{ "cells": [ { "cell_type": "markdown", "id": "f2d4dcef", "metadata": {}, "source": [ "## Calculation of electron-phonon matrix elements including quadrupoles from first principle\n", "Author: S. Ponce (v1, 10/27/2024)
\n", "Revision: S. Tiwari (v1.2, 10/29/2024)
\n", "\n", "We interpolate the electron-phonon matrix elements $|g_{nm\\nu}(\\mathbf{k,q})|$ using EPW and compare the results matrix elements computed with direct DFPT calculations.\n", "\n", "Below we define constants that will remain all accross the calculations\n", "\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "295a5af1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " \n", " \n", " -*#*- ...............- \n", " .+*= .+%*-=%%: .=#*- -===============-:.\n", " :*%=*%%- *%* #%* :+%+-%%+ .:. -=. :==-. \n", " -%S -%%*: :#%. -%%-. -##: #%* -=. :==- \n", " .. .%S: +%%%%*. :*%%%#= %%= -=. :==- \n", " :=#%%*- .#S- .. .%%= :*#*: -=. :==- \n", " -%S:.=#%%*==%# *%%=::=##-+%%. . .=-. :==- .= \n", " :%%- .-+++: -+##*=. =%S :-::==: .==- --.\n", " *%# #%+ -=--:. .----:. \n", " :%%- -%S. \n", " .-=*####SS%#########: -###########*+: +#######= =%SS####+::. \n", " =+#**%SSSSSSSSSSSSSSSS= =SSSSSSSSSSSSSSS= #SSSSSSS*. +SSSSSSSS%%%%- \n", " *%% =SSS.. .SSS= SSS=. .:+SSS+ -SSS:. .-::. .SSS+. #%* \n", " #%#. =SSS. *S# *S%: SSS= %SS%. .SSS= #SSS%. :SSS: =%#. \n", " *%%: =SSS#*#SSS- SSS= .+SSS+. %SS*.=SSSSS+ +SS%.:+%+ \n", " +%%:=SSSSSSSSS- SSSSSSSSSSSSS=. +SSS:SSS%SSS:%SS*-#%= \n", " ....#S==SSS:..SSS: =+- SSS%######+=. -SSS%SS%.#SS%SSS==%%=. \n", " .:+##%%#*- =SSS. ::. :SSS. SSS=. SSSSSS:..SSSSSS: :*%%%*=- \n", " #%+. -+#SSS*+++++++*SSS: .=+SSS#++++: %SSSS+. =SSSS%. :-+#%%+ \n", " #%* .SSSSSSSSSSSSSSSSSS: *SSSSSSSSSSS. +SSS%. %SSS*. . .%%= \n", " =%S :::::::::::::::::. .:::::::::. :::. :::. =+=-.#%+ \n", " -%S: =+===#S: \n", " ==*------------------------------=========+++++++++++++++++++++++========++-+## \n", " =+++++++++++*******++++++++++++++++========------------------==========+++++++- \n", "-- -- -- -- -- -- -- -- -- -- -- -- Structure Info -- -- -- -- -- -- -- -- -- -- -- -- -- \n", "1\n", "https://raw.githubusercontent.com/PseudoDojo/ONCVPSP-PBE-FR-PDv0.4/master/Si/Si.upf\n", "https://raw.githubusercontent.com/PseudoDojo/ONCVPSP-PBE-FR-PDv0.4/master/Si/Si_r.upf\n", "pseudo found at pseudodojo : ONCVPSP-PBE-FR-PDv0.4/Si_r.upf\n", "-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n" ] } ], "source": [ "import os\n", "import EPWpy\n", "from EPWpy import EPWpy\n", "from EPWpy.plotting import plot_bands\n", "from EPWpy.plotting import plot_g\n", "\n", "silicon=EPWpy.EPWpy({'prefix':'\\'si\\'','restart_mode':'\\'from_scratch\\'','ibrav':2,'nat':2,'calculation':'\\'scf\\'',\n", " 'atomic_species':['Si'],'mass':[28.0855],\n", " 'atoms':['Si','Si'],'ntyp':1,'pseudo':['Si.upf'],'ecutwfc':'40','ecutrho':'160',\n", " 'celldm(1)':'10.262','verbosity':'\\'high\\'','pseudo_auto':True, \n", " },env='mpirun')\n", "\n", "silicon.run_serial = True\n", "silicon.verbosity = 2\n" ] }, { "cell_type": "markdown", "id": "cdc1c3d1", "metadata": {}, "source": [ "### Self-consistent field (SCF) calculations\n", "\n", "Here we perform the self-consistent field calculation to obtain the electron charge density of silicon in the ground state. The calculation consists of three separate steps:\n", "1. Apply the method `scf` to the object `silicon`. This step specifies runtime parameters for an SCF calculation on siicon \n", "2. Based on the properties defined at step 1 as well as other properties that are set by default within EPWpy, the method `prepare` creates the input file needed by QE\n", "3. The method `run` applied to the object `silicon` instructs QE to perform the SCF calculation" ] }, { "cell_type": "code", "execution_count": 3, "id": "ca1c2189", "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "parallelization chosen: -nk 2\n", "-- -- -- -- -- -- -- -- -- -- -- Calculation: scf -- -- -- -- -- -- -- -- -- -- -- \n", "on 1: running: mpirun -np 4 /mnt/storage/sabya/For_video/epwpy/build/q-e-EPW-5.9s/bin/pw.x -nk 2 -in scf.in > scf.out\n", "Running scf |████████████████████████████████████████| in 2.0s (1.16/s) \n", "\n", "-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n" ] } ], "source": [ "silicon.scf(electrons={'conv_thr':'1E-13'},kpoints={'kpoints':[[4,4,4]], 'kpoints_type':'automatic'}, name='scf')\n", "silicon.prepare(0,type_run='scf')\n", "silicon.run(4, parallelization='-nk 2')" ] }, { "cell_type": "markdown", "id": "a705bdd2", "metadata": {}, "source": [ "### Band structure calculation\n", "\n", "In this step, we compute the band structure of silicon along some high-symmetry lines in the Brillouin zone.\n", "\n", "This calculation is not strictly necessary to compute the mobility, but it is useful to understand the electronic structure of the system under consideration.