New Light Harvesting Materials

Electronic bandgap calculations are presented for 2400 experimentally known materials from the Materials Project database and the bandgaps, obtained with different types of functionals within density functional theory and (partial) self-consistent GW approximation, are compared for 20 randomly chosen compounds forming an unconventional set of ternary and quaternary materials.

Ivano E. Castelli, Falco Hüser, Mohnish Pandey, Hong Li, Kristian S. Thygesen, Brian Seger, Anubhav Jain, Kristin Persson, Gerbrand Ceder, and Karsten W. Jacobsen

New Light Harvesting Materials Using Accurate and Efficient Bandgap Calculations

Advanced Energy Materials, Juli 22, 2014

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Key-value pairs

key	description	unit
gllbsc_dir_gap	Direct bandgap GLLB-SC.	eV
gllbsc_ind_gap	Indirect bandgap GLLB-SC.	eV
gllbsc_disc	Derivative discontinuity GLLB-SC.	eV
mpid	ID of materials in Materials project
icsd_id	ID of materials in ICSD
g0w0_gap	G0W0 gap at Gamma	eV
gw0_gap	GW0 gap at Gamma	eV
gw_gap	GW gap at Gamma	eV
hse06_gap	HSE06 gap at Gamma	eV
lda_gap	LDA gap at Gamma	eV
gllbsc_gap	GLLBSC gap at Gamma	eV

Band gaps

Here, we calculated the errors in the band gaps at \(\Gamma\) for a set of 20 ternary and quaternary materials releative to self-consitent GW:

import numpy as np
import ase.db

con = ase.db.connect('mp_gllbsc.db')

data = []
for row in con.select('g0w0_gap'):
    ref = row.gw_gap
    data.append([row.gw0_gap - ref,
                 row.g0w0_gap - ref,
                 row.lda_gap - ref,
                 row.gllbsc_gap - ref,
                 row.gllbsc_gap - row.gllbsc_disc - ref,
                 row.hse06_gap - ref])
errors = np.array(data).T

labels = ['`GW_0`', '`G_0W_0`', 'LDA', r'GLLB-SC - `\Delta_{xc}`',
          'GLLB-SC - KS', 'HSE06']
f = open('gaps.csv', 'w')
print('Material, Mean error [eV], Mean absolute error [eV]', file=f)
for label, e in zip(labels, errors):
    print('{}, {:.2f}, {:.2f}'.format(label, e.mean(), abs(e).mean()), file=f)

Material	Mean error [eV]	Mean absolute error [eV]
\(GW_0\)	-0.48	0.48
\(G_0W_0\)	-0.79	0.79
LDA	-2.34	2.34
GLLB-SC - \(\Delta_{xc}\)	-0.08	0.62
GLLB-SC - KS	-1.23	1.23
HSE06	-0.88	0.94

Here is how to make the plot:

# creates: gaps.svg
"""Plot the GLLB-SC, HSE06, GW approximations bandgaps for a
set of 20 ternary and quaternary materials"""

import re
import numpy as np
import matplotlib.pyplot as plt
import ase.db

# Connect to database:
con = ase.db.connect('mp_gllbsc.db')

# Extract gaps data:
data = []
for row in con.select('g0w0_gap', sort='gw_gap'):
    data.append([row.formula,
                 row.gw_gap,
                 row.gw0_gap,
                 row.g0w0_gap,
                 row.lda_gap,
                 row.gllbsc_gap,
                 row.gllbsc_gap - row.gllbsc_disc,
                 row.hse06_gap])

# Make a bar-chart:
fig = plt.figure(figsize=(12, 8))
ax = fig.add_subplot(1, 1, 1)

w = 0.25  # width of bars
x = np.arange(len(data))
i = 1
for color, shift, label in [('y', 0, 'GW'),
                            ('m', 0, 'GW$_0$'),
                            ('r', 0, 'G$_0$W$_0$'),
                            ('k', 0, 'LDA'),
                            ('b', w, r'GLLB-SC - $\Delta_{xc}$'),
                            ('c', w, 'GLLB-SC - KS'),
                            ('g', 2 * w, 'HSE06')]:
    rects = ax.bar(x + shift, [gaps[i] for gaps in data], w,
                   color=color, label=label)
    i += 1

plt.legend(loc=2)
ax.set_ylabel(r'Bandgap at $\Gamma$ [eV]')
ax.set_xticks(x + w)
names = [re.sub(r'(\d+)', r'$_\1$', gaps[0]) for gaps in data]
ax.set_xticklabels(names, rotation=60)
plt.tight_layout()
plt.savefig('gaps.svg')