# *G*{sup}`0`*W*{sup}`0` quasi-particle band structure with FHI-aims dataset This tutorial guides you through the process of setting up and running a calculation using FHI-aims for geometry and SCF computations, and LibRPA for quasi-particle energies by one-shot GW method. The silicon unit cell is used as test case. ## 1. **Prerequisites** Before starting, ensure that you have: - [FHI-aims](https://fhi-aims.org/get-the-code-menu/get-the-code) installed with `USE_GREENX` set to `ON`. - LibRPA [installed](../../../user_guide/install.md) with [LibRI enabled](). ## 2. **FHI-aims Input Files** These files are required to run the initial SCF and geometry optimization using FHI-aims: - **`control.in`**: This file contains control parameters for FHI-aims. Below is an example: ```text # Basic model xc pbe k_grid 4 4 4 occupation_type gaussian 0.001 # GW switches qpe_calc gw_expt freq_grid_type minimax frequency_points 16 anacon_type 1 # Output flags output librpa output band 0.50000 0.50000 0.50000 0.00000 0.00000 0.00000 13 L G output band 0.00000 0.00000 0.00000 0.50000 0.00000 0.50000 13 G X [light species default for Si] ``` - **`geometry.in`**: Contains the geometry of the system. For silicon: ```text lattice_vector 3.8301668167 0.0000000000 0.0000000000 lattice_vector 1.9150834084 3.3170217640 0.0000000000 lattice_vector 1.9150834084 1.1056739213 3.1273181102 atom_frac 0.0000000000 0.0000000000 0.0000000000 Si atom_frac 0.2500000000 0.2500000000 0.2500000000 Si ``` Then run FHI-aims by ```bash mpirun -np 4 /path/to/bin/aims.x > aims.out ``` It takes about 30 seconds to finish on an M2 Max Macbook Pro laptop. This will generate dataset files (~500 MB) for the LibRPA driver. ## 3. **LibRPA Input File** LibRPA requires **`librpa.in`** which specifies the parameters. For one-shot GW calculation for band structure, it looks like: ```text task = g0w0_band nfreq = 16 option_dielect_func = 0 replace_w_head = t parallel_routing = libri ``` Here `replace_w_head` is switched on, so that LibRPA uses the dielectric function directly computed in FHI-aims for the correction of dielectric matrix to speed up k-point convergence. ## 4. **Run GW with LibRPA** After obtaining the output files from FHI-aims and setting up the parameters in `librpa.in`, you can run the LibRPA driver at the same working directory to calculate the quasi-particle band structure: ```bash mpirun -np 4 /path/to/LibRPA/build/chi0_main.exe > LibRPA.out ``` On the same laptop, this takes about 1.7 hour. The calculation can be sped up if more MPI tasks and/or OpenMP threads are used. ## 5. **Analyze LibRPA Output** After successful run, you can find in `LibRPA.out` the quasi-particle energies and its compositions for states on the regular k-grid: ```text spin 1, k-point 1: (0.00000, 0.00000, 0.00000) ---------------------------------------------------------------------------------------------------------------------------- State occ e_mf v_xc v_exx ReSigc ImSigc e_qp ---------------------------------------------------------------------------------------------------------------------------- 1 2.00000 -1789.50277 -153.07760 -244.87703 8.90359 3.15362 -1872.39861 2 2.00000 -1789.50277 -153.07762 -244.87688 8.90214 3.15478 -1872.39990 ... 11 2.00000 -17.67291 -12.19859 -19.21812 6.69564 -0.86364 -17.99680 12 2.00000 -5.63619 -13.27559 -14.75075 1.24879 -0.00015 -5.86256 13 2.00000 -5.63548 -13.27912 -14.75356 1.24876 -0.00015 -5.86116 14 2.00000 -5.63533 -13.27943 -14.75386 1.24871 -0.00015 -5.86104 15 0.00000 -3.07993 -11.57831 -7.20939 -3.90052 -0.01063 -2.61152 16 0.00000 -3.07901 -11.57980 -7.21005 -3.90139 -0.01064 -2.61065 17 0.00000 -3.07776 -11.58158 -7.21096 -3.90154 -0.01066 -2.60869 18 0.00000 -2.14654 -14.88107 -9.67057 -4.69199 -0.01374 -1.62803 ... 49 0.00000 48.77341 -11.89143 -2.44414 -25.95775 -4.20613 32.26294 50 0.00000 94.46523 -19.21422 -6.75051 20.24488 -42.71633 127.17381 spin 1, k-point 2: (0.00000, 0.00000, 0.33333) ---------------------------------------------------------------------------------------------------------------------------- ... ``` The columns in the above output have the following meanings: - `State`: band index $n$ - `occ`: occupation number $f_{nk}$ (read from input) - `e_mf`: Kohn-Sham mean-field eigenvalue $E^{\mathrm{KS}}_{nk}$ (read from input) - `v_xc`: exchange-correlation potential $v^{\mathrm{xc}}_{nk}$ (read from input) - `v_exx`: exact-exchange potential $v^{\mathrm{exx}}_{nk}$ - `ReSigc`: real part of the correlation self-energy $\Re\Sigma^{\mathrm{c}}_{nk}$ - `ImSigc`: imaginary part of the correlation self-energy $\Im\Sigma^{\mathrm{c}}_{nk}$ - `e_qp`: resulting quasiparticle energy $E^{\mathrm{QP}}_{nk}$. It is computed as $$ E^{\mathrm{QP}}_{nk} = E^{\mathrm{KS}}_{nk} - v^{\mathrm{xc}}_{nk} + v^{\mathrm{exx}}_{nk} + \Re\Sigma^{\mathrm{c}}_{nk} $$ All energy quantities are given in eV. For band calculations with the `g0w0_band` task, LibRPA also writes the band-structure results to the following files: - `KS_band_spin_.dat`: input Kohn-Sham band structure, for reference - `EXX_band_spin_.dat`: non-self-consistent exact-exchange-only band structure - `GW_band_spin_.dat`: GW quasiparticle band structure All of these band-structure files use the same format as the corresponding FHI-aims output files and can therefore be post-processed in the same way using existing FHI-aims scripts. The **main difference** is in the energy reference: FHI-aims aligns the band energies to the Fermi level, whereas LibRPA uses its internal energy zero. The PBE and *GW* band structures of this case is plotted in {numref}`fig-band-si`. :::{figure-md} fig-band-si ![band](band.svg){align=center} Band structure of Silicon, one-shot GW from LibRPA :::