If you are using data from this database in your research, please cite the following papers:
Sten Haastrup, Mikkel Strange, Mohnish Pandey, Thorsten Deilmann, Per S. Schmidt, Nicki F. Hinsche, Morten N. Gjerding, Daniele Torelli, Peter M. Larsen, Anders C. Riis-Jensen, Jakob Gath, Karsten W. Jacobsen, Jens Jørgen Mortensen, Thomas Olsen, Kristian S. Thygesen
2D Materials 5, 042002 (2018)
Recent Progress of the Computational 2D Materials Database (C2DB)
M. N. Gjerding, A. Taghizadeh, A. Rasmussen, S. Ali, F. Bertoldo, T. Deilmann, U. P. Holguin, N. R. Knøsgaard, M. Kruse, A. H. Larsen, S. Manti, T. G. Pedersen, T. Skovhus, M. K. Svendsen, J. J. Mortensen, T. Olsen, K. S. Thygesen
2D Materials 8, 044002 (2021)
The database is provided upon request.
The database contains structural, thermodynamic, elastic, electronic, magnetic, and optical properties of around 4000 two-dimensional (2D) materials distributed over more than 40 different crystal structures. The properties are calculated by density functional theory (DFT) and many-body perturbation theory (\(G_0W_0\) and the Bethe- Salpeter Equation for around 300 materials) as implemented in the GPAW electronic structure code. The workflow was constructed using the Atomic Simulation Recipes (ASR) and executed with the MyQueue task manager. The workflow script and a table with the numerical settings employed for the calculation of the different properties are provided below.
If a parameter is not specified at a given step, its value equals that of the last step where it was specified:
Workflow step(s) |
Parameters |
|---|---|
Structure and energetics(*) (1-4) |
vacuum = 15 Å; \(k\)-point density = 6.0/Å\(^{-1}\); Fermi smearing = 0.05 eV; PW cutoff = 800 eV; xc functional = PBE; maximum force = 0.01 eV/Å; maximum stress = 0.002 eV/Å\(^3\); phonon displacement = 0.01Å |
Elastic constants (5) |
\(k\)-point density = \(12.0/\mathrm{Å}^{-1}\); strain = \(\pm\)1% |
Magnetic anisotropy (6) |
\(k\)-point density = \(20.0/\mathrm{Å}^{-1}\); spin-orbit coupling = True |
PBE electronic properties (7-10 and 12) |
\(k\)-point density = \(12.0/\mathrm{Å}^{-1}\) (\(36.0/\mathrm{Å}^{-1}\) for DOS) |
Effective masses (11) |
\(k\)-point density = \(45.0/\mathrm{Å}^{-1}\); finite difference |
Deformation potential (13) |
\(k\)-point density = 12.0/Å\(^{-1}\); strain = \(\pm\)1% |
Plasma frequency (14) |
\(k\)-point density = 20.0/Å\(^{-1}\); tetrahedral interpolation |
HSE band structure (8-12) |
HSE06@PBE; \(k\)-point density = 12.0/Å\(^{-1}\) |
\(G_0W_0\) band structure (8, 9) |
\(G_0W_0\)@PBE; \(k\)-point density = \(5.0/\mathrm{Å}^{-1}\); PW cutoff = \(\infty\) (extrapolated from 170, 185 and 200 eV); full frequency integration; analytical treatment of \(W({q})\) for small \(q\); truncated Coulomb interaction |
RPA polarisability (15) |
RPA@PBE; \(k\)-point density = \(20.0/\mathrm{Å}^{-1}\); PW cutoff = 50 eV; truncated Coulomb interaction; tetrahedral interpolation |
BSE absorbance (16) |
BSE@PBE with \(G_0W_0\) scissors operator; \(k\)-point density = \(20.0/\mathrm{Å}^{-1}\); PW cutoff = 50 eV; truncated Coulomb interaction; at least 4 occupied and 4 empty bands |
(*) For the cases with convergence issues, we set a (k)-point density of 9.0 and a smearing of 0.02 eV.
The C2DB project has received funding from the Danish National Research Foundation’s Center for Nanostructured Graphene (CNG) and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program Grant No. 773122 (LIMA) and Grant agreement No. 951786 (NOMAD CoE).
