Introduction

The interaction of hydrogen with transition-metal surfaces is of great importance in heterogeneous catalysis, metallurgy, energy storage, and fuel cell technology [1]. One can find differing studies in the literature regarding the preferred adsorption site of atomic hydrogen. Periodic DFT-GGA calculations by Eder et al. [1] suggested that H-atom favors the 2-fold bridge site on Fe(100), and the 4-fold hollow site is slightly higher in energy. Whereas, the study by Jiang and Carter [2] concludes that the fourfold-hollow site is the most stable while both the 2-fold bridge and the 4-fold hollow sites are true minima. In this post, spin-polarized density functional theory calculations are performed to characterize the atomic hydrogen (H) adsorption on the Fe (100) surface using the Vienna Ab initio Simulation Package (VASP).

Methodology 

We use the plane wave DFT calculations to evaluate the adsorption energy of atomic hydrogen on the Fe (100) surface on the bridge, hollow and on the top site as shown in Fig.1. All the calculations are performed using the Vienna Ab initio Simulation Package (VASP). The exchange and correlation energies were calculated using the PBE functional described within the projector augmented wave method (PAW). Electronic convergence tolerance of 1E-05 was used for all the calculations. The core electrons were treated using pseudo-potential with a core radius of 2.3 Bohrs (1.22 Angstrom) generated with a panel of 8 valence electrons ( 3d6 4s2). All the calculations are performed with the spin-polarized calculations. 

Cut-off Energy and K-Point Optimization 

The essential step before performing a plane-wave basis set calculation is to optimize the k-points and cut-off energy. This process is performed as follows:

K-point  

The numerically determined optimal lattice parameter for Fe bcc crystal structure is 2.835 Angstrom which agrees reasonably with the experimental value of 2.856 Angstrom [3]. The K-point optimization is performed at this lattice parameter with a 2×2 Fe (100) surface with 5 atomic layers containing 20 Fe atoms in the slab.

Table 1: K-point grid vs the number of K-points used

K-point grid	K-points used
3x3x1	5
4x4x1	8
5x5x1	13
6x6x1	18
7x7x1	25
8x8x1	32

Fig.2  shows the absolute change in the consecutive total energy (|ΔE|) with respect to the number of irreducible k-points. The corresponding K-point grid is shown in Table 1. As a convergence criterion of |ΔE| less than 0.002 eV is used for the K-point convergence. This corresponds to the optimal grid of 7x7x1. 

Cut-off energy 

In Fig. 3, the absolute change in the consecutive total energy (|ΔE|) is plotted as a function of the cut-off energy. As a convergence criterion, it is assumed that the total energy is converged if |ΔE| is less than 0.005 eV. From Figs. 3 and 4, it is clear that the cut-off energy of 600 eV sufficient considering both the functionals. A lattice parameter of 2.835 Angstrom and K-point grid of 7x7x1 is used for this convergence. 

H adsorption energy 

As mentioned earlier a 5 atomic layer 2×2 Fe (100) slab with a 10 Angstrom vacuum layer containing  20 Fe-atoms is constructed (see Fig.1). Later, the H-atom is placed on several probable surface sites and a geometry optimization is performed for 0.25 ML coverage. The adsorption energy of the H-atoms is calculated as per the following expression

E_{adsorption, H-atom} = E_Fe-H – E_Fe – 0.5E_H2

Based on the K-point and cut off energy convergence study, cut-off energy of 600 eV and a K-point grid of 7x7x1 is employed in these calculations.  

Results

Table 2 The adsorption energies of H-atom on a Fe (100) surface in eV.

Site	Top	Bridge	Hollow
Current	+0.217	-0.382	-0.327
Eder et al. [1]	+0.17	-0.36	-0.35
Jiang and Carter [2]	+0.23	-0.32	-0.38

Table. 2 shows the adsorption energy for the different sites on a Fe (100) surface. It also contains data from the references cited earlier. The current calculations match quite well with the literature data. The current calculations predict that the hollow site is energetically favored for H-atom adsorption. Additionally, calculations with more number of layers of Fe are also performed to assess its effect on the adsorption energy. Table. 3 lists the adsorption energies for different Fe layers for all the sites. The typical differences converge to within 0.01 eV or 2-5% of the adsorption energy value for 9 layers. 

Table 3 The adsorption energies of H-atom on a Fe (100) surface with different atomic layers.

Site	Top	Bridge	Hollow
5 layers	+0.217	-0.382	-0.327
7 layers	+0.200	-0.395	-0.339
9 layers	+0.197	-0.390	-0.347
11 layers	+0.194	-0.389	-0.355

Conclusions

This post investigates the preferred adsorption site of H-atom on the Fe (100) surface using DFT calculations. The calculations show consistent results with the previous theoretical studies. The results of current calculations predict that the hollow site to be slightly favorable compared to the bridge site for H-atom adsorption. The calculations also demonstrate the effect of using a bigger metal slab for the calculations. The adsorption energy change becomes less than 0.01 eV from 9 layers onwards.

 

References

1. Eder, M.; Terakura, K.; Hafner, J. Phys. ReV. B 2002, 64, 115426
2. Jiang, D. E., and Emily A. Carter. “Diffusion of interstitial hydrogen into and through bcc Fe from first principles.” Physical Review B 70.6 (2004): 064102.
3. Greenwood, Norman Neill, and Alan Earnshaw. Chemistry of the Elements. Elsevier, 2012.