Introduction
Adsorption of small molecules on transition metal surfaces is of great interest among chemists, since adsorption behavior could be essential to the catalytic process happening on transition metal surfaces. For adsorption on (111) surface of fcc metals, there are 4 different kinds of sites, as shown in figure 1. It is worth noticing that there are two different possible sites for threefold adsorption situations, which are called fcc and hcp site respectively. Since the bulk structure of Rh has been studied in previous work, in this work, the preference of adsorption of CO of low surface coverage on Rh (111) is assumed to be on-top site according former computational study[1]. Intuitively, CO adsorption on-top sites at low coverage is similar to the situation that CO bonds to central metal atom as a ligand, which should have a lower energy comparing to other adsorption sites.
Figure 1 (a) fcc site, (b) on-top site, (c) hcp site, (d) bridge site
Method
In this work, plane-wave based DFT code CASTEP is used. The exchange-correlation functional is described by a GGA-PBE functional, and pseudopotentials are kept default setting. As for pseudopotential, the “on the fly” generated ultrasoft pseudopotential for Rh is used with a core radius of 1.6 Bohr(0.847Å) and was generated with a 4d8 5s1 valence electronic configuration . The SCF tolerance is set to be 2e-6 eV per atom for all the optimization and single point energy calculations.
Optimized bulk structure of Rh is taken from previous work[2]. According to previous computational work[3], a 2×2 Rh(111) surface slab model of 4 layers of atoms is used to simulate the behavior of Rh surface. As for the optimization of surface slab model, energy cutoff is kept consistent with that for bulk calculation, while k points gird setting is set to 7x7x1. In order to get comparable energies for molecule and surfaces, the same setting is used for optimization of CO in vacuum. CO adsorption is modeled with single CO adsorbed on different sites of optimized surface model. The corresponding adsorption energy is calculated with the equation[4]
\begin{equation} E_{ads}=E_{Rh-CO}-E_{surface}-E_{CO} \end{equation}
Results
1. k points grid optimization
With an energy cutoff of 625 eV, single point energies of 1×1 slab models are calculated. In figure 2, the energies relative to 9x9x1 k points gird is shown. As a trade off of accuracy and efficiency, 7x7x1 k points grid is used to get valid results for surface calculations.
Figure 2 k points convergence test, energy relative to maximum k points grid is convergent for grid larger than 7x7x1 gird.
2. Surface optimization
Although 2×2 slab model will be used for adsorption of CO calculations in order to make sure a 1/4 ML coverage, here surface structure optimization is performed for 1×1 slab model. Due to the limitation of computation resources, 2×2 slab model optimization won’t converge in reasonable time, a 1×1 slab model is optimized instead. Since Rh surface slab model is periodic system, a 1×1 slab won’t introduce significant error to final results. Meanwhile, the energy of the supercell should be scalable, which makes it reasonable to get energy of 2×2 slab out of 1×1 slab. Only top two layers are relaxed while two layers at bottom are kept fixed to simulate bulk effect on surface atoms.
BFGS algorithm is used to perform the optimization with energy convergence of 2e-5 ev/atom and force convergence of 0.05 eV/A. The optimized structure has an energy of -12123.0410 eV.
3.Optimization of CO in vacuum
In order to obtain consistent value for molecular energy, CO configuration is optimized in the same lattice as the surface slab model. The optimized bond length is 1.138 A, with an energy of -596.123 eV.
4. Optimization of CO adsorption
A 2×2 slab model for Rh(111) surface is used to get a optimized structure of one single CO adsorption on- top site, which corresponds to a 1/4 ML coverage. Such systems would significantly increase the cost of computation if full optimization is performed. Thus, only the distance between CO molecule and Rh atom is allowed to relax to find the most stable configuration of CO adsorption on-top site. Such modelling of CO adsorption is based on the assumption that adsorption of CO with low coverage won’t induce significant surface structure reconstruction.
The optimization algorithm and convergence setting is consistent with those for surface structure optimization. The optimized distance between C and Rh atom is 1.843 A with a total energy of -49089.5603 eV. The CO adsorption energy for Rh on-top site is -1.273 eV. Meanwhile, C-O bond is stretched to 1.160 A, which suggests the weakening of bond strength between C and O.
Conclusion
The adsorption energy of CO on on-top site of Rh (111) surface is -1.273 eV with an optimized bond distance of 1.843 A, which is consistent with former computational results at 1/4 ML coverage, 1.83A [1] and 1.842 A[3], respectively. Since different levels of theory or different exchange-correlation functionals have been used, the bind energies are not comparable, it is reasonable to compare the bonding length between metal atoms and adsorbate to see if the optimized geometry is consistent with former study. Further work may focus on the influence of surface coverage on the adsorption energy and bond weakening of C-O bonds. On the other hand in order to get adsorption values comparable to experimental ones, a test for different exchange-correlation functionals and thermodynamic parameters are required.
Reference
[1] Mavrikakis, M., Rempel, J., Greeley, J., Hansen, L. B. & Nørskov, J. K. Atomic and molecular adsorption on Rh(111). J. Chem. Phys. 117, 6737–6744 (2002).
[2]Prediction of preferred structure and lattice parameters of Rh https://sites.psu.edu/dftap/2020/02/03/prediction-of-preferred-structure-and-lattice-parameters-of-rh/
[3] Krenn, G., Bako, I. & Schennach, R. CO adsorption and CO and O coadsorption on Rh(111) studied by reflection absorption infrared spectroscopy and density functional theory. J. Chem. Phys. 124, 144703 (2006).
[4] Sholl, D. & Steckel, J. A. Density functional theory: a practical introduction. (John Wiley & Sons, 2011).
