Influence of spin-orbit effects on structures and dielectric properties of neutral lead clusters

Abstract

Combining molecular beam electric deflection experiments and global optimization techniques has proven to be a powerful tool for resolving equilibrium structures of neutral metal and semiconductor clusters. Herein, we present electric molecular beam deflection experiments on PbN (N = 7-18) clusters. Promising structures are generated using the unbiased Birmingham Cluster Genetic Algorithm approach based on density functional theory. The structures are further relaxed within the framework of two-component density functional theory taking scalar relativistic and spin orbit effects into account. Quantum chemical results are used to model electric molecular beam deflection profiles based on molecular dynamics calculations. Comparison of measured and simulated beam profiles allows the assignment of equilibrium structures for the most cluster sizes in the examined range for the first time. Neutral lead clusters adopt mainly spherical geometries and resemble the structures of lead cluster cations apart from Pb10. Their growth pattern deviates strongly from the one observed for tin and germanium clusters.

Structural evolution and metallicity of lead clusters

“…This makes Pb 25 an interesting starting point for further investigations of the deflection behaviour and the dynamics of flexible clusters. 21 For Pb 54 a cuboctahedral geometry is assumed. 37 The metallicity of lead clusters has been evaluated in terms of their electron screening, their gaps and their structures.…”

“…The Pb 9 cluster on the other hand consists of two interpenetrating PBP. 21 However, the dipole moment of 36a is too small to explain the experimental beam broadening. Isomer 36b is only 0.03 eV higher in energy than 36a and has a dipole moment of 0.85 D. Its simulated beam profile resembles the experimental data very well.…”

“…Hence, a structural assignment is possible, as demonstrated for several group 14 clusters. [18][19][20][21] Former molecular beam deflection experiments on neutral lead clusters at 50 K indicated dipole moments or anomalies in the polarizability for several Pb N (N ≤ 40) without suggesting any structures for them. 22 We have repeated these measurements at 30 K to ensure the rigidity of the clusters.…”

Exploring the potential energy surface of small lead clusters using the gradient embedded genetic algorithm and an adequate treatment of relativistic effects

“…Our interest in these systems is due to the abundant experimental and theoretical studies concerning their structural elucidation when compared with our results. [15][16][17][18][19][20][21][22][23] From an experimental view, small lead clusters have been obtained via laser vaporization and determined by ion mobility, 16,24-28 gas phase ion electron diffraction, [27][28][29] and photoionization mass spectrometry. 21,[30][31][32] In these studies, "magic" numbers were observed in size distributions under a variety of ionization conditions.…”

Pool-BCGA: a parallelised generation-free genetic algorithm for the ab initio global optimisation of nanoalloy clusters

“…Since the electronic structure of large nanoparticles is expected to resemble the bulk phase, tailored model or empirical potentials (EPs) such as Gupta, 2 Sutton-Chen, 3 and Murrell-Mottram, 4 fitted to properties of the solid phase, enable a reasonable description of the PES. [11][12][13][14][15][16] For details on global optimisation algorithms, especially focused on genetic algorithms and basin hopping techniques, the reader is referred to the literature. nanoclusters, a quantum chemical treatment becomes necesa Eduard-Zintl-Institut, Technische Universität Darmstadt, Alarich-Weiss- Straße 8,64287 Darmstadt, Germany b Ernst-Berl-Institut, Technische Universität Darmstadt, Alarich-Weiss- Straße 8,64287 Darmstadt, Germany c School of Chemistry, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom Authors to whom correspondence should be addressed.…”