQpU/Dwww8jMzMTJ06cwJtvvol169YhMzPTU2/gwIF48MEHsXLlSk/Z9OnTcf78eTz33HNQKBRYt24dWJYVbPA4YcIEPPjgg0hKSoLVasUnn3yCgwcPYuHChcjJyenweAkhhBDS+YUsMQKAv//971i/fj2Ki4sRHx+PmTNnIisrS1AnJSUFDz30EFatWuUpM5lMePXVV3H48GE4nU6MGjUKL730EuLi4jx15s6di9OnT6O8vBwMw6Bfv36YPHky7r///g6LjxBCCCFdS0gTI0IIIYSQzkT8U9sJIYQQQlqIEiNCCCGEkDqUGBFCCCGE1KHEiBBCCCGkDiVGhBBCCCF1QnKIbFfG8zw4rn0W8rEs027X7gwovq5P7DGKPT5A/DFSfF0MDzgqKwDOzxmkLAtZZBTQhtO4QnJW2vWC43hUVlqCfl2plIVOp4LRWAOnM/iH1IYaxdf1iT1GsccHiD9Gii94eI4D73KCdzga/jndj7kmj92fNypv8hxX97yvazmNRjhKvM8/bSphwXPo1n9Aq+OJjFS1+JxTSowIIYSQToTnOK+kg3c44ORcMJVKYak0wWm1NZOsCBMQzsd1eIdTmMg0Ka+/bmfiNBg67LUCTozOnz+PFStW4NSpU1CpVHjggQcwd+5cyOVyv+14nkd+fj527tyJyspKDBgwAC+88AKGDh3qsz7HccjKysJ3332HDRs2YNy4cT7rFRUVYdKkSVAqlTh16pTguZSUFK/60dHROHbsWMuCJYQQcl3hOc53D0njhMNZl0QInnN6JSacoE3THhRfCYv7Obhcof4yCDEMGJkMjFQGRiYFI5OBbfS5u1zm+Zz1fC5tKK97zMqEde0lV1Gxd881b0Gq1XZAoHWvFUhlg8GAnJwc9O7dG3l5eSgpKcGqVatgtVqxaNEiv23z8/OxceNGLFiwACkpKdixYwemTZuGffv2ITEx0at+YWEhSkpK/F6T53ksX74ckZGRqKmp8Vln8uTJuO+++zyPZTJZCyIlhFxPeI6D5dwPcDprYZOGQZ7cFwxLa1M6mjApaX7IprnhHMblhFHKoMZkgcvmO+kQXst7uKczJyWsXAaJQg6elTRJRuqSlUYJR7MJiVeyImuSrDQ8z9Y9D4mkxfNzAsVzHAz/+ALOqqpm60h1kQjr593R0V4CSowKCwthsViwadMmREREAABcLheWLl2K3NxcwVlljdlsNmzZsgXTpk3D1KlTAQDDhg3DuHHjUFBQgCVLlgjqV1ZWYsOGDXj22WexcOHCZu9nz549qKqqwsSJE7F9+3afdXr06NFsrxQhhJj+8w3KCncIfjFLdTrEZD+G8GG3hvDOOhbvcvkflrnGkA3vdLZ8jonT2ST5cXbupKQ+UfCRjDQ8551wNE4uPL0rjR6zMnmjJEYq+NxXUlI/x6iqyiKaOVQMyyIm+zFceWtTs3Vish/t0P+oBJQYHTlyBGlpaZ6kCAAyMzOxePFiHDt2DBMmTPDZ7uTJkzCbzcjMzPSUyeVyjB07FocPH/aqv3btWowYMQIjRoxo9l6MRiPWrFmDlStXoqioKJAwCCEEgDsp8vUL2VlV5S7/01MdkhzxLtc1h1l89p549awIh3QaJx28wwE4nWA4J5xWOziHXXAtv6uCQoFhwMjl/ntDpMIkQqKQQ6kOg90F8BJpo6TEO/nwfs7HUI9EAsA9tcPl6rg5NzwAFwDwHNAoAeI4BlarBHa7DS6XeFamKYcMQexTT6Ny/ydwGYyecolWi8jx90E56CY4HHa/15BIpGCDlDwFlBjp9XpMnDhRUKbRaBATEwO9Xu+3HQAkJSUJypOTk7Ft2zZYrVYolUoAwOnTp/Hpp5/i008/9Xsv69evx6BBg3DXXXf5TYzefvttrF27FmFhYRg1ahSeffZZxMfH+732tUilwc9cJRJW8FFsKL6uT2wx8hyHssKdfuuU7ngfUlUY4HQ1m6AIekmaJDZNe1ca6jrBO+yex+hsZ3lLJF5JAtskiWCb9IA0HY5peCwX1m1yLbY+YWn6XF1SEthts9BowmA01sLlanuix/M8qqsrYLGY2nyt4GBQXl6/XL+Tfc+0VfcodJs2FbzDCQYceLBgZFJYAVgrrrToEipVOCIioto87BdQYmQ0GqHRaLzKtVotDH5mjBuNRsjlcigUCkG5RqMBz/MwGAxQKpXgOA5Lly7F448/joSEBFy6dMnn9c6dO4fdu3dj7969fu/3wQcfxOjRoxEdHY3//e9/eOutt/Doo49i37590LZyIhfLMtDpVK1q2xIaTVi7XbszoPi6PjHE6DCaUHrkSzirKv3WcxmNuPjG6x10V26MROJOEOTuhIKVycHKGxIMd7msrkzmeb4+ERE8Xzcvpdk6nus0tGFbmZR0JsH6Hr18+TJqay3QaiPr/n61zzwb0lY8bDYbTKZqKJWytnd+BOmuguLDDz9EeXk5Zs6c2WwdnuexdOlSPProo0hOTvZ7vddee83z+W233YZhw4ZhwoQJ+OCDDzBjxoxW3SPH8TAafU/0botg/0+ns6H4ur6uGCPvcsF+9SqsFy/CevECbBcvwHrhIpzVzU/0bEoaGQmpRuNzOEfY2yGvG57xPfTT0IPS+Hm59/BNO86laPweOpq+hy4AtS73vy4qmN+jHOdCRUUl1GodwsLCg3SHbcMw7hhdLq7TdTIGS2tjDAuTw+XiUVFRCYVCDZYVJvcaTViLe7sDSow0Gg1MJu8uRYPB4LcHRqPRwG63w2azCXqNjEYjGIaBVquFxWLB2rVrMW/ePDgcDjgcDpjNZgCA1WqF2WyGWq3G/v37odfrsWbNGhiN7rFIm83muZ5CofDqmarXv39/9OnTB999910gYXtpz0lvLhcnmkl1vlB8XV9njdFlscB28QJsly66/128CPvlX91DVT5ItBFwGaqved3u02a0aWO5lvAMjHDokLk+nfU9DJZgxOeo+76Ry33/PQmF+kRBrEkR0LYY698rm80Bmaz1vXsBJUZJSUlec4lMJhPKysq85g81bQcAxcXF6N+/v6dcr9cjPj4eSqUSly5dQnV1NRYvXozFixcL2j/33HOe/Yf0ej0MBgPGjBnj9Tq33XYbZsyYgQULFgQSFiGkC+E5Do7SEtguXhQkQs5K38NijEIBRUIiFAkJUCT0giLR/TkjV6D4uWc61TJh0vm01zJ1EnzBeq8CSowyMjKwefNmwVyjgwcPgmVZpKenN9suNTUVarUaBw4c8CRGDocDhw4dQkZGBgAgJiYG77//vqBdeXk55s+fj9mzZ+P2228HADz00EMYPny4oN7evXuxf/9+5Ofn+x1bPHfuHIqLi5tdPUcI6VxcNRbYLl2q6wG60NALZPe9QkUaHe1OghJ7eRIhWUxMs8NTnW2ZMCEk9AJKjLKzs7F9+3bMmjULubm5KCkpwerVq5GdnS3YwygnJweXL1/2LMVXKBTIzc1FXl4eIiMj0a9fP+zatQvV1dWYPn26p07T5fn1k69vvPFGpKamAgASEhKQkJAgqPevf/0LEolE0L6goAAXLlzAiBEjEBkZiR9//BGbN29G9+7dMWnSpEDCJoS0M57j4CgrdfcCeYbCLsBZUeGzPiOXQ9Ezoa73x50IyXsmQNKtW0CvGz7sVuBPT/nYxygSMdmPXlf7GBFC3AJKjLRaLbZt24bly5dj1qxZUKlUyMrKwrx58wT13Hs+CCfwzZgxAzzPY+vWrZ4jQQoKCnzueh0Mffr0waFDh3DgwAFYLBbodDrceeedmDt3rs+VdYSQjsFZa2G7eAm2SxcaEqFfL4GvmyvYlDQyyt37k1g/DNYLstjYoPXkhA+7FepbUmE//yMUtPM1IUEzdeqj6Nu3H158cUlA7RYvfhHffVeE8vIySKUyJCffiJyc6Rg+fGT73GgTDM+LeRpX8LlcHCorLUG/rhh3NG2M4uv6Ao2R5zg4KsoFc4Hsly7CUVbmsz4jk0HeM6FuPlCipzdIomq/7TEao/ew6wtmfA6HHRUVVxAV1QMymf+zQFuK5zjU/u8HOA0GSLVahPVLCTgBl0rZLvPetT4xegFDhw5DQkIi7HY7Pv10H7766v9h48bNuPnmW5pt5+89i4xUtc+qNEII8YWzWmH79ZJnNZjt4gXYf70Ezmr1WV+q0zWaC5QIeUIi5HFxXX7/HEKaQ0fPtNwrr7wmSP5Gjrwdkybdj4MH9/tNjIKFEiNCSIvxPA97WRlqfv5FsCzeUVbqc30tI5VCHt+zoQeoLhGSqNUhuHtCQqMzHD3zyitL8P33Z/H0089g06Z1uHjxIgYOHIQXX1wClUqF119/FSdOHEdERARyc2fh7rt/42n70Ud78Ne/7sDVq1cQFRWN++57AFOmTBMcwXHmzLdYt+51/PyzHj17JuDJJ+f4vI+iotN4++03cfZsESQSCdLSRmHOnGeg00U2e+8SiQTh4eFwOn1vvRFslBgRQnzibDbYfv3VMxfI/utF2C9dgqvG9wanEm1Eo8nQ7rlA8rg4MFL6NUPEg+f5ZldF+qzPcSjdtcNvnbLCHeg2cFCLhtV4ibLFr91UZWUFNm1ajylTpkEqlWL9+jewbNlLUCiUGDo0Ffff/yA+/vgjLFv2MgYNGozu3Xtg9+5CrF//BrKyHsHtt9+BM2e+xbvv5sNsNuOpp+YCACoqyjF//mwkJ9+IZctehclkwpo1q2C11qJv336e1y8qOo3Zs3MxcmQ6li59FVZrLfLz38Lzzz+DLVveFcbJ83C5XLBYzPjss09w8eJF/PnPzR8qH0z0G4uQ6xzP83BWVjYsia/vBSot8b3LmkQCRXy8Z08geV0iJA2nRQ1E3Hiex8VVr8B6/qegXtdZVYXzs//Uorphffsi4dmFrdqzx2g0Ii/vbSQluU+NKC8vw7p1r+Oxx3IwdeoTAID+/QfhyJEvceTIPzBx4sN47713cPfdv8HcuX8GAAwfPhJOpxOFhX/B5MlTodVG4IMPdoFhGLzxxkao63qDY2PjMGeOMKbNmzehf/8BWLnydc/9JyXdiClTHsHx40eRljbKU/fTT/fhtddWuGMO64Zly1bippuGBBxza1BiRMh1hLPbYb/8a10CdMnzkavxvaBAEq6pGwJLRNgNNyB2UD/YVDq4QCu2yHWqC2/4GB0d40mKACAx8QYAwK23NuwNGB4ejogIHUpLS/DLLz+juroaY8bcI7jOmDFjsX37uzh79jukpaXj7NkipKYO8yRFADBs2G3QaBpOxLBarThz5lvMmjVHsGo9MbEXYmPjcO7cWUFidMcdo9G3bz9UV1fjyy//hkWLXsArr7yOtLTm90wMFkqMCBEhnufhrK52T4L29ARdgv3qlWZ7geTde3jNBZI2OupHKmWh0qlgr7IAXWRVDCHBxDAMEp9bGNBQWs3/fsDlDWuvWS9+znx0a8Eu67JuSrhcrVtMrm4yt09aN8wdHi48C04mk8Fut3mOAGs6/ycy0v3YZHIfy1VRUY6EBO+td3Q6nedzk8kIl8uFjRvXYuNG769HaWmJ4HFERAQiIiIAuCdfG41GvPnmBkqMCCHXxjnssF+54tkZun5SNFd31mBTEnV4wxBYXSIk7xEPVibr4DsnpOthGAZMM+dx+qIadBOkOt01j55RDbqpRXOM3ENQHbPLTv2ef1VN7r2y7vid8Lrh86ioaFRVeR/J07idWh0OhmEwefLjyMgY7VVXq43wey8pKf1x4sRXgdx+q1FiREgXwfM8XAZD3WTohg0S7Vev+D54lGUh79690flg7iRIoo2g858I6SAMy3bZo2d69boBERE6fPnl33DnnXd5yr/44jBkMhkGDhwEABgwYBA++miP57B3APjPf/4No9HgaRMWFoabbhqMX34pRv/+TwZ8L6dPf4v4+J5tjKhlKDEipBPinU7Yr1xutDmiOxFy1XVtN8V2U3nmAnkmRcfHgw3SxnSEkNbrqkfPSCQSTJ06HevXvwGdLhJpaen47rsz2LnzfUya9HtPL8/DDz+KvXs/xIIFT+MPf8iByWRCQcEWaBsNxQPAk0/OwZw5f8KiRS/g7rt/g/DwcJSVleLf/z6B8eN/h9TUW/HVV0fx+eefIS1tFGJj42AyGXH48EH861/HsWTJKx0SNyVGhISY02hstBqsUS9Qk2N1AAAMA3lcd89KsPpESKrTUS8QIZ1Y/dEzbd35uqNlZWVDKpWisHAn9u79EFFR0Xj88RmYMmWap050dDTeeGMj1q9/HS+//Dx69kzA/PnP4e233xRca/Dgm/Hmm++goGALXn11KRwOB2Ji4nDrrbd55ij17JkAh8OBzZs3wWCohlYbgeTkvsjL24JbbhnWITHTkSABoiNBWofiq+sFunqlYXfoukTIZTT6rM+GhXkmQXvmAsX3BBvA/IZgovew6xN7jJ39SJBg6EpHgrRWa2OkI0EI6cRcJpPXvkD2K5fBO53elRkGsthYwREZisRESCOjqBeIEEI6WMCJ0fnz57FixQqcOnUKKpUKDzzwAObOnQu53H9GzfM88vPzsXPnTlRWVmLAgAF44YUXMHToUJ/1OY5DVlYWvvvuO2zYsAHjxo3zWa+oqAiTJk2CUqnEqVOnBM/Z7XasW7cOH3/8MSwWC2655Ra8/PLLSEpKCjRsQnziXS7YS67CcvkSDKVXUP2jHtaLF+CqrvZZn1UqG4bB6idF90wIWS8QIYQQoYASI4PBgJycHPTu3Rt5eXkoKSnBqlWrYLVasWjRIr9t8/PzsXHjRixYsAApKSnYsWMHpk2bhn379iEx0Xv/g8LCQpSUlPi4UgOe57F8+XJERkaixscxBStWrMD+/fvx/PPPIy4uDps3b8bUqVPx2Wefee3bQMi1uMxmwflgtosXYL/8q+9eIACymFivIzKk0dHUC0QIIZ1YQIlRYWEhLBYLNm3a5Nl4yeVyYenSpcjNzUVcXJzPdjabDVu2bMG0adMwdepUAMCwYcMwbtw4FBQUYMmSJYL6lZWV2LBhA5599lksXNj82Sh79uxBVVUVJk6ciO3btwueu3r1Knbv3o3FixcjKysLADB48GDcddddKCwsxIwZMwIJnVxHeI6Do+SqYE8g28WLcPrYpwMAGIUCysREaG9MAmLjIYvvCUVCAlhlWAffOSGEkLYKKDE6cuQI0tLSPEkRAGRmZmLx4sU4duwYJkyY4LPdyZMnYTabkZmZ6SmTy+UYO3YsDh8+7FV/7dq1GDFiBEaMGNHsvRiNRqxZswYrV65EUVGR1/NHjx4Fx3GCIbiIiAikp6fjyJEjlBgRAICrxtJwNEZdImS//GuzO9vKomMgT0hoNBeoF2TR0ZDJpaKe1EoIIdeLgBIjvV6PiRMnCso0Gg1iYmKg1+v9tgPgNbcnOTkZ27Ztg9VqhVLpPjH49OnT+PTTT/Hpp5/6vZf169dj0KBBuOuuu3wmRnq9HlFRUV77KCQnJ2P37t1+r30tUmnwl1fWz5Zv6az5ribU8fEcB3tpKWwXL8B64QKsdUNhjooKn/UZuRzKuiEwZWIvKHu5h8Qk3br5rB/q+DqC2GMUe3yA+GMMZnwc575GZ1q4XT8KzzC+T/YRg7bEWP9eSSRsm/5OB5QYGY1GzxbhjWm1WhgMBh8tGtrJ5XIomkww1Wg04HkeBoMBSqUSHMdh6dKlePzxx5GQkIBLly75vN65c+ewe/du7N271+9r+ppHpNFo/N7rtbAsA51O1er216LRiHv4pSPic9bUoObnX2D5+RdYfv4ZluKfUfPLBXA2m8/6iphodOvdG6o+vaHqfQNUvXtD2T0OjEQS8GuL/f0DxB+j2OMDxB9jMOJzuZSoqLgCl8sOqbRzfb3Emtg21poYa2vtkEhYREdrIGnF7+96nWq5/ocffojy8nLMnDmz2To8z2Pp0qV49NFHkZyc3Gy99sJxPIxG74nebSWRsNBowmA01sLlEt9QTHvEx3McHOVljXqALsJ68QIcZWU+6zMyGRQJCe4eoLqDUpWJiZCohImuFYDVaA3oXsT+/gHij1Hs8QHijzHY8SmVKhgMVXC5eMjlipAvnGAY93/OOY4XdY9RoDHyPA+73QazuRoqlRpGH7+/NZqw9tnHSKPReE7bbcxgMHgNWTVtZ7fbYbPZBL1GRqMRDMNAq9XCYrFg7dq1mDdvHhwOBxwOB8x1h2BarVbPGSz79++HXq/HmjVrYKzbGM9W1xNgNBqhUCigUCig0Wg87RszGo1+77Ul2nMOicvFiXqOSmvj46y1sP36a5ODUi+Bt/lOYKS6SCgEc4ESIYvr7rXLLI/gvp9if/8A8cco9vgA8ccYrPjUah04jofZ3PwBsB2NZVlwvs5GFJHWxhgWpoZarWvzex9QYpSUlOQ1l8hkMqGsrMzv3kD1zxUXF6N///6ecr1ej/j4eCiVSly6dAnV1dVYvHgxFi9eLGj/3HPPITo6GseOHYNer4fBYMCYMWO8Xue2227DjBkzsGDBAiQlJaG8vNwradPr9bSPUSfG8zyc5eWNVoO5EyFHWanP+oxUCnl8z7oEqCERktQdZEgIIa3l/o97FMLDdXC5fG/L0ZEkEgZabTcYDDVwucTZZdTaGCUSKdggHa8SUGKUkZGBzZs3C+YaHTx4ECzLIj09vdl2qampUKvVOHDggCcxcjgcOHToEDIyMgAAMTExeP/99wXtysvLMX/+fMyePRu33347AOChhx7C8OHDBfX27t2L/fv3Iz8/H/Hx8QCAUaNGgWVZHDp0CJMmTQLg7tk6evQonnwy8JN9SfBxNhtsv15qWA1WlwxxtbU+60u0EV77Asm7d2/VXCBCCGkplmXBsqE/FkQqZaFUKlFb6xJtj19niDGgxCg7Oxvbt2/HrFmzkJubi5KSEqxevRrZ2dmCPYxycnJw+fJlz1J8hUKB3Nxc5OXlITIyEv369cOuXbtQXV2N6dOne+o0XZ5fP/n6xhtvRGpqKgAgISEBCQkJgnr/+te/IJFIBO27d++OrKwsrF69GizLIi4uDlu2bEF4eDiys7MDCZu0Ec/zcFSUo/LHsyg/9yNqf/kFtkuX4Cgt8b3sQCKBIj6+YWfoxF6QJyRAGu498Z8QQggJpoASI61Wi23btmH58uWYNWsWVCoVsrKyMG/ePEE9juPganIy+IwZM8DzPLZu3eo5EqSgoMDnrtfB8tJLL0GlUmHNmjWwWCxITU3Fu+++S7tetyPObof910vCg1IvXQTnY2dyAJBoNIIeIEViIuTde4CRdqp1AYQQQq4TDN+ZNmnoAlwuDpWVlqBft6udes3zPJxVVbBdugB7ow0S7SVXm+0F6pbQE7L4BMh6NswFkrZxInxn0dXev9YQe4xijw8Qf4wUX9fXXjFGRqraZ1UauT5xDjvsly/X9QBd8OwUzVl8J4gSdXijuUDuYbBuiQmIio0Q9Q80IYSQro8SI+LB8zxchupGh6S6EyH71auAr6WTLAt59x4NQ2F1w2ESrdZrvw+2HXYLJ4QQQoKNEqPrFO90wnb514ZhsLpkyGX23qcKAFiVqmFJfP1coPh4sLLQr9QghBBCgoUSo+uA02Bo2BOoLgGyX70CNJkgDwBgGMjjugtWgykSekGq04V811dCCCGkvVFi1AnwHAfLuR/gdNbCJg2DPLmv1w7NLbqO0wn71SsNc4HqVoW56nYIb4rt1s09DOYZCusFeY94sE3OtCOEEEKuF5QYhZjpP9+grHAHnFUNW85LdTrEZD+G8GG3NtvOaTK6e34uNcwFsl2+3GwvkCw2rskRGb0gjYykXiBCCCGkEUqMQsj0n29w5a1NXuXOqip3+Z+egnroLbBfvSroAbJdvAiXodrnNdmwMCgSEiFv3BPUM4F6gQghhJAWoMQoRHiOQ1nhDr91rrz9lvsTX71AAGQxsZ4hsPohMWl0NPUCEUIIIa1EiVGI1P7vB8HwmU91CRGjUNatBmuYC6TomQBWqeyAOyWEEEKuH5QYhYjTYGhRvehHfg/d3WNbNRmbEEIIIYGhv7Yh0tKjMJSJvSgpIoQQQjoInZUWIJ7nwXFB+JLxgKOywveO0vVYFrLIKEAkU4YkEhYul3iPAxF7fID4YxR7fID4Y6T4ur72iJFlmRbPv6XEKIRcVisc1c0PqckitJDQPCJCCCGkw1BiRAghhBBShyavEEIIIYTUocSIEEIIIaQOJUaEEEIIIXUoMSKEEEIIqUOJESGEEEJIHUqMCCGEEELqUGJECCGEEFKHEiNCCCGEkDp0iGyAgnYkiA8sy7TbtTsDiq/rE3uMYo8PEH+MFF/XwvOA2WQF7ycmhmWgDleihSd6+BTIkSCUGAWI43hUVlqCfl2plIVOp4LRWAOnU3zn4FB8XZ/YYxR7fID4Y6T4QofnebicHFwuDk4nB5eTh8vFweV0P+Y85Zyn3OXiUFFqQdHJy9e8/v2/vxk9b4ho9f1FRqogkVBiRAghhIgex7mTEEHy4eTgcvE+kxGvMicHp4sD5+ThdDVu35DYuD/nfV/HybV7L1aNxd6u12+MEiNCCCGkleqTkuaTCXeC4lXWuK6njG+mfcN1wPOw21yC5zvj0JpUxkIiYSGRuj9KpfWPGXdZ3WO7zYnLF5o/TL1eN5W8A+7aLeDE6Pz581ixYgVOnToFlUqFBx54AHPnzoVc7v+meZ5Hfn4+du7cicrKSgwYMAAvvPAChg4d6rM+x3HIysrCd999hw0bNmDcuHE+6xUVFWHSpElQKpU4deqU4LmUlBSv+tHR0Th27FjLgiWEXBc4jseln6vwa3E1eIZHbLwGLNuGCQ2kQ3AcL0gcAMBp41BZaYHd7mxIMHz0dHgP7fDCJKVJAuNVt5MmJQwDYTIibZSgSFlIJO7ERCrxfk4qZcEKkphG9Ztcy1/dQObzcByPv7z1NSym5nuE1OEK9EjUButLdE0BJUYGgwE5OTno3bs38vLyUFJSglWrVsFqtWLRokV+2+bn52Pjxo1YsGABUlJSsGPHDkybNg379u1DYmKiV/3CwkKUlJT4vSbP81i+fDkiIyNRU1Pjs87kyZNx3333eR7LZLIWREoIuV7ofyjD0b/9JPjFrAqXY9Q9NyIpJSaEd9a5NU5KfA7NtGD4xavHpK5nxWteSpNkxf1c+y2Eaa36pETqlYywPpKVhp4TrySlUfLRuK5cLoVO1w01te7v1cbXr6/b1RJ6lmUw6p4b8fnes83WSb8nuUPjCigxKiwshMViwaZNmxAREQEAcLlcWLp0KXJzcxEXF+eznc1mw5YtWzBt2jRMnToVADBs2DCMGzcOBQUFWLJkiaB+ZWUlNmzYgGeffRYLFy5s9n727NmDqqoqTJw4Edu3b/dZp0ePHs32ShFCrm/6H8p8/kK2mOz4fO9Z3PvQwE6ZHNUnJb7mj/gbxuF5HnKZFGaTFQ6Hy3top/G8FB89J43L+c6Vk4BlGUFPhifxaKbnRCphwUqZhqSkaUIiSFIYr2THV49Je//xrp98XVVl6XSTr9siKSUG9z400Os/KOpwBdLvSe7wn8GAEqMjR44gLS3NkxQBQGZmJhYvXoxjx45hwoQJPtudPHkSZrMZmZmZnjK5XI6xY8fi8OHDXvXXrl2LESNGYMSIEc3ei9FoxJo1a7By5UoUFRUFEgYhhIDjeBz9209+6xz723n07hvt+YNXv12HoHfD19CMn+GX5uoG0nPSWZOSaw2/SJoOvUgZ3+WC4RrG5zBO07osy7Rb4sBxHFwuZzPP8gBccLlccLmC9pLN3AcDq1UCu93mnm8kIolJWjzyRCoqS80AzwAMj8hYNViWgcNx7YnXEokULBucrRkDSoz0ej0mTpwoKNNoNIiJiYFer/fbDgCSkpIE5cnJydi2bRusViuUSiUA4PTp0/j000/x6aef+r2X9evXY9CgQbjrrrv8JkZvv/021q5di7CwMIwaNQrPPvss4uPj/V77WqTS4O+LKZGwgo9iQ/F1fWKL8dLPVX7nNQCA2WTDto1fuf/0dfKkRNo0cfDxWCpjERYmB8dxYCWMsDel8ZCOVJiANK7j63FnGb4J9vcoz/Oorq6AxWIKyvXajkF5ef0+Rp3sGzFIGBnj2aupqsocUFuVKhwREVEtnt/UnIASI6PRCI1G41Wu1WphMDQ/q9xoNEIul0OhUAjKNRoNeJ6HwWCAUqkEx3FYunQpHn/8cSQkJODSpUs+r3fu3Dns3r0be/fu9Xu/Dz74IEaPHo3o6Gj873//w1tvvYVHH30U+/btg1bbuolcLMtAp1O1qm1LaDRh7XbtzoDi6/q6Yoyci0N5mQUll43uf1eMuPRLVYvaWq3N9RSgIfGQuZMFqVTi/ihjIan/3PO8pFGC0qiepPFjCaSS+vZsQ1ndtQWvVVeX6SRJSWcSrO/Ry5cvo7bWAq02su7vF32tOyceNpsNJlM1lEpZ2zs/gnRXQfHhhx+ivLwcM2fObLYOz/NYunQpHn30USQnJ/u93muvveb5/LbbbsOwYcMwYcIEfPDBB5gxY0ar7pHjeBiNvid6t4VEwkKjCYPRWAuXSzxjx/Uovq6vq8RYW+NARakZ5SV1/0rNqCyrafU93/XbFMQnahuSmkY9MW39n2ngeDhdLjhdLsDmCLh1V3kPWyuY8XGcCxUVlVCrdQgLCw/SHbYNw7hjdLk6X89lsLQ2xrAwOVwuHhUVlVAo1GBZieB5jSasxT2JASVGGo0GJpN3l6LBYPDbA6PRaGC322Gz2QS9RkajEQzDQKvVwmKxYO3atZg3bx4cDgccDgfMZnc3mtVqhdlshlqtxv79+6HX67FmzRoYjUYA7snd9ddTKBRePVP1+vfvjz59+uC7774LJGwv7TnprX4OglhRfF1fZ4mR43gYKmtQXmpBRZkZFaUWVJSamx0ek8kliIpRISpWjahYFSKjVTi87ywsZv/LhPsNivM5VOSe49E1/zp1lvewvQQjPofDnXjK5b7/noRCfaIg1qQIaFuM9e+VzeaATNb6/7QElBglJSV5zSUymUwoKyvzmj/UtB0AFBcXo3///p5yvV6P+Ph4KJVKXLp0CdXV1Vi8eDEWL14saP/cc8959h/S6/UwGAwYM2aM1+vcdtttmDFjBhYsWBBIWISQTs5mdaCi1ILy0voEyILKcotn75qmNBHKRkmQGtFxKoRrlV49PKPGdq5lwqTz6fheQdJawXqvAkqMMjIysHnzZsFco4MHD4JlWaSnpzfbLjU1FWq1GgcOHPAkRg6HA4cOHUJGRgYAICYmBu+//76gXXl5OebPn4/Zs2fj9ttvBwA89NBDGD58uKDe3r17sX//fuTn5/sdWzx37hyKi4ubXT1HCAktjuNhrK5tSIJKzKgos8BstPmsL5Wxgl6gqFg1omJUkCta9qutsy0TJoSEXkCJUXZ2NrZv345Zs2YhNzcXJSUlWL16NbKzswV7GOXk5ODy5cuepfgKhQK5ubnIy8tDZGQk+vXrh127dqG6uhrTp0/31Gm6PL9+8vWNN96I1NRUAEBCQgISEhIE9f71r39BIpEI2hcUFODChQsYMWIEIiMj8eOPP2Lz5s3o3r07Jk2aFEjYhJB2YLM6UVFmRmWpxT0cVmpGZbkFTofvXqBwjUKYAMWqoNWFtfl/iUkpMejdNxqll41geIZ2vibkOhdQYqTVarFt2zYsX74cs2bNgkqlQlZWFubNmyeo597zQbihw4wZM8DzPLZu3eo5EqSgoMDnrtfB0KdPHxw6dAgHDhyAxWKBTqfDnXfeiblz5/pcWUcIaR88z8NYbUV5iRkVpe4eoIpSC0wGq8/6UimLyBiVIAGKilFDoWy/tSIsyyCht06Um+eRzoPjeFy5aECNxY5uKjl6JGpFnYBPnfoo+vbthxdfXNLqa3zwwU5s3LgWt98+CqtXrw/avfnD8LyYp3EFn8vlPocn2MS6o2k9iq/ra0mMdpsTlWUNPUAVZRZUllngsPve+U6tUXgNhWl1YSH5Y0HvYdcXzPgcDjsqKq4gKqoHZLK2H2AarKNnpFK2y7x3rU2M6mOsqCjHY49Ngkwmw4ABA6+ZGPl7zyIjVe2zKo0QQgB3L5DJYG0yIdoMY7XvXiCJhKnrBVILEiFlGJ1dSMSvqx49E2pvvrkRo0Zl4OrVKx36upQYEUL8cthdqCizoLqiBqZqK369UI3yUnOzvUAqtdxrLlBEZDdRDxmQ6wvP883OhWuK43gcPez/6Jmjf/sJPW/QtehnRCJp3c/RK68swfffn8XTTz+DTZvW4eLFixg4cBBefHEJVCoVXn/9VZw4cRwRERHIzZ2Fu+/+jaftRx/twV//ugNXr15BVFQ07rvvAUyZMk1wBMeZM99i3brX8fPPevTsmYAnn5zj8z6Kik7j7bffxNmzRZBIJEhLG4U5c56BThcpqPftt//F//t//8TOnXuwZEnzZ6a2B0qMCCEA3L/szUaboAeootQCQ1Wtz/qshEFkVJO5QLFqhHWjXiAiXjzP46O//BdXfzUG7ZoWkx1b1x9rUd0eCVo88NjNrVp0UFlZgU2b1mPKlGmQSqVYv/4NLFv2EhQKJYYOTcX99z+Ijz/+CMuWvYxBgwaje/ce2L27EOvXv4GsrEdw++134MyZb/Huu/kwm8146qm5AICKinLMnz8byck3YtmyV2EymbBmzSpYrbXo27ef5/WLik5j9uxcjByZjqVLX4XVWov8/Lfw/PPPYMuWdz31XC4X1q1bjSlTHkd0dHTAcbYVJUaEXIccDheqyuvmApXUJUJlZthtvnuBuqnkiI5To2evCIRrFYiIViEisuU7yRIiKl2089NoNCIv720kJblPjSgvL8O6da/jscdyMHXqEwCA/v0H4ciRL3HkyD8wceLDeO+9d3D33b/B3Ll/BgAMHz4STqcThYV/weTJU6HVRuCDD3aBYRi88cZGqNVqAEBsbBzmzPmT4PU3b96E/v0HYOXK1z2JXVLSjZgy5REcP34UaWmjAAB79nwIq7UWjzzyWId8XZqixIgQEeN5HhaTrWEydN1HQ1Wtz51lWZaBLqpbox4gdy9QN5Vc9BN3CWkJhmHw4GNDWzyUdvliNfZ/2PxB5/XGT7oJ8YkR16ynDJPW7boeuOjoGE9SBACJiTcAAG69tWFvwPDwcERE6FBaWoJffvkZ1dXVGDPmHsF1xowZi+3b38XZs98hLS0dZ88WITV1mCcpAoBhw26DRtNwIobVasWZM99i1qw5glXriYm9EBsbh3PnziItbRSqqiqRn/8WXnxxKWSy0PQ+U2JEiEg4nZy7F6hRD1BFqQW2Zg5BVXaTITq20e7QsSpERHWjXiBCroFhGMjkkmtXBJDYJxKqcHmzR9UA7g1FE/tEtmiOkbunpXWJUePEBQCkUncKEB4uPAtOJpPBbrd5jgBrOv8nMtL92GRyDydWVJQjIcF76x2dTuf53GQywuVyYePGtdi4ca1X3dLSEgDAO+9sxo039sXNN9/ieX2XywWn0wWTyYSwsDDPfbcXSowI6WJ4nkeN2S6cC1Q3OdpXLxDDALpoVd1qMFVdEqRGN3XblyATQvxjWQaj7umaR8/U7/lXVVUlKK+srAQAhIe7n4+KikZVVaVX+8bt1OpwMAyDyZMfR0bGaK+6Wm0EAOCXX37Gf/97EpmZd3nVycy8C2+8sREjR97eqnhaihIjQjoxl5NDZbmlblPEhkTIWttML1CYVLApYv1hqRIp9QIREipd9eiZXr1uQESEDl9++TfceWdDovLFF4chk8kwcOAgAMCAAYPw0Ud7PIe9A8B//vNvGI0GT5uwsDDcdNNg/PJLMfr3f7LZ15wz5xnU1FjgcjUMVW7cuLbuBI1ZuPHGvsEO0wslRoR0Eg29QA27Q1dX1IDjvLuBGAaIiOzmtSJMpZbToZeEdEL1R890pZ2vJRIJpk6djvXr34BOF4m0tHR8990Z7Nz5PiZN+r2nl+fhhx/F3r0fYsGCp/GHP+TAZDKhoGALtFqt4HpPPjkHc+b8CYsWvYC77/4NwsPDUVZWin//+wTGj/8dUlNvRd++KV6bWKrVanTr1g2pqbd2SNyUGBHSwVwuDtUVNY0mRLt7gmprHD7ryxXSRnOBVIiOU0MX1Q1SWcvmOBBCOgeWZdDzhohQ30ZAsrKyIZVKUVi4E3v3foioqGg8/vgMTJkyzVMnOjoab7yxEevXv46XX34ePXsmYP785/D2228KrjV48M148813UFCwBa++uhQOhwMxMXG49dbbfM5RChU6EiRAdCRI61yv8dVY7O4jMkoahsGqmukFAoCIyDBBD1B0rAqqcEWn6AW6Xt9DMRF7jJ35SJBg6UpHgrRWa2MM2ZEg58+fx4oVK3Dq1CmoVCo88MADmDt3LuRy/984PM8jPz8fO3fu9Bwi+8ILL2Do0KE+63Mch6ysLHz33XfYsGEDxo0b57NeUVERJk2aBKVSiVOnTgmes9vtWLduHT7++GNYLBbccsstePnll5GUlBRo2IT45XJxKL1ihP7HMpRebegFqrH4XokiV0g8c4Ci4tzHZETGqCCjXiBCCAmpgBIjg8GAnJwc9O7dG3l5eSgpKcGqVatgtVqxaNEiv23z8/OxceNGLFiwACkpKdixYwemTZuGffv2ITHRuwutsLAQJSUlfq/J8zyWL1+OyMhI1NTUeD2/YsUK7N+/H88//zzi4uKwefNmTJ06FZ999pnX8kRCWspa6/BaEl9ZbgHXzN4iWl2Y10nx4drO0QtECCFEKKDEqLCwEBaLBZs2bUJERAQA9/4CS5cuRW5uLuLi4ny2s9ls2LJlC6ZNm4apU6cCAIYNG4Zx48ahoKAAS5YsEdSvrKzEhg0b8Oyzz2LhwubPSNmzZw+qqqowceJEbN++XfDc1atXsXv3bixevBhZWVkAgMGDB+Ouu+5CYWEhZsyYEUjo5DrEcTwMlTXCzRHLzM3uRyJXSD09P55EKEbV4v1OCCGEhF5AidGRI0eQlpbmSYoAIDMzE4sXL8axY8cwYcIEn+1OnjwJs9mMzMxMT5lcLsfYsWNx+PBhr/pr167FiBEjMGLEiGbvxWg0Ys2aNVi5ciWKirx3FT169Cg4jhMMwUVERCA9PR1HjhyhxIgI2KwOlJc09ABVlJpRWV4DVzPj3JoIpaAHKC4+HDf0jkK1oUb04/+EECJmASVGer0eEydOFJRpNBrExMRAr9f7bQfAa25PcnIytm3bBqvVCqVSCQA4ffo0Pv30U3z66ad+72X9+vUYNGgQ7rrrLp+JkV6vR1RUlNdyweTkZOzevdvvta9F2g57wtRPChPrrsOdJT6O42GoqkV5idn9r9T90Wy0+awvk0k8K8Gi4+pWhcWqIVcIf3QkEhYMy4Q8vvbUWd7D9iL2+ADxxxjM+DjOfY3OtD6pfvSdYeBzM1cxaEuM9e+VRMK26e90QImR0Wj07ITZmFarhcFg8NGioZ1cLodCoRCUazQa8DwPg8EApVIJjuOwdOlSPP7440hISMClS5d8Xu/cuXPYvXs39u7d6/c1fc0j0mg0fu/1WliWgU6nanX7a9Fowtrt2p1BR8ZnrXWg5IoRJZcb/pVeNTV7xlFEZBhie2gQF69B93j3R11kNzAB7DMi9vcPEH+MYo8PEH+MwYjP5VKiouIKXC47pNLO9fUSa2LbWGtirK21QyJhER2tgUTS+ikMnWofow8//BDl5eWYOXNms3V4nsfSpUvx6KOPIjk5udl67YXjeBiN3hO920oiYaHRhMForBXs+CkW7RkfzzftBXIvjzcZrD7rS6WspxcoKtbdExQdq4ZC6f3jUG1o2Xst9vcPEH+MYo8PEH+MwY5PqVTBYKiCy8VDLg/9ggmGcf/nnON4UfcYBRojz/Ow220wm6uhUqlhNHr/7tdowtpnub5Go/Ec6taYwWDwGrJq2s5ut8Nmswl6jYxGIxiGgVarhcViwdq1azFv3jw4HA44HA6YzWYA7lN567ca379/P/R6PdasWQOj0X2Anc1m81xPoVBAoVBAo9F42jdmNBr93mtLtOccEpeLE/UclbbGZ7c5vY7HqCizNNsLpNYo3GeE1S2Jj4pVQ6sL87nbbDC+7mJ//wDxxyj2+ADxxxis+NRqHTiOh9lcde3KHYRlWXCceN87oPUxhoWpoVbr2vzeB5QYJSUlec0lMplMKCsr87s3UP1zxcXF6N+/v6dcr9cjPj4eSqUSly5dQnV1NRYvXozFixcL2j/33HOIjo7GsWPHoNfrYTAYMGbMGK/Xue222zBjxgwsWLAASUlJKC8v90ra9Ho97WPUBfA8D5PB6p4Q3eiYDGO1714giYSpWw3WMA8oMkYFZZisg++cECIW7v+4RyE8XAeXy/f5hB1JImGg1XaDwVADVzPbg3R1rY1RIpGCZYMzxBhQYpSRkYHNmzcL5hodPHgQLMsiPT292XapqalQq9U4cOCAJzFyOBw4dOgQMjIyAAAxMTF4//33Be3Ky8sxf/58zJ49G7ff7j5N96GHHsLw4cMF9fbu3Yv9+/cjPz8f8fHxAIBRo0aBZVkcOnQIkyZNAuDu2Tp69CiefLL5A+xIx3PYXT57gRx2l8/6qnB5w+aIdbtDayO7deozhwghXRfLsmDZ0O9+LZWyUCqVqK11ibbHrzPEGFBilJ2dje3bt2PWrFnIzc1FSUkJVq9ejezsbMEeRjk5Obh8+bJnKb77VNxc5OXlITIyEv369cOuXbtQXV2N6dOne+o0XZ5fP/n6xhtvRGpqKgAgISEBCQkJgnr/+te/IJFIBO27d++OrKwsrF69GizLIi4uDlu2bEF4eDiys7MDCZsECc/zMFbXouSySZAIGapqfdZnJQwio1WCk+KjYtUI60a9QIQQQtpHQImRVqvFtm3bsHz5csyaNQsqlQpZWVmYN2+eoB7HcXC5hP/bnzFjBniex9atWz1HghQUFPjc9TpYXnrpJahUKqxZswYWiwWpqal49913adfrDuBwuFBZd0J8RanZ/XmZBTar7+7obiq510nxEZEtnyxHCCGEBAMdIhsgOkRWiOd5WEw2we7Q5aVmGCqb6QViGeiiuglOio+MUaGbKvTd1G3RVd+/QIg9RrHHB4g/Roqv62uvGNv1EFly/XI6XKgsr/GaC9RcL1BYN5knAYrtHo6kvjGQyBnRLjMlhBDS9VFiRLzwPA+L2S5MgEotqK6s8ZnUsCyDiKhugvPBomPV6KZu6AW6Hv6nQwghpOujxOg653JyqCy3CHqAKkrNsNb67gVShkkF84CiY9XQRXWDpB2OSSGEEEI6GiVG1wme51FjsQt6gMpLzaiu8N0LxDBw9wI12Ruom1oe8t1fCSGEkPZCiVEnwHE8Lv1chV+Lq8EzPGLjNW3ak8fl4lBVPxeorgeovNQCa43DZ32FUiocBotTQxetapfDcgkhhJDOjBKjENP/UIajf/sJFpPdU6YKl2PUPTciKSXmmu3dvUDCuUBVFTXgOO9uIIYBtLqwJkNhKqjCQ38GECGEENIZUGIUQvofyvD53rNe5RaTHZ/vPYt7HxroSY5cLg7VFTVNdoi2oMZi92oPAHKFpGFTxDh3AqSLVkEma/2Jw4QQQojYUWIUIhzH4+jffvJb58v9P6D4f+WoLKtBZYUFXDPnxrh7gYRzgdQa6gUihBBCAkWJUYhcuWgQDJ/5Yre58L/vSj2PZXKJYAgsMsY9J0gmp14gQgghJBgoMQqR5obAmuqTEo2UQXGIilUhXKukXiBCCCGkHVFiFCItPQJjcGpP9Lwhon1vhhBCCCEA6Ky0gPE873PFV+DXAcwmK3g/12JYBupwJcTSSSSRsHC5xLvrtdjjA8Qfo9jjA8QfI8XX9bVHjCzLtHjEhRKjELLbnLCYbc0+r1IrIFdQpx4hhBDSUSgxIoQQQgipQ1sbE0IIIYTUocSIEEIIIaQOJUaEEEIIIXUoMSKEEEIIqUOJESGEEEJIHUqMCCGEEELqUGJECCGEEFKHEiNCCCGEkDq0rXKAgnUkiC8sy7TbtTsDiq/rE3uMYo8PEH+MFF/X43TYYa0xNvu8spsGUlnLzhdtTiBHglBiFCCO41FZaQn6daVSFjqdCkZjDZxO8Z2DQ/F1fWKPUezxAeKPkeLrOjiOA+dywmm34fO/vAarpfnEKCw8AvdNXwKWbf0gV2SkChIJJUaEEEIIacKdlDjgcjrBuZxwOR1wuRx1n7sfcy4nXC4nOKcDrsaf1z1uaNdQh3M64Wp83frPPW3cj10uB3iu5Yldraka5b+eR2xi33b8qjSgxIgQQgjpIBzn8pGA1CcTTZMVYeICzgW5jIHZXAOnw9HQvi7ZEHzudMDlctV9FCYrgSQlnUWtnx6lYAs4MTp//jxWrFiBU6dOQaVS4YEHHsDcuXMhl/sf/+N5Hvn5+di5cycqKysxYMAAvPDCCxg6dKjP+hzHISsrC9999x02bNiAcePG+axXVFSESZMmQalU4tSpU4LnUlJSvOpHR0fj2LFjLQuWEEKIaHCcq0kCUt+D0ejzRr0l7s8b9Ya0qLekSfsm1+f5zpWUMAwLiVQKViKr+yiFRCqDRCIFW/dRIpGBlTb+6K7DShp9Xlfuvk5d+/pr1V9fIm30Wu72FVd+xj/3/J9r3meYStMBXw23gBIjg8GAnJwc9O7dG3l5eSgpKcGqVatgtVqxaNEiv23z8/OxceNGLFiwACkpKdixYwemTZuGffv2ITEx0at+YWEhSkpK/F6T53ksX74ckZGRqKmp8Vln8uTJuO+++zyPZTJZCyIlhFxPOI5DyYWfUPaLDRyjgK57UpvmMxAhnufBc1yjBMHHcIu/oR1XQ4LhNczTqLeEcznBwAWbzd4oKWm4bqdLSlgWksYJiURWl4xI6j4Kn5PKZejWLQxOJ8CwEk/iUp+0NE1IhB/rri9IVqRgWUlIvwaxiX0Rpo5Arbm62Tph4RGI7pncYfcUUGJUWFgIi8WCTZs2ISIiAgDgcrmwdOlS5ObmIi4uzmc7m82GLVu2YNq0aZg6dSoAYNiwYRg3bhwKCgqwZMkSQf3Kykps2LABzz77LBYuXNjs/ezZswdVVVWYOHEitm/f7rNOjx49mu2VIoSQSz9+i5Nf7hH8Yg5TRyD1rolI6Htz6G4sSBqSEgecdhfMrA2mKiNsNptXb4bPoR2/vSWNh22azElpNMzDuRzg+c61koplJZ6EoXEPhsSTZDROVrx7SwQJiKdnpaGXpXEC0jghafwx0OS7fvJ1VZWly0++rseyLFLvmohjnxQ0Wyd19MQO/Y9KQInRkSNHkJaW5kmKACAzMxOLFy/GsWPHMGHCBJ/tTp48CbPZjMzMTE+ZXC7H2LFjcfjwYa/6a9euxYgRIzBixIhm78VoNGLNmjVYuXIlioqKAgmDEEIAuJMiX7+Qa83VOPZJAdJ/N71NyZF7ew9Xo8mn3kmFVy/JNYd2rjERVjCE46jrKemESUmjXg62SVLhNbRT/7lXAiJMVmRyObRaNWqtTvCQeA0JtTYp4ep6u4KFB+oSycDacRwDq1UCu90Gl6tzvadtEdd7AG6//wmcPXFIsGxfqdJg4PDfIO6G/nA47H6vIWlFotmcgBIjvV6PiRMnCso0Gg1iYmKg1+v9tgOApKQkQXlycjK2bdsGq9UKpVIJADh9+jQ+/fRTfPrpp37vZf369Rg0aBDuuusuv4nR22+/jbVr1yIsLAyjRo3Cs88+i/j4eL/XvhapNPiZq0TCCj6KDcXX9YktRo7jcOofe/zW+dfnO1Bx9WfwjRKTxj0pgseNh3o8vSZOuP8Mdh4NvSQNCUfjngyJxN/j+jIfc00a9Y40Tmy85qtIpWCY9vkekkhYaDRhMBpr4XK1vUeF53lUV1fAYjEF4e6CgUF5ef0+Rp3r+6qtZGotbr57kjsB5XmAYSCRuFOUioorLbqGShWOiIioFu9X1JyAEiOj0QiNxnsClFarhcFg8NtOLpdDoVAIyjUaDXieh8FggFKpBMdxWLp0KR5//HEkJCTg0qVLPq937tw57N69G3v37vV7vw8++CBGjx6N6Oho/O9//8Nbb72FRx99FPv27YNWq21BxN5YloFOp2pV25bQaMLa7dqdAcXX9XXlGF0uJ6rKrqDiyiUUf/9f1Jiq/dZ32K34/t9/D9rrexIHmQxSqawhmZA297gusaivX9e26fNebWX1j5vUlUjBXAdzp4L1PXr58mXU1lqg1UbW/f1q2x9c0l542Gw2mEzVUCplbe/8CNJdBcWHH36I8vJyzJw5s9k6PM9j6dKlePTRR5Gc7H8y1muvveb5/LbbbsOwYcMwYcIEfPDBB5gxY0ar7pHjeBiNvid6t0Ww/6fT2VB8XV9Xi9FaY0Z12a+oKr2E6rLLqCr9FYaKq+ACHBKJTxoEXVyCoHdFuGKn0TyT+l4USZPHUhlYiaTdekqa4wLgcgJ2Jw/AAYnE1aXew0AF83uU41yoqKiEWq1DWFh4kO6wbRjGHaPLxaGTjY4GTWtjDAuTw+XiUVFRCYVC7TWpXKMJa3Fvd0CJkUajgcnk3aVoMBj89sBoNBrY7XbYbDZBr5HRaATDMNBqtbBYLFi7di3mzZsHh8MBh8MBs9kMALBarTCbzVCr1di/fz/0ej3WrFkDo9E9Fmmz2TzXUygUXj1T9fr3748+ffrgu+++CyRsL+056c3l4kQzqc4Xiq/r62wxcpwLpqpSVJddRnXZr6gu+xWGssuotfjuxZbJldDGxEOuVOHy+TPXvH7KsDFt3ljOPacEADrH162zvYfBFoz4HA4HAEAu9/33JBTqEwWxJkVA22Ksf69sNgdkstb37gWUGCUlJXnNJTKZTCgrK/OaP9S0HQAUFxejf//+nnK9Xo/4+HgolUpcunQJ1dXVWLx4MRYvXixo/9xzz3n2H9Lr9TAYDBgzZozX69x2222YMWMGFixYEEhYhJAuwlZrgaG8IQGqLvPfC6TWRiMipiciYuKhjemJiJieUGkiwTAMOI7Dp+8s6VTLhEnn09b5KqTjBOu9CigxysjIwObNmwVzjQ4ePAiWZZGent5su9TUVKjVahw4cMCTGDkcDhw6dAgZGRkAgJiYGLz//vuCduXl5Zg/fz5mz56N22+/HQDw0EMPYfjw4YJ6e/fuxf79+5Gfn+93bPHcuXMoLi5udvUcIaRz4DgO5uqyuuSnIRFqLomRyhTQRveoS4Lc/7TRPSCTK5t9jc64TJgQEnoBJUbZ2dnYvn07Zs2ahdzcXJSUlGD16tXIzs4W7GGUk5ODy5cve5biKxQK5ObmIi8vD5GRkejXrx927dqF6upqTJ8+3VOn6fL8+snXN954I1JTUwEACQkJSEhIENT717/+BYlEImhfUFCACxcuYMSIEYiMjMSPP/6IzZs3o3v37pg0aVIgYRNC2pHdWoPqcuEwmKHiClxOh8/6Km0UIqLdvUD1vUEqbVSr5u8k9L0Z6b+b7r2PUXgEUkeLYx8jQkhgAkqMtFottm3bhuXLl2PWrFlQqVTIysrCvHnzBPXcez4IN2iYMWMGeJ7H1q1bPUeCFBQU+Nz1Ohj69OmDQ4cO4cCBA7BYLNDpdLjzzjsxd+5cnyvrCCHti+c5mKvLvXqBakxVPutLpPJGvUDxdb1A8ZArgrsqLqHvzYhPHoyqq3qwPO18TUiwTJ36KPr27YcXX1wSULsHH/wtrl71XqL/978fa3YOcTAxfGfb+auTc7k4VFZagn5dMe5o2hjF1/UFEqPDVlvXC9SoJ6j8ClxO35u0dQvXNRoGcydBKm10x+52S+9hlxfM+BwOOyoqriAqqgdkMv9ngbYUx3Eo//U8ai1GhKk0iO6Z3Krdr7vKe9faxCgr63fo338gsrP/ICgfNOgmv/OI/L1nkZGq9lmVRgghjfE8B4uholECdBnV5b/CYqjwWV8ikUET3aPRMFhPRETHQ67s1sF3TkjHEvvRM8EWGRmJm24aHJLXpsSIENIiDpsVV365ggvnf0JlySVPL5DTYfNZP0wdIegBiojpCXVEDA1RketOex890xKvvLIE339/Fk8//Qw2bVqHixcvYuDAQXjxxSVQqVR4/fVXceLEcURERCA3dxbuvvs3nrYffbQHf/3rDly9egVRUdG4774HMGXKNMHP8pkz32Ldutfx88969OyZgCefnOPzPoqKTuPtt9/E2bNFkEgkSEsbhTlznoFOF9mu8QeCEiNCiADP87AYK2HwLIl39waZDeU+67MSKbRR3RutBnMnQoqw9tshnpBQ4nm+2WFhr7och5Nf7vZb5+SXexDXq1+LdiWXSJpfaXktlZUV2LRpPaZMmQapVIr169/AsmUvQaFQYujQVNx//4P4+OOPsGzZyxg0aDC6d++B3bsLsX79G8jKegS3334Hzpz5Fu++mw+z2YynnpoLAKioKMf8+bORnHwjli17FSaTCWvWrILVWou+fft5Xr+o6DRmz87FyJHpWLr0VVittcjPfwvPP/8Mtmx5V3Cvhw4dxCeffASpVIqbb74Ff/rT00hOvrHVsQeCEiNCrmNOhw2G8iuCYTBD2WU47Faf9buFR0AbHe9JfiJi4hGui/XaZZYQseJ5Hn//63pUXC4O2jVrzdX4v//nuRbVjemZhLsentOqPXuMRiPy8t5GUpJ7b67y8jKsW/c6HnssB1OnPgEA6N9/EI4c+RJHjvwDEyc+jPfeewd33/0bzJ37ZwDA8OEj4XQ6UVj4F0yePBVabQQ++GAXGIbBG29shFqtBgDExsZhzpw/CV5/8+ZN6N9/AFaufN1z/0lJN2LKlEdw/PhRpKWNAgDcccedGDBgEOLiuuPy5V+xbdtWPPnkdGzdugM9ewpXpbcHSowIuQ7wPI8aU5WgB8hQfhmmqjL4OoySlUigiewuGAqL6p6AHj27i3biLiEtxXTRM9Oio2M8SREAJCbeAAC49daGvQHDw8MREaFDaWkJfvnlZ1RXV2PMmHsE1xkzZiy2b38XZ89+h7S0dJw9W4TU1GGepAgAhg27DRpNw4kYVqsVZ858i1mz5ghWrScm9kJsbBzOnTvrSYyeeeZZz++Ym2++BbfdNhKPPTYRu3b9BQsWPB/Er4hvlBgRIjJOhx2GiiswNFoRVl1+GQ5brc/6ym7hXsNgmsg4sBJhL5BUSnODCGEYBmMemdPiobSyS+dxZO/ma9bLeOiPiEm49i7rCqUSLlfrFpM3TlwAQCp1pwDh4cKz4GQyGex2m+cIsKbzfyIj3Y9NJvexXBUV5UhI8N56R6fTeT43mYxwuVzYuHEtNm5c61W3tLSk2fuOjo7GkCFD8cMP55qtE0yUGBHSRfE8j1pztWcIzDMXqKoUvnbhYFi2rhco3rMaLCKmJ5Qq2teLkEAwDAOprGX76cTd0B9h6ohrHj0Td0P/Fi1McA9BdcwuO/V7/lVVCfcaq6ysBACEh7ufj4qKRlVVpVf7xu3U6nAwDIPJkx9HRsZor7pabUSQ7rrtKDEipAtwOR0wVFxttCeQOwmyW2t81leEqdw9QI2OyNDoYiGRyjr4zgm5vnXlo2d69boBERE6fPnl33DnnXd5yr/44jBkMhkGDhwEABgwYBA++miP57B3APjPf/4No7HhIOewsDDcdNNg/PJLMfr3fzKg+ygvL8Pp0//FvfeOD0JU10aJESGdyP9v786jojryPYB/u5t9aWgWUUCf24O4oIA6uBAXEqNGR40rcVwxqG/cRuMk6kSRiUdzfHF3XEDMM4qaxHVEdMiMMU44HHXGjI4mJ75I5gkS2Xthb7vv+4OmtacbpJulF7+fc/oo91Y19bO47Y+6dasEQUBNpfK5TVLrR4NUZUUQBON5PSKRGN5+QfWjQAHPHot385Ry80siG2GvW89IJBLMn78Qu3Z9DJnMD0OGDMP9+//EiROfYvr0t/WjPDNmzMK5c19gzZoVmD17HlQqFdLSDsHHx8fg/X7965VYufK/sHHjOrz22hvw9vZGcXERbt26gTff/CWiowfiyy+vICcnG4MHD0VAQCAKCvJx7Nj/QCyWGC342FaYGBFZiUbzFMrSJ/p9whoej6+tNr2yuoubh9FcIB//jhwFIrIDDVvPtHTl6/Y2bVo8nJyccOrUCZw79wX8/QOwYEEi5s5N0JcJCAjAxx/vwa5d/40NG9YiJCQUq1e/j5SU/QbvFRHRH/v3H0Za2iFs3ZoMtVqNwMAgDBw4SD9HqVOnEJSUFGPPnu1QqVTw9vZGdPQgvPPOYgQHh7RLzNwSxEzcEsQyL3t8z0aBns0HUpY9gaA1NQokgpesw7MnwnQbprp7+Vp1FOhl70NH4Ogx2vqWIK3BnrYEsZSlMVptS5CHDx9i8+bN+Pbbb+Hp6YlJkybhN7/5DVxcmv7BEQQBqampOHHihH4T2XXr1iEyMtJkea1Wi2nTpuH+/fvYvXs3xo4da7LcvXv3MH36dLi5ueHbb781OFdXV4edO3fij3/8IyorKxEVFYUNGzage/fu5oZN1CxajQby4p+fexqsfl2gmiqVyfLOru4GE6F9A0Mg9e8IJxv6ICYiepmYlRgpFArMmzcPXbt2xd69e1FYWIiPPvoINTU12LhxY5N1U1NTsWfPHqxZswbh4eFIT09HQkICLly4gM6djR/zO3XqFAoLG398D6hPtj788EP4+fmhqsp4EurmzZuRmZmJtWvXIigoCAcPHsT8+fNx6dIlo8cTicxVU6WCvLgAihLdmkBlP6OssABarcZEaRG8ZYEGu8T7BobAw1vGuUBERDbErMTo1KlTqKysxL59++Dr6wsA0Gg0SE5OxuLFixEUFGSyXm1tLQ4dOoSEhATMnz8fADBgwACMHTsWaWlp2LRpk0H5srIy7N69G++99x7Wr1/faHvOnDmD8vJyTJ06FceOHTM49+TJE5w+fRpJSUmYNm0aACAiIgKjRo3CqVOnkJiYaE7o9BLTajVQlRXp1wNqGA2qqVSaLO/s4gYf/S2w+ttgPgGdmv14LxERWY9ZidH169cxZMgQfVIEAOPGjUNSUhKys7MxZcoUk/Vu376NiooKjBs3Tn/MxcUFo0ePxpdffmlUfseOHYiJiUFMTEyjbVEqldi+fTu2bNmCe/fuGZ3/5ptvoNVqDW7B+fr6YtiwYbh+/ToTIzKptrpSfwtMXlwARfFjKEqfQKt5arK8l08AfAND4BcUitDu3eHsEQBXD+vOBSIiIsuZlRjl5uZi6tSpBsekUikCAwORm5vbZD0ARnN7evTogaNHj6KmpgZubvUb4929excZGRnIyMhosi27du1Cnz59MGrUKJOJUW5uLvz9/Y0eF+zRowdOn256Q78XaYsVgBsmhTV3cpi9sbX4tFotVOVFKC+qH/0pL6p/NbYIm5OzK3w7hECmuxUm61A/GuTsUj8KJJGIIZW6Q6mshkbjmBMjba0PW5ujxwc4foytGZ9WW/8etvR8UsPvWyIRYEPNalUtibGhryQScYv+nzYrMVIqlfqVMJ/n4+MDhUJhosazei4uLnB1NbyVIJVKIQgCFAoF3NzcoNVqkZycjAULFiA0NBT5+fkm3+/777/H6dOnce7cuSa/p6l5RFKptMm2vohYLIJM1na7hkul7m323rbAGvHVVFei9Oc8lPych9Inuj8LH0PzVG2yvFQWiIBOneHfqTMCOoYioFMXSGUBzdr52tH7D3D8GB09PsDxY2yN+DQaN5SW/gyNpg5OTrb17+Woie3zLImxuroOEokYAQFSSCSWb2xtU+sYffHFFygpKcGiRYsaLSMIApKTkzFr1iz06PHifWVam1YrQKk0vdpwSzj6iEN7xKfValEhL64f/Sl+DLnuzyplucnyEmcX+AYEQ9bh2QiQLDAYzq6GH4JaAHKF6X3G9O/l4P0HOH6Mjh4f4PgxtnZ8bm6eUCjKodEIcHFxtfotcpGo/pdzrVZw6BEjc2MUBAF1dbWoqJDD09MLSmWNURmp1L1tHteXSqX6TeWep1AojG5Z/Xu9uro61NbWGowaKZVKiEQi+Pj4oLKyEjt27MCqVaugVquhVqtRUVEBoH5X3oalxjMzM5Gbm4vt27dDqayf/FpbW6t/P1dXV7i6ukIqlerrP0+pVDbZ1uZoyzUkNBqtQ69R0VrxqWurn5sI3bBb/M+NbuzoIfV77pH4+j89fQJMLq7WkvY5ev8Bjh+jo8cHOH6MrRWfl5cMWq2AigrTv1xZg1gshtbE+meOxNIY3d294OUla3Hfm5UYde/e3WgukUqlQnFxcZNrAzWc++mnn/DKK6/oj+fm5iI4OBhubm7Iz8+HXC5HUlISkpKSDOq///77CAgIQHZ2NnJzc6FQKBAXF2f0fQYNGoTExESsWbMG3bt3R0lJiVHSlpuby3WM7IggaFEhL9XvDdbwqlQab1gIABInZ/j4d9LtE/Zss1QXN492bjkR2bv6X9z94e0tg6aRBzDak0Qigo+PBxSKKmg0jjlkZGmMEolTq60iblZiNHz4cBw8eNBgrtGVK1cgFosxbNiwRutFR0fDy8sLly9f1idGarUaWVlZGD58OAAgMDAQn376qUG9kpISrF69GsuXL8fQoUMBAG+99RZ+8YtfGJQ7d+4cMjMzkZqaiuDgYABAbGwsxGIxsrKyMH36dAD1I1vffPMNfv1r8zawo/ahrqt5LgF6Ngr0VF1rsry7l69+UcSGUSAv30CbX2KfiOyLWCyGWGz9RVednMRwc3NDdbXGYUf8bCFGsxKj+Ph4HDt2DEuXLsXixYtRWFiIbdu2IT4+3mANo3nz5qGgoED/KL6rqysWL16MvXv3ws/PD2FhYTh58iTkcjkWLlyoL/Pvj+c3TL7u2bMnoqOjAQChoaEIDQ01KHfz5k1IJBKD+h07dsS0adOwbds2iMViBAUF4dChQ/D29kZ8fLw5YVMrEwQBlcoygxEgRXEBKhQlJsuLJU7w8e/4XBJUv0Ciq3vbTYInIqKXk1mJkY+PD44ePYoPP/wQS5cuhaenJ6ZNm4ZVq1YZlNNqtdBoDFf/TUxMhCAIOHLkiH5LkLS0NJOrXreWDz74AJ6enti+fTsqKysRHR2NTz75hKtet6On6lrIi+tXha5WFuFJ3r9QXvwYT+saGQXy9DG8DRYYDG9ZB4jFlj