{ "cells": [ { "cell_type": "markdown", "id": "e69d043c", "metadata": {}, "source": [ "# 1.4.2 EPCE and ZPR using FP: Post-processing the inputs.\n", "In this step we would write a post-processing script to compute electron-phonon coupling energies (EPCE), zero-point renormalization (ZPR) or renormalization at finite temperature.\n", "\n", "We need electron-phonon from finite difference (epfd) module, numpy and os. Lets import them first.\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "dc33cf46", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " \n", " ███████████ \n", " ░░███░░░░░███ \n", " ░███ ░███ █████ ████ \n", " ░██████████ ░░███ ░███ \n", " ░███░░░░░░ ░███ ░███ \n", " ░███ ░███ ░███ \n", " █████ ░░███████ \n", " ░░░░░ ░░░░░███ \n", " ███ ░███ \n", " ░░██████ \n", " ░░░░░░ \n", " ██████████ ███████████ ███████████ ██████████ \n", "░░███░░░░░█░░███░░░░░███░░███░░░░░░█░░███░░░░███ \n", " ░███ █ ░ ░███ ░███ ░███ █ ░ ░███ ░░███\n", " ░██████ ░██████████ ░███████ ░███ ░███\n", " ░███░░█ ░███░░░░░░ ░███░░░█ ░███ ░███\n", " ░███ ░ █ ░███ ░███ ░ ░███ ███ \n", " ██████████ █████ █████ ██████████ \n", "░░░░░░░░░░ ░░░░░ ░░░░░ ░░░░░░░░░░ \n", "PyEPFD version : 1.1\n", "Author : Arpan Kundu\n", "Author Email : arpan.kundu@gmail.com\n", "Today : 2024-12-18 17:25:04.685580\n", "*************************************************\n", " CITATIONS \n", "=================================================\n", "Please cite the following 3 references: \n", "(1) A. Kundu et al, Phys. Rev. Mater (2021), 5, \n", "L070801, \n", "(2) A. Kundu and G Galli, \n", "J. Chem. Theory. Comput. (2023), 19, 4011\n", "(3) https://pyepfd.readthedocs.io/en/latest/\n", "*************************************************\n" ] } ], "source": [ "import os\n", "import numpy as np\n", "import pyepfd.epfd as ep" ] }, { "cell_type": "markdown", "id": "09a0ce11", "metadata": {}, "source": [ "Now we will define the directories where all input files are present as well as where the outputs would be written. Within the electron-phonon class there are objects \"inp_dir\" and \"out_dir\" for that purpose. Our input directory is the current one, i.e. \"./\", lets name the output directory as \"epfd_out\". We further tell that if epfd_directory does not exist then it will create that directory\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "b9988a18", "metadata": {}, "outputs": [], "source": [ "ep.inp_dir = \"./\"\n", "ep.out_dir = \"epfd_out\"\n", "if not os.path.isdir(ep.out_dir):\n", " os.system(\"mkdir \"+ep.out_dir)" ] }, { "cell_type": "markdown", "id": "ddbc442f", "metadata": {}, "source": [ "Now we will define a linear temperature grid from 0.0 K to 1100.0 K with 111 points in it. We will use temp_grid method available within ep class defined above. " ] }, { "cell_type": "code", "execution_count": 3, "id": "a84cbb54", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0. 10. 20. 30. 40. 50. 60. 70. 80. 90. 100. 110.\n", " 120. 130. 140. 150. 160. 170. 180. 190. 200. 210. 220. 230.\n", " 240. 250. 260. 270. 280. 290. 300. 310. 320. 330. 340. 350.\n", " 360. 370. 380. 390. 400. 410. 420. 430. 440. 450. 460. 470.\n", " 480. 490. 500. 510. 520. 530. 540. 550. 560. 570. 580. 590.\n", " 600. 610. 620. 630. 640. 650. 660. 670. 680. 690. 700. 710.\n", " 720. 730. 740. 750. 760. 770. 780. 790. 800. 810. 820. 830.\n", " 840. 850. 860. 870. 880. 890. 900. 910. 920. 930. 940. 950.\n", " 960. 970. 980. 990. 1000. 1010. 1020. 1030. 1040. 1050. 1060. 1070.\n", " 1080. 1090. 1100.]\n" ] } ], "source": [ "T = ep.temp_grid( T_start = 0.0, T_end = 1100.0, NT = 111 )\n", "print(T)" ] }, { "cell_type": "markdown", "id": "964e2f22", "metadata": {}, "source": [ "Now we will define a \"homo\" class with the available input files using frozen-phonon harmonic class (fph) available within epfd object (imported here as ep). HOMO is 2-fold degenerate at equilibrium geometry, however, when we displace it degeneracies may be lost. In the displaced cooddinates we will assume them to be degenerate if the energy difference is less than 0.002 eV.\n", "\n", "After defining the homo class, we will compute the renormalized band energies using a method named eigval_at_temp. This will create a list of renormalized eigenvalues / band energies and store them within an object homo.renorm_eigval" ] }, { "cell_type": "code", "execution_count": 4, "id": "17ea109c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Process-id0: Time spent on read_pyepfd_info class: 0.0012581348419189453 s.