Version |
rows |
comment |
2018-06-01 |
1888 |
Initial release |
2018-08-01 |
2391 |
Two new prototypes added |
2018-09-25 |
3084 |
New prototypes |
2018-12-10 |
3331 |
Some BSE spectra recalculated due to small bug affecting absorption strength of materials with large spin-orbit couplings |
2021-04-22 |
4049 |
Major update including several hundreds new monolayers from experimentally known crystals (from the ICSD/COD databases), new crystal prototype characterization scheme, improved properties (stiffness tensor, effective masses, optical absorbance), and new properties (exfoliation energies, Bader charges, spontaneous polarisations, Born charges, infrared polarisabilities, piezoelectric tensors, band topology invariants, exchange couplings, Raman- and second harmonic generation spectra). See Gjerding et al. for a full description. |
2021-06-24 |
4056 |
Updated MARE for effective masses. |
2022-09-08 |
15686 |
Added 11.630 materials from lattice decoration and a deep generative model (see arXiv:2206.12159). Corrected symmetry threshold used to define band structure path to be consistent with the threshold used to define the space group. |
2022-11-30 |
15733 |
Shift currents for selected materials. Improved deformation potentials. |
key |
description |
unit |
|---|---|---|
A |
Single-ion anisotropy (out-of-plane) |
meV |
E_B |
Exciton binding energy from BSE |
eV |
E_x |
Soc. total energy, x-direction |
meV/unit cell |
E_y |
Soc. total energy, y-direction |
meV/unit cell |
E_z |
Soc. total energy, z-direction |
meV/unit cell |
J |
Nearest neighbor exchange coupling |
meV |
N_nn |
Number of nearest neighbors |
|
Topology |
Band topology |
|
a |
Cell parameter a |
Å |
age |
Time since creation |
|
alpha |
Cell parameter alpha |
deg |
alphax |
Static total polarizability (x) |
Å |
alphax_el |
Static interband polarizability (x) |
Å |
alphax_lat |
Static lattice polarizability (x) |
Å |
alphay |
Static total polarizability (y) |
Å |
alphay_el |
Static interband polarizability (y) |
Å |
alphay_lat |
Static lattice polarizability (y) |
Å |
alphaz |
Static total polarizability (z) |
Å |
alphaz_el |
Static interband polarizability (z) |
Å |
alphaz_lat |
Static lattice polarizability (z) |
Å |
asr_id |
Material unique ID |
|
b |
Cell parameter b |
Å |
beta |
Cell parameter beta |
deg |
c |
Cell parameter c |
Å |
c_00 |
Stiffness tensor, 00-component |
N/m<sup>dim-1</sup> |
c_01 |
Stiffness tensor, 01-component |
N/m<sup>dim-1</sup> |
c_02 |
Stiffness tensor, 02-component |
N/m<sup>dim-1</sup> |
c_03 |
Stiffness tensor, 03-component |
N/m<sup>dim-1</sup> |
c_04 |
Stiffness tensor, 04-component |
N/m<sup>dim-1</sup> |
c_05 |
Stiffness tensor, 05-component |
N/m<sup>dim-1</sup> |
c_10 |
Stiffness tensor, 10-component |
N/m<sup>dim-1</sup> |
c_11 |
Stiffness tensor, 11-component |
N/m<sup>dim-1</sup> |
c_12 |
Stiffness tensor, 12-component |
N/m<sup>dim-1</sup> |
c_13 |
Stiffness tensor, 13-component |
N/m<sup>dim-1</sup> |
c_14 |
Stiffness tensor, 14-component |
N/m<sup>dim-1</sup> |
c_15 |
Stiffness tensor, 15-component |
N/m<sup>dim-1</sup> |
c_20 |
Stiffness tensor, 20-component |
