Structural evolution and metallicity of lead clusters

Abstract

The evolution of the metallic state in lead clusters and its structural implications are subject to ongoing discussions. Here we present molecular beam electric deflection studies of neutral PbN (N = 19-25, 31, 36, 54) clusters. Many of them exhibit dipole moments or anomalies of the polarizability indicating a non-metallic state. In order to resolve their structures, the configurational space is searched using the Pool Birmingham Cluster Genetic algorithm based on density functional theory. Spin-orbit effects on the geometries and dipole moments are taken into account by further relaxing them with two-component density functional theory. Geometries and dielectric properties from quantum chemical calculations are then used to simulate beam deflection profiles. Structures are assigned by the comparison of measured and simulated beam profiles. Energy gaps are calculated using time-dependent density functional theory. They are compared to Kubo gaps, which are an indicator of the metallicity in finite particles. Both, experimental and theoretical data suggest that lead clusters are not metallic up to at least 36 atoms.

How metallic are noble-metal clusters? Static screening and polarizability in quantum-sized silver and gold nanoparticles

“…1,2 This has led to a number of studies, theoretical and experimental, that determine the dipole moment of small clusters. [3][4][5] These studies conclude that the dipole moments of simple-metal clusters are very small and essentially consistent with zero value which characterizes the clusters as metallic.…”

A Global Optimizer for Nanoclusters

“…The global minima of atomic clusters (Davis et al, 2015; Shayeghi et al, 2015a) are essential as these are often the most likely structure to be formed in the experiment. Thus, finding the global minimum and other low-lying minima on the PES is helpful to interpret the experimental results (Shayeghi et al, 2014, 2015b; Götz et al, 2016).…”

First principles global optimization of metal clusters and nanoalloys

“…Even if the experimental structure is not the GM, typically it is a very low energy isomer [46]. In combined experimental and theoretical studies, the presence of one or more low lying isomers have been found to explain experimental results very well [49][50][51]. The approach in such combined studies is: (i) to measure a physico-chemical property of a particular cluster; (ii) to use a GO technique to search for the GM and other low energy structures and (iii) to calculate the same property for these isomers.…”

“…In the optimization of clusters, a cost-saving approach (which sometimes gives good results) involves first performing GO at a lower level of theory (EP or DFT with a small basis set) and looser convergence criteria. This is followed by refinement (reoptimization) of a set of low-energy and structurally distinct isomers using a more rigorous ab initio method, such as CCSD(T), or DFT with larger basis sets and/or more computationally expensive hybrid exchange-correlation (xc) functionals [10,50,51,[98][99][100][101][102][103]. Particular attention must be paid to the fact that the relative energy differences between the isomers, as well as their energetic order, can change (especially in DFT with the use of different xc functionals and basis sets) so that an originally energetically higher isomer can become the GM after refinement (see Figure 2) [51].…”

“…The GM cluster geometries were mainly spherical and showed a strongly deviating growth pattern compared to tin clusters: whereas tin cluster adopts mainly prolate geometries, lead prefers a denser packing and forms more spherical structures. In a later study, Götz et al investigated the structure of larger neutral Pb n (n = 19-25, 31, 36, 54) clusters with BPGA-DFT, finding that Pb n clusters with up to 36 atoms are not metallic [50]. They found oblate structures for the GM of Pb 19 and Pb 20 , while prolate structures were obtained for Pb 21 to Pb 25 .…”