Density-functional theory with screened van der Waals interactions applied to atomic and molecular adsorbates on close-packed and non-close-packed surfaces

Modeling the adsorption of atoms and molecules on surfaces requires efficient electronic-structure methods that are able to capture both covalent and noncovalent interactions in a reliable manner. In order to tackle this problem, we have developed a method within density-functional theory (DFT) to model screened van der Waals interactions (vdW) for atoms and molecules on surfaces (the so-called DFT+${\text{vdW}}^{\mathrm{surf}}$ method). The relatively high accuracy of the DFT+${\text{vdW}}^{\mathrm{surf}}$ method in the calculation of both adsorption distances and energies, as well as the high degree of its reliability across a wide range of adsorbates, indicates the importance of the collective electronic effects within the extended substrate for the calculation of the vdW energy tail. We examine in detail the theoretical background of the method and assess its performance for adsorption phenomena including the physisorption of Xe on selected close-packed transition metal surfaces and 3,4,9,10-perylene-tetracarboxylic acid dianhydride (PTCDA) on Au(111). We also address the performance of DFT+${\text{vdW}}^{\mathrm{surf}}$ in the case of non-close-packed surfaces by studying the adsorption of Xe on Cu(110) and the interfaces formed by the adsorption of a PTCDA monolayer on the Ag(111), Ag(100), and Ag(110) surfaces. We conclude by discussing outstanding challenges in the modeling of vdW interactions for studying atomic and molecular adsorbates on inorganic substrates.

Figure 1

Geometry of the atom-surface system.

Figure 2

Adsorption energies $E_{\mathrm{ads}}$ calculated with PBE+${\text{vdW}}^{\mathrm{surf}}$ for Xe on transition-metal surfaces. The contributions of PBE and vdW interactions after relaxing the system with the PBE+${\text{vdW}}^{\mathrm{surf}}$ method are shown in red and blue, respectively. Total adsorption energies after relaxation are displayed in green. Top sites are displayed with plain color filled bars whereas fcc hollow sites are displayed with pattern filled bars.

Figure 3

Potential-energy curve as a function of vertical distance $d$ of a Xe monolayer on top of Pt(111) with different approximations within DFT. The blue shaded regions correspond to the experimental adsorption distance [91] of 3.4 $\pm$ 0.1 Å and to the interval of experimental adsorption energy [38] that ranges from $-260$ to $-280$ meV.

Figure 4

(a) Chemical structure of PTCDA. The distinction between carbon atoms belonging to the perylene core (${\mathrm{C}}_{\mathrm{peryl}}$, black) and to the functional groups (${\mathrm{C}}_{\mathrm{funct}}$, dark gray) is also displayed. In a similar fashion, oxygen atoms are shown in red for the case of the carboxylic oxygen (${\mathrm{O}}_{\mathrm{carb}}$) and blue for the anhydride oxygen (${\mathrm{O}}_{\mathrm{anhyd}}$). (b) Top view of the relaxed structure of PTCDA on Ag(111). Both inequivalent molecules of the structure are labeled A and B. (c) Top view of the relaxed structure of PTCDA on Ag(100). (d) Top view of the relaxed structure of PTCDA on Ag(110). The topmost metal layer is displayed in dark gray while the sublayer is light gray. Images of the structures were produced using the visualization software vesta [106].

Figure 5

(a) Adsorption energy $E_{\mathrm{ads}}$ as a function of vertical distance $d$ for PTCDA on Au(111). The distance $d$ is evaluated with respect to the position of the unrelaxed topmost metal layer. The blue shaded region corresponds to the experimental adsorption distance of 3.25 $\pm$ 0.1 Å as determined by Wagner and co-workers [79]. The error bar corresponds to typical experimental error estimates. (b) Contribution of vdW interactions to the adsorption energy as a function of vertical distance $d$ for PTCDA on Au(111), which is defined as the difference between either the PBE+${\text{vdW}}^{\mathrm{surf}}$ or the PBE+vdW energy and the PBE energy.

Figure 6

(a) Changes in the $C_6^{\mathrm{AuC}}$ coefficient with respect to the adsorption distance $d$ for a single PTCDA molecule on Au(111) calculated with the PBE+${\text{vdW}}^{\mathrm{surf}}$ method. (b) Variations of the damping function $f_{\mathrm{damp}}$ with respect to the adsorption distance $d$ when using the PBE+vdW and PBE+${\text{vdW}}^{\mathrm{surf}}$ methods. The onset of $f_{\mathrm{damp}}$ occurs at a smaller distance in the PBE+${\text{vdW}}^{\mathrm{surf}}$ method.

Figure 7

Potential-energy curve as a function of vertical distance $d$ of a Xe monolayer on top of Cu(110) with different approximations within DFT. The blue shaded regions correspond to the experimental adsorption distance [85] of 3.3 $\pm$ 0.1 Å and experimental adsorption energy [86] of $-218\pm$ 6 meV (see also Table 3).

Figure 8

(a) Changes in the $C_6^{\mathrm{XeCu}}$ coefficient with respect to the adsorption distance $d$ for Xe on Cu(110) (blue) and Cu(111) (red) calculated with the PBE+${\text{vdW}}^{\mathrm{surf}}$ method. (b) Potential-energy curve as a function of vertical distance $d$ of Xe on top of Cu(110) (blue) and Cu(111) (red) calculated with the PBE+${\text{vdW}}^{\mathrm{surf}}$ method. The blue dashed line corresponds to the experimental adsorption distance [85] of 3.3 $\pm$ 0.1 Å for Xe on Cu(110). The red dashed line corresponds to the experimental adsorption distance [84] of 3.60 $\pm$ 0.08 Å for Xe on Cu(111).

Figure 9

Geometry of PTCDA when adsorbed on (a) Ag(111), (b) Ag(100), and (c) Ag(110). The equilibrium distances $d$ for each chemically inequivalent atom calculated with the PBE+${\text{vdW}}^{\mathrm{surf}}$ method are displayed. Experimental results [44] from NIXSW studies are also shown for comparison. The distinction between carbon atoms belonging to the perylene core (${\mathrm{C}}_{\mathrm{peryl}}$, black) and to the functional groups (${\mathrm{C}}_{\mathrm{funct}}$, dark gray) is also displayed. In a similar fashion, oxygen atoms are shown in red for the case of the carboxylic oxygen (${\mathrm{O}}_{\mathrm{carb}}$) and blue for the anhydride oxygen (${\mathrm{O}}_{\mathrm{anhyd}}$). Images of the structures were produced using the visualization software vesta [106].