We have evaluated various density functional theory (DFT) methods to simulate geometric, energetic, electronic, and hydrogen adsorption properties of metal-nanoparticles supported on metal surfaces. We used Pt and Pd nanoislands on Au(111) as model systems. The evaluated DFT methods include GGA (PW91, PBE, RPBE, revPBE, and PBESol), GGA with van der Waals (vdW) corrected (PBE-D3), GGA with optimized vdW functionals (revPBE-vdW), meta-GGA (SCAN and MS2), and the machine learning-based method BEEF-vdW. The results show that the various DFT methods yield similar geometric and electronic properties for Pt (or Pd) nanoislands on Au(111). The DFT methods also produce similar relative energetics for small Pt (or Pd) clusters with different conformations on Au(111). The results show that a triatomic cluster of Pt on Au(111) is more stable with a linear conformation. In contrast, a triatomic cluster of Pd is more stable with a triangular conformation. For clusters with four or more atoms, Pt and Pd clusters on Au(111) prefer non-linear conformation. We found that the various DFT methods yield different results only for the adsorption energy of hydrogen.

我们评估了各种密度泛函理论 (DFT) 方法来模拟金属表面负载的金属纳米粒子的几何、能量、电子和氢吸附特性。我们使用 Au(111) 上的 Pt 和 Pd 纳米岛作为模型系统。评估的 DFT 方法包括 GGA（PW91、PBE、RPBE、revPBE 和 PBESol）、经过范德华 (vdW) 校正的 GGA (PBE-D3)、具有优化 vdW 泛函的 GGA (revPBE-vdW)、meta-GGA (SCAN)和MS2），以及基于机器学习的方法BEEF-vdW。结果表明，各种 DFT 方法对 Au(111) 上的 Pt（或 Pd）纳米岛产生相似的几何和电子特性。DFT 方法还对 Au(111) 上具有不同构象的小 Pt（或 Pd）簇产生类似的相对能量。结果表明，Au(111)上的Pt三原子团簇具有更稳定的线性构象。相比之下，具有三角形构象的三原子簇 Pd 更稳定。对于具有四个或更多原子的簇，Au(111) 上的 Pt 和 Pd 簇更喜欢非线性构象。我们发现不同的 DFT 方法仅针对氢的吸附能产生不同的结果。