.. _adsorption:
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} \rightarrow \mathrm{OH/slab} +
\frac{1}{2} \mathrm{H}_2`
2) `\mathrm{CH}_4 + \mathrm{slab} \rightarrow \mathrm{CH/slab} +
\frac{3}{2} \mathrm{H}_2`
3) `\mathrm{NO} + \mathrm{slab} \rightarrow \mathrm{NO/slab}`
4) `\mathrm{CO} + \mathrm{slab} \rightarrow \mathrm{CO/slab}`
5) `\mathrm{N}_2 + \mathrm{slab} \rightarrow \mathrm{N_2/slab}`
6) `\frac{1}{2}\mathrm{N}_2 + \mathrm{slab} \rightarrow \mathrm{N/slab}`
7) `\frac{1}{2}\mathrm{O}_2 + \mathrm{slab} \rightarrow \mathrm{O/slab}`
8) `\frac{1}{2}\mathrm{H}_2 + \mathrm{slab} \rightarrow \mathrm{H/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).
.. container:: article
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
__ http://dx.doi.org/10.1021/acs.jpcc.7b12258
The data can be obtained from the files:
* Download raw data :download:`adsorption.db` and :download:`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}} = \frac12 \bigg( E_{\text{slab}}
- N_{\text{layers}} E_{\text{bulk}}\bigg)`, 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} \rightarrow \mathrm{CH/Sc} + \frac32
\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/Sc}} -(E_{\mathrm{Sc}} + E_{\mathrm{CH}_4\mathrm{(g)}} -
\frac32 E_{\mathrm{H}_2\mathrm{(g)}})`.
Key-value pairs
---------------
Database of adsorption energies:
.. csv-table::
:file: keytable.csv
:header-rows: 1
:widths: 3 10 1
Similar for the surface energies:
.. csv-table::
:file: keytable_surfaces.csv
:header-rows: 1
:widths: 3 10 1
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):
.. literalinclude:: plot_example.py
Which should generate the following figure showing the adsorption versus
surface energy for NO adsorption on four different transition metals:
.. image:: database_example.svg
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\times6\times6` Å `^3` box fully relaxing the geometry with the PBE
functional.
.. _materialsproject.org: https://materialsproject.org/
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\times6\times1` 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\times12\times1` (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\times12\times1` ensures that the
exchange + correlation energy is converged to within 0.02 eV with respect to
the k-point density.
.. image:: RPA_conv.png