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, S. Manti, T. G. Pedersen, T. Skovhus, M. K. Svendsen, J. J. Mortensen, T. Olsen, K. S. Thygesen

arXiv:2102.03029 [cond-mat.mtrl-sci]

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.

../_images/workflow.png

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.

Key-value pairs

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

eV/unit cell

E_y

Soc. total energy, y-direction

eV/unit cell

E_z

Soc. total energy, z-direction

eV/unit cell

J

Nearest neighbor exchange coupling

meV

N_nn

Number of nearest neighbors

Topology

Band topology

age

Time since creation

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

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_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_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>

calculator

ASE-calculator name

cbm

Conduction band minimum

eV

cbm_gw

Conduction band minimum (G₀W₀)

eV

cbm_hse

Conduction band minimum (HSE06)

eV

cell_area

Area of unit-cell

\(Ų\)

charge

Net charge in unit cell

|e|

class

Material class

cod_id

Related COD id

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

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.

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)

efermi

Fermi level

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_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>

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/Ang

folder

Path to collection folder

formula

Chemical formula

gap

Band gap

eV

gap_dir

Direct band gap

eV

gap_dir_gw

Direct band gap (G₀W₀)

eV

gap_dir_hse

Direct band gap (HSE06)

eV

gap_dir_nosoc

Direct gap w/o soc.

eV

gap_gw

Band gap (G₀W₀)

eV

gap_hse

Band gap (HSE06)

eV

gap_nosoc

Gap w/o soc.

eV

has_inversion_symmetry

Material has inversion symmetry

hform

Heat of formation

eV/atom

icsd_id

Related ICSD id

id

Uniqe row ID

is_magnetic

Material is magnetic

lam

Anisotropic exchange (out-of-plane)

meV

magmom

Magnetic moment

au

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

pbc

Periodic boundary conditions

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

smax

Maximum stress on unit cell

eV/Ang<sup>3</sup>

spacegroup

Space group

speed_of_sound_x

Speed of sound (x)

m/s

speed_of_sound_y

Speed of sound (y)

m/s

spgnum

Space group number

spin

Maximum value of S_z at magnetic sites

spin_axis

Magnetic easy axis

stoichiometry

Stoichiometry

thermodynamic_stability_level

Thermodynamic stability level

uid

Unique identifier

unique_id

Random (unique) ID

user

Username

vbm

Valence band maximum

eV

vbm_gw

Valence band maximum (G₀W₀)

eV

vbm_hse

Valence band maximum (HSE06)

eV

volume

Volume of unit cell

Ang<sup>3</sup>

workfunction

Work function (avg. if finite dipole)

eV

Examples

Band alignment

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
import ase.db

# Connect to database
db = ase.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

../_images/band-alignment.png

Polarizability

In this example we reproduce figure 18 from Gjerding et al.. See asr.polarizability.Result and asr.infraredpolarizability.Result for more information.

# creates: fig18.png
import matplotlib.pyplot as plt
from ase.db import connect
from asr.infraredpolarizability import Result as InfraredPolarizabilityResult
from asr.polarizability import Result as PolarizabilityResult
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.

../_images/fig18.png

Extracting VBM and CBM positions in the BZ

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.hse.Result. Once we have a Result object we can get the data from the attributes kvbm and kcbm:

from ase.db import connect
from asr.hse import Result

db = connect('c2db.db')

# Select a row that has HSE06 data:
for row in db.select(has_asr_hse=True):
    break

dct = row.data['results-asr.hse.json']
result = Result(**dct['kwargs'])

print(result.kvbm)
print(result.kcbm)

Tools for creating the “Computational 2D materials” database

Requirements

Python 3.6+ and up-to-date versions of ASE, ASR and GPAW.

Workflow

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