9hQERE1FzcRNZM3ETWNEEQUKUqN7gNJi9+jAp5CQDjHzGxRAKpX0ejW2Gu7l7t3/hWYO/91xyOHqOjxwc4foyMz/61VYxtuoks0VN1HRSlP+uTIIVuqwx1relH2t08vCHrEIKOXbrB3bsDvP07QSoLgrgF60wQERG1BSZG1ChBEFBdITcYAaofBSo2uRqsSCzWjQI92yneNyAYbp7Sl+I3HSIisn9MjAgAoHmqNjkKVFdjejFLV3evZxOhdYmQ1C8IEgl/pIiIyH7xf7GXjCAIqKlUPjcCVAB5yWOoyoogCMYjOSKRGN5+Qc9GgXSLJLp5Sq2+CiwREVFrY2LkwDRP1VCWFRokQYqSx6itNj153MXNw+CReN/AYEj9OkLi5NzOLSciIrIOJkY2QKvVovDRjyj+v1poRa6Qdexu9iKF1bpRIMVz84GU5YUQTCyrLhKJ4C3r8Ow2WEB9IuTu5cNRICIieqkxMbKy/P+9g9tfnUF1hVx/zN3LF9GjpiL0P/sblddonkKlHwWqvw0mLy5AbZXxHnYA4OzqbjAR2jcwBFL/jnBytv4qrkRERLaGiZEV5f/vHWRfTDM6Xl0hR/bFNAx6YxY8vGXPVocuKYCy9Am0Wo2JdxPBWxZo8ESYT0AwPLxlHAUiIiJqJiZGVqLVanH7qzNNlrmVdcLkcWcXN33i8ywJ6sRRICIiohZiYmQlJY8fGtw+a4ybpw8Cgrvqb4P5BobAQ+rHUSAiIqI2wMTISqorlc0qFzliMv7jlQFt3BoiIiICuFea2QRBgFbb8n8yzVM1qisVLyzn7unjMI/LSyRiaDSOu+q1o8cHOH6Mjh4f4PgxMj771xYxisWiZt9pYWJkJYIgoEJR1shE6npisQRePrxtRkRE1F6YGBERERHpmLeKIBEREZEDY2JEREREpMPEiIiIiEiHiRERERGRDhMjIiIiIh0mRkREREQ6TIyIiIiIdJgYEREREekwMSIiIiLSYWJEREREpMPEiIiIiEiHiRERERGRDhOjdlRZWYnhw4cjPDwc//znP5ssKwgCUlJSMHLkSPTr1w8zZ87EP/7xj/ZpaAuYE2NcXBzCw8ONXrW1te3U2uY5e/asyXZ+/PHHTdazlz60ND576b8G586dw+TJkxEREYGYmBi88847qKmpabLOF198gTFjxiAiIgITJ07EV1991U6ttYy5Mc6ZM8dkHz58+LAdW/1ijbUzPDwcly5darSevVyDlsZnb9fgX/7yF0yfPh1RUVGIjY3FypUrkZeX98J67d2PTm32zmRk//790Gg0zSqbmpqKPXv2YM2aNQgPD0d6ejoSEhJw4cIFdO7cuY1bajlzYgSAMWPGICEhweCYi4tLazerVRw+fBje3t76r4OCgposb299aG58gP3034EDB5CamoolS5YgMjIS5eXlyMnJafJn9dKlS9iwYQOWLFmCwYMHIzMzE8uWLUN6ejoiIyPbr/HNZEmMABAdHY3333/f4FhoaGhbNtVsSUlJqKioMDh29OhRZGVlYciQIY3Ws5dr0NL4APu5Bm/cuIFly5Zh8uTJWLVqFeRyOXbv3o2EhARcvHgRbm5ujdZt934UqF38+OOPQmRkpHDy5EkhLCxMuHv3bqNla2pqhOjoaGH79u36Y7W1tcKoUaOEpKSkdmitZcyJURAEYdSoUUJycnI7tc5yZ86cEcLCwoTS0tJm17GnPrQkPkGwn/57+PCh0Lt3b+HatWtm1XvjjTeE1atXGxybOXOm8M4777Rm81qFpTHOnj1bWLRoURu1qm3FxcUJiYmJjZ63p2vQlBfFJwj2cw0KgiBs2LBBiIuLE7Rarf5YTk6OEBYWJty6davRetboR95KayebN29GfHw8unXr9sKyt2/fRkVFBcaNG6c/5uLigtGjR+P69ett2cwWMSdGR2evfeiIzp49i9DQUIwYMaLZdfLy8vCvf/3LoP8A4M0330ROTg7q6upau5ktYkmM9uz27dvIz8/HL3/5yybL2Os12Jz47M3Tp0/h6ekJkUikP9YwQi0IQqP1rNGPTIzawZUrV/DgwQMsXbq0WeVzc3MBAN27dzc43qNHDxQUFLxwXoQ1mBtjg4sXL6Jv376IiopCYmIifvjhhzZqYctNmDABvXr1wmuvvYZDhw41eYvCHvvQnPga2EP/3blzB2FhYdi/fz+GDBmCvn37Ij4+Hnfu3Gm0TkP//XuS36NHD6jV6mbNi2hPlsTY4ObNm4iMjERERARmz56NW7dutUOLWyYjIwMeHh547bXXGi1jj9dgg+bE18AerkEAmDJlCh4+fIj09HSoVCrk5eVhx44d6N27N6KjoxutZ41+5ByjNlZdXY2PPvoIq1atgpeXV7PqKJVKuLi4wNXV1eC4VCqFIAhQKBRN3o9tb5bECNRPHOzXrx+Cg4ORl5eHgwcPYtasWTh//rxN3f8PDAzE8uXL0b9/f4hEIly9ehW7du1CYWEhNm7caLKOPfWhJfEB9tN/xcXFuHfvHh48eICkpCS4u7vj4MGDSEhIQFZWFvz9/Y3qKBQKAPX99byGrxvO2wpLYgSAQYMGYdKkSejatSuKioqQlpaGBQsW4NixY4iKimrnKJrn6dOnuHz5MuLi4uDh4dFoOXu6Bp/X3PgA+7kGAWDgwIHYt28f3n33Xfz+978HAPTq1QuHDx+GRCJptJ41+pGJURs7cOAA/P39MXXqVGs3pc1YGuMHH3yg//vAgQMxbNgwjBs3Dmlpadi0aVMrt9Jyr776Kl599VX917GxsXB1dcXRo0exZMkSdOjQwYqtazlL47OX/hMEAVVVVdi9ezdeeeUVAED//v0RFxeH48ePY+XKlVZuYctZGuOKFSsMvh45ciQmTJiA/fv3IzU1tc3bbYns7GyUlZVhwoQJ1m5KmzAnPnu5BoH6W2LvvfceZsyYgZEjR0Iul2P//v1YtGgRTpw4YVNJKm+ltaHHjx/jyJEjWLFiBVQqFZRKJaqqqgAAVVVVqKysNFlPKpWirq7O6JFLpVIJkUgEHx+fNm97c1kaoykdOnTAgAEDcP/+/bZqbqsZN24cNBoNvv/+e5Pn7akPTXlRfKbYav9JpVL4+vrqEwYA8PX1Re/evfHjjz+arNPQPyqVyuC4Uqk0OG8rLInRFA8PD4wYMcLm+vB5GRkZ8PX1RWxsbJPl7PUabG58ptjqNQjUz0EdPHgw1q5di8GDB2Ps2LFISUnBd999hwsXLjRazxr9yBGjNpSfnw+1Wo1FixYZnZs7dy769++Pzz//3Ohcw73Un376yeCDLjc3F8HBwTaVWVsao6Ozpz50dD179sSjR49MnmtsvZeG/svNzTWY25CbmwtnZ2ebu01hSYz2qKamBn/+858xceJEODs7N1nWHq9Bc+KzNw8fPjSaM9WxY0fIZLJGf3YB6/QjR4zaUK9evfDpp58avNatWwcASE5ORlJSksl60dHR8PLywuXLl/XH1Go1srKyMHz48HZpe3NZGqMphYWF+Pvf/46IiIi2am6ryczMhEQiQe/evU2et6c+NOVF8Zliq/03atQoyOVyg9Gv8vJy3L9/H3369DFZp3PnzujatSuuXLlicDwzMxNDhgyxuXViLInRlKqqKly7ds3m+rDB1atXUVVV1ayntezxGjQnPlNs9RoEgODgYHz33XcGxx4/fozy8nKEhIQ0Ws8a/cgRozYklUoRExNj8lyfPn30H1jz5s1DQUEBvvzySwCAq6srFi9ejL1798LPzw9hYWE4efIk5HI5Fi5c2G7tbw5LY8zIyMBXX32FESNGoEOHDsjLy0NKSgokEgkWLFjQbu1vjoULFyImJgbh4eEA6ldv/fzzzzF37lwEBgYCsO8+tCQ+e+q/119/HREREVixYgVWrVoFV1dXpKSkwMXFBbNmzQIArF+/HufPnzf44F6+fDnWrFmDLl26ICYmBpmZmbh79y6OHz9urVAaZUmMf/vb33D48GGMHj0aISEhKCoqwieffILi4mLs3r3bmuE06uLFiwgODsaAAQOMztnzNdjAnPjs6RoEgPj4eGzZsgWbN29GXFwc5HK5fn7q84/i20I/MjGyAVqt1ujR6MTERAiCgCNHjqCsrAy9evVCWlqazQ3hN9e/xxgaGoqioiJs2bIFKpUK3t7eGDx4MFasWGFzMXbr1g1nzpzBkydPoNVq0bVrV6xfvx5z5szRl7HnPrQkPnvqP7FYjJSUFGzduhUbN26EWq3GwIEDkZ6erk/8TPXfhAkTUF1djdTUVKSkpKBbt27Yt2+fTT6tZUmMgYGBUKvV2LlzJ+RyOdzd3REVFYXk5GT069fPWqE0SqFQ4K9//SvmzZtnsBZOA3u+BgHz47OnaxCon1rh4uKCkydP4syZM/D09ERkZCR27doFmUymL2cL/SgSmlpZiYiIiOglwjlGRERERDpMjIiIiIh0mBgRERER6TAxIiIiItJhYkRERESkw8SIiIiISIeJEREREZEOEyMiIiIiHSZGRERERDpMjIiIWuDrr7/G3r17rd0MImolTIyIiFrg66+/xr59+6zdDCJqJUyMiIiIiHSYGBGRQyksLMS6deswdOhQ9O3bF+PHj8fp06cNytTW1mLv3r0YM2YMIiIiEBsbi2XLluHRo0cAgBs3biA8PBw3btwwqJefn4/w8HCcPXsWALB27Vqkp6cDAMLDw/UvIrJfTtZuABFRaykpKcGMGTMgEonwq1/9Cn5+frh+/Tp+97vfoaKiAvPnz4dGo8HixYuRk5OD8ePHY+7cuaisrER2djYePHiALl26NPv7zZw5E0VFRcjOzsa2bdvaMDIiai9MjIjIYezcuRMajQYXL16ETCYDALz99ttYvXo19u3bh/j4eFy6dAk5OTlYt24d5s+fr6+7aNEiCIJg1veLiopC165dkZ2djUmTJrVmKERkJbyVRkQOQRAEZGVlIS4uDoIgoKysTP+KjY2FSqXC/fv3kZWVBZlMhtmzZxu9h0gkskLLiciWcMSIiBxCWVkZlEolPvvsM3z22WeNlnn06BG6desGJyd+/BGRMX4yEJFD0Gq1AICJEyfirbfeMlmmuROjGxs5avgeROS4mBgRkUPw8/ODp6cntFothg4d2mi5Ll264M6dO1Cr1XB2djZZRiqVAgBUKpXB8cePHxuV5e03IsfCOUZE5BAkEgnGjBmDP/3pT3jw4IHR+bKyMgDAG2+8gfLycv1j9s9rmHwdEhICiUSCW7duGZw/efKkUR13d3cAgFKpbHEMRGR9HDEiIofx7rvv4saNG5gxYwamT5+Onj17QqFQ4P79+8jJycHNmzcxefJknD9/Hlu3bsXdu3cxYMAAVFdXIycnB2+//TZef/11eHt7Y+zYsTh+/DhEIhE6d+6Ma9euobS01Oh79unTBwCwefNmxMbGQiKRYPz48e0dOhG1EpFg7vOpREQ2rLS0FH/4wx9w9epVlJSUwNfXFz179sSbb76JGTNmAABqampw4MABZGRkoLCwEL6+voiOjsZvf/tbdO7cGUD9CNOmTZtw/fp1uLi4YOzYsZgzZw4mTJiArVu3YsqUKQAAjUaDrVu34tKlSygvL4cgCPjhhx+sFj8RtQwTIyIiIiIdzjEiIiIi0mFiRERERKTDxIiIiIhIh4kRERERkQ4TIyIiIiIdJkZEREREOkyMiIiIiHSYGBERERHpMDEiIiIi0mFiRERERKTDxIiIiIhIh4kRERERkc7/A1RtWmR6ju99AAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data_gamma.plot(x=\"ecut\", y=[k for k in data_gamma if k.startswith(\"mode\")], subplots=True, style=\"-o\");" ] }, { "cell_type": "markdown", "id": "53ca8cfc", "metadata": {}, "source": [ "This convergence study at $\\Gamma$ thus reveals that our pseudos require\n", "{{ecut}} >= 6 Ha to get reasonably converged phonon frequencies at $\\Gamma$.\n", "In what follows, we assume that also the modes at the other $q$-points present a similar\n", "convergence behaviour and we use {{ecut}} = 6 Ha to keep the computational cost low." ] }, { "cell_type": "markdown", "id": "6512670d", "metadata": {}, "source": [ "For a quick introduction to Pandas, see:\n", "\n", "* [Pandas cookbook](https://github.com/jvns/pandas-cookbook)\n", "* [Pandas cookbook Chapter 1 Reading data from a csv file](https://nbviewer.jupyter.org/github/jvns/pandas-cookbook/blob/master/cookbook/Chapter%201%20-%20Reading%20from%20a%20CSV.ipynb)" ] }, { "cell_type": "markdown", "id": "9902087d", "metadata": {}, "source": [ "## Phonon band structure of AlAs\n", "\n", "Now we are finally ready for the calculation of the vibrational spectrum of $AlAs$.\n", "We already managed to run DFPT calculations at $\\Gamma$ with different values of {{ecut}} and the\n", "steps required to get a full band structure are not that different, provided that\n", "the following differences are taken into account:\n", "\n", "- we need the dynamical matrix $D(q)$ on a homogeneous mesh so that it is possible to calculate $D(R)$\n", " in anaddb via Fourier transform and then phonon frequencies for arbitrary q-points via Fourier interpolation\n", "\n", "- $AlAs$ is a polar semiconductor so we need to include the LO-TO splitting for $q \\rightarrow 0$ that, in turns,\n", " requires the DFPT computation of the Born effective charges and of the dielectric constant.\n", "\n", "\n", "In AbiPy, these concepts are translated in an easy-to-use API in which you pass an initial `AbinitInput` object,\n", "you specify the q-mesh for phonons in terms of `ph_nqpt` and activate the computation of the\n", "Born effective charges with the boolean flag `with_becs`.\n", "\n", "Let's have a look at the code (as usual there are more comments than lines of code):" ] }, { "cell_type": "code", "execution_count": 23, "id": "14979e58", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "

\n", "\n", "
def build_flow_alas_phonons(options):\n",
       "    """\n",
       "    Build and return a Flow to compute the dynamical matrix on a (2, 2, 2) qmesh\n",
       "    as well as DDK and Born effective charges.\n",
       "    The final DDB with all perturbations will be merged automatically and placed\n",
       "    in the Flow `outdir` directory.\n",
       "    """\n",
       "    scf_input = make_scf_input(ecut=6, ngkpt=(4, 4, 4))\n",
       "    return flowtk.PhononFlow.from_scf_input("flow_alas_phonons", scf_input,\n",
       "                                            ph_ngqpt=(2, 2, 2), with_becs=True)\n",
       "
\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from lesson_dfpt import build_flow_alas_phonons\n", "abilab.print_source(build_flow_alas_phonons)" ] }, { "cell_type": "markdown", "id": "e1a6fb0e", "metadata": {}, "source": [ "We can finally construct the flow with:" ] }, { "cell_type": "code", "execution_count": 24, "id": "cfe07964", "metadata": {}, "outputs": [], "source": [ "flow_phbands = build_flow_alas_phonons(options=None)" ] }, { "cell_type": "markdown", "id": "0d4ecbd1", "metadata": {}, "source": [ "and visualize the connections with:" ] }, { "cell_type": "code", "execution_count": 25, "id": "f73d5024", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "flow\n", "\n", "PhononFlow, node_id=85, workdir=flow_alas_phonons\n", "\n", "clusterw0\n", "\n", "Work (w0)\n", "\n", "\n", "clusterw1\n", "\n", "PhononWork (w1)\n", "\n", "\n", "\n", "w0_t0\n", "\n", "w0_t0\n", "ScfTask\n", "\n", "\n", "\n", "w1_t0\n", "\n", "w1_t0\n", "DdkTask\n", "\n", "\n", "\n", "w0_t0->w1_t0\n", "\n", "\n", "WFK\n", "\n", "\n", "\n", "w1_t1\n", "\n", "w1_t1\n", "DdkTask\n", "\n", "\n", "\n", "w0_t0->w1_t1\n", "\n", "\n", "WFK\n", "\n", "\n", "\n", "w1_t2\n", "\n", "w1_t2\n", "DdkTask\n", "\n", "\n", "\n", "w0_t0->w1_t2\n", "\n", "\n", "WFK\n", "\n", "\n", "\n", "w1_t3\n", "\n", "w1_t3\n", "BecTask\n", "\n", "\n", "\n", "w0_t0->w1_t3\n", "\n", "\n", "WFK\n", "\n", "\n", "\n", "w1_t4\n", "\n", "w1_t4\n", "BecTask\n", "\n", "\n", "\n", "w0_t0->w1_t4\n", "\n", "\n", "WFK\n", "\n", "\n", "\n", "w1_t5\n", "\n", "w1_t5\n", "PhononTask\n", "\n", "\n", "\n", "w0_t0->w1_t5\n", "\n", "\n", "WFK\n", "\n", "\n", "\n", "w1_t6\n", "\n", "w1_t6\n", "PhononTask\n", "\n", "\n", "\n", "w0_t0->w1_t6\n", "\n", "\n", "WFK\n", "\n", "\n", "\n", "w1_t7\n", "\n", "w1_t7\n", "PhononTask\n", "\n", "\n", "\n", "w0_t0->w1_t7\n", "\n", "\n", "WFK\n", "\n", "\n", "\n", "w1_t8\n", "\n", "w1_t8\n", "PhononTask\n", "\n", "\n", "\n", "w0_t0->w1_t8\n", "\n", "\n", "WFK\n", "\n", "\n", "\n", "w1_t9\n", "\n", "w1_t9\n", "PhononTask\n", "\n", "\n", "\n", "w0_t0->w1_t9\n", "\n", "\n", "WFK\n", "\n", "\n", "\n", "w1_t10\n", "\n", "w1_t10\n", "PhononTask\n", "\n", "\n", "\n", "w0_t0->w1_t10\n", "\n", "\n", "WFK\n", "\n", "\n", "\n", "w1_t0->w1_t3\n", "\n", "\n", "DDK\n", "\n", "\n", "\n", "w1_t0->w1_t4\n", "\n", "\n", "DDK\n", "\n", "\n", "\n", "w1_t1->w1_t3\n", "\n", "\n", "DDK\n", "\n", "\n", "\n", "w1_t1->w1_t4\n", "\n", "\n", "DDK\n", "\n", "\n", "\n", "w1_t2->w1_t3\n", "\n", "\n", "DDK\n", "\n", "\n", "\n", "w1_t2->w1_t4\n", "\n", "\n", "DDK\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "flow_phbands.get_graphviz()\n", "#flow_phbands.plot_networkx();" ] }, { "cell_type": "markdown", "id": "f9a0078b", "metadata": {}, "source": [ "Note that there are a lot of things happening under the hood here.\n", "\n", "First of all, AbiPy generates `PhononTasks` only for the $q$-points in the\n", "irreducible wedge of the Brillouin zone corresponding to `ph_ngqpt`.\n", "Moreover, for a given $q$-point, only the irreducible atomic perturbations are explicitly computed\n", "since the other atomic perturbations can be reconstructed by symmetry.\n", "Fortunately you do not have to care about all these technical details as AbiPy and Abinit\n", "will automate the whole procedure.\n", "\n", "Remember that the $q$-point mesh cannot be chosen arbitrarily\n", "since all $q$ wavevectors should connect two $k$ points of the grid used for the electrons.\n", "\n", "It is also worth stressing that the computational cost of the DFPT run depends on the q-point\n", "since only those symmetries that preserve the q-point as well as the direction of the perturbation\n", "can be employed (calculations at $\\Gamma$ are therefore much faster than other q-points)." ] }, { "cell_type": "code", "execution_count": 26, "id": "4f970730", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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rfphonrfatpolrfdirqptkptoptclass
w0_t0NoneNoneNoneNoneNoneScfTask
w1_t0NoneNone(1, 0, 0)(0, 0, 0)2DdkTask
w1_t1NoneNone(0, 1, 0)(0, 0, 0)2DdkTask
w1_t2NoneNone(0, 0, 1)(0, 0, 0)2DdkTask
w1_t31[1, 1][1, 0, 0](0, 0, 0)2BecTask
w1_t41[2, 2][1, 0, 0](0, 0, 0)2BecTask
w1_t51[1, 1][1, 0, 0][0.5, 0.0, 0.0]3PhononTask
w1_t61[1, 1][0, 1, 0][0.5, 0.0, 0.0]3PhononTask
w1_t71[2, 2][1, 0, 0][0.5, 0.0, 0.0]3PhononTask
w1_t81[2, 2][0, 1, 0][0.5, 0.0, 0.0]3PhononTask
w1_t91[1, 1][1, 0, 0][0.5, 0.5, 0.0]3PhononTask
w1_t101[2, 2][1, 0, 0][0.5, 0.5, 0.0]3PhononTask
\n", "
" ], "text/plain": [ " rfphon rfatpol rfdir qpt kptopt class\n", "w0_t0 None None None None None ScfTask\n", "w1_t0 None None (1, 0, 0) (0, 0, 0) 2 DdkTask\n", "w1_t1 None None (0, 1, 0) (0, 0, 0) 2 DdkTask\n", "w1_t2 None None (0, 0, 1) (0, 0, 0) 2 DdkTask\n", "w1_t3 1 [1, 1] [1, 0, 0] (0, 0, 0) 2 BecTask\n", "w1_t4 1 [2, 2] [1, 0, 0] (0, 0, 0) 2 BecTask\n", "w1_t5 1 [1, 1] [1, 0, 0] [0.5, 0.0, 0.0] 3 PhononTask\n", "w1_t6 1 [1, 1] [0, 1, 0] [0.5, 0.0, 0.0] 3 PhononTask\n", "w1_t7 1 [2, 2] [1, 0, 0] [0.5, 0.0, 0.0] 3 PhononTask\n", "w1_t8 1 [2, 2] [0, 1, 0] [0.5, 0.0, 0.0] 3 PhononTask\n", "w1_t9 1 [1, 1] [1, 0, 0] [0.5, 0.5, 0.0] 3 PhononTask\n", "w1_t10 1 [2, 2] [1, 0, 0] [0.5, 0.5, 0.0] 3 PhononTask" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "flow_phbands.get_vars_dataframe(\"rfphon\", \"rfatpol\", \"rfdir\", \"qpt\", \"kptopt\")" ] }, { "cell_type": "markdown", "id": "ea2c9918", "metadata": {}, "source": [ "Now we can generate the directories and the input files of the `Flow`.\n", "Change lesson_dfpt.py so that the build_flow_alas_phonons function is called in main\n", "instead of build_flow_alas_ecut_conv.\n", "Run the script to generate the directory with the flow.