Source code for asr.hse

"""HSE band structure."""
from ase import Atoms
from asr.calculators import Calculation
import asr
from asr.core import (
    command, option, ASRResult, prepare_result,
)
import typing
from ase.spectrum.band_structure import BandStructure
from asr.bandstructure import legend_on_top
from asr.database.browser import (
    fig, table, describe_entry, make_panel_description)
from asr.gs import calculate as calculategs
from asr.bandstructure import main as bsmain
from asr.bandstructure import calculate as bscalculate


panel_description = make_panel_description(
    """The single-particle band structure calculated with the HSE06
xc-functional. The calculations are performed non-self-consistently with the
wave functions from a GGA calculation. Spin–orbit interactions are included
in post-process.""",
    articles=['C2DB'],
)


[docs]@prepare_result class HSECalculationResult(ASRResult): hse_eigenvalues: typing.List[float] hse_eigenvalues_soc: typing.List[float] calculation: Calculation key_descriptions = dict( calculation='Calculation object', hse_eigenvalues='HSE eigenvalues without SOC.', hse_eigenvalues_soc='HSE eigenvalues with SOC.', )
[docs]@command(module='asr.hse') @asr.atomsopt @asr.calcopt @option('--kptdensity', help='K-point density', type=float) @option('--emptybands', help='number of empty bands to include', type=int) def calculate( atoms: Atoms, calculator: dict = calculategs.defaults.calculator, kptdensity: float = 8.0, emptybands: int = 20, ) -> HSECalculationResult: """Calculate HSE corrections.""" eigs, calc, hse_nowfs = hse( atoms=atoms, calculator=calculator, kptdensity=kptdensity, emptybands=emptybands, ) eigs_soc = hse_spinorbit(atoms, calculator, eigs, calc) results = { 'hse_eigenvalues': eigs, 'hse_eigenvalues_soc': eigs_soc, 'calculation': hse_nowfs, } return HSECalculationResult(data=results)
# XXX move to utils? [also in asr.polarizability]
[docs]def get_kpts_size(atoms, kptdensity): """Find reasonable monkhorst-pack size which hits high symmetry points.""" from gpaw.kpt_descriptor import kpts2sizeandoffsets as k2so size, offset = k2so(atoms=atoms, density=kptdensity) size[2] = 1 for i in range(2): if size[i] % 6 != 0: size[i] = 6 * (size[i] // 6 + 1) kpts = {'size': size, 'gamma': True} return kpts
[docs]def hse(atoms, calculator, kptdensity, emptybands): import numpy as np from gpaw.hybrids.eigenvalues import non_self_consistent_eigenvalues convbands = int(emptybands / 2) gsresult = calculategs(atoms=atoms, calculator=calculator) calc = gsresult.calculation.load(parallel={'band': 1, 'kpt': 1}) atoms = calc.get_atoms() pbc = atoms.pbc.tolist() ND = np.sum(pbc) if ND == 3 or ND == 1: kpts = {'density': kptdensity, 'gamma': True, 'even': False} elif ND == 2: kpts = get_kpts_size(atoms=atoms, kptdensity=kptdensity) calc.set(nbands=-emptybands, fixdensity=True, kpts=kpts, convergence={'bands': -convbands}, txt='hse.txt') calc.get_potential_energy() hse_nowfs = calc.save(id='hse_nowfs') nb = calc.get_number_of_bands() result = non_self_consistent_eigenvalues(calc, 'HSE06', n1=0, n2=nb - convbands, snapshot='hse-snapshot.json') e_scf_skn, vxc_scf_skn, vxc_hse_skn = result e_hse_skn = e_scf_skn - vxc_scf_skn + vxc_hse_skn dct = dict(vxc_hse_skn=vxc_hse_skn, e_scf_skn=e_scf_skn, vxc_scf_skn=vxc_scf_skn, e_hse_skn=e_hse_skn) return dct, calc, hse_nowfs
