Clusters

The computational prediction of thermodynamically stable metal cluster structures has developed into a sophisticated and successful field of research. To this end, research groups have developed, combined and improved algorithms for the location of energetically low-lying structures of unitary and alloy clusters containing several metallic species. In this chapter, we review the methods by which global optimisation is performed on metallic alloy clusters, with a focus on binary nanoalloys, over a broad range of cluster sizes. Case studies are presented, in particular for noble metal and coinage metal nanoalloys. The optimisation of chemical ordering patterns is discussed, including several novel strategies for locating low-energy permutational isomers of fixed cluster geometries. More advanced simulation scenarios, such as ligand-passivated, and surface-deposited clusters have been developed in recent years, in order to bridge the gap between isolated, bare clusters, and the situation observed under experimental conditions. We summarise these developments and consider the developments necessary to improve binary cluster global optimisation in the near future.

A comprehensive review on geometric and electronic structures, spectroscopic and energetic properties of small niobium clusters in the range from two to twenty atoms, Nb_n, n = 2–20, in three different charged states is presented including a systematic comparison of quantum chemical results with available experimental data to assign the lowest-lying structures of Nb_n clusters and their IR spectra and some basic thermochemical parameters including total atomization (TAE) and dissociation (D _e) energies based on DFT and CCSD(T) results. Basic energetic properties including electron affinities, ionization energies, binding energies per atom, and stepwise dissociation energies are further discussed. Energetic parameters of small sizes often exhibit odd–even oscillations. Of the clusters considered, Nb₂, Nb₄, Nb₈ and Nb₁₀ were found to be magic as they hold the numbers of valence electrons corresponding to the closed-shell in the electron shells [1S/1P/2S/1D/1F…..]. Nb₁₀ has a spherically aromatic character, high chemical hrT high chemical hardness and large HOMO–LUMO gap. The open-shell Nb₁₅ system is also particularly stable and can form a highly symmetric structure in all charged states. For species with an encapsulated Nb atom, an electron density flow is present from the cage skeleton to the central atom, and the greater the charge involved the more stabilized the cluster is.

Alkali dopants interact with helium droplets very differently depending on their size and ionization state, leading to non-wetting behavior for small neutral impurities or to more homogeneous embedding in the case of ionized or large neutral systems. In the present contribution we examine by means of atomistic computer modeling the equilibrium state and out-of-equilibrium submersion kinetics of sodium atoms and dimers in helium clusters containing between 55 and 560 atoms in the normal fluid state, after ionization typically produced by appropriate laser excitation. Our modeling relies on the path-integral molecular dynamics framework, using simple but realistic pair potentials to describe all interactions. Ring-polymer molecular dynamics trajectories shed light onto the various stages of the submersion process, namely initial shell formation around the impurity followed by the slower sinking of this ‘snowball’ to the droplet center and accompanied by the evaporation of several helium atoms in the process. Characteristic times are evaluated as a function of impurity and cluster sizes.

Transition metal (TM) doped silicon and germanium clusters have been studied widely over the last two-three of decades. The initial motivation was to understand metal-semiconductor interfaces, and to couple magnetism in the TM atoms with the semiconducting properties of silicon. However, later on, the focus shifted to production of stable, TM encapsulated silicon or germanium cage clusters, possibly having magnetic moment. The most fundamental question the experiments threw up is, what are the most stable clusters in these series? And, how to understand their stability? Like other branches of physics and chemistry, simple electron counting rules, such as the 18-electron rule of inorganic and organometallic chemistry, and the idea of shell filling in a spherical electron gas, were invoked to explain stability of some of the clusters. However, different clusters were found to be most stable under different experimental conditions, making it somewhat unclear whose stability one has to explain. Faced with such challenges, a large number of experimental and theoretical studies were devoted to elucidating these issues. Quite early on, some authors (Sen and Mitas, e.g.) argued that electron counting rules may not explain all the observations in TM–Silicon clusters, though some of the observations can ostensibly be explained by such rules. The most recent works from Bandyopadhyaya and Sen, and Khanna and co-workers show that electron counting rules only have limited applicability to these clusters. A detail review of the literature discussing these issues is presented, and the still open questions are pointed out.