\n", "\n", "Also in this case, we use **three instructions** to specify runtime parameters, prepare the input file, and execute the QE calculation." ] }, { "cell_type": "code", "execution_count": 4, "id": "6d16a983", "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-- -- -- -- -- -- -- -- -- -- -- Calculation: bs -- -- -- -- -- -- -- -- -- -- -- \n", "on 1: running: mpirun -np 4 /mnt/storage/sabya/For_video/epwpy/build/q-e-EPW-5.9s/bin/pw.x -nk 2 -nt 2 -in bs.in > bs.out\n", "Running bs |████████████████████████████████████████| in 4.5s (0.35/s) \n", "\n", "-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n" ] } ], "source": [ "silicon.scf(control={'calculation':'\\'bands\\''},system={'nbnd':12},electrons={'conv_thr':'1E-11'},\n", " kpoints={'kpoints':[['0.5', '0.5', '0.5', '20'],\n", " ['0.0','0.0','0.0','20'],\n", " ['0.0','0.5','0.5','20']],\n", " 'kpoints_type':'{crystal_b}'},\n", " name='bs')\n", "silicon.prepare(type_run='bs')\n", "silicon.run(4,type_run='bs')" ] }, { "cell_type": "markdown", "id": "2ce7b068", "metadata": {}, "source": [ "### Band structure plot\n", "\n", "We now plot the electronic band structure computed at the previous step. The zero of the energy axis is set to the value specified manually via `ef0`.\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "983d506b", "metadata": {}, "outputs": [ { "data": { "image/png": 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nVIRN+LEIdBf8D37gPN9tFDhZXLUyzWOZpIjw88+br5+oBl6YZrarJrj2yZgaGqJp/xtv9HfflRERrjERdrpYzznH+YlsxymsbenS4MTOyyi3pUuZr7yycl7Xpibmj33MPN9r0sU5LhG2/i777ed8/UT18HUa9Wlv33Jqb4+mje1WbWenswC7mZpSRLjGRDjI2GIvE+K4ETu3YtvU5G1VkWqppcX7ZNxRE4cIm/yrhx4a3Ugy6zWRz6tpWJ0scaeJ88PG6d6aPNn7/VVGRDjEFIcIM1c+rU85xXzxOD2pTQJpGoufy1W+EjY3M19zDfPVV1d2UuRyZssmilS27JJgJcchwlOmmH+XKH4Tr51sTisaR+EqMb0lZDJqezXfrwkR4RBTXCKsw+nidiKueXudhNNkoftZMPWcc5Kx2GTYImxtxwMOYD7hBPNvEoag2a+j665To9p059ct4dXcbF52yPpADRO/91A1RIRDTEkSYSeBOuEEb09wr/P2+klO8/ma/MWmNducJnGJ86a2EqYIe7U4w1gw1cv5iUZalZnMvoidAw+M56F52WXm+rpdksiEiHCIKUkiHKSv2M+8vSbhria2QURH6Orb0sJ84YXOQuBn0VC/hCnCptf48eODnbxc99s//7zZ4jW9UemuCYD5Qx9i3r49+g640dwrbhARDjElSYSZK31W551nvrCqPd29ztsb9+TppnP4WTQ0DIJod/t3XLKEecEC5+8X1G+va183bisvD/Oo4pRNBkuhwPz5z/vz+zohIlxHIqzD6QYZHvZenh/rNU5M8y+blr+ZOjWZa8z5GUnm1+1g//433GAWTiJzpIupAzDu1WFGuxKyV0SE61yEnV65xo9nnjs3+Cd/0vDa+RiGheyl3XX1Na2VN2YM83e+493t4OTusftknVLZ2nZ7/h/8wPzbR+GnX7PG+fuEgYhwnYtwkPNQ1BJeOx87Ophfesm/laxrd7cun2oPDFNZXs7R2Mj84Q+bV2mpJpxuzm8dkmw3DsJyBVlddNXcJ2IJpzClQYSZ9fGNL7wQ/cWYJEzWmxvLz/q5pcXZ770vv1iRbz9fc7P3QSxOImjqsPQ6P4Pp93Fjbet+03nzout88/JACcv4EBEOMSVNhL3Ot+B0w82YMfLznDmhVTs2dL+LyUJubnb2Zdp9zI2NzB//eOUAlqYmFbVhGhnmlOyDaBobnTtFJ0zwfo5Jk/T5fgZ4mH7LqMIDRzPpTpCICIeYvIiwk0XkdaIaL5EL552nF4KFC70PyqhFIbbj5N+McxBLR0elq6ChQU0uYxJOr6l8LQUR1lYsms8TRQfc1q3O3zVKRIRDTG5F2OvgA11+c7MKKF+4sNIiymbNvrygUxIjIILGT7ib12Qazm3KD7J9nWK3nb6/W955h/nss83nD9sSfuQRZ7dO1O42EeEQk1sRjmIEWlwpl6s9ITa9qs6Zo/8NTOFuTilIq9o014ffgTJ+sJZXnl9ENw9JGB1wXjrfgOg7nkWEQ0xuRTjO11inOYODejiMGePqZ0gFps6cefP8iW3YqZoLIaqBMrqIjmuvDf/8pvZqa2Nety5a368JEeEQ02gtYdNN7Uc4TVaPyeXh5Ec+4gjvYjAwUGkpJt2HrLtB/UwSFEVqawvXhTAapk0zX69hE/XACz+ICIeYovQJj2Z4sJ9RbjpB9SMec+bEb43ozu8nfjqo1NvrfdKhjo5k+uNXrzbXOewOuNdec/7NkoKIcIgpSdERURCkW6UshEGJs6msoMS2XKZum+nNYeR3LI6oV39/ZWebkxUe1ZBeJ6zXXT6vQvCcromgLWH7zGtO5xZLuE5S0uKEw8YkQj09oxc5q3CVz2USVbdWrZ9Y3CDrZcXtiDmTu4mI+fTT1YxpSVsF+fTTg52tTUeQswRGjYhwiKneRJjZLDZBiR3AfMgh+nzTlIlBprAC+d22u07sTH0HUU5Ob3o4TJq0r95hvp0lZeCFH0SEQ0z1KMIm/PqMw05eXShJGLqqEzTTgIyurnDqa6VYjHfms+Fh5zZLOkGLcAaCoOGRR4A5c0bmHX88kM3GUx9AnXvBAv223l6VyvXLZtXnZcuiq5+J7m5g3TqgWFR/u7uBjRv1+27YAHzpS8DNNwPTpwOZjPo7MOD//AMD+8qaOhX4m79Rcqcjn/d/Hjc8/TSw//7m7XFeX7FhUud6TGIJV8ePJRpUmJhbf20UjLbdvcZ0+3VVmHy/DQ2VHYlRzHwW15tLkIg7IsQkIlwdpxhpe1RBOa54dFEIteMXtGIKTVy82Dz/b1eXt+ibnTuZ99/fe1lBYmr7s85KfhubEBEWEY4Vvx1NfqMQkkoYyxuVfyuntw37b22KQ89mnafyjCpEzvRdkhRy5hURYRHh2NGJh9OiobVImO0e5NwkpomCwm6X9evNUTHllFakY06IHV1H05tv6vcdGoqyZrXB4sVAa+vIPPtnNxABd92lL2vxYv/109HXB+Ry6pyZDDBtGvCnP5n3r8sOOAMiwkIgOPWq33wz0N8fXG9/rdPdDSxfDhQKStQKhX2fdZgELZ83l9XdHVx9+/qAW24BhofVZ+Z99TrlFP0xPT3BnT/1mEzkekzijvCPzlds7RHX+TKTMFeCX+Jod69zlkT1+1abdCetfn8T4o4QEonO4rrnHuBHP1LWb7E4cv9t24BFi+Kpa1oxWbXLloVv7Zp48819FrCdcv6yZcCePUqa9+xJRux2ksjFXQGhduju1t/45ddTO+Iv9o7pNzblB01fnxL44WH1cDW1LSB+X7eIJSyEjslfPGGC800sJAu777dYdG4/8fu6Q0RYCB1dbz+gXmXf+16gq0s67NLA8uX6/PIQ8SQOGU8DNSXCRDSLiFiT3oq7bvWM3ZeZz6ubtKUFeOYZ4KWXlEU1OKisJxHi5PHGG86+X/H7+seVT5iImgAcB+ADAKYCaAHwBoDnATzBzC+EVkN/XAzg15bPe+KqiKDQ+Sx/8hMlwFbKHXZR+DcFM+L7jQ5HESaigwEsBNANYD8ARQBvA9gOoB1AMwAmorUAlgFYycxFfWmR8hwzr4m7EoIzL7+sz5cOu3gp+37L2CNb7Ijvd3QY3RFEdDOAZwEcA+DK0t9mZu5g5i5mbgUwBcAZAH4H4DoAfySiY0OvtVATmDrsmIEPfUiNuhJfcfSI7zdanHzCUwG8n5mPZebvMfNaZh7xWs/MrzHzj5m5B0qQbwHwNyHW1y0DRDRMRJuI6F+IKORZUgU/6DrsGhqU8D71lJpbV3zF0fKXv4jvN2qMIszMf8fMv3NbEDPvZOYbmNnwHI2EtwF8F8B8ACcC+CaAuQB+SUSdMdZL0KAbfHDXXcDkyZX7yuCO4LHO95DLqcne3/Uu8/7i+w