1. COLLEGE OF ENGINEERING Chemical, Biological & Environmental Engineering
A DFT Study of Adsorbate-Adsorbate Interactions as
a Function of Coverage and Hubbard U on RuO2
Yousif Almulla1,2 and Líney Árnadóttir3
1Department of Physics
2Department of Mathematics
3School of Chem., Bio., & Enviro. Engineering
Oregon State University, Corvallis, Oregon
Results
An interaction energy, Eint, can be defined as in
Figure 6. A negative Eint (green shading) implies
that the 1ML higher coverage bonding is less
favorable than the ½ ML bonding at the Ueff value.
The majority of data points in Figure 6 take a
negative interaction energy, essentially saying
that a higher O concentration is destabilizing to
surface adsorption.
We conjectured that the change in surface
structure brought about by individual lattice
parameter optimization at each Ueff could affect
the adsorbate-adsorbate interaction at higher
coverage. As such, all calculations were repeated
at fixed lattice parameters, based on Ueff = 0 eV.
Figure 7 shows the interaction energy calculated
from fixed lattice parameters, and the high
variance remains in the Ueff = 2 to Ueff = 5 domain,
leading us to dismiss the possibility that
sensitivity to U value is based only on interatomic
distances.
Introduction
Conclusion and Discussion
The variance is not limited to adsorptions
energies but also affects the adsorbate-
adsorbate interactions. Although most DFT+U
calculations predict repulsive interactions at
higher coverage, it is not universal and also
varies with choice of lattice parameters.
It should be noted that in previous studies, U
values ranging from 2 eV to 7 eV have been used
for RuO2 calculations, but larger variations are
seen between this U values here. Studies such as
this one call into question the fidelity of DFT+U
calculations, and even comparison of trends
between different studies.
The sensitivity to U value in energy calculations
highlights the importance of obtaining a more
complete grasp of the +U Hubbard energy term
for DFT.
Acknowledgements
• Dr. Líney Árnadóttir
• Graduate Students Lynza H. Sprowl, Kofi
Oware Sarfo, and Qin Pang
References
Xu et al. A Linear Response DFT+U Study of Trends in the Oxygen
Evolution Activity of Transition Metal Rutile Dioxides. J. Phys. Chem. C
119(9) 4827-4833, 2015.
Huang et al. Surface-Specific DFT + U Approach Applied to α-
Fe2O3(0001). J. Phys. Chem. C 120(9) 4919-4930, 2016.
Wang et al. Oxidation energies of transition metal oxides within the GGA
+ U framework. Phys. Rev. B. Vol. 17. 2006.
Motivation
The DFT+U approach is common for calculating
band-gaps and reaction mechanisms on TMO
surfaces, but the effects of the Hubbard U on
surface-adsorbate and adsorbate-adsorbate
interactions are not yet fully explored. For
example, Xu et al. found that adsorption energies
on TMO surfaces vary with U value, while Huang et
al. showed that although DFT+U improves band gap
predictions, it also effects the surface energy
calculations and bulk properties.
In this study we analyze how the addition of the
Hubbard U affects adsorbate-adsorbate interactions
of adsorbed O on rutile (110) RuO2, as a function of
adsorbate coverage and U value.
Figure 1.
Above is a top-down view of the bare surface, ½ and 1
monolayer (ML) O coverage surfaces, respectively. To
the right is an example of a complete RuO2 unit cell
used in our calculations, with a 1 ML O coverage.
Methods
The Vienna ab-initio Simulation Package was used to
conduct spin-polarized DFT calculations for all
systems. RuO2 system energy calculations of ½ ML, 1
ML and 0 ML (bare surface) were conducted at each
Ueff from 0 eV to 7 eV, in 0.5 eV intervals. The
adsorbed O is in the on-top position for all
coverages.
On-top adsorption sites.
Future Work
Further calculations for other metal oxide
surfaces are under way. We would also like to
conduct similar studies for other less strongly
bonding adsorbates. It is possible that the
variance in adsorbate energy here is affected by
the fact that O bonds very strongly to surfaces.
Measuring this variance for other adsorbates will
help surface scientists develop a clearer picture
of how the +U should be utilized and provide
insights into how results and trends can be
compared for different values of +U.
COLLEGE OF SCIENCE
Systems Modeled:
Background
Density Functional Theory (DFT) is widely used in
the field of surface science as an approximation to
the many-bodied Schrödinger equation and as the
canonical tool for chemical modelling. When
modelling transition metal oxide (TMO) surfaces, a
Hubbard energy term, U, is added to the
Hamiltonian for DFT to improve the treatment of d-
orbital electrons. The Hubbard U explicitly factors
in on-site Coulombic repulsion of electrons, and has
been shown to model the band-structures of
strongly correlated systems with better empirical
agreement than previous methods.
“U–effective” = Ueff
Hubbard U Notation
J is normally constant for a specific element, hence
we vary only U value and define U – J as the
effective U.
Figure 6. We have defined the interaction energy to be a
metric for destabilization of oxygen adsorption w.r.t. the
higher coverage:
𝐸𝑖𝑛𝑡 = 2 ∗ 𝐸 𝑎𝑑𝑠
1
2
𝑀𝐿 − 𝐸 𝑎𝑑𝑠(1𝑀𝐿)
Repulsive interactions
Attractive interactions
Figures 2 and 3. Adsorption energies seem to follow a similar
path, merging at Ueff = 5. Total energies increase linearly.
Figure 4. Note the trend for 1ML
O is not as smooth as in Fig. 2.
Figure 5. Comparing to Fig. 3, we
see that +U smoothens trends.
Figure 7. While smoother than Fig. 6’s Eint plot,
there is still a mysterious high variance.