This chapter consists of a review on the geometric, electronic structure and chemical bonding in a number of small boron clusters doped by two transition metal elements. First-row transition metals introduce not only new class of boron clusters but also particular growth patterns. In the bimetallic cyclic motif, the two metals are vertically coordinated to the planar B_n strings along the symmetry axis. The same M–M axis persist in double ring tubular forms. A bimetallic configuration model has been used to rationalize the electronic structure and stability for both bimetallic cyclic and tubular boron clusters. The anti-bonding π* and δ* MOs of dimeric metals enjoy stabilizing interactions with the B₇, B₈ strings and B₁₄ double ring, thus inducing an enhanced stability for the doped cluster. Formation of bimetallic tube requires the occupancy of the molecular orbital configuration of [(σ_4s)² (π)⁴ (π*)⁴ (δ)⁴ (σ_3d)² (δ*)⁴]. At least 20 electrons are thus needed to populate the electron shell. However, there is no fixed electron count, but this rather depends on the nature of the metallic dopants.

In this chapter we provide a brief overview of bottom-up modelling of nanosilicate clusters, particularly with respect to their astronomical relevance. After providing some general background, we highlight the importance of computational modelling for obtaining unprecedentedly detailed insights into the low energy structures of nanosilicates of a range of compositions and sizes. Later we show how such insights can be useful in understanding the formation of nanosilicates through nucleation around stars, and their role as seeds for further nucleation of water ice.

The binary clusters of transition metal atoms form an interesting platform for studying the effects of shape, size, chemical compositions, and ordering on its magnetic properties. Notably, mixed clusters often show higher magnetic moments compared to pure elemental clusters. Due to the reduced dimension of the clusters, they tend to behave as single domain particles. One important parameter of their magnetic behavior is the magnetic anisotropy energy. In this chapter we review previous works on the magnetic anisotropy energy of binary alloy clusters, along with a density functional theory based method to compute the anisotropy energy with applications to binary metal clusters. The clusters of transition metal atoms often show high spin moments but generally are also reactive with the environment. Passivation of the surface atoms can lead to more stable clusters. We have explored one such avenue for passivation in this work. We consider the As@Ni₁₂@As₂₀ cluster which in the neutral state has a magnetic moment of 3 μ_B. We dope this cluster by substituting various numbers of Ni atoms by Mn atoms. The substitutional doping leads to spin moments located mostly on the Mn atoms. The doping also leads to symmetry breaking and as a consequence the number of structural isomers and spin ordered states for each isomer becomes very large. We have investigated all possible ferromagnetic isomers for a given number of dopants and subsequently all the possible anti-ferromagnetic states for the lowest energy structure were examined. The results show that the encapsulation within the As₂₀ cage stabilizes the clusters and the atomization energy of the clusters increases as the number of dopant increases. These clusters have small energy barrier for reversal of magnetization and also have rich variation in configuration and spin states with many low-lying spin states.

In this chapter we review the structural evolution of lead-chalcogenide (PbX) _n (X = S, Se, and Te; n = 1–32) nanoclusters and how various properties of these clusters change with increasing cluster size. We first give an overview of different experimental techniques that are used to synthesize or generate lead sulfide clusters. The growth mechanism and size-dependent electronic structure and stabilities of these clusters obtained from density functional theory (DFT) based computational studies are also discussed in detail. The importance of the synergy between computational study and experiments is demonstrated by focusing on lead sulfide clusters.

Industrial heterogeneous catalysts are complex multi-component systems which typically contain different transition metal particles supported on porous materials. For the future design of new tailor-made catalytic materials, a molecular level insight into the reaction mechanisms, energetics, and kinetics of the catalytic processes are mandatory. Furthermore, the detailed investigation of the nature of the interaction between different elements in alloy materials and their influence on the catalytic properties is essential. Free clusters in the gas phase represent simplified but suitable model systems which allow to obtain insight into catalytic processes on a rigorously molecular level. In this chapter we summarize experimental and theoretical studies on the reactivity and catalytic activity of free gold clusters and the change of their chemical properties caused by doping these clusters with transition metal atoms. In particular, we focus on three selected catalytic reactions, the oxidation of carbon monoxide, the conversion of methane, and the coupling of methane and ammonia, which have all been shown to be catalyzed by small binary gold clusters.