Size-dependent properties of transition metal clusters: from molecules to crystals and surfaces – computational studies with the program ParaGauss

Abstract

In the so-called scalable regime the size-dependent behavior of the physical and chemical properties of transition metal clusters is described by scaling relationships. For most quantities this scalable regime is reached for cluster sizes between a few tens and a few hundreds of atoms, hence for systems for which an accurate treatment by density functional theory is still feasible. Thus, by invoking scaling relations one is able to obtain properties of very large nanoparticles and even the bulk limit from the results of a series of smaller cluster models. In this invited review we illustrate this strategy by exploiting results from computational studies that mostly were carried out with the density functional theory software ParaGauss. We address mainly the size-dependent behavior of the properties of transition metal clusters. To this end, we first present benchmark studies probing various approximations that are used in such density functional calculations. Subsequently we show how physical insight may be gained by exploring less understood types of systems. These applications range from bare clusters to nanoislands and nanoalloys to adsorption complexes.

Comparison of the periodic slab approach with the finite cluster description of metal–organic interfaces at the example of PTCDA on Ag(110)

“…Please note that energetically close lying electronic states were occasionally reported and the use of this method in Ref. and related work of these authors. We checked that reducing the Fermi temperature to zero does not change structural parameters and adsorption energies presented in this work by more than 0.01 Å and 0.01 eV, respectively.…”

“…for adsorbates on silver and other metals . Recently, cluster models of transition metals containing a very large number of atoms (up to 300 atoms) constructed in accordance with the Wulff construction method have been extensively studied by Rösch and coworkers . Generally, it is more difficult to design a proper cluster than to set up a periodic slab calculation as it is not clear how the lateral extension of the cluster and the corresponding borders influence the metal‐adsorbate properties.…”

Size-Dependence of the Adsorption Energy of CO on Pt Nanoparticles: Tracing Two Intersecting Trends by DFT Calculations

“…Indeed, E ads values deviate notably from trend 1 (Figure b), and therefore, scaling trend 1 is only approximate in the case of Pd, being applied in the nonscalable size regime . In the nonscalable regime, particles are small enough for quantum effects to alter properties with the smallest change in size, i.e., “every atom counts”, in contrast to the regime of larger particles, where scaling relationships can be applied to quantify how properties depend on particle size and approach the bulk limit . For Pt, in contrast to Pd, the transition from the descending trend 2 to the ascending trend 1 (with decreasing nuclearity) occurs at cluster sizes of about 200 atoms, which commonly is assigned to the scalable size regime .…”

Transformations of Organic Molecules over Metal Surfaces: Insights from Computational Catalysis

“…An alternative way of modeling active centers of a transition‐metal catalyst relies on finite sub‐nanometer cluster models 8. While the latter approach might be particularly advantageous for modeling nanostructured catalysts,9–13 periodic models employed in the studies covered in this Personal Account are more suitable for describing larger catalyst particles in the “scalable‐to‐bulk regime”,14,15 i.e., showing crystallite‐like characteristics.…”