0HYoPHnYg+A+DfmHlbtFUKFiI6GsB/AfgWM39ds70HQA8ATJo06X2rVq3yVP6WLVswZsyYIKoqlDjxxBPATJotjMceezzy+uhIe7tff/3B+PGPDwBQ+Ttns0UMD5NtG+O0017CwoV/jqqKicVP28+ePXstM8/QbjSNZ4bqhHsHwN0AZpv2S0OC8m0/WG0/mTsiGThN5Th/PvOKFeFPRl6NtLe7ab4HIubdu2tvvocgiXLuiA8D+HeojrdHiGiQiK4iIocXlkQjY7NSgslXnM0Ct9+u/MODg+IvHg0mvy+zck2I7zc6nHzCjzLzuQAmA/gsVEzwpQCeI6JfEtECIhofSS1HARHNAHAolEtCSAEmX/EzzwCNjZUxq+Ivdsbu+500ybyv+H2jp+qIOWbexsz3MvNJAKYBuAxAG1Rc8CtE9EMi+njI9XQFEQ2UrPUziOhEIroEwM8AvATghpirJ3hAN3H8kUcCu3fr96+X2GLrysnW0D1Tvn2+h+Fh80rPgMT8xoGnYcvM/Aozf4eZ3wPgaAD3QLkr/iOEuvnhvwF8AsBdAB6EGmhyH4BjmfmNGOslBIQptri5GbjpptqeOH5gQO+K6eurzD//fOCii4DbbtOXlclIzG9iMDmLnRJU+NddUCFhRQDP+yknaUk65pKPaQl3XQpzYvOw2123jt8BB7j73m6T4I/YJnUnosOJ6BoiGgLwMIDTAXwfwAeZ+dCgHw6CoEPnL77hBjUZkJ20+op1Fu9nPlM5z8ZoyNTU1F3pptrcEfsD+AcA8wC8F8rqfQjAlwH8mJl3hl5DQbChmwzoi1/U75tGX/Fll6kHiBWn+RuIvM/LrHtoCfHgNHfE/wfVofU9AI0AvgJgGjN/jJn/VQRYSBJOC43+/d8rizlpvmJ7Z9qSJcqPu369+RjdysleBRgAtm5VESe17ENPDSY/BYCNAK4H8F7TPrWWxCecXqotNBq0r3i07e7Ft11OZd+w1Vd8773Ox3R0uC8/7YuvRkWUPuGpzLyQmX8bwbNAEEaFaaHRTs2MIdu2AV/7WnR104WPXXpppcsBAMaMAa65Rm/xLl48cmKj9etVFISJbBZYurSyrKYmfTxwWn3oacdpsMaIGdOI6AAiuo6IniaiF4jo/5TyF8r0lenFHsjf1+duWxLRxRa//rp+36Eh4PrrgTvuCPeVXNfJdu65Skh1bN2qBFq3evJTT1Wu8bZrl/ncPT36h9Mdd5h9zGn0oacek4lsTQCOBPAmgNcB/ATAMICjS9u+B+Bf3JST9JQWd4TTuH7TNl1+b6/+tdTNNrfniBuneSicXsl1IWJWdO2uO8br+QsF83cxuVcyGe+/vVO9TjmF+TvfiX9+jqQStDvCrQj/DMBTAMZARVQULSJ8FoAX3JST9ORFhPdd9EVXQhSFcC5YoN82caI3IfCTDj/cXK9q3z9MdL7X1lbmL32JualJX+exY5lbWiqPGSnOxRHipDtPLuf8m+nqVS7P/nsdeKBzWUH8Lg0N5t9E/MX7iEuEtwA4tfR/1ibCMwFsc1NO0pNbETYJ4RFHeMufP5953jz9tvZ255suLYmI+YMf1G9zsqqDxGTVEnn7LuPGMTc3j8xramK+6CLmCRO8laXrZLMKsJeystngfpdXX2UeM8ZcZyE+EX7HQYTPALDJTTlJT25F2PRaWCuJyLtABZmiEmevrgK/ycniDeL6Cvq3MbU9UXU3TT0Qlwg/AuC+0v92EV4F4Cduykl6civCcYukLmWzwT0cnNwecYtzkJhcFV7Cuspp7Fh9fjWL1/qgOe885k9+svpvEOfDyX6N1aObIi4RPgHAbqjRcp8tdcx9BWoCn51QE+S4KivJKWpLOCrhNLlDqlmcXnzSTucI8vcy1csvOoH0Ks7l47xYvF5dDtbvHzYmf7GpXvXmpohFhFUZ+BiAP5Ws4HJ6AcBH3ZaR9BS1Tzgq4XTK94PXcwRpVZuOCdqF4UWcrZ1zbl/VnR5MRx1l/o5RofsuTm6KeiI2Ed57AHAwgL8FcKjXY5Oe0hAdkVa8WNVBujzCE+eia5+o9fyZDHM+71xn0+8VNyY3RS7HfPHF6nvVg684dhGu5ZSWOOFawos4n3desOLMzDxnzsj8OXNUvp84YS/fxZSicjn4QfcmYHpg1rKvODIRBnCGaZvDMVMAfMDrcUlJIsLJwWQJBhmZMmWKPv+IIypjfHM5JSr7RLs4QrT9+HidHg5Jxf5wWrnSHE5Zq77iKOeOuJGIfldaS67dYT8Q0fFEtBzAnwG8x2lfQXDDBz8IdHWpobZdXeozAMyaFdw5XnlFn//ss2pxSyt79gDnnAM8+mg5Ry0H/+ijar6HW27xfv40rmxhHxo+bx6webN+38FB4MUXzUsvCQqn+YQPgZo3+EooQX4OwDNQQ5d3ApgA4CAAMwDsB+AJAB9m5v8bao2FmmJgQE0aMzSkpqNcvFjl9/Tsm+BmcBCYPx9Yuxb4zW/iq6uJrVu9H5PJqAfLT3+qvrv1QZM28nnVRjoOPlh91/JDrbwkE1A5J3TdYjKRywlqLuGzAdwJ4FkAbwHYATXX8KMALgdwWLVy0pDEHREebqMNGhsrhwyHkaI4R7VkD/vyG2kRN7p2bGkxj5RMu6tCOuZCTCLCo8MkHF7nKXBKpiG1Jl9xR4eKSLDmZTJ2/+7oU1tbMOVMmMB8xRXeR9nFjdeh4WkefSciHGISEXaHW6u2oYH5xBP9ia3JejLF6vb2moXL6WbXRUeYOtmmTtXnz5mjytSJvZ/Rd9W+f5qEqxZH34kIh5jqUYSdbmqT2Npf5XM55xFVXlNHh79BEUEKlCk6wxQd4fR7eRl9Z7L0rQ+2NAmXlxVPyg+apCMiLCLsCy8Ccc89zN/7XqUFm8n4G0jR2anPdxLbpFt8Xtrd6+g7rxMLTZ2a7N/L6+i7lSuT+12YRYRFhNmf9Wq/4ZubzZPOBJmqzauQZPFwIoh29+JDr9aRaBe1pHfyOT1onL5LEhARTogIO03u7fVV2csxJkG7807m66+vnO82l1MRB2GLrV8XQloJ++Gr+728Wsj77cf8zW8ms5PP1Idg96uXUz6/77i4ryMR4RCTWxH22jlUrdNIZ6V+8pOV7oCGhkqRDSPl8+YbPs0uhCCJ6w1I99v7aeMkdPJ5cVMAagEE04onURLXVJb/F8A8AE1u9k9rcivCJoFy8nPp8rNZ85M/ilRNUEVszcTVF+DFQq7WyWd/yCfBQvYz0X7UnXlxifBqqKkrNwG4rlYGZ9iTWxGOc2JzUwrDehWxNZOkDlmnB2a1Gdt011G5zDja3vRdLr7YXGci5nvvja6+cc4nfFhJgN+AmtR9dWkkXYPbMpKeRmsJm6xaU/7UqcxdXfptToMPxHqNnySJMLO3Tr5qcdvvfa85FC6K68h0jqR05sXuEwbQVHJNPFkS49cAfAvAQV7LSlpKik94NIMPRGyjIWki7EQQnXyAWug0zk4+3b2Sy5mNnIkTmVesCP5+iF2E9x4IHG1xUxQB7AHwQwCT/ZYZd0pDdISQDNIkwjpMD/+lS72Lc5SdfF478+wpiIidWEUYQAuAzwH4r5IV/CyAiwBMBnBBeVIfL2UmKaUlTliIn1podz+v/abkNAQ5bIH2Wt+WFuZ/+IfKSCO3Lpe4OubeDeAmAJsB7CpZvLM1+50KYIebMpOYRIQFt9Ryu5usZK/zYLS2Mp99tjkKIyhxDjJ0b/x4s8vFtKSZG4IQ4SKADaVpK6c47Hc4gMfclJnEJCIsuKXW293LQCE/YtfS4k+cvbjunKKFvNbXNEueWyEOQoTPAJB1s2+ak4iw4JZ6bXcvYmda9sgpNTZWRma0tKgQNK/RP/39laNFGxv9d0zqkts1AZ1E2Glljb0w831u9ksCRDQNwPcAfBhqDZpHACxk5qFYKyYINUB3t35FDOtKKADQ2grccINaNcW06oaOXbsq87ZvV8soZTJqWSUr27YBF1ygVu7YvVvlDQ4Cn/ucWgpreHjk/sPDwOrVzquBeMFevh9ciTARfcNhcxHA2wB+w8xPjb5K/iGiVgA/h1p+6VwADOAqAI8R0XuY2cdCNIIgOFEWZfsyVeV8nUC3tACbNnk7j12Ay2zfXpm3axfw0EOV+cPDwO23ezuvE+U1AkeDKxEGcAWUoJFmWzmfieiXAD7GzG+Pvmq+uABq3btDmfnPAEBEvwfwJwCfhxpsIghCwJgsZJNAA97EOZ9XAvrSS8HX3Q1tbfq1BMvr5Y0Gp9WWrRwOtZLyJQAKAJpLf/+plP+3UKPnDgdw9eir5ZtPAFhTFmAAYOYXATwF4LTYaiUIdYx9heayYC9fDhQKakXtQkF9XrpUibGV1lbg6quBb39bv62jQ39ek5VaKKiko6NDf47bbrOujs3Bro5tchZbE5Rf9SuGbV9BKTa49P96N2WGkQC8CuA2Tf4yAK9XO1465oQyvb29nM1mGQBns1nuLXWDz5kzh6He/hgAz7EsrWE6RvCG1+gIv6NO/Q7xDzpOmNR2Z4hoK4BPMPOjmm1zAfyYmduI6EQADzBz06ieDD4hol0ArmPmS235VwG4lJkr3C9E1AOgBwAmTZr0vlWrVnk655YtWzBmzBj/lRZC5/rrr8f999+PYrGITCaDU089FQsXLjRuA4Af//jHFeV0dHRgk+Zd+eijj8a0adO0x5x22ml7zyWExyOPdOL22w/Cxo1N6OzcifnzX8DcuRuN+U7HVMPPPT979uy1zDxDu9GkztYE4GUAVxu2fQvAy6X/T4ELizOsBDWQ5Fua/KsA7Kl2vFjC6UZnifb29o6wXMvpox/