GW with scissors operator¶
This example shows how to generate an energy-dependent scissors operator by fitting the GW corrections as function of the KS eigenvalues. We then use the scissors operator to correct the KS band structure computed on a high symmetry k-path. Finally, the LDA and the QPState band structure are plotted with matplotlib.
KS fermie 5.598313017568332 eV --> QP fermie 5.40710713209731 eV Delta(QP-KS)= -0.1912058854710219 eV KS fermie 5.598453325290463 eV --> QP fermie 5.407251265916601 eV Delta(QP-KS)= -0.19120205937386192 eV
import abipy.data as abidata from abipy.abilab import abiopen, ElectronBandsPlotter # Get the QP results from the SIGRES.nc database. sigma_file = abiopen(abidata.ref_file("si_g0w0ppm_nband30_SIGRES.nc")) # Let's have a look at the QP correction as function of the KS energy. # Don't shift KS eigenvalues to have zero energy at the Fermi energy. # because we need the absolute values for the fit. # The qpeme0(e0) curve consists of two branches: # the one in the [-6, 5.7] eV interval associated to valence states # and the one in the [6.1, 15] eV interval associated to conduction bands. # We will fit these results with 2 functions defined in these two domains. sigma_file.plot_qps_vs_e0(e0=None) sigma_file.plot_qps_vs_e0() qplist_spin = sigma_file.qplist_spin # Define the two domains and construct the scissors operator domains = [[-10, 6.1], [6.1, 18]] scissors = qplist_spin.build_scissors(domains, bounds=None) # Read the KS band energies computed on the k-path ks_bands = abiopen(abidata.ref_file("si_nscf_GSR.nc")).ebands # Read the KS band energies computed on the Monkhorst-Pack (MP) mesh # and compute the DOS with the Gaussian method ks_mpbands = abiopen(abidata.ref_file("si_scf_GSR.nc")).ebands ks_edos = ks_mpbands.get_edos() # Apply the scissors operator first on the KS band structure # along the k-path then on the energies computed with the MP mesh. qp_bands = ks_bands.apply_scissors(scissors) qp_mpbands = ks_mpbands.apply_scissors(scissors) # Compute the DOS with the modified QPState energies. qp_edos = qp_mpbands.get_edos() # Plot the LDA and the QPState band structure with matplotlib. plotter = ElectronBandsPlotter() plotter.add_ebands("LDA", ks_bands, edos=ks_edos) plotter.add_ebands("LDA+scissors(e)", qp_bands, edos=qp_edos) # By default, the two band energies are shifted wrt to *their* fermi level. # Use e=0 if you don't want to shift the eigenvalus # so that it's possible to visualize the QP corrections. plotter.combiplot(title="Silicon band structure") plotter.gridplot(title="Silicon band structure") sigma_file.close()
Total running time of the script: ( 0 minutes 1.888 seconds)