{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Back to the main [Index](../index.ipynb) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Bethe-Salpeter calculations with AbiPy and Abinit" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This lesson discusses how to calculate the macroscopic dielectric function, $\\epsilon_\\infty(\\omega)$, including excitonic effects within the Bethe-Salpeter equation (BSE). \n", "Crystalline silicon is used as test case. \n", "\n", "For a more detailed description of the Abinit implementation, see the official Abinit \n", "[BSE tutorial](https://docs.abinit.org/tutorial/bse/).\n", "A brief description of the formalism can be found in the [BSE_notes](https://docs.abinit.org/theory/bse/).\n", "\n", "## Table of Contents\n", "[[back to top](#top)]\n", "\n", "- [Typical BSE flowchart](#Typical-BSE-flowchart)\n", "- [AbiPy flow for BSE with the model dielectric function](#AbiPy-flow-for-BSE-with-the-model-dielectric-function)\n", "- [Analyzing the results](#Analyzing-the-results)\n", "- [Converge study with respect to the $k$ point sampling](#Converge-study-with-respect-to-the-$k$-point-sampling)\n", "- [Exercises](#Exercises)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Typical BSE flowchart \n", "[[back to top](#top)]\n", "\n", "The flowchart of a typical Bethe-Salpeter run is schematically depicted in the diagram below: " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"bse_flowchart\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The WFK file (KSS file in old versions of Abinit) contains the Kohn-Sham (KS) wavefunctions and energies and is represented with an ellipsis. \n", "The path on the left indicated with blue arrows represents the RPA calculation (`optdriver=3`) that produces the SCR file (see also the first lesson of the $GW$ tutorial). \n", "Once the WFK (KSS) and the SCR file are available, we can finally contruct the BSE Hamiltonian \n", "and solve the Bethe-Salpeter problem (the green rectangle at the bottom of the flowchart).\n", "The construction of the Bethe-Salpeter Hamiltonian represents a significant portion of the overall CPU time due to the large number of transitions (bands and in particular $k$-points) needed for an accurate description of the frequency-dependence of the polarizability.\n", "\n", "For BSE computations, it is common practice to simulate the self-energy corrections by employing the scissors operator whose value can be obtained either from experiments or from *ab-initio* calculations. The scissors operator allows one to avoid a costly $GW$ calculation that should performed for all the $k$-points and bands included in the transition space (the optional path on the right indicated with yellow arrows that corresponds to `optdriver=4`).\n", "\n", "For this reason, in this lesson, we will employ two commonly used approximations that will\n", "reduce considerably the computational cost of the BSE flowchart while giving reasonably accurate results:\n", "\n", " * The *ab-initio* $W$ is replaced by a model dielectric function \n", " that is constructed from the GS density $n(r)$ and the additional variable `mdf_epsinf`\n", " that gives the value of the static limit $\\epsilon_\\infty(\\omega=0)$.\n", " This approximation allows us to bypass the blue boxes in the diagram above (`optdriver=3`)\n", " \n", " * The modifications introduced by the $GW$ self-energy on the initial KS band structure\n", " are approximated with a scissor operator (`mbpt_sciss`).\n", " This approximation allows us to bypass the yellow boxes in the diagram above (`optdriver=4`).\n", " \n", "Under these assumptions, the BSE flowchart reduces to a simple GS-SCF run to get $n(r)$ plus\n", "a NSCF calculation of the band structure on a dense $k$-mesh and, finally, the solution\n", "of the BSE problem (the green box)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## AbiPy flow for BSE with the model dielectric function\n", "[[back to top](#top)]\n", "\n", "After the standard imports:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\") # to get rid of deprecation warnings\n", "\n", "import abipy.abilab as 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", "metadata": {}, "source": [ "We import from `lesson_bse` the function that builds the 3 input objects we are going to use to build the `Flow`:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "

\n", "\n", "
def make_scf_nscf_bse_inputs(ngkpt=(6, 6, 6), ecut=6, ecuteps=3,\n",
       "                             mdf_epsinf=12.0, mbpt_sciss="0.8 eV"):\n",