[docs]def hse_spinorbit(atoms, calculator, dct, calc): from gpaw.spinorbit import soc_eigenstates from asr.magnetic_anisotropy import get_spin_axis, get_spin_index e_skn = dct.get('e_hse_skn') dct_soc = {} theta, phi = get_spin_axis(atoms=atoms, calculator=calculator) soc = soc_eigenstates(calc, eigenvalues=e_skn, theta=theta, phi=phi) dct_soc['e_hse_mk'] = soc.eigenvalues().T dct_soc['s_hse_mk'] = soc.spin_projections()[ :, :, get_spin_index(atoms=atoms, calculator=calculator)].T return dct_soc
[docs]def MP_interpolate( atoms, calculator, bsrestart, kptpath, npoints, calc, delta_skn, lb, ub ): """Interpolate corrections to band patch. Calculates band stucture along the same band path used for SCF by interpolating a correction onto the SCF band structure. """ import numpy as np from gpaw.spinorbit import soc_eigenstates from ase.dft.kpoints import (get_monkhorst_pack_size_and_offset, monkhorst_pack_interpolate) from asr.core import singleprec_dict from asr.magnetic_anisotropy import get_spin_axis bandrange = np.arange(lb, ub) # read SCF (without SOC) results_bandstructure = bsmain( atoms=atoms, calculator=calculator, bsrestart=bsrestart, kptpath=kptpath, npoints=npoints, ) path = results_bandstructure['bs_nosoc']['path'] e_scf_skn = results_bandstructure['bs_nosoc']['energies'] size, offset = get_monkhorst_pack_size_and_offset(calc.get_bz_k_points()) bz2ibz = calc.get_bz_to_ibz_map() icell = calc.atoms.cell.reciprocal() eps = monkhorst_pack_interpolate(path.kpts, delta_skn.transpose(1, 0, 2), icell, bz2ibz, size, offset) delta_interp_skn = eps.transpose(1, 0, 2) e_int_skn = e_scf_skn[:, :, bandrange] + delta_interp_skn dct = dict(e_int_skn=e_int_skn, path=path) # add SOC from bs.gpw bscalculateres = bscalculate( atoms=atoms, calculator=calculator, bsrestart=bsrestart, kptpath=kptpath, npoints=npoints, ) calc = bscalculateres.calculation.load() theta, phi = get_spin_axis( atoms=atoms, calculator=calculator, ) soc = soc_eigenstates(calc, eigenvalues=e_int_skn, n1=lb, n2=ub, theta=theta, phi=phi) dct.update(e_int_mk=soc.eigenvalues().T) results = {} results['bandstructure'] = singleprec_dict(dct) return results
[docs]def plot_bs_hse(row, filename): data = row.data['results-asr.hse.json'] return plot_bs(row, filename=filename, bs_label='HSE06', data=data, efermi=data['efermi_hse_soc'], vbm=row.get('vbm_hse'), cbm=row.get('cbm_hse'))
[docs]def plot_bs(row, filename, *, bs_label, efermi, data, vbm, cbm): import matplotlib.pyplot as plt import matplotlib.patheffects as path_effects figsize = (5.5, 5) fontsize = 10 path = data['bandstructure']['path'] reference = row.get('evac') if reference is None: reference = efermi label = r'$E - E_\mathrm{F}$ [eV]' else: label = r'$E - E_\mathrm{vac}$ [eV]' emin_offset = efermi if vbm is None else vbm emax_offset = efermi if cbm is None else cbm emin = emin_offset - 3 - reference emax = emax_offset + 3 - reference e_mk = data['bandstructure']['e_int_mk'] - reference x, X, labels = path.get_linear_kpoint_axis() # with soc style = dict( color='C1', ls='-', lw=1.0, zorder=0) ax = plt.figure(figsize=figsize).add_subplot(111) for e_m in e_mk: ax.plot(x, e_m, **style) ax.set_ylim([emin, emax]) ax.set_xlim([x[0], x[-1]]) ax.set_ylabel(label) ax.set_xticks(X) ax.set_xticklabels([lab.replace('G', r'$\Gamma$') for lab in labels]) xlim = ax.get_xlim() x0 = xlim[1] * 0.01 ax.axhline(efermi - reference, c='C1', ls=':') text = ax.annotate( r'$E_\mathrm{F}$', xy=(x0, efermi - reference), ha='left', va='bottom', fontsize=fontsize * 1.3) text.set_path_effects([ path_effects.Stroke(linewidth=2, foreground='white', alpha=0.5), path_effects.Normal() ]) # add KS band structure with soc from asr.bandstructure import add_bs_ks if 'results-asr.bandstructure.json' in row.data: ax = add_bs_ks(row, ax, reference=row.get('evac', row.get('efermi')), color=[0.8, 0.8, 0.8]) for Xi in X: ax.axvline(Xi, ls='-', c='0.5', zorder=-20) ax.plot([], [], **style, label=bs_label) legend_on_top(ax, ncol=2) plt.savefig(filename, bbox_inches='tight')
[docs]def webpanel(result, row, key_descriptions): if row.get('gap_hse', 0) > 0.0: hse = table(row, 'Property', ['gap_hse', 'gap_dir_hse'], kd=key_descriptions) if row.get('evac'): hse['rows'].extend( [['Valence band maximum wrt. vacuum level (HSE06)', f'{row.vbm_hse - row.evac:.2f} eV'], ['Conduction band minimum wrt. vacuum level (HSE06)', f'{row.cbm_hse - row.evac:.2f} eV']]) else: hse['rows'].extend( [['Valence band maximum wrt. Fermi level (HSE06)', f'{row.vbm_hse - row.efermi:.2f} eV'], ['Conduction band minimum wrt. Fermi level (HSE06)', f'{row.cbm_hse - row.efermi:.2f} eV']]) else: hse = table(row, 'Property', [], kd=key_descriptions) from asr.utils.hacks import gs_xcname_from_row xcname = gs_xcname_from_row(row) title = f'Electronic band structure (HSE06@{xcname})' panel = {'title': describe_entry(title, panel_description), 'columns': [[fig('hse-bs.png')], [fig('bz-with-gaps.png'), hse]], 'plot_descriptions': [{'function': plot_bs_hse, 'filenames': ['hse-bs.png']}], 'sort': 15} if row.get('gap_hse'): bandgaphse = describe_entry( 'Band gap (HSE)', 'The electronic single-particle band gap calculated with ' 'HSE including spin–orbit effects.\n\n', ) rows = [[bandgaphse, f'{row.gap_hse:0.2f} eV']] summary = {'title': 'Summary', 'columns': [[{'type': 'table', 'header': ['Electronic properties', ''], 'rows': rows}]], 'sort': 11} return [panel, summary] return [panel]
[docs]@prepare_result class Result(ASRResult): vbm_hse_nosoc: float cbm_hse_nosoc: float gap_dir_hse_nosoc: float gap_hse_nosoc: float kvbm_nosoc: typing.List[float] kcbm_nosoc: typing.List[float] vbm_hse: float cbm_hse: float gap_dir_hse: float gap_hse: float kvbm: typing.List[float] kcbm: typing.List[float] efermi_hse_nosoc: float efermi_hse_soc: float bandstructure: BandStructure key_descriptions = { "vbm_hse_nosoc": "Valence band maximum w/o soc. (HSE) [eV]", "cbm_hse_nosoc": "Conduction band minimum w/o soc. (HSE) [eV]", "gap_dir_hse_nosoc": "Direct gap w/o soc. (HSE) [eV]", "gap_hse_nosoc": "Band gap w/o soc. (HSE) [eV]", "kvbm_nosoc": "k-point of HSE valence band maximum w/o soc", "kcbm_nosoc": "k-point of HSE conduction band minimum w/o soc", "vbm_hse": "KVP: Valence band maximum (HSE) [eV]", "cbm_hse": "KVP: Conduction band minimum (HSE) [eV]", "gap_dir_hse": "KVP: Direct band gap (HSE) [eV]", "gap_hse": "KVP: Band gap (HSE) [eV]", "kvbm": "k-point of HSE valence band maximum", "kcbm": "k-point of HSE conduction band minimum", "efermi_hse_nosoc": "Fermi level w/o soc. (HSE) [eV]", "efermi_hse_soc": "Fermi level (HSE) [eV]", "bandstructure": "HSE bandstructure." } formats = {"ase_webpanel": webpanel}
