Surface energetics of alkaline-earth metal oxides: Trends in stability and adsorption of small molecules

We present a systematic theoretical investigation of the surface properties, stability, and reactivity of rocksalt type alkaline-earth metal oxides including MgO, CaO, SrO, and BaO. The accuracy of commonly used exchange-correlation density functionals (LDA, PBE, RPBE, PBEsol, BEEF-vdW, and hybrid HSE) and random-phase approximation (RPA) is evaluated and compared to existing experimental values. Calculated surface energies of the four most stable surface facets under vacuum conditions, the (100) surface, the metal and oxygen terminated octopolar (111), and the (110) surfaces, exhibit a monotonic increase in stability from MgO to BaO. On the MgO(100) surface, adsorption of CO, NO, and ${\text{CH}}_4$ is characterized by physisorption while ${\text{H}}_2\text{O}$ chemisorbs, which is in agreement with experimental findings. We further use the on-top metal adsorption of CO and NO molecules to map out the surface energetics of each alkaline-earth metal oxide surface. The considered functionals all qualitatively predict similar adsorption energy trends. The ordering between the adsorption energies on different surface facets can be attributed to differences in the local geometrical surface structure and the electronic structure of the metal constituent of the alkaline-earth metal oxide. The striking observation that CO adsorption strength is weaker than NO adsorption on the (100) terraces as the period of the alkaline-earth metal in the oxide increases is analyzed in detail in terms of charge redistribution within the $\sigma$ and $\pi$ channels of adsorbates. Finally, we also present oxygen adsorption and oxygen vacancy formation energies in these oxide systems.

Figure 1

Calculated lattice constants $a$, bulk moduli $M$, and atomization energies $\Delta E^{\mathrm{AE}}$ for six different DFT functionals together with experimental values adapted from Refs. [54, 55, 56]. Note that, in our simplified comparison to experimental data, we have neglected anharmonic ZPE corrections, which can be as large as $\Delta a=-0.02$ Å for bulk MgO [57].

Figure 2

Calculated surface energies of stoichiometric low-index terminated alkaline-earth metal-oxide surfaces in eV normalized to $1\times 1$ surface area. The results for the (100), (110), and two octopolar (111) terminated (M-Oct, O-oct) surfaces obtained using six different DFT functionals are shown. The corresponding primitive cell of the surfaces used in the calculations are also shown as insets, where larger spheres represent the metal atoms. For clarity, only the top layer was rendered in color.

Figure 3

Upper panel: adsorption energies of CO, NO, ${\text{CH}}_4$, and ${\text{H}}_2\text{O}$ molecules on the MgO(100) surface. The $2\times 2$ unit cells are shown as insets with geometries discussed in the text. Except for the case of ${\text{CH}}_4$ with one monolayer coverage, all other adsorbates are in the limit of low coverage (up to coverage of $\Theta =1/8$) as discussed in text. The experimental and calculated values are summarized in Table 2. Lower panel: associated atomization errors of each molecular species for the different methods relative to the ZPE corrected experimental atomization energies as adapted from NIST CCCBD [68].

Figure 4

Adsorption energies of CO (top panel) and NO (bottom panel) in the on-top surface metal site on the (100), (111)-M-oct, and (110) surfaces of the AEMO series plotted as function of surface energy. For clarity, only the BEEF-vdW results are shown for NO on (111)-M-oct.

Figure 5

Charge density difference plots for CO@MgO(100) (left) and CO@BaO(100) (right) projected along the $\langle 110\rangle$ direction obtained with the BEEF-vdW functional. The positive (negative) values of this quantity indicate regions with gain (loss) of electronic charge. The numeric labels indicate the change in the Bader charge upon adsorption relative to the free gas-phase molecule. Small red and black spheres indicate positions of oxygen and carbon atoms, respectively.

Figure 6

Charge density difference contour plots for NO@MgO(100) (left) and NO@BaO(100) (right) projected along the $\langle 100\rangle$ direction calculated at the BEEF-vdW level. Small blue sphere indicate positions of the nitrogen atom while the rest of the labels are identical to Fig. 5. Insets: full three-dimensional shapes of charge density difference contours at values of $\pm 0.001$.

Figure 7

Projected density of states of CO (left panel) and NO (right panel) adsorbed on the MgO(100) and BaO(100) surfaces compared to their gas-phase spectra as calculated within the BEEF-vdW functional. All spectra are aligned relative to the Fermi level $E_F$, except for the gas-phase spectrum of CO, which was aligned to match the position of the $5\sigma$ peak to an experimental spectrum (adapted from Fig. 43 of Ref. [71]). For NO, the spin-minority channel is indicated as negative values. The atomic projections to $\sigma$ and $\pi$ contributions of molecules have been enhanced by a factor of 2 for CO and 4 for NO for clarity.

Figure 8

Upper panel: adsorption energy of atomic oxygen $E_{\mathrm{ads}.}^{\mathrm{O}}$, for adsorbate coverage $\Theta =0.25$, on the surfaces of the AEMO series shown as function of surface energy. As in Fig. 4, the reported results are for six DFT functionals and two RPA methods. For on-top and bridge sites, only the PBE results are shown. The inset depicts the geometry of the MOM site. Lower panel: same as above but for oxygen vacancy formation energy $E_{\mathrm{f}}^{\mathrm{O}}$.

Figure 9

Linear dependence of $E_{\mathrm{f}}^{\mathrm{O}}$ in (110) and O-oct (111) surfaces relative to $E_{\mathrm{f}}^{\mathrm{O}}$ of (100) surfaces. Inset: similar linear dependence between on-top $E_{\mathrm{ads}}^{\mathrm{O}}$ and $E_{\mathrm{f}}^{\mathrm{O}}$ using only the PBE data of Fig. 8.