N/m<sup>dim-1</sup> |
c_21 |
Stiffness tensor, 21-component |
N/m<sup>dim-1</sup> |
c_22 |
Stiffness tensor, 22-component |
N/m<sup>dim-1</sup> |
c_23 |
Stiffness tensor, 23-component |
N/m<sup>dim-1</sup> |
c_24 |
Stiffness tensor, 24-component |
N/m<sup>dim-1</sup> |
c_25 |
Stiffness tensor, 25-component |
N/m<sup>dim-1</sup> |
c_30 |
Stiffness tensor, 30-component |
N/m<sup>dim-1</sup> |
c_31 |
Stiffness tensor, 31-component |
N/m<sup>dim-1</sup> |
c_32 |
Stiffness tensor, 32-component |
N/m<sup>dim-1</sup> |
c_33 |
Stiffness tensor, 33-component |
N/m<sup>dim-1</sup> |
c_34 |
Stiffness tensor, 34-component |
N/m<sup>dim-1</sup> |
c_35 |
Stiffness tensor, 35-component |
N/m<sup>dim-1</sup> |
c_40 |
Stiffness tensor, 40-component |
N/m<sup>dim-1</sup> |
c_41 |
Stiffness tensor, 41-component |
N/m<sup>dim-1</sup> |
c_42 |
Stiffness tensor, 42-component |
N/m<sup>dim-1</sup> |
c_43 |
Stiffness tensor, 43-component |
N/m<sup>dim-1</sup> |
c_44 |
Stiffness tensor, 44-component |
N/m<sup>dim-1</sup> |
c_45 |
Stiffness tensor, 45-component |
N/m<sup>dim-1</sup> |
c_50 |
Stiffness tensor, 50-component |
N/m<sup>dim-1</sup> |
c_51 |
Stiffness tensor, 51-component |
N/m<sup>dim-1</sup> |
c_52 |
Stiffness tensor, 52-component |
N/m<sup>dim-1</sup> |
c_53 |
Stiffness tensor, 53-component |
N/m<sup>dim-1</sup> |
c_54 |
Stiffness tensor, 54-component |
N/m<sup>dim-1</sup> |
c_55 |
Stiffness tensor, 55-component |
N/m<sup>dim-1</sup> |
calculator |
ASE-calculator name |
|
cbm |
Conduction band minimum |
eV |
cbm_gw |
Conduction band minimum (G₀W₀) |
eV |
cbm_gw_nosoc |
Conduction band minimum w/o soc. (G₀W₀) |
eV |
cbm_hse |
Conduction band minimum (HSE06) |
eV |
cbm_hse_nosoc |
Conduction band minimum w/o soc. (HSE06) |
eV |
cell_area |
Area of unit-cell [\(Ų\)] |
|
charge |
Net charge in unit cell |
|e| |
charge_state |
Charge state |
|
class |
Material class |
|
cod_id |
COD id of parent bulk structure |
|
crystal_type |
Crystal type |
|
dE_zx |
Magnetic anisotropy (E<sub>z</sub> - E<sub>x</sub>) |
meV/unit cell |
dE_zy |
Magnetic anisotropy (E<sub>z</sub> - E<sub>y</sub>) |
meV/unit cell] |
defect_name |
Defect name {type}_{position} |
|
defect_pointgroup |
Defect point group |
|
dim_nclusters_0D |
Number of 0D clusters. |
|
dim_nclusters_1D |
Number of 1D clusters. |
|
dim_nclusters_2D |
Number of 2D clusters. |
|
dim_nclusters_3D |
Number of 3D clusters. |
|
dim_primary |
Dim. with max. scoring parameter |
|
dim_primary_score |
Dimensionality scoring parameter of primary dimensionality. |
|
dim_score_0123D |
Dimensionality score of dimtype=0123D |
|
dim_score_012D |
Dimensionality score of dimtype=012D |
|
dim_score_013D |
Dimensionality score of dimtype=013D |
|
dim_score_01D |
Dimensionality score of dimtype=01D |
|
dim_score_023D |
Dimensionality score of dimtype=023D |
|
dim_score_02D |
Dimensionality score of dimtype=02D |
|
dim_score_03D |
Dimensionality score of dimtype=03D |
|
dim_score_0D |
Dimensionality score of dimtype=0D |
|
dim_score_123D |
Dimensionality score of dimtype=123D |
|
dim_score_12D |
Dimensionality score of dimtype=12D |
|
dim_score_13D |
