Computational 2D Materials Database (C2DB)

If you are using data from this database in your research, please cite the following papers:

The Computational 2D Materials Database: High-Throughput Modeling and Discovery of Atomically Thin Crystals

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)

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• The full dataset is provided upon request.

Brief description

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.

Overview of methods and parameters used

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.

Funding acknowledgements

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).

Versions

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.
2024-05-01	16789	New webpages. Restructuring of the search page (removed HIGH, MEDIUM, LOW characterization of thermodynamic stability). Added various properties for the 3.330 most stable of the 11.630 structures that were added in version 2022-09-08. Added ca. 100 self-intercalated bilayers. Spontaneous polarisations for 63 ferroelectrics. Symmetry classification according to layer groups in addition to space groups of the AA-stacked bulk.

Key-value pairs

name	description	unit
A	Single-ion anisotropy (out-of-plane)	meV
J	Nearest neighbor exchange coupling	meV
N_nn	Number of nearest neighbors
alphax	Static polarizability (phonons + electrons) (x)	Å
alphax_el	Static interband polarizability at (x)	Å
alphax_lat	Static polarizability (phonons) (x)	Å
alphay	Static polarizability (phonons + electrons) (y)	Å
alphay_el	Static interband polarizability at (y)	Å
alphay_lat	Static polarizability (phonons) (y)	Å
alphaz	Static polarizability (phonons + electrons) (z)	Å
alphaz_el	Static interband polarizability at (z)	Å
alphaz_lat	Static polarizability (phonons) (z)	Å
area	Unit cell area	Å\(^{2}\)
cod_id	COD id of parent bulk structure
dE_zx	Magnetic anisotropy energy, xz	meV/unit cell
dE_zy	Magnetic anisotropy energy, yz	meV/unit cell
doi	Mono/few-layer report(s)
dyn_stab	Dynamically stable
efermi	Fermi level	eV
ehull	Energy above convex hull	eV/atom
energy	Energy	eV
evac	Vacuum level	eV
folder	Original file-system folder
formula	Formula
gap	Band gap	eV
gap_gw	Band gap (G₀W₀)	eV
gap_hse	Band gap (HSE06)	eV
halfmetal_gap	Half-metal gap (PBE)	eV
halfmetal_gap_hse	Half-metal gap (HSE06)	eV
has_inversion_symmetry	Inversion symmetry
hform	Heat of formation	eV/atom
icsd_id	ICSD id of parent bulk structure
label	Structure origin
lam	Anisotropic exchange (out-of-plane)	meV
layergroup	Layer group
lgnum	Layer group number
magmom	Total magnetic moment	μ\(_{B}\)
magstate	Magnetic state
natoms	Number of atoms
nspecies	Number of species
olduid	Old uid
plasmafrequency_x	Plasma frequency (x)	Å\(^{0.5}\)
plasmafrequency_y	Plasma frequency (y)	Å\(^{0.5}\)
reduced	Reduced formula
spin	Maximum value of S\(_{z}\) at magnetic sites
spin_axis	Spin axis
stoichiometry	Stoichiometry
uid	Unique ID

Using the data

Here is an example using the c2db.db ASE-DB file:

import matplotlib.pyplot as plt
from ase.db import connect

db = connect('c2db.db')
rows = db.select('gap_gw')

gw = []
hse = []
pbe = []
for row in rows:
    gw.append(row.gap_gw)
    hse.append(row.gap_hse)
    pbe.append(row.gap)

fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.plot(pbe, hse, 'o', label='HSE06')
ax.plot(pbe, gw, 'x', label='GW')
x = [0, max(pbe)]
ax.plot(x, x, label='PBE')
ax.set_xlabel('PBE-gap [eV]')
ax.set_ylabel('gap [eV]')
ax.legend()
plt.savefig('gaps.png')

Alternatively, one can unpack the c2db.tar.gz file with tar -xf c2db.tar.gz and extract the gaps like this:

from pathlib import Path
import json

gw = []
hse = []
pbe = []
for path in Path().glob('materials/A*/*/*'):
    data = json.loads((path / 'data.json').read_text())
    if 'gap_gw' in data:
        gw.append(data['gap_gw'])
        hse.append(data['gap_hse'])
        pbe.append(data['gap'])