       "    """\n",
       "    Build and returns three `AbinitInput` objects to perform a\n",
       "    GS-SCF + GS-NSCF + BSE calculation with model dielectric function.\n",
       "\n",
       "    Args:\n",
       "        ngkpt: Three integers giving the number of divisions for the k-mesh.\n",
       "        ecut: Cutoff energy for the wavefunctions.\n",
       "        ecuteps: Cutoff energy for the screened interation W_{GG'}.\n",
       "        mdf_epsinf: Static limit of the macroscopic dielectric functions.\n",
       "            Used to build the model dielectric function.\n",
       "        mbpt_sciss: Scissors operator energy (used to open the initial KS gap).\n",
       "    """\n",
       "    multi = abilab.MultiDataset(structure=abidata.structure_from_ucell("Si"),\n",
       "                                pseudos=abidata.pseudos("14si.pspnc"), ndtset=3)\n",
       "    multi.set_mnemonics(True)\n",
       "\n",
       "    # Variables common to the three datasets.\n",
       "    multi.set_vars(\n",
       "        ecut=ecut,\n",
       "        nband=8,\n",
       "        istwfk="*1",\n",
       "        diemac=12.0,\n",
       "        #iomode=3,\n",
       "    )\n",
       "\n",
       "    # SCF run to get the density.\n",
       "    multi[0].set_vars(tolvrs=1e-8)\n",
       "    multi[0].set_kmesh(ngkpt=ngkpt, shiftk=(0, 0, 0))\n",
       "\n",
       "    # NSCF run on a randomly shifted k-mesh (improve the convergence of optical properties)\n",
       "    multi[1].set_vars(\n",
       "        iscf=-2,\n",
       "        nband=15,\n",
       "        tolwfr=1e-8,\n",
       "        chksymbreak=0,  # Skip the check on the k-mesh.\n",
       "    )\n",
       "\n",
       "    # This shift breaks the symmetry of the k-mesh.\n",
       "    multi[1].set_kmesh(ngkpt=ngkpt, shiftk=(0.11, 0.21, 0.31))\n",
       "\n",
       "    # BSE run with Haydock iterative method (only resonant + W + v)\n",
       "    multi[2].set_vars(\n",
       "        optdriver=99,                 # BS calculation\n",
       "        chksymbreak=0,                # To skip the check on the k-mesh.\n",
       "        bs_calctype=1,                # L0 is constructed with KS orbitals and energies.\n",
       "        mbpt_sciss=mbpt_sciss,        # Scissors operator used to correct the KS band structure.\n",
       "        bs_exchange_term=1,           # Exchange term included.\n",
       "        bs_coulomb_term=21,           # Coulomb term with model dielectric function.\n",
       "        mdf_epsinf=mdf_epsinf,        # Parameter for the model dielectric function.\n",
       "        bs_coupling=0,                # Tamm-Dancoff approximation.\n",
       "        bs_loband=2,                  # Lowest band included in the calculation\n",
       "        nband=6,                      # Highest band included in the calculation\n",
       "        bs_freq_mesh="0 6 0.02 eV",   # Frequency mesh for the dielectric function\n",
       "        bs_algorithm=2,               # Use Haydock method.\n",
       "        zcut="0.15 eV",               # Complex shift to avoid divergences in the continued fraction.\n",
       "        ecutwfn=ecut,                 # Cutoff for the wavefunction.\n",
       "        ecuteps=ecuteps,              # Cutoff for W and /bare v.\n",
       "        inclvkb=2,                    # The commutator for the optical limit is correctly evaluated.\n",
       "    )\n",
       "\n",
       "    # Same shift as the one used in the previous dataset.\n",
       "    multi[2].set_kmesh(ngkpt=ngkpt, shiftk=(0.11, 0.21, 0.31))\n",
       "\n",
       "    scf_input, nscf_input, bse_input = multi.split_datasets()\n",
       "\n",
       "    return scf_input, nscf_input, bse_input\n",
       "
\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from lesson_bse import make_scf_nscf_bse_inputs\n", "abilab.print_source(make_scf_nscf_bse_inputs)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "scf_inp, nscf_inp, bse_inp = make_scf_nscf_bse_inputs(ngkpt=(4, 4, 4), ecut=6, ecuteps=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function `make_scf_nscf_bse_inputs` returns three `AbinitInput` objects:\n", "\n", " * The first input (`scf_inp`) solves the KS equations on a Monkhorst-Pack mesh \n", " to obtain the groud-state density $n(r)$.\n", "\n", " * The second input (`nscf_inp`) uses the density produced by `scf_inp` to compute \n", " the KS band structure on a **randomly-shifted** $k$-mesh in order to accelerate \n", " the convergence of the optical properties with respect to the $k$-sampling.\n", "\n", " * Finally, the third input (`bse_inp`) uses the `WFK` file produced in the previous step \n", " to solve an approximated BSE equation in which the ab-initio \n", " screened interation $W$ is approximated\n", " by a model dielectric function that depends only on $n(r)$ and the input variable `mdf_epsinf`\n", " that gives the value of $\\epsilon_\\infty(0)$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The variables governing the BSE run are those in the `vargw` section of `bse_inp`:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "############################################################################################