Dimensionality score of dimtype=13D |
|
dim_score_1D |
Dimensionality score of dimtype=1D |
|
dim_score_23D |
Dimensionality score of dimtype=23D |
|
dim_score_2D |
Dimensionality score of dimtype=2D |
|
dim_score_3D |
Dimensionality score of dimtype=3D |
|
dim_threshold_0D |
0D dimensionality threshold. |
|
dim_threshold_1D |
1D dimensionality threshold. |
|
dim_threshold_2D |
2D dimensionality threshold. |
|
dim_threshold_3D |
3D dimensionality threshold. |
|
dipz |
Out-of-plane dipole along +z axis |
e · Å/unit cell |
doi |
Monolayer reported DOI |
|
dos_at_ef_nosoc |
Density of states at the Fermi level w/o soc. |
states/(eV · unit cell) |
dos_at_ef_soc |
Density of states at the Fermi level |
states/(eV · unit cell) |
dynamic_stability_phonons |
Phonon dynamic stability (low/high) |
|
dynamic_stability_stiffness |
Stiffness dynamic stability (low/high) |
|
e_11 |
Piezoelectric tensor |
Å<sup>-1</sup> |
e_12 |
Piezoelectric tensor |
Å<sup>-1</sup> |
e_13 |
Piezoelectric tensor |
Å<sup>-1</sup> |
e_14 |
Piezoelectric tensor |
Å<sup>-1</sup> |
e_15 |
Piezoelectric tensor |
Å<sup>-1</sup> |
e_16 |
Piezoelectric tensor |
Å<sup>-1</sup> |
e_21 |
Piezoelectric tensor |
Å<sup>-1</sup> |
e_22 |
Piezoelectric tensor |
Å<sup>-1</sup> |
e_23 |
Piezoelectric tensor |
Å<sup>-1</sup> |
e_24 |
Piezoelectric tensor |
Å<sup>-1</sup> |
e_25 |
Piezoelectric tensor |
Å<sup>-1</sup> |
e_26 |
Piezoelectric tensor |
Å<sup>-1</sup> |
e_31 |
Piezoelectric tensor |
Å<sup>-1</sup> |
e_32 |
Piezoelectric tensor |
Å<sup>-1</sup> |
e_33 |
Piezoelectric tensor |
Å<sup>-1</sup> |
e_34 |
Piezoelectric tensor |
Å<sup>-1</sup> |
e_35 |
Piezoelectric tensor |
Å<sup>-1</sup> |
e_36 |
Piezoelectric tensor |
Å<sup>-1</sup> |
edft |
DFT total enrgy |
eV |
efermi |
Fermi level |
eV |
efermi_gw_nosoc |
Fermi level w/o soc. (G₀W₀) |
eV |
efermi_gw_soc |
Fermi level (G₀W₀) |
eV |
efermi_hse_nosoc |
Fermi level w/o soc. (HSE06) |
eV |
efermi_hse_soc |
Fermi level (HSE06) [eV] |
|
ehull |
Energy above convex hull |
eV/atom |
emass_cb_dir1 |
Conduction band effective mass, direction 1 |
m<sub>e</sub> |
emass_cb_dir2 |
Conduction band effective mass, direction 2 |
m<sub>e</sub> |
emass_cb_dir3 |
Conduction band effective mass, direction 3 |
m<sub>e</sub> |
emass_vb_dir1 |
Valence band effective mass, direction 1 |
m<sub>e</sub> |
emass_vb_dir2 |
Valence band effective mass, direction 2 |
m<sub>e</sub> |
emass_vb_dir3 |
Valence band effective mass, direction 3 |
m<sub>e</sub> |
energy |
Total energy |
eV |
etot |
Total energy |
eV |
evac |
Vacuum level |
eV |
evacdiff |
Vacuum level difference |
eV |
first_class_material |
A first class material marks a physical material. |
bool |
fmax |
Maximum force |
eV/Å |
folder |
Path to collection folder |
|
forces |
Forces on atoms |
eV/Å |
formula |
Chemical formula |
|
gamma |
Cell parameter gamma |
deg |
gap |
Band gap |
eV |
gap_dir |
Direct band gap |
eV |
gap_dir_gw |
Direct band gap (G₀W₀) |
eV |
gap_dir_gw_nosoc |
Direct gap w/o soc. (G₀W₀) |
eV |
gap_dir_hse |
Direct band gap (HSE06) |
eV |
gap_dir_hse_nosoc |
Direct gap w/o soc. (HSE06) [eV] |
|
gap_dir_nosoc |