9KB933HHabUGmTCYjFnKNEbQl7LZj7k4AlxHRWAD/BmAjgE4AZwFYAOCa0n7HAvhvl2WGwWYAEzT57aVtQg3Q19eH5cuXY3h4GNlsFj2l3pFbbrll7z7Dw8MjPtt54IEHQq8nABSLRcd62b/HskCcjEKqMKkzj7QkM1DW5F+h5owYhgpN+yuAbwJ73RrvB3CEmzLDSFDhab/Q5K8G8Hi148USTg4m69Fk2dZKEis5+cQ9gc94AMcD+FTp73gvx4edACyEms3tIEvedAC7AVxS7XgR4ejx4kJoaGgITOzK5/SSiEibP2fOHG5rawusXkKyiVyEATQCeBOqYy52oa1S1zaokLk/QIWkfQLAMwBeADCm2vEiwqPDyfep29bT0xObxVnt3JlMpuJzf3+/MTqiv79fe4yfun33u9/lnp4e8SMnlLhmUdsI4CQ3+8adAOQB/AjAO1Dukv8AMN3NsSLC7vBivfb09PDpp58emHh6Fbbe3t4K4TzyyCO5UCgYjykUCtzf38+FQoGJaO9nK7p21x0TlIVc/i5C/MQlwssBLHezb5qTiPBIvIhtFKlcB5NA6erb39/Pra2t2mO6urq4qalpRF5ra2uF4Opw2+4mC9nkDjG5PMrHLViwQCzkmIlLhP8OwHqoyIhzAMwBcKI1uSkn6amWRdipoystHWDV6qzDZPG2t7fznj17qlq8Jry0u+4cTmLr93cRoiEuES4aUjlKYthNOUlPaRFhr75Xk6AeccQRRoEKSiCy2aznTjCTVeuVYrFoPAcRjaoNRtvuTu4Qr0likaMlLhE+oVpyU07SUxAi7NXi9HpMtdfxoG7soJKbOgclHlaLc+rUqXzkkUca61UoFHyfh3n0Iqxzk7S2tvKFF14Y6G8vBE9iFvqsxeRFhIOwOJ2OOeSQQ2IVT6+vy9UENWxLzeT7bWxs5MbGxgqxc+t2MBHEG5DJFRKUq6Ic7iZWcrDEHSc8EcDHoebqbS/lNQPIeCknqcmtCCfR4gwy+ekAixvT631XV5dvv68TYbqhgnRVmDolk9BmaSUudwQBuBbADuzzBR9d2vYggH92U07Sk1sR9hPoH3bKZDKew7ecLHTm9FhQw8PDxu84Wt+viTBFWGfVm9rWT7tb2zMN7Zs04hLhrwHYXvp7TEmIyyJ8IYBfuSkn6cmtCMcpnKbk1/eaxhvRatkecMABfNhhhxl/l9H6fk2E3SGrs947Ojq039EUi3zGGWf4uo4EZ+IS4RcAXFb6P2sT4ZMBvOGmnKSnsCxhPz7hasfE5XuNG5Pvt7m52XfMrx/iiIox+YqJyNjuXq9V8SNXJy4R3glgNutF+EQA292Uk/Q0Wp+wX4uzlqzUsIna92siDhF28hUfe+yx3NXVVfHd/fRfHHrooWIlOxCnJXwR60X4SwCedVNO0tNooyOE8HGyBqMkDhHWvQU0NDRoXVrWtwDdteqnX0P8yIq4RPjbAF4H8EGLCL8XwLsAbADwDTflJD2lZbBGPbJ161ZesGCBUSDC8v2aiKvdddb+AQcc4Pk3MVnIBx98sGdxrjchjkuEWwA8CRUV8UJJhP8M5aZ4DECjm3KSnkSEk4NVbCZPnsyTJ0/ea33Zp7QM0/drIknt7hRXvHv3buNxQfqR68lCji1OuGQBzwPQD+AhAN+HihfOuS0j6UlEOBmYOt+mTp3Kv/vd7yL1/ZpIUrs7+YpnzJjB11xzjaffK6g4+Frt25ARcyLCNY9JVKZNmxZ31faSpHbXPbSampqMc4C4eXMIwo9MRMYwuTQLsYiwiHDNk5TONyeS1u66t4O3336bx4wZE5gPPciRoml2YQQtwhm4gIgaiehyIvofItpGRMO2tMdNOYJgZ2BgANOnT0cmk0E+n8fMmTOVdaAhn89HXLv00N3djXXr1qFYLGLdunXo7u7GuHHjsHXrVu3+Q0NDns+xbNky9Pb2IpvNAgCy2eyIz14oL3g6PDw84nNfXx/6+vqQy+VARMjlcujr6/NcfqowqbM1AVgKtXbb/QCuBnC5PbkpJ+lJLOFoMfl+iSiUSXeCJC3tbnLtNDQ08JVXXhmIb90pbj6oIf5J8i/HFR3xEoBFbvZNcxIRjhaTQEyZMiURnW9OpKXddQ86k7tnNA+6KBYHOOqoo4wCHaU4xyXCb6NGVs9wSiLC0ZIG36+JNLW7/YF255138tixYwPzFVcjqMEifqznIEeqjkbogxDhfgBXuNk3zUlEODqclviJeuCFH9Le7nE/AE0WcpDLPpnS8ccfz6eccop2m2nOlmozDlYjCBE+FsDzAL4BYAaAg+zJTTlJTyLC4WG1xqyvx3aLKGm+XxNpb3cnX/HatWsjcQd5XTkmiVPIlic8qkYQImxfV64iuSkn6UlEOBxMHXDnn39+4n2/JtLe7k6+YiKKdVSiV/9yFNazU3KDkwiT2u4MEX22dEIjzHxP1YISzowZM/jpp5/2dMzq1asxa9ascCpUIxQKBW1IVKFQwLp166KvUADUQrsPDAxg0aJFGBoaQj6fx+WXX45nnnkGS5cu1e6fhPbq6+vD8uXLMTw8jGw2i56eHgDALbfcUrEvEUGnb+WQunJ43GjIZrPYs6d6hC4RrWXmGdqNJnWuxySWcPA8++yzRgsiDR1wJmq53eP2F/shqEVxE+sTdkoAMiitN5f2JCI8OqyuhXw+z+eeey43NzcbRTgNHXAmarndnUIH00aqoyMAvInSnMGlzwTgJ7B1wkF12olPuM4x+X0B1Rvd0tISm48xDGq53U1tmc1m+dOf/jTn8/nU+fCDJMphy+MB5CyfM1ArLY93OEaoUxYtWoRt27ZV5E+cOBFPPPEEVqxYgUKhACJCoVDA8uXL0d3dHUNNhWp0d3dj+fLle9tr2rRpOOGEEzA8PIzvf//7GBoaAjNjcHAQPT09GBgYiLvKqcbV3BGCUA3TXASbNm0CoJ/bQEgu1vYaGhrC6tWrsf/++1fst23bNixatCiGGtYOIsLCqHn44YeRyegvJZl0p3Z44403tPl+JgMS9iEiLHjGOvPZ2LFjcdJJJ2F4eLhCiFtbW7F48eKYaikEjdMD9YILLkChUEAmk8H06dPFReGBaiJ8ABEdRETlkXEj8kr5XeFWUUgSAwMD6OnpweDgIJgZW7ZsAQCcddZZuPvuu8XvW8MsXrwYra2tI/Ky2SyYGbfffrv4iv1i6rGDfnScMc9UTpqSREdUZ9q0aTUXbuaHemv3MroRjh0dHXV1TQQdHWGNfrBzXuCKL6SaNWvWYP369dpt4hesD7q7uyvebubNm6fdV64JdxhFmGtgGLIwOqzDWseOHYt33nnHuK90wNUv+Xweg4ODFflEhPvuuw/bt28fMTx68eLF4qayUFMdc0S0johYk06Pu25pw+77LQvwUUcdVeEXlA64+kbnK85kMigWi/jkJz+Jc889d+91JP7iSmpKhEs8COA4W3o81hqlkMsuu0w7+GLz5s0jAvmlA06wD+4oFAq45557cOONN4KIKibKkdjikTj5hNPKG8y8Ju5KpJmHHnrI0fer8wsK9Y3pmrj44ou1+4u/eB+1aAkLHrDG/E6bNg0zZ87ERz7yEeP+4vsVvGC6XnSj7+qVWhThU4loGxHtJKI14g82Y/f7btiwAU8++SRyuRzOPvts8f0Ko0bnLwaAjRs3Ys6cOcjn83U/wKPWRPh+ABcB+AiAbgA7APw7EZ0Ta60SimnSnc7OTqxatUp8v8KosfuL8/k8zjrrLGQyGfz85z/H+vXr677DztXKGnFARHMBPOxi18eZeZahjCyANQAmM/M0wz49AHoAYNKkSe9btWqVp3pu2bIFY8aM8XRMEti9ezdOOukk7TYiws9//vOIa5Qu0truSeHMM8/cO7mTlUmTJsHrPRg1ftp+9uzZxpU1kizCrQDcOCC3MbPRy09EXwHwbQBTmfkVp4JqeXkja8xvZ2cnstksXn75Ze2+SVjGJumkpd2TSiaTgU57iAjFYjGGGrnHT9s7LW+UWHcEM29j5v9xkdx2sybzaRMBdt/va6+9hpdffhnjxo1DU1PTiH3F7ytEganDjplx8skn15WvOLEiHARElANwNoAhZn417vrExde+9jWt73e//fbDHXfcIX5fIXJ0HXYNDQ0AgAcffLCufMU1I8JE9GkiWkVEnyGi2UT09wAeA3A0gK/GXL3YePjhh40xmRs2bJDJ1oVY0A3wuOuuuzB58uSKfWt9cEfNiDCAFwF0ArgWwEMAbgWwE8DJzJxsT3+AWON+W1tbjZ1vgMT8CvGiMwBee+017b61PLijZkSYmdcw84nMPImZG5h5PDPPZeYH465bVAwMDOCCCy7Y6/vdvn07AODYY4+VmF8hFTj5ii+++GLceeede42MWvEX14wI1zu7du3CRRddtFd4rbz66qsS8yukApOvmIhw4403Yv78+TU3GZCIcAqxuhwKhQIuvPBCHH744di8ebN2//J8D+L7FZKOyVf8m9/8Bg0NDRVhbbXgL67FCXxqmnK4WTnaYWhoCDfffDMAIJfLYc+ePRXHiO9XSBOmyYB01zaQfn+xWMIpwxRu1t7ejjvvvFN8v0LNYjImWltbcdttt6XWVywinGDsbodLL73U+NTfvHkz5s2bJ75foWYxTQa0detWLFiwIL2+YtPic/WYkrTQZ39/P7e2tmoXUNSlWl1UManU60KfcWNfaHTJkiXc1NQU6T0R9EKfYgknFNPKFi0tLWhpaRmRJy4HoV6wdzBfcskl2LVrl3bftPiKRYQTgNXt0NXVhVNPPdW4ssWOHTuwYsUKcTkIQgmTr7ixsRHf