Geometrical frustration of an argon monolayer adsorbed on the MgO (100) surface: An accurate periodic ab initio study

We present an accurate first-principles method for calculating the energy of physisorption, based on a fully periodic local Møller-Plesset second order perturbation theory (LMP2) treatment. The LMP2 inter-surface-adsorbate interaction energy is scaled with a factor, obtained by comparing the method error of LMP2 versus coupled cluster singles doubles theory with perturbative triples at the basis set limit in small clusters mimicking the system under study. This method is applied to the investigation of geometrical frustration in argon monolayers adsorbed on the MgO (100) surface. It is found that several arrangements of the argon monolayer, i.e., $3\times 2$, $4\times 2$, optimal hexagonal, and $\zeta \times 2$ 1D noncommensurate have very similar adsorption energies, which agrees with the experimental observations. Moreover, this study provides further insight in to the Ar-MgO adsorption process and sheds light on a controversy among different experiments. The calculated adsorption energy of 2.3 kcal/mol is in a very good agreement with the experimental values, which range from 2.0 to 2.3 kcal/mol, and provides a new benchmark for this system.

Figure 1

CCSD(T) and LMP2 potential curves for the equilateral argon trimer.

Figure 2

HF, LMP2, CCSD(T), and corrected LMP2 potential curves for the argon - planar Na${}_2$Mg${}_3$O${}_4$ dimer in the perpendicular orientation. The intra- and intercomponents of the LMP2 and corrected LMP2 curves are also shown.

Figure 3

Corrected LMP2 Ar-MgO potential curves and its components, calculated in the $2\times 2$ arrangement for 3 adsorption positions: on top of Mg atoms (red, triangles, solid), on top of oxygen atoms (blue, circles, dashed) and on top of Mg-Mg midpoint (green, starts, dash-dotted).

Figure 4

The competing arrangements of argon monolayer on MgO surface, studied in the present work. Small blue spheres correspond to the Mg atoms, intermediate-sized red spheres to the oxygen atoms, and large grey spheres to the argons. The crystallographic unit cells are brightened. The detailed specification is given in Appendix .

Figure 5

The MgO (100)-surface corrugation potential for the argon atoms at the equilibrium Ar-MgO distance. The 2D surface has been fitted via a cubic interpolation to the energies for 12 symmetry unique adsorption sites, calculated within the $2\times 2$ supercell. The maximal and minimal energy values are $-$1.381 kcal/mol (on-O adsorption) and $-$1.709 kcal/mol (on-Mg adsorption). The contour isoline step is 0.02 kcal/mol.

Figure 6

The MgO (100)-surface corrugation potential curve along the Mg-(Mg|Mg)-Mg direction as from the 2D 12-point cubic fit, Fig. 5 (blue dashed line) or from Eq. (3) (red solid line). The energies of explicitly calculated points within this direction are also shown (circles).

Figure 7

The formation energy of the planar argon monolayer per one argon atom $E_{\parallel }$ as a function of the surface concentration $\sigma$, i.e., the number of Ar atoms per MgO surface unit cell (unity concentration corresponds to an arrangement with the amount of Ar atoms equal to that of surface Mg or O atoms). Two types of arrangements are considered: the continuous rectangular $\zeta \times 2$ arrangement (and $n\times 2$ with the $2\times 2$, $3\times 2,$ and $4\times 2$ geometries as particular cases): blue squares; and a regular hexagonal monolayer with different inter-argon distances: red stars. The symbols represent the explicitly calculated points, the values in between are spline interpolated. The crosses correspond to the energies of the five commensurate argon monolayer arrangements studied in the paper, calculated with the actual off-planarity of the argon atoms in the monolayers (cf. Sec. 2c) taken into account.

Figure 8

Ar-Na${}_2$Mg${}_3$O${}_4$ dimer used in the LMP2$\to$CCSD(T) correction scheme.