Direct gap w/o soc. |
eV] |
gap_gw |
Band gap (G₀W₀) |
eV |
gap_gw_nosoc |
Gap w/o soc. (G₀W₀) |
eV |
gap_hse |
Band gap (HSE06) |
eV |
gap_hse_nosoc |
Band gap w/o soc. (HSE06) [eV] |
|
gap_nosoc |
Gap w/o soc. |
eV] |
has_inversion_symmetry |
Material has inversion symmetry |
|
hform |
Heat of formation |
eV/atom |
host_name |
Host formula |
|
icsd_id |
ICSD id of parent bulk structure |
|
id |
Uniqe row ID |
|
is_magnetic |
Material is magnetic |
|
kcbm |
k-point of HSE06 conduction band minimum |
|
kcbm_nosoc |
k-point of HSE06 conduction band minimum w/o soc |
|
kvbm |
k-point of HSE06 valence band maximum |
|
kvbm_nosoc |
k-point of HSE06 valence band maximum w/o soc |
|
lam |
Anisotropic exchange (out-of-plane) |
meV |
layergroup |
Layer group |
|
lgnum |
Layer group number |
|
magmom |
Magnetic moment |
μ_B |
magstate |
Magnetic state |
|
mass |
Sum of atomic masses in unit cell |
au |
minhessianeig |
Minimum eigenvalue of Hessian |
eV/Ų |
natoms |
Number of atoms |
|
nspins |
Number of spins in calculator |
|
origin |
Label specifying generation procedure or origin of material |
|
pbc |
Periodic boundary conditions |
|
pdos_nosoc |
Projected density of states w/o soc. |
|
pdos_soc |
Projected density of states |
|
phi |
Easy axis, polar coordinates, phi |
radians |
phi0_km |
Berry phase spectrum localized in k0 |
|
phi0_pi_km |
Berry phase spectrum at k2=pi localized in k0 |
|
phi1_km |
Berry phase spectrum localized in k1 |
|
phi2_km |
Berry phase spectrum localized in k2 |
|
plasmafreq_vv |
Plasma frequency tensor |
Hartree |
plasmafrequency_x |
2D plasma frequency (x) |
eV/Å<sup>0.5</sup> |
plasmafrequency_y |
2D plasma frequency (y) |
eV/Å<sup>0.5</sup> |
pointgroup |
Point group |
|
s0_km |
Spin of berry phases localized in k0 |
|
s0_pi_km |
Spin of berry at phases at k2=pi localized in k0 |
|
s1_km |
Spin of berry phases localized in k1 |
|
s2_km |
Spin of berry phases localized in k3 |
|
sct |
Spin coherence time T2 |
ms |
smax |
Maximum stress on unit cell |
eV/ų |
spacegroup |
Space group (AA stacking) |
|
speed_of_sound_x |
Speed of sound (x) |
m/s |
speed_of_sound_y |
Speed of sound (y) |
m/s |
spgnum |
Space group number (AA stacking) |
|
spin |
Maximum value of S_z at magnetic sites |
|
spin_axis |
Magnetic easy axis |
|
spos |
Array: Scaled positions |
|
stiffness_tensor |
Stiffness tensor |
N/m<sup>dim-1</sup> |
stoichiometry |
Stoichiometry |
|
stresses |
Stress on unit cell |
eV/Å<sup>dim-1</sup> |
symbols |
Array: Chemical symbols |
|
thermodynamic_stability_level |
Thermodynamic stability level |
|
theta |
Easy axis, polar coordinates, theta |
radians |
uid |
Unique identifier |
|
unique_id |
Random (unique) ID |
|
user |
Username |
|
vbm |
Valence band maximum |
eV |
vbm_gw |
Valence band maximum (G₀W₀) |
eV |
vbm_gw_nosoc |
Valence band maximum w/o soc. (G₀W₀) |
eV |
vbm_hse |
Valence band maximum (HSE06) |
eV |
vbm_hse_nosoc |
Valence band maximum w/o soc. (HSE06) |
eV |
volume |
Volume of unit cell |
ų |
workfunction |
Work function (avg. if finite dipole) |
eV |
The following Python script shows how to plot the VBM and CBM.