# SECTION: basic
############################################################################################
# <Energy CUToff>
ecut 6
# <Number of BANDs>
nband 6
# <Number of Grid points for K PoinTs generation>
ngkpt 4 4 4
# <KPoinTs OPTion>
kptopt 1
# <Number of SHIFTs for K point grids>
nshiftk 1
# <SHIFT for K points>
shiftk 0.11 0.21 0.31
############################################################################################
# SECTION: bse
############################################################################################
# <Bethe-Salpeter CALCulation TYPE>
bs_calctype 1
# <Bethe-Salpeter EXCHANGE TERM>
bs_exchange_term 1
# <Bethe-Salpeter COULOMB TERM>
bs_coulomb_term 21
# <Bethe-Salpeter COUPLING>
bs_coupling 0
# <Bethe-Salpeter Lowest Occupied BAND>
bs_loband 2
# <Bethe-Salpeter FREQuency MESH>
bs_freq_mesh 0 6 0.02 eV
# <Bethe-Salpeter ALGORITHM>
bs_algorithm 2
############################################################################################
# SECTION: dev
############################################################################################
# <Integer for choice of STorage of WaveFunction at each k point>
istwfk *1
############################################################################################
# SECTION: gstate
############################################################################################
# <model DIElectric MACroscopic constant>
diemac 12.0
# <OPTions for the DRIVER>
optdriver 99
# <CHecK SYMmetry BREAKing>
chksymbreak 0
############################################################################################
# SECTION: gw
############################################################################################
# <Many Body Perturbation Theory SCISSor operator>
mbpt_sciss 0.8 eV
# <Model Dielectric Function, EPSilon INFinity>
mdf_epsinf 12.0
# <Z-CUT>
zcut 0.15 eV
# <Energy CUT-off for WaveFunctioNs>
ecutwfn 6
# <Energy CUT-off for EPSilon (the dielectric matrix)>
ecuteps 3
# <INCLude VKB>
inclvkb 2
############################################################################################
# STRUCTURE
############################################################################################
# <Number of ATOMs>
natom 2
# <Number of TYPes of AToms>
ntypat 1
# <TYPe of AToms>
typat 1 1
# <charge -Z- of the NUCLeus>
znucl 14
# <vectors (X) of atom positions in REDuced coordinates>
xred
0.0000000000 0.0000000000 0.0000000000
0.2500000000 0.2500000000 0.2500000000
# <CELL lattice vector scaling>
acell 1.0 1.0 1.0
# <Real space PRIMitive translations>
rprim
0.0000000000 5.1085000000 5.1085000000
5.1085000000 0.0000000000 5.1085000000
5.1085000000 5.1085000000 0.0000000000" ], "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bse_inp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once we have our three input objects, we can create a flow to automate the calculation.\n", "Note that AbiPy already provides the `BseMdfWork` class that is explicitly designed for this kind of calculation:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "

\n", "\n", "
def build_bse_flow(options):\n",
       "    """\n",
       "    Build a flow to solve the BSE with default parameters.\n",
       "\n",
       "    Args:\n",
       "        options: Command line options.\n",
       "\n",
       "    Return:\n",
       "        Flow object.\n",
       "    """\n",
       "    workdir = options.workdir if (options and options.workdir) else "flow_bse"\n",
       "    flow = flowtk.Flow(workdir=workdir)\n",
       "\n",
       "    # Build a Work for BSE calculation with the model dielectric function ...\n",
       "    scf_inp, nscf_inp, bse_inp = make_scf_nscf_bse_inputs()\n",
       "\n",
       "    work = flowtk.BseMdfWork(scf_inp, nscf_inp, bse_inp)\n",
       "\n",
       "    # and add it to the flow\n",
       "    flow.register_work(work)\n",
       "\n",