\n", "Finally, use\n", "\n", " abirun.py flow_alas_phonons scheduler\n", "\n", "to launch the entire calculation." ] }, { "cell_type": "markdown", "id": "2d08dc1c", "metadata": {}, "source": [ "## Post-processing the results\n", "\n", "Our flow is completed and we have the final DDB file with all the $q$-points and all the independent atomic perturbations.\n", "Let's open this DDB file with:" ] }, { "cell_type": "code", "execution_count": 27, "id": "ae08275e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "================================= File Info =================================\n", "Name: out_DDB\n", "Directory: /home/runner/work/abipy_book/abipy_book/abipy_book/dfpt/flow_alas_phonons/outdata\n", "Size: 28.11 kB\n", "Access Time: Sun Oct 27 17:41:29 2024\n", "Modification Time: Sun Oct 27 17:38:46 2024\n", "Change Time: Sun Oct 27 17:38:46 2024\n", "\n", "================================= Structure =================================\n", "Full Formula (Al1 As1)\n", "Reduced Formula: AlAs\n", "abc : 3.970101 3.970101 3.970101\n", "angles: 60.000000 60.000000 60.000000\n", "pbc : True True True\n", "Sites (2)\n", " # SP a b c\n", "--- ---- ---- ---- ----\n", " 0 Al 0 0 0\n", " 1 As 0.25 0.25 0.25\n", "\n", "Abinit Spacegroup: spgid: 0, num_spatial_symmetries: 24, has_timerev: True, symmorphic: False\n", "\n", "================================== DDB Info ==================================\n", "\n", "Number of q-points in DDB: 3\n", "guessed_ngqpt: [2 2 2] (guess for the q-mesh divisions made by AbiPy)\n", "ecut = 6.000000, ecutsm = 0.000000, nkpt = 128, nsym = 24, usepaw = 0\n", "nsppol 1, nspinor 1, nspden 1, ixc = 1, occopt = 1, tsmear = 0.010000\n", "\n", "Has total energy: False\n", "Has forces: False\n", "Has stress tensor: False\n", "\n", "Has (at least one) atomic pertubation: True\n", "Has (at least one diagonal) electric-field perturbation: True\n", "Has (at least one) Born effective charge: True\n", "Has (all) strain terms: False\n", "Has (all) internal strain terms: False\n", "Has (all) piezoelectric terms: False\n", "Has (all) dynamical quadrupole terms: False\n" ] } ], "source": [ "ddb = abilab.abiopen(\"flow_alas_phonons/outdata/out_DDB\")\n", "print(ddb)" ] }, { "cell_type": "markdown", "id": "57f28863", "metadata": {}, "source": [ "The `DdbFile` object provides an easy-to-use interface that invokes `anaddb` to post-process\n", "the data stored in the DDB file.\n", "\n", "`anacompare_phdos`, for example, computes the phonon DOS with different $q$-meshes.\n", "Each mesh is defined by a single integer, `nqsmall`, that gives the number of\n", "divisions used to sample the smallest reciprocal lattice vector.\n", "The number of divisions along the other directions are chosen so that proportions are preserved:" ] }, { "cell_type": "code", "execution_count": 28, "id": "12421f38", "metadata": {}, "outputs": [], "source": [ "c = ddb.anacompare_phdos(nqsmalls=[8, 10, 12, 14, 16])" ] }, { "cell_type": "code", "execution_count": 29, "id": "9493eca9", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://chart-studio.plotly.com", "responsive": true, "showLink": true }, "data": [ { "mode": "lines", "name": "DOS: nqsmall 8", "showlegend": true, "type": "scatter", "x": [ -0.0037195256267313916, -0.0036947287892198487, -0.0036699319517083063, -0.0036451351141967635, -0.0036203382766852206, -0.0035955414391736786, -0.0035707446016621357, -0.0035459477641505937, -0.003521150926639051, -0.003496354089127508, -0.0034715572516159656, -0.0034467604141044227, -0.00342196357659288, 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "c.plotter.combiplotly();" ] }, { "cell_type": "markdown", "id": "5a017e91", "metadata": {}, "source": [ "A 16x16x16 $q$-mesh with the tetrahedron method gives a well converged phonon DOS." ] }, { "cell_type": "markdown", "id": "713bff28", "metadata": {}, "source": [ "To function `anaget_phbst_and_phdos_files` allows one to compute the phonon band structure on\n", "an automatically defined $q$-path as well as the phonon DOS:" ] }, { "cell_type": "code", "execution_count": 30, "id": "55efa81f", "metadata": {}, "outputs": [], "source": [ "phbst_file, phdos_file = ddb.anaget_phbst_and_phdos_files(ndivsm=10, nqsmall=16, lo_to_splitting=False)\n", "\n", "# Extract the phonon bands and the phonon DOS from phbst_file and phdos_file\n", "phbands = phbst_file.phbands\n", "phdos = phdos_file.phdos" ] }, { "cell_type": "markdown", "id": "77c944ed", "metadata": {}, "source": [ "Let's plot the phonon bands with plot:" ] }, { 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "phbands.qpoints.plotly();" ] }, { "cell_type": "markdown", "id": "cfd59736", "metadata": {}, "source": [ "Do you see the two strange dips for the highest phonon band, at the $\\Gamma$ point?\n", "They are due to the lack of LO-TO splitting for the ANADDB treatment of the first list of vector.\n", "See also the discussion in the [second DFPT lesson](https://docs.abinit.org/tutorial/rf2/index.html)." ] }, { "cell_type": "markdown", "id": "bd25002f", "metadata": {}, "source": [ "For years, Abinit users had to patch manually the output frequencies to include the LO-TO splitting.\n", "These days are finally gone and we can plot the LO-TO splitting with AbiPy by just setting\n", "lo_to_splitting=True`:" ] }, { "cell_type": "code", "execution_count": 33, "id": "34dff971", "metadata": {}, "outputs": [], "source": [ "phbst_file, phdos_file = ddb.anaget_phbst_and_phdos_files(ndivsm=10, nqsmall=16, lo_to_splitting=True)\n", "\n", "# Extract the phonon bands and the phonon DOS from phbst_file and phdos_file\n", "phbands = phbst_file.phbands\n", "phdos = phdos_file.phdos" ] }, { "cell_type": "code", "execution_count": 34, "id": "1cc2a892", "metadata": {}, "outputs": [], "source": [ "#phbst_file.phbands.qpoints.plot();" ] }, { "cell_type": "markdown", "id": "f82b294c", "metadata": {}, "source": [ "The band structure plot now correctly shows the non-analytical behaviour around $\\Gamma$:" ] }, { "cell_type": "code", "execution_count": 35, "id": "1772958b", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://chart-studio.plotly.com", "responsive": true, "showLink": true }, "data": [ { "legendgroup": "", "line": { "color": "black", "width": 2.0 }, "mode": "lines", "name": "", "showlegend": false, "type": "scatter", "x": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "phbands.plotly();" ] }, { "cell_type": "markdown", "id": "c894a19f", "metadata": {}, "source": [ "```{warning}\n", "`lo_to_splitting=True` works only when the DDB contains the Born effective charges\n", "and the dielectric constant, that must be computed in the Abinit run.\n", "```" ] }, { "cell_type": "markdown", "id": "aedfafd4", "metadata": {}, "source": [ "To plot bands and DOS on the same figure:" ] }, { "cell_type": "code", "execution_count": 36, "id": "7361d837", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://chart-studio.plotly.com", "responsive": true, "showLink": true }, "data": [ { "legendgroup": "", "line": { "color": "black", "width": 2.0 }, "mode": "lines", "name": "", "showlegend": false, "type": "scatter", "x": [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "phbands.plotly_fatbands(phdos_file=phdos_file);" ] }, { "cell_type": "markdown", "id": "758b6775", "metadata": {}, "source": [ "The highest frequency modes have a strong Al-character while the low frequency modes originate from As.