/e53k+8rNpnI9ZjicEeI2yGdiDsiOXi5h1pbW7m/v39U5xN3REqxWrvTp0/Hvffei8cffxwLFizQuh3GjRsnkQ6C4AJdbPGtt96Ktra2in0TGVdsUud6TEFYwvaOg/7+fs/WLgAmIm1ZQjIQSzj5EJHx3hoNQVvCsQtfkpIXEXYrtk1NTdzS0qK9GHK5HI8bN07cDilERDj5FAoF7b2VzWb5vvvu823kiAgnQIT7+/srhLWhoYGbm5t9Wbt24Q7CbyWEi4hw8tHdW5lMZoQY+7nvxCecABYtWlQxUc7u3buxY8cOT+Xk83mtP0uiHQRh9Ojurbvvvhs33XQTiAjDw8Mj9o/LX5zYNebiwO0ac6b1sUx0dHRg+/btIzrgWltbRWxTjKwxl25Gs8Zd3awxl2RMcYkdHR3aiIalS5eKtSsICcJ0D7e1tUU/D4XJT1GPyYtP2OTHlYiG+kB8wulmNLHF0jGXABFm1kdHCPWDiHD6sd/D3/nOd1zNQxG0CItP2IJbn7AV8Q3WJ9LutYkbX7H4hAVBEELC5CsmIpxwwgnI5XKYPXs2crkc+vr6AjmniLAgCEIJ3ZzFmUwGxWIRTzzxxN6wtuHhYdxyyy2BCLGIsCAIQgldbPHKlSuRyeilcvny5aM+p4iwIAiCA+X5i3XYB3z4QRb6FARBKGFfSHdwcBBf//rXjftns9lRn1MsYUEQhBKLFi3STi1rEtuenp5Rn1NEWBAEAUCxWMTg4KBxW29v714xzmaz6O3txbJly0Z9XhFhQRDqEutCC5MmTcJBBx1k3Defz2PZsmXYs2cPHnvsMezZsycQAQbEJywIQh1i9/1u3LgRgFpId3h4eMTioWGvaCOWsCAIdcdXv/pVre934sSJuPPOOyOdbEssYUEQapaBgQEsWrQIQ0NDyOfzuPTSS/GnP/0JL730knb/DRs2oLu7O9IZDkWEBUGoSXThZr29vY7HmIYth4m4IwRBqElM4WbNzc246qqrErOauYiwIAg1x44dO4zhZjt37sSiRYsSs9CCiLAgCKnHGm7W3t6OKVOmGPctuxy6u7v3Dklet25dbCvdiE9YEIRUY/f9bt68GQDQ3t6OrVu3YufOnXv3jcvl4EQqLGEi+kciup+IXiEiJqIrHPY9nYh+S0Q7iGiQiL5ORKMf4C0IQuLYsmULLrzwQq3vd8yYMbjjjjsS4XJwIhUiDOACAJ0A/sNpJyL6CIAfAfg1gI8CWArg6wCuDrpC5defE088ccRigNbXokgWCRSEOsJ6f40fPx6TJ0/GW2+9pd13/fr1iXE5OGJa9yhJCUCm9DcHtebTFYb9fgvgcVveNwDsAjC52nlGu9Bnb2+vLABaJ8gac9HT39/PLS0tFeu/5XK5quvCBUldL/TpJMIAppW2XWDLP7CUf1618t2KcKFQ0DY6EWnz29vbjeIspBMR4fDQGSx/+MMfuK2tLRH3V9AinBZ3hBuOLP39b2smM78IYBuAI4I60dDQkDZf/daVvPnmmxU+q23btuFrX/saAHFhCEKZcifb4OAgmBmDg4P4zGc+g3e/+93YunWr9pjNmzcnJtzMD7UUHdFe+rtZs22zZfuoyefz2hjE8lpUbhkaGsKMGTPw+9//Hrt37wagRvVY5yi1DrlcvHhxai4sQfCDboBFsVgEEaGtrQ1btmypOCafz0c+1DhIIhdhIpoL4GEXuz7OzLNCrg6IqAdADwBMmjQJq1evrnrMOeecgyVLlowIfWlqasLJJ5+Mn/3sZxX5TU1NeOedd7RlrV27tiJv27Zt6OnpwfDw8N6yBgcHcf755+O5557D3LlzvXxFIQS2bNni6loRzDzyyCO4/fbbsXHjRnR2duJTn/qUcYAFAHzxi1/U3nfnnHNOpG0ReNub/BRhJQCtAA5zkfKaY518wh8tbTtOs20rgGur1c2tT5hZ77cy5Zs68pYsWaL1cTmlcpnSyRcv4hMeHbp7otp1Xz4u7mtfOubMIpwvbZtvy5+OgDvmrLhtENPFY+rkc0pNTU3SyRczIsKjo6urS3ttNzQ0JP76lo45A8w8BOAZAHbH0DkAdgN4IPJKWTDFKy5evFg7kUhHR4exLOvrGCCdfEKysV6TkydPxsyZM7Fhwwbtvnv27EnFAItAMalzkhKAGQDOBPApqKfjv5Y+nwmg1bLfKQCKAG4DMAvAlwDsgAtXBIdsCTvh1oXR3NzsaCGfeOKJibciagWxhN1hiu01pbBie4OkLt0RAO52aLjptn3PgLKIdwIYghqskXVznrhE2IROnP24L/L5fCJ8abWEiPBI7NfX3XffzT/60Y+MAjx+/PjUxs7XpQhHlZImwjpMnXzf/OY3HYXYPqooLRd8UhER3ofXTjZADWxKq2EgIlznIswcXCff5MmTeeXKlam8EeKmXkVYd+1NmTLF2Mk2YcKE1LodTIgIiwgbMVnJXoTZaiGn1VKJgiS1e1Tori/TUH2rtZtWt4MJEWERYUeC8CO3tbVxX19fhT8v7TdPkCSt3YPGfh2tXLmSJ02a5Ok6SlJsb5CICIsIeyYIC9l6Y9XaTeWHNLS7X/z4eGvN2nVC4oQFz3R3d2snOCkUCtr9x48fbyxrcHAQ55577ogJVnp6ejAwMCAxyilD117PPfccLrroIu0k6Sas11PdxPYGiUmd6zHVqiVswslf59WF0dLS4hijXGvWc5ra3W0cupN/F3Vo8ZoQd4SIcKA4zYERhAtjypQpvHLlypq7edPS7rp2bGxsNA78yWQyxnYWV5RCRFhEODKCGixisrDSfFMnrd11v+Pu3buN4WNObVWLEQ1BIiIsIhwrphu0o6NDe1Oblp4pp2w2q73ZncQ5CcIdV7u7dS1kMhluaGjw/MCs1YiGIBERFhGOHS/Tdfb39xtnzHKyxuzi3NLSUvU8UQpH2O3u9jfOZrOODzrTto6ODrF2fSIiLCKcWML2LxOR0bpzmovAj1XtNT/IsnST3lQTWz+uBbF2/SEiLCKcSoLyL3tNzc3NFcLd3NzMt956q7HD0LRqdrXVtN0e09zczJ/4xCe4sbFxRH4mk+HOzs7Avru4FsJBRFhEuGbw6l/u6uriyZMnhy7cTpalLr+trc24EnAUSVwL0SKDNYSawTSIZOnSpdqJ7r/1rW9hyZIlnifBDwp1L1WydetW40rAXiEiTJs2Tbuto6ND+92XLl0qgyXSjEmd6zGJJZwcvPpevVrVhUKB8/m8dlsmk/GU397ebjyPvYOxWn75+4gfN7mIO0JEWDDgNWrDix83SJ9wtbJM30VIBiLCIsKCR9IWHSEkm6BFmNR2AQBmzJjBTz/9tKdjVq9ejVmzZoVTISGxSLvXL37anojWMvMM3TbpmBMEQYgREWFBEIQYEREWBEGIERFhQRCEGBERFgRBiBERYUEQhBgRERYEQYgREWFBEIQYkcEaFojodQCDHg+bCOCNEKojJBtp9/rFT9sXmHl/3QYR4VFCRE+bRsIItYu0e/0SdNuLO0IQBCFGRIQFQRBiRER49CyPuwJCLEi71y+Btr34hAVBEGJELGFBEIQYERH2CBH9gIjeJKLJtvwsEf2aiP5ERC1x1U8QhOAhos8SERPRwUGXLSLsnYuglqNZZsv/MoD3AZjPzNsjr5UQOpYbUZf+O+76CekkF3cF0gYzbySiLwG4h4jOYuYfEtG7AFwB4DZmfjzeGgoRcBaADba8bXFUREg/IsI+YOaVRPRpADcR0WMA7gDwOoCvxFszISJ+x8x/jrsSQm0gIuyfzwP4I4BfATgIwMeY+a/xVkkQhLQhPmGfMPMQgJugBPg+Zv5pzFUSBCGFiAj7hIjGAZgH1Ul3DBGNjblKgiCkEBFh/1wLYAKAjwHoBHBNvNURBCGNiAj7gIhmAbgAwNeZ+QEAVwHoJaK/jbNegiCkDxFhj5QGYqwA8GsAS0vZ34bqpLudiBrjqpsgCOlDoiO8cyWAAoAzmLkIAMy8m4jmA/glgEUALo+xfoIghMfJRPSqLe9tZn7Yb4Eiwh4gohkAvgTgamb+g3UbM/8XES0FcCkR/Ssz/zGWSgqCECY3avL+COD/+C1QZlETBJcQ0WcB3AXgEBmsIQSFiLAgCEKMSMecIAhCjIgIC4IgxIiIsCAIQoyICAuCIMSIiLAgCEKMiAgLgiDEiIiwEBtE9OnS0kAzbfmTSvmvaY75Qmmb7+D4tEBERxHRFUTUHnddhPAQERbi5InS35m2/JlQywV1EtFhmm2boEYp1TpHQQ2BFxGuYUSEhdhg5pcA/AV6Ef65YdvxAH7BMsrIF0TUFHcdhJGICAtx8wSA44jIOo/JTABPAvgFLCJMRIcAmALgcSI6hoj+jYg2ENF2InqeiK4uzXJX3v9mInrNVjaIqImINpfm+ijn7U9EtxLRS0S0k4j+h4h6LNuPKblBPmH/AkS0jIheJ6IGS14PET1DRDuI6A0iusPuViCiHBF9lYieLe33OhH9jIgOswyRBoA/WVZ1nl46dhwR3UREL5fq+zwRfYmIyFL+rNIxZxDRCiJ6HUCFi0eIFxFhIW6eADAGwNEAQETjoSZDebKUjrfsO9NyTB7A7wAsAHAy1LSin8M+4QKAe6Em3D/Jds6PAxgPYGXpnOOgBP8UqFWzPwbgfgC3ENFFAMDMvwbwPIBzrAWVpi49G8AqZt5dyvsWgJsBPALgEwD+qVTHB4goazl8FYDFAH4K4HSoOaqfhXrQ/CfUPNWAWt35uFJ6hYgype3nAfgugFMB/AzAdaXy7NwIgKBWgvmsZrsQJ8wsSVJsCcCBUEtEfbn0+VQof3AjgHeVtk0vbbsHwNsAsrYyCGpGwHMAFAF0WLb9L4Dv2/b/DwDPWj7/M4AdUBPzWPdbAeANALnS50UAtgPYz7LP6aU6vr/0eTqAYQDfsJX1wdJ+p5c+n1j6fLHDb/PZ0j4H2/I/Xsr/rC3/dgA7AUwsfZ5V2u/f425nSeYklrAQK8z8IoAN2GflzgTwK2bexcz/C2CjbdtTzDxceh3/NhH9BUp4dkNZvgTgEMsp7gVwWnkNQCLqgLJ477XsczLUqtkvllwEuZIL40EAHQCOKO3XD6AJyjItMw/A88z8X6XPH4Z6wxywlfUrAH+1fJeToARyhcefrPw7FAH8iy2/H+rhdZwt/999nEOICBFhIQk8AeBDJX9m2R9c5hcAZhJRF5SVWY6ouAvKFXEDlPAdA+ALpW3NluP7S5/PLH0+G8pq7rfs01k6725b+mFpewcAMPNg6fzzgL2uk49hpKB3lv7+WVPe2HJZpb9vMvN2889ipL107C5b/quW7VZe8XEOISJkUnchCTwO4B8AfADKN/x1y7YnAfQBOKH0+QkiagZwGoArmNnaufZue8HM/CIRPQXlqrir9Hc1M6+37LYJyuL+oqF+z1v+vxfACiIqAPgIlOVpFfRNpb8nAdisKau8/Q0A7UTU4kOI3ywd22gT4smW7VYkkiTBiCUsJIGydXsplDvhl5Ztv4ByL3wKylf8ayiXQBbKurTyWUP5KwHMKi3QehxGWq6A6tQ6DMAQMz+tSX+17PtDKPdHN5RF/GTJQi7zMJSrIG8o68XSfg+Vvut8Q51ROg8AtNjyH4e6d8+y5XcD2IWRv5+QcMQSFmKHmf+HiDZCdcqtZeYtls2/BbCltO0xVhEIbxPRGgCXENErUFbl5wAcYDjFD6EiBPqhOtb+zbb9e1BuiieJ6HtQlm8blDAfz8ynWer6DhH9GMr1MQUqosH6Xf5CRN8GcBMRHQolmDsATINym9zOzI8x82NE9CMA1xHRNKi46AYot8h/MvNqqEgJAPgCEd0D9dD5PYAHoB5OtxLR/lADV06BEvRrmPkNw+8gJJG4ewYlSWJmQAklA7hOs+2h0rbLLXnTocTor1CuhJug/LMMYJZD+f9iOP8EKDF+Ecqa3AjlClmo2bd8nhGRErZ95gFYA2Ar1EPkuVIduyz75KAiLv63dM7XocLVDrXsczmAl6AiLqyRIuNK5b1SOvZ/odY/JMuxs0rHzI27fSWZkyxvJAiCECPiExYEQYgREWFBEIQYEREWBEGIERFhQRCEGBERFgRBiBERYUEQhBgRERYEQYgREWFBEIQYEREWBEGIkf8fnt6wtjAbtOwAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "silicon.scf_file = 'scf' # Tell which file was used \n", "\n", "silicon.pw_util = silicon.PW_utilities()\n", "ef0 = silicon.pw_util.efermi\n", "\n", "Band=plot_bands.plot_band_scf('./si/bs/bs.out') \n", "plot_bands.plot_band_prod(Band,\n", " ef0=6.45,\n", " xticks=['X','$\\Gamma$','L'],\n", " xlabel = 'Wavevector',\n", " ylabel = 'Energy (eV)', \n", " first = True,color_c= 'b',marker = 'o'\n", " )" ] }, { "cell_type": "markdown", "id": "84e8cfff", "metadata": {}, "source": [ "### Phonon dispersion relations\n", "\n", "To compute phonon-limited mobilities, we need to determine vibrational frequencies and eigenmodes. This operation consists of three steps\n", "1. We compute these properties on a uniform and centered Brillouin zone grid\n", "2. We perform a Fourier transform of the results in order to obtain the interatomic force constants (IFCs)\n", "3. We interpolate the IFCs along specified Brillouin zone paths to obtain phonon dispersions.\n", "\n", "This plot of phonon dispersions is only meant for us to develop a qualitative understanding of the vibrational properties of the system under consideration. The phonon interpolation needed for transport calculations is performed once again later by EPW." ] }, { "cell_type": "code", "execution_count": 6, "id": "8f6bcede-5ab2-4ef8-a6e7-a8ae66c983d1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-- -- -- -- -- -- -- -- -- -- -- Calculation: ph -- -- -- -- -- -- -- -- -- -- -- \n", "on 1: running: mpirun -np 1 /mnt/storage/sabya/For_video/epwpy/build/q-e-EPW-5.9s/bin/ph.x -pd .true. -nk 1 -nt 1 -in ph.in > ph.out\n", "Running ph |████████████████████████████████████████| in 15.2s (0.09/s) \n", "\n", "-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n" ] } ], "source": [ "silicon.ph(phonons={'fildyn':'\\'si.dyn\\'',\n", " 'qplot':'.true.',\n", " 'electron_phonon':'\\'prt\\'',\n", " 'fildvscf':'\\'dvscf\\''},\n", " qpoints={'nqs':3,\n", " 'qpoints':[[-0.5,0.5,0.5,'2'],\n", " [0,0,0,'2'],\n", " [1.0,0.0,0.0,'1']]})\n", "silicon.prepare(type_run='ph')\n", "silicon.run(1,type_run='ph')" ] }, { "cell_type": "code", "execution_count": 7, "id": "19c3e0f4", "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-- -- -- -- -- -- -- -- -- -- -- Calculation: ph2 -- -- -- -- -- -- -- -- -- -- -- \n", "on 1: running: mpirun -np 1 /mnt/storage/sabya/For_video/epwpy/build/q-e-EPW-5.9s/bin/ph.x -pd .true. -nk 1 -nt 1 -in ph2.in > ph2.out\n", "Running ph2 |████████████████████████████████████████| in 15.0s (0.09/s) \n", "\n", "-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n" ] } ], "source": [ "############Phonon run on a grid ############\n", "del silicon.ph_params['qplot'] \n", "del silicon.ph_params['electron_phonon'] \n", "silicon.ph_qpoints={}\n", "silicon.ph(phonons={'fildyn':'\\'si.dyn\\'',\n", " 'nq1':2,\n", " 'nq2':2,\n", " 'nq3':2,\n", " 'fildvscf':'\\'dvscf\\''},name = 'ph2')\n", "silicon.prepare(type_run='ph',infile = 'ph2.in',name='ph2')\n", "\n", "silicon.run(1,type_run='ph',infile = 'ph2',name='ph2')\n" ] }, { "cell_type": "markdown", "id": "02d67e82", "metadata": {}, "source": [ "We can plot the phonon spectra using the matdyn.x but we will directly plot the interpolated phonon spectra in a later step." ] }, { "cell_type": "markdown", "id": "cb059152", "metadata": {}, "source": [ "### Non-self consistent field (NSCF) calculations\n", "\n", "We now solve the non-self-consistent DFT calculation for a k-point grid of $4\\times4\\times4$" ] }, { "cell_type": "code", "execution_count": 8, "id": "ffcd0ce2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-- -- -- -- -- -- -- -- -- -- -- Calculation: nscf -- -- -- -- -- -- -- -- -- -- -- \n", "on 1: running: mpirun -np 4 /mnt/storage/sabya/For_video/epwpy/build/q-e-EPW-5.9s/bin/pw.x -nk 2 -nt 2 -in nscf.in > nscf.out\n", "Running nscf |████████████████████████████████████████| in 5.9s (0.26/s) \n", "\n", "-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n" ] } ], "source": [ "############nscf run############\n", "\n", "silicon.nscf(system={'nbnd':12},\n", " kpoints={'grid':[4,4,4],\n", " 'kpoints_type': 'crystal'})\n", "silicon.prepare(type_run='nscf')\n", "silicon.run(4,type_run='nscf')\n" ] }, { "cell_type": "markdown", "id": "529baaa5", "metadata": {}, "source": [ "### Wannierization of electronic and phonon part (EPW I)\n", "\n", "Now, we have the phonon spectra, the dynamical matrices, and the electron-phonon interactions.\n", "We next interpolate these using the EPW code (https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.89.015003). \n", "The first step consists of finding the Wannier functions.\n", "In the second step one uses the Wannier functions for obtaining electron-phonon matrix elements on a fine grid.\n", "We also use a scissor shifted eigenvalue file for interpolation si.eig\n" ] }, { "cell_type": "code", "execution_count": 9, "id": "ae1c7413", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "obtaining nscf and ph attributes\n", "(4, 3)\n", "[51, 51, 51]\n", "-- -- -- -- -- -- -- -- -- -- -- Calculation: epw1 -- -- -- -- -- -- -- -- -- -- -- \n", "on 1: running: mpirun -np 1 /mnt/storage/sabya/For_video/epwpy/build/q-e-EPW-5.9s/bin/epw.x -nk 1 -in epw1.in > epw1.out\n", "Running epw1 |████████████████████████████████████████| in 34.4s (0.04/s) \n", "\n", "-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n" ] } ], "source": [ "############epw run############\n", "\n", "########Generate epw1 file############\n", "silicon.reset()\n", "silicon.epw(epwin={'wdata':['guiding_centres = .true.',\n", " 'dis_num_iter = 500',\n", " 'num_print_cycles = 10',\n", " 'dis_mix_ratio = 1',\n", " 'use_ws_distance = T'],\n", " 'proj':['\\'Si : sp3\\''],\n", " 'band_plot':'.true.',\n", " 'filkf':'\\'LGX.txt\\'',\n", " 'filqf':'\\'LGX.txt\\'', \n", " 'prtgkk':'.true.', \n", " 'fsthick':'10',\n", " 'calc_nelec_wann':'.false.'},\n", " name='epw1')\n", "\n", "######################################################################################\n", "######## Generate filkf if needed with the same name as the filkf key above##########\n", "silicon.filkf(path=[[0.5,0.5,0.5],\n", " [0,0,0],[0.0,0.5,0.5]],length=[51,51],name='LGX.txt')\n", "######################################################################################\n", "\n", "silicon.prepare(0,type_run='epw1') \n", "silicon.run(1,type_run='epw1')\n" ] }, { "cell_type": "markdown", "id": "1420b1e0", "metadata": {}, "source": [ "### Plot electron and phonon dispersion obtained from EPW\n", "\n", "At this point, we plot the electronic and phonon bandstructure obtained from the Wannier interpolation" ] }, { "cell_type": "code", "execution_count": 11, "id": "dfe583d4", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "silicon.pw_util = silicon.PW_utilities()\n", "ef_from_file = silicon.pw_util.efermi \n", "silicon.prefix='si'\n", "\n", "Band_QE=plot_bands.plot_band_scf(f'./{silicon.prefix}/bs/bs.out')\n", "Band_EPW=plot_bands.plot_band_eig(f'./{silicon.prefix}/epw/band.eig')\n", "\n", "xticks=['X','$\\Gamma$','L']\n", "ef0=6.2757\n", "plot_bands.plot_band_prod(Band_EPW,\n", " ef0=ef_from_file,\n", " xlabel='Wavevector', \n", " ylabel='Electron energy (eV)',\n", " xticks=['L','$\\Gamma$','X'],linestyle='--',color_c='b',color_v='b',first = True)\n", "plot_bands.plot_band_prod(Band_QE,\n", " ef0=ef_from_file,\n", " xlabel='Wavevector', \n", " ylabel='Electron energy (eV)',\n", " xticks=['L','$\\Gamma$','X'],first = False) # False controls if this is the first set of plots \n", "\n", "\n", "####Phonon from EPW #################\n", "#######inputs###############\n", "Band_EPW = plot_bands.plot_band_eig(f'./{silicon.prefix}/epw/phband.freq')\n", "xticks=['L','$\\Gamma$','X']\n", "ef0=0\n", "plot_bands.plot_band_freq(Band_EPW,xticks=xticks,color='red')\n", "############################\n" ] }, { "cell_type": "markdown", "id": "c3835227", "metadata": {}, "source": [ "### Electron-phonon matrix elements with EPW and PH\n", "\n", "We can also plot the electron-phonon matrix elements and compare with QE. " ] }, { "cell_type": "code", "execution_count": 17, "id": "3d5dd3d4", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from EPWpy.plotting import plot_g\n", "\n", "silicon.ph_fold = 'ph' # Folder in which the path calculation of