Density-Functional Calculations on Platinum Nanoclusters:  Pt₁₃, Pt₃₈, and Pt₅₅

Abstract

The results of an accurate density-functional study of the structure, energetics and electronic structure of Pt n clusters (with n = 13, 38, and 55) are presented. For Pt38, a truncated octahedral geometry is considered; for Pt13 and Pt55, icosahedral, truncated decahedral, and cuboctahedral geometries are considered. In each case, the structure of the neutral and positively and negatively charged clusters is fully optimized within the given symmetry group. For Pt13, allowing symmetry breaking starting from the symmetrical structures derives additional local minima. The computational procedure is thoroughly tested to keep numerical accuracy under control. From the electronic structure point of view, it is found that these systems start developing metallic characteristics, with ionization introducing small changes. From the structural point of view, for Pt13 the icosahedral configuration is not favored, whereas it becomes the ground state for Pt55, in agreement with the predictions of atom−atom potentials. Moreover, the lowest energy configuration of Pt13 is a symmetry-broken D 4 h one, while for Pt38 and Pt55 a peculiar rearrangement is found, corresponding to an expansion (reconstruction) of the atoms lying on (111) or (100) faces.

Study of 40-atom Pt–Au clusters using a combined empirical potential-density functional approach

“…Charge density fitting was adopted for calculation of the Coulomb potential (Weigend et al 1998) for Pt (9s4p3d3f4g)/[9s4p3d3f2g] and for Au (9s4p4d3f4g)/[8s4p3d3f2g]. Dealing with transition metal-containing systems like Pt-Au, a Gaussian-smearing technique for the fractional occupation of the energy levels (with a broadening factor of 0.82 eV) is applied to tackle degeneracy problems (Elsässer et al 1994;Warren & Dunlap 1996;Aprà & Fortunelli 2003). The calculations were performed on the University of Birmingham's BlueBEAR high performance computer (http://www.bear.bham.ac.uk).…”

First-Principles Study on Stability and Electronic Structures of Pt-Rh Bimetallic Nanoparticles

“…Recent first-principles-based investigation by the authors elucidate that Pt-Rh stable surface significantly destabilize CO adsorption with respect to hydrogen, which indicates the Pt-Rh surface to be potential candidate for electrode in polymer electrolyte fuel cells (PEFC): The destabilization is reasonably attributed to the d-state electronic contribution of top-layer Pt atoms, particularly to the d-band center measured from the Fermi energy. DFT-based studies on Pt and Rh nanoparticles have also been carried out to understand stable atomic configurations: [30][31][32][33][34][35][36] Up to now, nanoparticles consisting of $ 300 atoms are extensively studied, and a number of stable or metastable structures including icosahedron, octahedron, cuboctahedron, biplanar, and lower-symmetry shapes are proposed, where their relative stability is still under discussion. Particularly, icosahedral and cubohedral Pt and Rh nanoparticles have been considered interesting since they are Platonic and Archimedean solids in uniform polyhedra, and they are linked to each other by Mackay transformation with small energy difference.…”

“…With these considerations, further theoretical assessment for electronic structure and catalytic properties of the Pt-Rh nanoparticles based on firstprinciples calculation is highly desirable in order to design suitable alloy nanoparticles. In the present study, we concentrate on study of Pt-Rh nanoparticle consisting of 55 atoms with cuboctahedron shape where the 55-atom nanoparticle is considered interesting due to its intermediate size between finite molecules and fully metallic systems 34) and cuboctahedron nanoparticle has been studied based on semiempirical model for segregation in Pt-Rh system, and is also synthesized for 55 Pt atoms. [38][39][40] We perform firstprinciples calculation on Pt 1 Rh 54 and Pt 2 Rh 53 nanoparticles: Energetically preferred single site of Pt atom, Pt electronic structure and ordering tendency for the Pt-Rh nanoparticles are discussed.…”

Stability and Electronic Structures of Pt-Rh Icosahedral Nanoparticles

“…[30][31][32][33][34][35][36] Up to now, nanoparticles consisting of $300 atoms are extensively studied, and a number of stable or metastable structures including icosahedron, octahedron, cuboctahedron, biplanar, and lower-symmetry shapes are proposed, while their relative stability is still under discussion.…”

“…In the present study, we focus on Pt-Rh icosahedral nanoparticle consisting of 55 atoms, because: (i) The 55-atom nanoparticles are considered interesting due to their intermediate size between finite molecules and fully metallic systems. 35) (ii) Icosahedral nanoparticles are linked to cuboctahedral nanoparticles by Mackay transformation with small energy difference, and they are Platonic and Archimedean solids in uniform polyhedra. 32) (iii) The numbers of surface atoms for icosahedron and cuboctahedron are the same while the numbers of symmetry-equivalent sites and their coordination numbers are different.…”