Benchmark adsorption and surface energies with RPA

This database contains the adsorption energies of 200 reactions involving 8 different adsorbates on 25 different transition metal surfaces at full coverage as well as the surface energies for the same surfaces. Various DFT functionals have been employed and compared to the results from many-body perturbation theory within the random phase approximation.

The adsorption reactions are

1. ${\mathrm{H}}_2\mathrm{O}+\mathrm{slab}\to \mathrm{OH}/\mathrm{slab}+\frac{1}{2}{\mathrm{H}}_2$

2. ${\mathrm{CH}}_4+\mathrm{slab}\to \mathrm{CH}/\mathrm{slab}+\frac{3}{2}{\mathrm{H}}_2$

3. $\mathrm{NO}+\mathrm{slab}\to \mathrm{NO}/\mathrm{slab}$

4. $\mathrm{CO}+\mathrm{slab}\to \mathrm{CO}/\mathrm{slab}$

5. ${\mathrm{N}}_2+\mathrm{slab}\to {\mathrm{N}}_2/\mathrm{slab}$

6. $\frac{1}{2}{\mathrm{N}}_2+\mathrm{slab}\to \mathrm{N}/\mathrm{slab}$

7. $\frac{1}{2}{\mathrm{O}}_2+\mathrm{slab}\to \mathrm{O}/\mathrm{slab}$

8. $\frac{1}{2}{\mathrm{H}}_2+\mathrm{slab}\to \mathrm{H}/\mathrm{slab}$

and the surfaces include 3d transition metals from Scandium (Sc) to Zink (Zn), 4d from Yttrium (Y) to Cadmium (Cd) excluding Technetium (Tc) and 5d from Hafnium (Hf) to Gold (Au).

Per S. Schmidt and Kristian S. Thygesen

Benchmark Database of Transition Metal Surface and Adsorption Energies from Many-Body Perturbation Theory

The Journal of Physical Chemistry C Article ASAP

The data can be obtained from the files:

• Download raw data adsorption.db and surfaces.db

And browsed online:

• Browse adsorption energies

• Browse surface energies

The adsorption energy is defined with respect to the adsorbate in its gas phase: $E_{\text{ads}}=E_{\text{adsorbate@slab}}-(E_{\text{slab}}+E_{\text{adsorbate(g)}})$

And the surface energy as: $E_{\text{surf}}=\frac{1}{2}(E_{\text{slab}}-N_{\text{layers}}{E}_{\text{bulk}})$, where the number of atomic layers in the slab is $N_{\text{layers}}=3$.

One example reaction that the adsorption energy is calculated for is:

${\mathrm{CH}}_4(\mathrm{g})+\mathrm{Sc}\to \mathrm{CH}/\mathrm{Sc}+\frac{3}{2}{\mathrm{H}}_2(\mathrm{g})$

In the database the adsorbate is then $\mathrm{CH}$, the surface material is $\mathrm{Sc}$, reference molecule 1 is ${\mathrm{CH}}_4$ and reference molecule 2 is ${\mathrm{H}}_2$. The adsorption energy is then $E_{\text{ads}}=E_{\mathrm{CH}/\mathrm{Sc}}-(E_{\mathrm{Sc}}+E_{{\mathrm{CH}}_4(\mathrm{g})}-\frac{3}{2}{E}_{{\mathrm{H}}_2(\mathrm{g})})$.

Key-value pairs

key	description	unit
surf_mat	Surface Material
adsorbate	Adsorbate
mol	Reference molecule 1
mol2	Reference molecule 2
LDA_adsorp	Adsorption energy with LDA	eV
PBE_adsorp	Adsorption energy with PBE	eV
RPBE_adsorp	Adsorption energy with RPBE	eV
BEEFvdW_adsorp	Adsorption energy with BEEF-vdW	eV
vdWDF2_adsorp	Adsorption energy with vdW-DF2	eV
mBEEF_adsorp	Adsorption energy with mBEEF	eV
mBEEFvdW_adsorp	Adsorption energy with mBEEF-vdW	eV
EXX_adsorp	Adsorption energy with EXX	eV
RPA_adsorp	RPA correlation adsorption energy extrapolated	eV

Reading data

In the following script it is shown how to extract and plot adsorption and surface energies from the database files (adsorption.db, surfaces.db):