Phonon was performed\n", "silicon.ph_file = 'ph' # Phonon output file which contaions the e-p coupling\n", "silicon.EPW_util = silicon.EPW_utilities()\n", "silicon.PH_util = silicon.PH_utilities()\n", "g_noquad=silicon.EPW_util.gkk\n", "g_ph = silicon.PH_util.gkk\n", "xticks=['L','$\\Gamma$','X']\n", "\n", "# this function takes ibnd,jbnd,g,ik #\n", "plot_g.plot_gkk_mode_q(0,0,g_noquad,ik=49,color='crimson')\n", "plot_g.plot_gkk_mode_q(0,0,g_ph,ik=0,color='royalblue',linestyle=' ',marker='o',\n", " xticks=['L','G','X'],ylabel='e-p coupling (meV)',first = False)\n", "\n" ] }, { "cell_type": "markdown", "id": "2e6dde38-0d43-4d3b-aa1e-8871e6ff3953", "metadata": {}, "source": [ "### Effect of quadrupoles on the interpolation quality\n", "\n", "Even in the case of non-polar materials such as Silicon, the material has a non-zero quadrupole tensor, which generate long-range fields.\n", "These long-range component should be removed before performing the Wannier/Fourier interpolation for an accurate interpolation. \n", "\n", "See https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.043022 (for 3D materials) and https://journals.aps.org/prb/abstract/10.1103/PhysRevB.107.155424 (for 2D materials) for more information. \n", "\n", "To include quadrupole, we need to provide a quadrupole.fmt file which could be computed with the Abinit software. \n", "To compute the quadrupole with Abinit and convert them in EPW/QE format, you can follow the tutorial at https://docs.abinit.org/tutorial/lw_quad/\n" ] }, { "cell_type": "code", "execution_count": 18, "id": "2d87bdb1-b1f2-4a8d-b059-2f3c1a21111b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(4, 3)\n", "[51, 51, 51]\n", "-- -- -- -- -- -- -- -- -- -- -- Calculation: epw2 -- -- -- -- -- -- -- -- -- -- -- \n", "on 1: running: mpirun -np 1 /mnt/storage/sabya/For_video/epwpy/build/q-e-EPW-5.9s/bin/epw.x -nk 1 -in epw2.in > epw2.out\n", "Running epw2 |████████████████████████████████████████| in 7.0s (0.21/s) \n", "\n", "-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n" ] } ], "source": [ "############epw run############\n", "\n", "########Generate epw2 file############\n", "PWD=os.getcwd()\n", "silicon.epw(epwin={'wdata':['guiding_centres = .true.',\n", " 'dis_num_iter = 500',\n", " 'num_print_cycles = 10',\n", " 'dis_mix_ratio = 1',\n", " 'use_ws_distance = T'],\n", " 'proj':['\\'Si : sp3\\''],\n", " 'band_plot':'.true.',\n", " 'filkf':'\\'LGX.txt\\'',\n", " 'filqf':'\\'LGX.txt\\'', \n", " 'prtgkk':'.true.', \n", " 'fsthick':'10'},\n", " name='epw2')\n", "\n", "######################################################################################\n", "######## Generate filkf if needed with the same name as the filkf key above##########\n", "silicon.transfer_file=[f'{PWD}/quadrupole.fmt']\n", "silicon.filkf(path=[[0.5,0.5,0.5],\n", " [0,0,0],[0.0,0.5,0.5]],length=[51,51],name='LGX.txt')\n", "######################################################################################\n", "\n", "silicon.prepare(0,type_run='epw2') \n", "silicon.run(1,type_run='epw2')" ] }, { "cell_type": "markdown", "id": "7f26b644-b2cb-4912-a931-7999ec2df86f", "metadata": {}, "source": [ "\n", "\n", "By looking at the epw2.out, you can verify that the quadrupole was correctly read by looking at the following lines:\n", "\n", " ------------------------------------\n", " Quadrupole tensor is correctly read: \n", " ------------------------------------ \n", " atom dir Qxx Qyy Qzz Qyz Qxz Qxy\n", " 1 x 0.00000 0.00000 0.00000 13.66000 0.00000 0.00000\n", " 1 y 0.00000 0.00000 0.00000 0.00000 13.66000 0.00000\n", " 1 z 0.00000 0.00000 0.00000 0.00000 0.00000 13.66000\n", " 2 x 0.00000 0.00000 0.00000 -13.66000 0.00000 0.00000\n", " 2 y 0.00000 0.00000 0.00000 0.00000 -13.66000 0.00000\n", " 2 z 0.00000 0.00000 0.00000 0.00000 0.00000 -13.66000\n", "\n", "\n" ] }, { "cell_type": "markdown", "id": "1d5f8e8c-8c0c-4b36-bd9f-d32a9faf9aa0", "metadata": {}, "source": [ "### Electron-phonon matrix elements with EPW\n", "\n", "We can also plot the electron-phonon matrix elements. " ] }, { "cell_type": "code", "execution_count": 21, "id": "c43cf301-c3c6-464f-90ed-503cadc9454c", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "\n", "silicon.EPW_util2 = silicon.EPW_utilities()\n", "g_quad = silicon.EPW_util2.gkk # e-p matrix with quadrupole correction\n", "\n", "xticks=['L','$\\Gamma$','X']\n", "plot_g.plot_gkk_mode_q(0,0,g_noquad,ik=49,color='crimson')\n", "plot_g.plot_gkk_mode_q(0,0,g_quad,ik=49,color='royalblue',linestyle='--',\n", " ylabel='e-p coupling (meV)',first = False,xticks=xticks)\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "id": "708a610b", "metadata": {}, "outputs": [], "source": [ "\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": {}, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 5 }