# creates: band-alignment.png
from math import floor
import numpy as np
import matplotlib.pyplot as plt
from ase.db import connect
# Connect to database
db = connect('c2db.db')
rows = db.select('gap>0,class=TMDC-H', sort='gap')
labels = []
vbms = []
cbms = []
for row in rows:
M, X = row.symbols[:2]
label = M + X + '$_2$'
labels.append(label)
vbms.append(row.vbm)
cbms.append(row.cbm)
x = np.arange(len(vbms)) + 0.5
emin = floor(min(vbms)) - 1.0
# Width and height in pixels
ppi = 100
figw = 800
figh = 400
fig = plt.figure(figsize=(figw / ppi, figh / ppi), dpi=ppi)
ax = fig.add_subplot(1, 1, 1)
ax.bar(x, np.array(vbms) - emin, bottom=emin)
ax.bar(x, -np.array(cbms), bottom=cbms)
ax.set_xlim(0, len(labels))
ax.set_ylim(emin, 0)
ax.set_xticks(x)
ax.set_xticklabels(labels, rotation=90, fontsize=10)
plt.title("2H-TMD's: Positions of VBM and CBM (PBE+SOC)", fontsize=12)
plt.ylabel('Energy relative to vacuum [eV]', fontsize=10)
plt.tight_layout()
plt.savefig('band-alignment.png')
This produces the figure
In this example we reproduce figure 18 from
Gjerding et al..
See asr.c2db.polarizability.Result and
asr.c2db.infraredpolarizability.Result for more information.
# creates: fig18.png
import matplotlib.pyplot as plt
from asr.infraredpolarizability import \
Result as InfraredPolarizabilityResult
from asr.polarizability import Result as PolarizabilityResult
from ase.db import connect
from scipy.interpolate import interp1d
db = connect('c2db.db')
row = db.get(formula='BN')
dct = row.data['results-asr.infraredpolarizability.json']
irpol = InfraredPolarizabilityResult(**dct['kwargs'])
freq = irpol.omega_w
iralpha = irpol.alpha_wvv[:, 0, 0] # xx-component
dct = row.data['results-asr.polarizability.json']
elpol = PolarizabilityResult(**dct['kwargs'])
x = elpol.frequencies
y = elpol.alphax_w
# Interpolate to IR frequency grid:
elalpha = (interp1d(x, y.real)(freq) +
interp1d(x, y.imag)(freq) * 1j)
alpha = iralpha + elalpha
ax = plt.subplot()
ax.plot(freq * 1000, alpha.real, label='real')
ax.plot(freq * 1000, alpha.imag, label='imag')
ax.set_xlabel('Energy [meV]')
ax.set_ylabel(r'Polarizability [$\mathrm{\AA}$]')
ax.set_xlim(0, 500)
ax.legend()
plt.tight_layout()
plt.savefig('fig18.png')
The figure shows the total polarizability, including both electrons and phonons, of monolayer hBN in the infrared frequency regime.
In this example, we want to extract the k-points of HSE valence band
maximum and conduction band minimum. We do that by creating an instance of
asr.c2db.hse.Result. Once we have a Result
object we can get the data from the attributes
kvbm and kcbm:
from asr.database import connect
db = connect('c2db.db')
# Select a row that has HSE06 data:
for row in db.select(has_asr_hse=True):
break
record = row.cache.get(name='asr.c2db.hse:main')
result = record.result
print(result.kvbm)
print(result.kcbm)
The workflow for each material is described in this
workflow.py file
As an example, let’s do MoS\(_2\) in the CdI2 prototype (T-phase).
Create a main folder and a subfolder:
$ mkdir TMD
$ cd TMD
$ mkdir MoS2-CdI2
Create a structure.json file containing something close to the groundstate
structure:
$ python3
>>> from ase.build import mx2
>>> a = mx2('MoS2', '1T', a=3.20, thickness=3.17, vacuum=7.5)
>>> a.write('MoS2-CdI2/structure.json')
Start the workflow with:
$ mq workflow ~/cmr/docs/c2db/workflow.py MoS2-CdI2/
Note
The \(mq\) tool is described here
Once the first part of the workflow has finished,
one or more folders will appear (nm/, fm/, afm/) if the material
was thermodynimically stable. You can then run the remaining part of the
workflow:
$ mq workflow ~/cmr/docs/c2db/workflow.py MoS2-CdI2/*m/
When everything is ready you can collect the results in a database file and inspect the results in a web-browser:
$ python3 -m asr.database.fromtree MoS2-CdI2/*m/
$ python3 -m asr.app