[docs]@command(module='asr.hse') @asr.atomsopt @asr.calcopt @option('--kptdensity', help='K-point density', type=float) @option('--emptybands', help='number of empty bands to include', type=int) @asr.calcopt( aliases=['-b', '--bsrestart'], help='Bandstructure Calculator params.', matcher=asr.matchers.EQUAL, ) @option('--kptpath', type=str, help='Custom kpoint path.') @option('--npoints', type=int, help='Number of points along k-point path.') def main( atoms: Atoms, calculator: dict = calculategs.defaults.calculator, bsrestart: dict = bscalculate.defaults.bsrestart, kptpath: typing.Union[str, None] = bscalculate.defaults.kptpath, npoints: int = bscalculate.defaults.npoints, kptdensity: float = 8.0, emptybands: int = 20, ) -> Result: """Interpolate HSE band structure along a given path.""" import numpy as np from asr.utils import fermi_level from ase.dft.bandgap import bandgap # interpolate band structure results_hse = calculate( atoms=atoms, calculator=calculator, kptdensity=kptdensity, emptybands=emptybands, ) calc = results_hse.calculation.load() data = results_hse['hse_eigenvalues'] nbands = data['e_hse_skn'].shape[2] delta_skn = data['vxc_hse_skn'] - data['vxc_scf_skn'] results = MP_interpolate( atoms, calculator, bsrestart, kptpath, npoints, calc, delta_skn, 0, nbands) # get gap, cbm, vbm, etc... eps_skn = results_hse['hse_eigenvalues']['e_hse_skn'] ibzkpts = calc.get_ibz_k_points() efermi_nosoc = fermi_level(calc, eigenvalues=eps_skn, nspins=eps_skn.shape[0]) gap, p1, p2 = bandgap(eigenvalues=eps_skn, efermi=efermi_nosoc, output=None) gapd, p1d, p2d = bandgap(eigenvalues=eps_skn, efermi=efermi_nosoc, direct=True, output=None) if gap: kvbm_nosoc = ibzkpts[p1[1]] # k coordinates of vbm kcbm_nosoc = ibzkpts[p2[1]] # k coordinates of cbm vbm = eps_skn[p1] cbm = eps_skn[p2] subresults = {'vbm_hse_nosoc': vbm, 'cbm_hse_nosoc': cbm, 'gap_dir_hse_nosoc': gapd, 'gap_hse_nosoc': gap, 'kvbm_nosoc': kvbm_nosoc, 'kcbm_nosoc': kcbm_nosoc} else: subresults = {'vbm_hse_nosoc': None, 'cbm_hse_nosoc': None, 'gap_dir_hse_nosoc': gapd, 'gap_hse_nosoc': gap, 'kvbm_nosoc': None, 'kcbm_nosoc': None} results.update(subresults) eps = results_hse['hse_eigenvalues_soc']['e_hse_mk'] eps = eps.transpose()[np.newaxis] # e_skm, dummy spin index efermi_soc = fermi_level(calc, eigenvalues=eps, nspins=2) bzkpts = calc.get_bz_k_points() gap, p1, p2 = bandgap(eigenvalues=eps, efermi=efermi_soc, output=None) gapd, p1d, p2d = bandgap(eigenvalues=eps, efermi=efermi_soc, direct=True, output=None) if gap: kvbm = bzkpts[p1[1]] kcbm = bzkpts[p2[1]] vbm = eps[p1] cbm = eps[p2] subresults = {'vbm_hse': vbm, 'cbm_hse': cbm, 'gap_dir_hse': gapd, 'gap_hse': gap, 'kvbm': kvbm, 'kcbm': kcbm} else: subresults = {'vbm_hse': None, 'cbm_hse': None, 'gap_dir_hse': gapd, 'gap_hse': gap, 'kvbm': None, 'kcbm': None} results.update(subresults) subresults = {'efermi_hse_nosoc': efermi_nosoc, 'efermi_hse_soc': efermi_soc} results.update(subresults) return Result(data=results)
if __name__ == '__main__': main.cli()