\n", "This behaviour is somehow expected. Could you explain it in terms of a simple physical model?" ] }, { "cell_type": "markdown", "id": "f7c48785", "metadata": {}, "source": [ "## Macroscopic dielectric tensor and Born effective charges\n", "\n", "Our calculations includes the response of the system to an external electric field.\n", "The code below extracts the macroscopic dielectric tensor (`emacro`)\n", "and the Born effective charges (`becs`) from the DDB file:" ] }, { "cell_type": "code", "execution_count": 39, "id": "60f24c96", "metadata": {}, "outputs": [], "source": [ "emacro, becs = ddb.anaget_epsinf_and_becs()" ] }, { "cell_type": "code", "execution_count": 40, "id": "7c65503f", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ "DielectricTensor([[ 1.03961652e+01 -0.00000000e+00 -0.00000000e+00]\n", " [-0.00000000e+00 1.03961652e+01 1.19611765e-15]\n", " [-0.00000000e+00 1.19611765e-15 1.03961652e+01]])" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "emacro" ] }, { "cell_type": "code", "execution_count": 41, "id": "9f6cbcaf", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/share/miniconda/envs/abipy/lib/python3.12/site-packages/spglib/spglib.py:115: DeprecationWarning:\n", "\n", "dict interface (SpglibDataset['equivalent_atoms']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead\n", "\n", "/usr/share/miniconda/envs/abipy/lib/python3.12/site-packages/spglib/spglib.py:115: DeprecationWarning:\n", "\n", "dict interface (SpglibDataset['wyckoffs']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead\n", "\n", "/usr/share/miniconda/envs/abipy/lib/python3.12/site-packages/spglib/spglib.py:115: DeprecationWarning:\n", "\n", "dict interface (SpglibDataset['equivalent_atoms']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead\n", "\n", "/usr/share/miniconda/envs/abipy/lib/python3.12/site-packages/spglib/spglib.py:115: DeprecationWarning:\n", "\n", "dict interface (SpglibDataset['wyckoffs']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead\n", "\n" ] }, { "data": { "text/html": [ "
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elementsite_indexfrac_coordscart_coordswyckoffxxyyzzyzxzxy
0Al0[0.0, 0.0, 0.0][0.0, 0.0, 0.0]1a2.1680532.1680532.1680530.00.00.0
1As1[0.25, 0.25, 0.25][1.40364, 1.40364, 1.40364]1d-2.168053-2.168053-2.1680530.00.00.0
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" ], "text/plain": [ "Born effective charges in Cartesian coordinates (Voigt notation)\n", " element site_index frac_coords cart_coords wyckoff xx yy zz yz xz xy\n", "0 Al 0 [0.0, 0.0, 0.0] [0.0, 0.0, 0.0] 1a 2.168053 2.168053 2.168053 0.0 0.0 0.0\n", "1 As 1 [0.25, 0.25, 0.25] [1.40364, 1.40364, 1.40364] 1d -2.168053 -2.168053 -2.168053 0.0 0.0 0.0\n", "\n", "Born effective charge neutrality sum-rule with chneut: 1\n", "\n", "[[0.00000000e+00 0.00000000e+00 0.00000000e+00]\n", " [0.00000000e+00 0.00000000e+00 0.00000000e+00]\n", " [2.40741243e-35 2.40741243e-35 0.00000000e+00]]" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "becs" ] }, { "cell_type": "markdown", "id": "d1cb5063", "metadata": {}, "source": [ "As explained in the references, the Born effective charges must fulfill\n", "the charge neutrality sum-rule.\n", "This rule is usually broken due to the discretization introduced by the FFT mesh,\n", "and `anaddb` will enforce it if {{chneut}} is set to 1 (default behaviour).\n", "Let's check it out!" ] }, { "cell_type": "code", "execution_count": 42, "id": "ec6864e8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Born effective charges in Cartesian coordinates (Voigt notation)\n", " element site_index frac_coords cart_coords wyckoff xx yy zz yz xz xy\n", "0 Al 0 [0.0, 0.0, 0.0] [0.0, 0.0, 0.0] 1a 2.168053 2.168053 2.168053 0.0 0.0 0.0\n", "1 As 1 [0.25, 0.25, 0.25] [1.40364, 1.40364, 1.40364] 1d -2.168053 -2.168053 -2.168053 0.0 0.0 0.0\n", "\n", "Born effective charge neutrality sum-rule with chneut: 1\n", "\n", "[[0.00000000e+00 0.00000000e+00 0.00000000e+00]\n", " [0.00000000e+00 0.00000000e+00 0.00000000e+00]\n", " [2.40741243e-35 2.40741243e-35 0.00000000e+00]]\n" ] } ], "source": [ "print(becs)" ] }, { "cell_type": "markdown", "id": "86adaebc", "metadata": {}, "source": [ "Let's repeat the same calculation but without enforcing the sum-rule:" ] }, { "cell_type": "code", "execution_count": 43, "id": "fb41273e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Born effective charges in Cartesian coordinates (Voigt notation)\n", " element site_index frac_coords cart_coords wyckoff xx yy zz yz xz xy\n", "0 Al 0 [0.0, 0.0, 0.0] [0.0, 0.0, 0.0] 1a 2.127295 2.127295 2.127295 0.0 0.0 0.0\n", "1 As 1 [0.25, 0.25, 0.25] [1.40364, 1.40364, 1.40364] 1d -2.208811 -2.208811 -2.208811 0.0 0.0 0.0\n", "\n", "Born effective charge neutrality sum-rule with chneut: 0\n", "\n", "[[-8.15163891e-02 0.00000000e+00 0.00000000e+00]\n", " [ 0.00000000e+00 -8.15163891e-02 0.00000000e+00]\n", " [ 5.81483171e-19 5.81483171e-19 -8.15163891e-02]]\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/usr/share/miniconda/envs/abipy/lib/python3.12/site-packages/spglib/spglib.py:115: DeprecationWarning:\n", "\n", "dict interface (SpglibDataset['equivalent_atoms']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead\n", "\n", "/usr/share/miniconda/envs/abipy/lib/python3.12/site-packages/spglib/spglib.py:115: DeprecationWarning:\n", "\n", "dict interface (SpglibDataset['wyckoffs']) is deprecated.Use attribute interface ({self.__class__.__name__}.{key}) instead\n", "\n" ] } ], "source": [ "emacro, becs_chneut0 = ddb.anaget_epsinf_and_becs(chneut=0)\n", "print(becs_chneut0)" ] }, { "cell_type": "markdown", "id": "5ac1577e", "metadata": {}, "source": [ "## Thermodynamic properties within the harmonic approximation\n", "\n", "The thermodynamic properties of an ensemble of non-interacting phonons can be\n", "expresses in terms of integrals of the DOS.\n", "\n", "\\begin{equation} %\\label{eq:helmholtz}\n", "\\Delta F = 3nNk_BT\\int_{0}^{\\omega_L}\\text{ln}\\left(2\\text{sinh}\\frac{\\hbar\\omega}{2k_BT}\\right)g(\\omega)d\\omega\n", "\\end{equation}\n", "\n", "\\begin{equation} %\\label{eq:free_en}\n", "\\Delta E = 3nN\\frac{\\hbar}{2}\\int_{0}^{\\omega_L}\\omega\\text{coth}\\left(\\frac{\\hbar\\omega}{2k_BT}\\right)g(\\omega)d\\omega\n", "\\end{equation}\n", "\n", "\\begin{equation} %\\label{eq:c_v}\n", "C_v = 3nNk_B\\int_{0}^{\\omega_L}\\left(\\frac{\\hbar\\omega}{2k_BT}\\right)^2\\text{csch}^2\\left(\\frac{\\hbar\\omega}{2k_BT}\\right)g(\\omega)d\\omega\n", "\\end{equation}\n", "\n", "\n", "\\begin{equation} %\\label{eq:entropy}\n", "S = 3nNk_B\\int_{0}^{\\omega_L}\\left(\\frac{\\hbar\\omega}{2k_BT}\\text{coth}\\left(\\frac{\\hbar\\omega}{2k_BT}\\right) - \\text{ln}\\left(2\\text{sinh}\\frac{\\hbar\\omega}{2k_BT}\\right)\\right)g(\\omega)d\\omega,\n", "\\end{equation}\n", "\n", "where $k_B$ is the Boltzmann constant.\n", "\n", "This should represent a reasonable approximation especially in the low temperature\n", "regime in which anharmonic effects can be neglected.\n", "\n", "Let's plot the vibrational contributions thermodynamic properties as function of $T$:" ] }, { "cell_type": "code", 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