van der Waals effects at molecule-metal interfaces

We present the results of plane-wave pseudopotential periodic density functional theory (DFT) calculations on the geometries, energetics, and electronic structure of small molecules on Au(111). The chosen molecules—benzene, ammonia and cytosine—are representative of different adsorption regimes and interaction strengths. The chosen substrate is a prototype noble-metal surface that is widely employed as a support for organic materials. We assess the relevance of van der Waals effects in the adsorption process and the accuracy of different first-principle density functionals that have been recently developed to embody such effects. We find that there is no unique functional that is optimal for any system. In particular, our results reveal that functionals designed to reduce the short-term repulsion between the adsorbate and the substrate usually overestimate the adsorption strength and may even predict the wrong adsorption orientation. We show that an accurate description of the substrate does not ensure an accurate evaluation of the adsorption energetics, while the electronic structure is less sensitive to the specific choice. We propose the best choice for DFT calculations of DNA bases on Au(111) and similar systems in which both short-range and long-range interactions exist.

Figure 1

Top view of the most energetically favorable optimized geometries of (a) ${\mathrm{C}}_6{\mathrm{H}}_6$ and (b) ${\mathrm{NH}}_3$ adsorbed on Au(111). Side view of the (c) horizontal and (d) vertical optimized adsorption geometries for cytosine on Au(111). In all images: only the top gold layer is shown; spheres of increasing size represent H, N, and Au atoms. These relaxed configurations were obtained by vdW-DF calculations.

Figure 2

Formation energy of ${\mathrm{C}}_6{\mathrm{H}}_6@\mathrm{Au}\left(111\right)$ obtained with four different vdW functionals: (left) vdW-DF and vdW-DF2; (right) C09-vdW-DF and C09-vdW-DF2. The energy is presented as a function of molecule-surface distance at fixed internal coordinates of the molecule and of the surface, obtained from single-point self-consistent DFT calculations with different vdW functionals, as indicated in the legends. The molecule-surface distance was calculated between the closest atoms in the substrate and in the adsorbate.

Figure 3

Formation energy of ${\mathrm{NH}}_3@\mathrm{Au}\left(111\right)$ obtained with four different vdW functionals: (left) vdW-DF and vdW-DF2; (right) C09-vdW-DF and C09-vdW-DF2. The energy is presented as a function of molecule-surface distance at fixed internal coordinates of the molecule and of the surface, obtained from single-point self-consistent DFT calculations with different vdW functionals, as indicated in the legend. The molecule-surface distance was calculated between the closest atoms in the substrate and in the adsorbate.

Figure 4

Formation energy of cytosine@Au(111) obtained with two different vdW functionals: vdW-DF and C09-vdW-DF2. The energy is presented as a function of molecule-surface distance at fixed internal coordinates of the molecule and of the surface, obtained from single-point self-consistent DFT calculations with different vdW-DF functionals, as indicated in the legend. The molecule-surface distance was calculated between the closest atoms in the substrate and in the adsorbate.

Figure 5

Density of states of cytosine adsorbed horizontally on the Au(111) surface, computed with the (left panel) vdW-DF and (right panel) C09-vdW-DF2 functionals, using a Gaussian broadening of 0.054 eV. The Fermi level of the system is set at the origin of the energy scale in each plot. The deepest energy level, which is associated with the same orbital in the gas-phase molecule and in the adsorbed molecule, is used for alignment of the two curves in each plot. The solid orange (dashed blue) line is the DOS of the gas-phase molecule (total DOS of the interface projected onto the molecule). For the gas-phase molecule, the double highest occupied molecular orbital peak is split by 0.14 (0.08) eV in vdW-DF (C09-vdW-DF2) calculations. In the inset, a bonding orbital is shown, with the atoms represented with the same color code and size as in Fig. 1.