\n", "ZPR (meV) for homo:\n", "Orbital-7 49.63074301665274\n", "Orbital-8 58.95381558176698\n" ] } ], "source": [ "homo = ep.fph(phonon_info_file='enmfdphonon.xml',\n", " eigval_file = \"homo.eigval.dat\",\n", " overlap_file = \"orbital-0.overlap\",\n", " degeneracy_cutoff = 0.002,\n", " output_prefix = \"homo\"\n", " )\n", "homo.eigval_at_temp(T)\n", "\n", "#print(\"\\nRenormalized Eigenvalues for band 7 & 8\\n\")\n", "#print(homo.renorm_eigval)\n", "# deleting the homo object for completeing file writing\n", "del homo" ] }, { "cell_type": "markdown", "id": "bb40fe92", "metadata": {}, "source": [ "Similarly we can compute the renormalized energies for LUMO. We do not need overlap_file as it is singly degenerate at equilibrium geometry. Neither we do need the degeneracy cutoff." ] }, { "cell_type": "code", "execution_count": 5, "id": "0640d68f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Process-id0: Time spent on read_pyepfd_info class: 0.0004923343658447266 s.\n", "ZPR (meV) for lumo:\n", "Orbital-9 -88.48019533017887\n" ] } ], "source": [ "lumo = ep.fph(\n", " phonon_info_file='enmfdphonon.xml',\n", " eigval_file = \"lumo.eigval.dat\",\n", " output_prefix = \"lumo\"\n", " )\n", "lumo.eigval_at_temp(T)\n", "\n", "#print(\"\\nRenormalized Eigenvalues for band 9\\n\")\n", "#print(lumo.renorm_eigval)\n", "# deleting lumo object for completing file writing\n", "del lumo" ] }, { "cell_type": "markdown", "id": "21f4ab45", "metadata": {}, "source": [ "Now we have obtained two ZPR values for HOMO, 49 meV and 59 meV. This is because of splitting of degeneracy. The average HOMO renormalization without considering the splitting would be (49+59)/2 meV = 54 meV. \n", "Now let us have a look at the directory epfd_out\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "574eb3f8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "homo.epce.dat\n", "homo.pyepfd.log\n", "homo.tscan.eigval\n", "lumo.epce.dat\n", "lumo.pyepfd.log\n", "lumo.tscan.eigval\n" ] } ], "source": [ "%%bash\n", "ls epfd_out/" ] }, { "cell_type": "markdown", "id": "774bcff6", "metadata": {}, "source": [ "homo.epce.dat file contains the electron-phonon coupling energy for band 7 and 8 along each mode. homo.tscan.eigval contains the renormalized band-energies. " ] }, { "cell_type": "code", "execution_count": 7, "id": "0cb479d6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "# Column-1 ==> Normal Mode Number\n", "# Column-2 ==> Normal Mode Frequency (cm-1)calculated based on normal mode hessian.\n", "# Column-3 ==> EPCE: value(meV) [percentage] for Orbital-7\n", "# Column-4 ==> EPCE: value(meV) [percentage] for Orbital-8\n", " 6 676.086354 10.7385 [ 10.818 ] 20.0616 [ 17.015 ] \n", " 7 676.087602 10.7386 [ 10.818 ] 20.0617 [ 17.015 ] \n", " 8 1345.456097 0.499236 [ 0.503 ] 0.499236 [ 0.423 ] \n", " 9 2361.832806 77.2852 [ 77.860 ] 77.2852 [ 65.547 ] \n", "# EPCE SUM (meV) = 99.2615 [ 100.000 ] 117.908 [ 100.000 ] \n", "# ZPR (meV) = 49.6307 [ 100.000 ] 58.9538 [ 100.000 ] \n", "\n" ] } ], "source": [ "homo_epce_file = open(\"epfd_out/homo.epce.dat\",\"r\").read()\n", "print(homo_epce_file) " ] }, { "cell_type": "code", "execution_count": 8, "id": "c8f32f2d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "# Thermally averaged energies (eV) are sorted in increasing order.\n", "# Column-1 ==> Temperature(K)\n", "# Column-2 ==> Orbital-7\n", "# Column-3 ==> Orbital-8\n", " 0.00 -10.459491 -10.450168 \n", " 10.00 -10.459491 -10.450168 \n", " 20.00 -10.459491 -10.450168 \n", " 30.00 -10.459491 -10.450168 \n", " 40.00 -10.459491 -10.450168 \n", " 50.00 -10.459491 -10.450168 \n" ] } ], "source": [ "%%bash\n", "head epfd_out/homo.tscan.eigval" ] }, { "cell_type": "markdown", "id": "8e92984d", "metadata": {}, "source": [ "We can plot the band gap renormalization as a function of temperature using tscan.eigval files." ] }, { "cell_type": "code", "execution_count": 9, "id": "63f86355", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "static_gap = 9.5794 ### in eV; clamped nuclei\n", "homo = np.genfromtxt(\"epfd_out/homo.tscan.eigval\")\n", "temp = homo[:,0] #First column is temperature\n", "### Average energy of orbitals 7 and 8; called center gap\n", "homo_center = 0.5*(homo[:,1] + homo[:,2])\n", "homo_edge = homo[:,2]\n", "# 2nd column of the following file have LUMO energies\n", "lumo = np.genfromtxt(\"epfd_out/lumo.tscan.eigval\")[:,1]\n", "#Renormalized band gap without considering degeneracy lifting\n", "gap_center = lumo - homo_center\n", "renorm_center = (gap_center - static_gap) * 1000 #eV to meV\n", "#Renormalized band gap when splitting is considered; i.e.\n", "# shortest band gap\n", "gap_edge = lumo - homo_edge\n", "renorm_edge = (gap_edge - static_gap) * 1000 #ev to meV\n", "\n", "## plotting\n", "plt.xlabel(\"Temperature (K)\")\n", "plt.ylabel(\"Gap renorm. (meV)\")\n", "plt.plot(temp,renorm_center,label=\"Center\")\n", "plt.plot(temp,renorm_edge,label=\"Edge\")\n", "plt.legend()\n", "plt.show()" ] } ], "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }