Large-scale surface reconstruction energetics of Pt(100) and Au(100) by all-electron density functional theory

The low-index surfaces of Au and Pt all tend to reconstruct, a fact that is of key importance in many nanostructure, catalytic, and electrochemical applications. Remarkably, some significant questions regarding their structural energies remain even today, specifically for the large-scale quasihexagonally reconstructed (100) surfaces: rather dissimilar reconstruction energies for Au and Pt in available experiments and experiment and theory do not match for Pt. We here show by all-electron density functional theory that only large enough “$\left(5\times N\right)$” approximant supercells capture the qualitative reconstruction energy trend between Au(100) and Pt(100), in contrast to what is often done in the theoretical literature. Their magnitudes are then in fact similar and closer to the measured value for Pt(100); our calculations achieve excellent agreement with known geometric characteristics and provide direct evidence for the electronic reconstruction driving force.

Figure 1

(Color online) Structure and distortion of the quasihexagonal layer. Circles: topmost (hex) layer, crosses: second (square) layer. Unit vectors of the coincidence lattice of both planes are shown by arrows. (a) $\left(5\times 1\right)$ and (b) $\left(5\times 20\right)$ superstructure. The hex layer is compressed by 4% with respect to bulk (111) in both dimensions and rotated by $1°$ in one dimension. (c) $\left(5\times 20\right)$-type superstructure, rotated in both dimensions.

Figure 2

(Color online) Change in surface energy with reconstruction, compared to $\left(1\times 1\right)$ [negative of $\Delta E_{5\times N}$, Eq. (1)], for Pt(100) (upper panel) and Au(100) (lower panel) using DFT-LDA/PBE, as a function of the lateral atomic packing density $\theta$. Dashed-dotted lines: experimental estimates for the packing density from SXRD, (Refs. 35, 36) and for the Pt(100) reconstruction energy from the reanalysis (Ref. 44) of CO titration calorimetry data (Refs. 45, 46).

Figure 3

(Color online) (a) Top view of the hex layer on an $\text{Au}\left(100\right)\text{−}\left(5\times 20\right)$ reconstruction model (LDA). $z$ coordinates of all atoms are in different gray scales in units of $d_{\text{bulk}}$, relative to the average $z$ position of the plane. (b) Height profiles through the most corrugated and least corrugated surface areas.