# creates: database_example.svg
import numpy as np
import matplotlib.pyplot as plt
import ase.db

adsorbate = 'NO'
slabs = ['Sc', 'Ti', 'Cu', 'Pd']
db = ase.db.connect('adsorption.db')
db_surf = ase.db.connect('surfaces.db')

labels = ['LDA', 'PBE', 'RPBE', 'BEEF-vdW', 'RPA']
markers = ['o', 's', 'v', 'D', 'x']
markersize = [10, 10, 10, 10, 12]
mews = [1, 1, 1, 1, 4]
cols = ['r', 'k', 'b', 'g']

plt.figure()
for ii, slab in enumerate(slabs):
    rows = db.select(adsorbate=adsorbate)
    adss = []
    for row in rows:
        if row.symbols[0] == slab:
            adss.append(row.LDA_adsorp)
            adss.append(row.PBE_adsorp)
            adss.append(row.RPBE_adsorp)
            adss.append(row.BEEFvdW_adsorp)
            adss.append(row.RPA_EXX_adsorp)

    rows_surf = db_surf.select(surf_mat=slab)
    surfs = []
    for row in rows_surf:
        surfs.append(row.LDA_surf)
        surfs.append(row.PBE_surf)
        surfs.append(row.RPBE_surf)
        surfs.append(row.BEEFvdW_surf)
        surfs.append(row.RPA_EXX_surf)

    for i in range(len(adss)):
        if ii == 0:
            plt.plot(surfs[i], adss[i], color='darkgray',
                     marker=markers[i], markersize=markersize[i],
                     mew=mews[i], label=labels[i])

        plt.plot(surfs[i], adss[i], color=cols[ii],
                 marker=markers[i], markersize=markersize[i], mew=mews[i])

    p = np.polyfit(surfs[:-1],
                   adss[:-1],
                   deg=1)

    plt.plot([surfs[2], surfs[0]],
             p[0] * np.array([surfs[2], surfs[0]]) + p[1],
             color=cols[ii])
    plt.annotate(slabs[ii], (surfs[-1] + 0.02, adss[-1]), color=cols[ii],
                 size=14)

plt.legend(loc='lower left', numpoints=1, prop={'size': 14})
plt.title('NO adsorption', size=18)

plt.ylim([-3.5, 0])
plt.xlim([0.3, 1.1])

plt.xlabel(r'$E_{\sigma}$ (eV)', size=22)
plt.ylabel(r'$E_{\mathrm{ads}}$ (eV)', size=22)

plt.xticks(size=18)
plt.yticks(size=18)
plt.tight_layout()
plt.savefig('database_example.svg', dpi=500)

Which should generate the following figure showing the adsorption versus surface energy for NO adsorption on four different transition metals:

Computational details

The surfaces were modeled using three layers with the bottom two layers fixed at the fcc PBE lattice constants from materialsproject.org and the position of the top layer relaxed. The position of the adsorbate was relaxed keeping all three surface layers fixed at the position found previously. All relaxations were carried out with the BFGS algorithm using the PBE approximation to the xc-functional with a force convergence criteria of 0.05 eV/Å. The electron temperature was 0.01 eV and spin-polarized calculations were performed for calculations involving Fe, Ni or Co. 5 Å of vacuum was added to either side of the adsorbate to avoid artificial interactions between neighboring layers following convergence tests at both the DFT and RPA level. The adsorption energies are relative to the molecule in its gas phase and the calculations for the isolated molecules were carried out in a $6\times 6\times 6$ Å ${}^3$ box fully relaxing the geometry with the PBE functional.

The RPA calculations were carefully converged with respect to plane wave basis using the following extrapolation scheme: In the following figure, the black dots are from a calculation with $6\times 6\times 1$ k-points (not enough to achieve convergence) but high cutoff energies (300, 400, 500 eV). The green circle is a calculation at a much denser k-point sampling of $12\times 12\times 1$ (converged). From these four circles, the two green crosses are predicted which allow for an extrapolation to infinite cutoff energy. The red dots represent actual calculations with both a dense k-point grid and high cutoff energies to test the extrapolation scheme. The error introduced by the extrapolation scheme for this particular system is seen to be 0.013 eV. The k-point grid of $12\times 12\times 1$ ensures that the exchange + correlation energy is converged to within 0.02 eV with respect to the k-point density.