       "    return flow\n",
       "
\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from lesson_bse import build_bse_flow\n", "abilab.print_source(build_bse_flow)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's build the flow:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "flow = build_bse_flow(options=None)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The graphical representation of the flow reveals that the `BseTask` depends on the `NscfTask` that \n", "in turns depends on the initial `ScfTask`." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "flow\n", "\n", "Flow, node_id=345805, workdir=flow_bse\n", "clusterw0\n", "\n", "BseMdfWork (w0)\n", "\n", "\n", "w0_t0\n", "\n", "w0_t0\n", "ScfTask\n", "\n", "\n", "w0_t1\n", "\n", "w0_t1\n", "NscfTask\n", "\n", "\n", "w0_t0->w0_t1\n", "\n", "\n", "DEN\n", "\n", "\n", "w0_t2\n", "\n", "w0_t2\n", "BseTask\n", "\n", "\n", "w0_t1->w0_t2\n", "\n", "\n", "WFK\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "flow.get_graphviz()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "#flow.plot_networkx(with_edge_labels=True);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you are working with python, you can build the directories of the Flow with:\n", "\n", " flow.build_and_pickle_dump()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now you can execute the lesson_bse.py script to generate the flow and then use:\n", "\n", " abirun.py flow_bse scheduler\n", " \n", "
\n", "Please make sure that AbiPy is properly configured by running abicheck --with flow\n", "
\n", "\n", "Alternatively, one can use the files in the github repository and use AbiPy \n", "to analyze the data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analyzing the results\n", "[[back to top](#top)]\n", "\n", "Now we can finally analyze the results. In this case, we are mainly interested in the \n", "frequency-dependent macroscopic dielectric function, $\\epsilon_\\infty(\\omega)$, produced\n", "by the `BseTask`" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# The BseTask is the last task in the first work \n", "# i.e. flow[0][2] or, much better, flow[0][-1]\n", "bse_task = flow[0][-1]\n", "bse_task" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `BseTask` has produced a netcdf file (`MDF.nc`) containing the most important results of the run. Let's open the file with:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "run_control": { "marked": true } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "================================= File Info =================================\n", "Name: out_MDF.nc\n", "Directory: /Users/gmatteo/git_repos/abitutorials/abitutorials/bse/flow_bse/w0/t2/outdata\n", "Size: 122.77 kb\n", "Access Time: Sun Aug 12 00:58:11 2018\n", "Modification Time: Fri Oct 13 18:12:44 2017\n", "Change Time: Fri Oct 13 18:12:44 2017\n", "\n", "================================= Structure =================================\n", "Full Formula (Si2)\n", "Reduced Formula: Si\n", "abc : 3.823046 3.823046 3.823046\n", "angles: 60.000000 60.000000 60.000000\n", "Sites (2)\n", " # SP a b c\n", "--- ---- ---- ---- ----\n", " 0 Si 0 0 0\n", " 1 Si 0.25 0.25 0.25\n", "\n", "Abinit Spacegroup: spgid: 0, num_spatial_symmetries: 48, has_timerev: True, symmorphic: True\n", "================================== Q-points ==================================\n", "0) [+0.939, +0.000, +0.000], weight: 0.000\n", "1) [+0.000, +0.939, +0.000], weight: 0.000\n", "2) [+0.000, +0.000, +0.939], weight: 0.000\n", "3) [+0.000, +0.813, +0.813], weight: 0.000\n", "4) [+0.813, +0.000, +0.813], weight: 0.000\n", "5) [+0.813, +0.813, +0.000], weight: 0.000\n" ] } ], "source": [ "mdf_file = abilab.abiopen(\"flow_bse/w0/t2/outdata/out_MDF.nc\") \n", "print(mdf_file)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and use `matplotlib` to plot the imaginary part of $\\epsilon_\\infty(\\omega)$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mdf_file.plot_mdfs();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Meaning of the three curves:\n", "\n", " * EXC is $\\epsilon_\\infty(\\omega)$ computed from the BSE with excitonic effects included\n", " * KS-RPA is the analogous quantity computed within the RPA and the KS band structure\n", " * GW-RPA corresponds to the RPA expression but computed with modified band energies obtained\n", " by \"opening\" the KS eigenvalues with a constant scissor operator that tries to mimic \n", " the $GW$ corrections (`soenergy` variable)\n", " \n", "It is worth stressing that:\n", "\n", "1) The RPA-KS spectrum underestimates the experimental optical threshold due to the well-know band-gap problem of DFT. Most importantly, the amplitude of the first peak is underestimated.\n", "\n", "2) The RPA-GW results with QP corrections simulated with `soenergy` does not show any significant improvement over RPA-KS: the RPA-GW spectrum is just shifted towards higher frequencies due to opening of the gap, but the shape of the two spectra is very similar, in particular the amplitude of the first peak is still underestimated.\n", "\n", "3) On the contrary, the inclusion of the BSE kernel leads to important changes both in the optical threshold as well as in the amplitude of the first peak. This simple analysis tells us that the first peak in the absorption spectrum of silicon has a strong excitonic character that is not correctly described within the RPA. Our first BS spectrum is not converged at all and it barely resembles the experimental result, nevertheless this unconverged calculation is already able to capture the most important physics. \n", "\n", "The difference among the three approaches is schematically depicted in the figure below:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"schematic" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To plot the real part of $\\epsilon_\\infty(\\omega)$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mdf_file.plot_mdfs(cplx_mode=\"re\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It should be stressed that the screened interaction $W$ is the fundamental ingredient that leads\n", "to the attractive interaction between electrons and holes (excitonic effects).\n", "In a metallic system, the dielectric function is large, $W$ is small and excitonic effects are strongly damped.\n", "\n", "To understand this point, we can do a test calculation with a very large value of `mdf_epsinf`\n", "so that our BSE Hamiltonian will be constructed with a metallic $W$:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "

\n", "\n", "
def build_bse_metallicW_flow(options):\n",
       "    """\n",
       "    Build a flow to solve the BSE with metallic screening.\n",
       "    Note the value of `mdf_epsinf`.\n",
       "\n",
       "    Args:\n",
       "        options: Command line options.\n",
       "\n",
       "    Return:\n",
       "        Flow object.\n",
       "    """\n",
       "    workdir = options.workdir if (options and options.workdir) else "flow_bse_metallicW"\n",
       "    flow = flowtk.Flow(workdir=workdir)\n",
       "\n",
       "    # Model dielectric function with metallic screening\n",
       "    scf_inp, nscf_inp, bse_inp = make_scf_nscf_bse_inputs(ngkpt=(4, 4, 4), ecut=6, ecuteps=3,\n",
       "                                                          mdf_epsinf=1.0e+12)\n",
       "\n",
       "    flow.register_work(flowtk.BseMdfWork(scf_inp, nscf_inp, bse_inp))\n",
       "\n",
       "    return flow\n",
       "
\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from lesson_bse import build_bse_metallicW_flow\n", "abilab.print_source(build_bse_metallicW_flow)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "metalW_flow = build_bse_metallicW_flow(options=None)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's assume we have already executed the flow and let's have a look at the results:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with abilab.abiopen(\"flow_bse_metallicW/w0/t2/outdata/out_MDF.nc\") as mdf_file:\n", " mdf_file.plot_mdfs();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the EXC curve computed with a metallic $W$ \n", "is similar to the results obtained in GW-RPA.\n", "In particular the first peak is now shifted towards higher frequencies and its amplitude\n", "is decreased when compared to the previous results. \n", "\n", "This behaviour can be easily understood if we consider that \n", "the BSE formalism reduces to the RPA if $W$ tends to 0.\n", "The EXC curve is still shifted towards higher frequencies when compared with KS-RPA \n", "but this effect is mainly due to the scissor operator that opens the KS gap.\n", "A similar calculation done with `soenergy=0` would give an EXC curve similar to KS-RPA.\n", "This test is left as an optional exercise. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Convergence study with respect to the $k$-point sampling\n", "[[back to top](#top)]\n", "\n", "The most important parameter that should be checked for convergence is the number of $k$-points. \n", "This convergence study represents the most tedious and difficult part since it requires the generation of new WFK files for each k-mesh \n", "(the list of $k$-points for the wavefunctions and the set of $q$-points in the screening must be consistent with each other).\n", "\n", "In the previous section, we have shown how to build a flow for BSE calculation with a fixed \n", "$k$-points sampling. \n", "We can thus reuse the same logic to construct a `Flow` made of multiple `BseMdfWorks`, \n", "each `Work` will have a different $k$-point sampling.\n", "\n", "Let's create, for example, a `Flow` that solves that BSE equation on \n", "a `4x4x4`, `6x6x6` and a `8x8x8` $k$-mesh:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "

\n", "\n", "
def build_bse_kconv_flow(options):\n",
       "    """\n",
       "    Build a flow to analyze the convergence of the BSE spectrum wrt k-point sampling.\n",
       "\n",
       "    Args:\n",
       "        options: Command line options.\n",
       "\n",
       "    Return:\n",
       "        Flow object.\n",
       "    """\n",
       "    workdir = options.workdir if (options and options.workdir) else "flow_bse_kconv"\n",
       "    flow = flowtk.Flow(workdir=workdir)\n",
       "\n",
       "    # 3 works with differet ngkpt.\n",
       "    for nk in [4, 6, 8]:\n",
       "        scf_inp, nscf_inp, bse_inp = make_scf_nscf_bse_inputs(ngkpt=3 * [nk], ecut=6, ecuteps=3)\n",
       "        work = flowtk.BseMdfWork(scf_inp, nscf_inp, bse_inp)\n",
       "        flow.register_work(work)\n",
       "\n",
       "    return flow\n",
       "
\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from lesson_bse import build_bse_kconv_flow\n", "abilab.print_source(build_bse_kconv_flow)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "flow_kconv = build_bse_kconv_flow(options=None)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "flow\n", "\n", "Flow, node_id=345815, workdir=flow_bse_kconv\n", "clusterw0\n", "\n", "BseMdfWork (w0)\n", "\n", "clusterw1\n", "\n", "BseMdfWork (w1)\n", "\n", "clusterw2\n", "\n", "BseMdfWork (w2)\n", "\n", "\n", "w0_t0\n", "\n", "w0_t0\n", "ScfTask\n", "\n", "\n", "w0_t1\n", "\n", "w0_t1\n", "NscfTask\n", "\n", "\n", "w0_t0->w0_t1\n", "\n", "\n", "DEN\n", "\n", "\n", "w0_t2\n", "\n", "w0_t2\n", "BseTask\n", "\n", "\n", "w0_t1->w0_t2\n", "\n", "\n", "WFK\n", "\n", "\n", "w1_t0\n", "\n", "w1_t0\n", "ScfTask\n", "\n", "\n", "w1_t1\n", "\n", "w1_t1\n", "NscfTask\n", "\n", "\n", "w1_t0->w1_t1\n", "\n", "\n", "DEN\n", "\n", "\n", "w1_t2\n", "\n", "w1_t2\n", "BseTask\n", "\n", "\n", "w1_t1->w1_t2\n", "\n", "\n", "WFK\n", "\n", "\n", "w2_t0\n", "\n", "w2_t0\n", "ScfTask\n", "\n", "\n", "w2_t1\n", "\n", "w2_t1\n", "NscfTask\n", "\n", "\n", "w2_t0->w2_t1\n", "\n", "\n", "DEN\n", "\n", "\n", "w2_t2\n", "\n", "w2_t2\n", "BseTask\n", "\n", "\n", "w2_t1->w2_t2\n", "\n", "\n", "WFK\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "flow_kconv.get_graphviz()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "#flow_kconv.plot_networkx();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Change the lesson_bse.py script so that build_bse_kconv_flow is called in main instead of build_bse_flow.\n", "Run the script and submit the calculation with abirun.py FLOWDIR scheduler as usual." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our `Flow` has three `BseTasks` and therefore three different `MDF.nc` files containing $\\epsilon_\\infty(\\omega)$.\n", "The MDF files are available in the github repository. \n", "\n", "In order to plot the three $\\epsilon_\\infty(\\omega)$ on the same graph, we have use the `MdfRobot`\n", "that will gather the results for us:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
    \n", "
  1. w0/t2/outdata/out_MDF.nc
  2. \n", "
  3. w1/t2/outdata/out_MDF.nc
  4. \n", "
  5. w2/t2/outdata/out_MDF.nc
  6. \n", "
" ], "text/plain": [ "Label Relpath\n", "------------------------ ---------------------------------------\n", "w0/t2/outdata/out_MDF.nc flow_bse_kconv/w0/t2/outdata/out_MDF.nc\n", "w1/t2/outdata/out_MDF.nc flow_bse_kconv/w1/t2/outdata/out_MDF.nc\n", "w2/t2/outdata/out_MDF.nc flow_bse_kconv/w2/t2/outdata/out_MDF.nc" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "robot = abilab.MdfRobot.from_dir(\"flow_bse_kconv\")\n", "robot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now finally compare the imaginary and the real part of $\\epsilon_\\infty(\\omega)$ with `matplotlib`:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "plotter = robot.get_multimdf_plotter()" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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