Search for global-minimum geometries of medium-sized germanium clusters. II. Motif-based low-lying clusters Ge21–Ge29

Dielectric Behavior and Prolate Growth Patterns of Silicon Clusters SiN with N = 12-30 by Cryogenic Electric Beam Deflection

We present a comprehensive investigation of the dielectric behavior and geometric structures of cold neutral SiN clusters of intermediate size with N = 12-30 atoms. For this, cryogenic electric beam deflection experiments were carried out for the first time for Si clusters at nozzle temperatures below 30 K. In combination with quantum chemical calculations based on density functional theory and classical trajectory simulations of the rotational dynamics in the electric field, the geometric structures of the clusters are discriminated. Clusters with N < 15 favor a single-capped square antiprism as a nucleus for cluster growth, forming compact geometries in the molecular beam. Starting with 15 atoms, a prolate-like growth is observed. The prolate structures are based on stable building blocks which reappear for numerous sizes throughout the cluster growth. Finally, the transition from prolate to quasi-spherical shapes is shown to take place around Si29/Si30 as predicted theoretically by the literature. The influence of the exchange-correlation functional on the predicted structure and dielectric properties is discussed in detail for some clusters. Relaxation of the electric-dipole moment and therefore quenching of the observed electric response due to vibrational excitation and collisions with the background gas are also considered, which explains deviations between experiment and theory.

A database of low-energy atomically precise nanoclusters

The chemical and structural properties of atomically precise nanoclusters are of great interest in numerous applications, but the structures of the clusters can be computationally expensive to predict. In this work, we present the largest database of cluster structures and properties determined using ab-initio methods to date. We report the methodologies used to discover low-energy clusters as well as the energies, relaxed structures, and physical properties (such as relative stability, HOMO-LUMO gap among others) for 63,015 clusters across 55 elements. We have identified clusters for 593 out of 1595 cluster systems (element-size pairs) explored by literature that have energies lower than those reported in literature by at least 1 meV/atom. We have also identified clusters for 1320 systems for which we were unable to find previous low-energy structures in the literature. Patterns in the data reveal insights into the chemical and structural relationships among the elements at the nanoscale. We describe how the database can be accessed for future studies and the development of nanocluster-based technologies.

Symmetry collapse due to the presence of multiple local aromaticity in Ge244

Understanding the structural changes taking place during the assembly of single atoms leading to the formation of atomic clusters and bulk materials remains challenging. The isolation and theoretical characterization of medium-sized clusters can shed light on the processes that occur during the transition to a solid-state structure. In this work, we synthesize and isolate a continuous 24-atom cluster Ge₂₄⁴⁻, which is characterized by X-ray diffraction analysis and Energy-dispersive X-ray spectroscopy, showing an elongated structural characteristic. Theoretical analysis reveals that electron delocalization plays a vital role in the formation and stabilization of the prolate cluster. In contrast with carbon atoms, 4 s orbitals of Ge-atoms do not easily hybridize with 4p orbitals and s-type lone-pairs can be localized with high occupancy. Thus, there are not enough electrons to form a stable symmetrical fullerene-like structure such as C₂₄ fullerene. Three aromatic units with two [Ge₉] and one [Ge₆] species, connected by classical 2c-2e Ge-Ge σ-bonds, are aligned together forming three independent shielding cones and eventually causing a collapse of the global symmetry of the Ge₂₄⁴⁻ cluster.

Gaining insight on the structural transformations from atomic clusters to bulk materials is challenging. Here the authors synthesize a continuous cluster of germanium Ge₂₄⁴⁻, which can be viewed as two terminal Ge₉ units bridged via a Ge₆ central fragment, and characterize it by several techniques including X-ray diffraction; theoretical analysis indicates the presence of three aligned independent aromatic fragments.

A remarkable mixture of germanium with phosphorus and arsenic atoms making stable pentagonal hetero-prisms [M@Ge5E5]+, E = P, As and M = Fe, Ru, Os

A pentagonal hetero-prismatic structural motif was found for singly transition metal doped M@Ge₅E₅⁺ clusters, where the transition metal atom is located at the centre of a (5/5) Ge₅E₅ prism in which Ge is mixed with either P or As atoms. Structural characterization indicates that each (5/5) Ge₅E₅ prism is established by joining of two Ge₃E₂ and Ge₂E₃ strings in a prismatic fashion rather than two Ge₅ and E₅ strings. Each string results from a remarkable mixture of Ge and E atoms and contains only one E–E connection due to the fact that Ge–E bonds are much stronger than E–E connections. From the donor–acceptor perspective, the Ge₅E₅ tube donates electrons to the M center, which behaves as an acceptor. NBO atomic charge and ELI_D analyses demonstrate such electrostatic interactions of the M dopant with a Ge₅E₅⁺ tube which likely induce thermodynamic stability for the resulting M@Ge₅E₅⁺ cluster. CMO analysis illustrates that the conventional 18 electron count is recovered in the M@Ge₅E₅⁺ cations.

Geometric shape of the lowest-energy structure M@Ge₅E₅⁺.

Transformation between Hexagonal Prism and Antiprism of the Singly and Doubly Cr-Doped Ge12 Clusters

Structural transformation is a unique characteristic of atomic clusters, but it turns out very different from cluster to cluster. This theoretical study proves that the isomeric transformation between hexagonal prism and hexagonal antiprism is found for the doubly doped Cr₂Ge₁₂ cluster but not for singly doped CrGe₁₂ cluster. We confirm that the ground state of CrGe₁₂ is the distorted hexagonal prism C_2h at the ³B_g triplet state instead of various shapes predicted in the previous studies. Upon comparison between the estimation at the B3P86/6-311+G(d) level of theory and the detachment energies measured by photoelectron spectroscopy, hexagonal antiprismatic shape is identified as the most stable isomer of the Cr₂Ge₁₂ cluster and it is easy to transform to the hexagonal prism-a less stable isomer by the rotation of the hexagonal rings. That is the first evidence for the structural transformation between a hexagonal prism and an antiprism of the germanium clusters, referring to the ability of Ge-based clusters in the formation of tubular geometry by doping Cr atoms. All the low-energy isomers of both Cr-doped germanium clusters have high magnetic moments. Interestingly, there is a tuning in magnetic properties of Cr₂Ge₁₂ from the ferromagnetism of the lowest-lying hexagonal antiprism to the ferrimagnetism of the higher-energy hexagonal prism. The stronger Cr-Cr bond and stronger interaction between the Cr₂ moiety and the antiprism cage are accounted for by the higher stability of the hexagonal antiprismatic isomer.

Structure, Stability, and Electronic and Magnetic Properties of VGen (n = 1-19) Clusters

We systematically study the equilibrium geometries and electronic and magnetic properties of Ge_n+1 and VGe_n (n = 1-19) clusters using the density functional theory approach within the generalized gradient approximation. Endohedral structures in which the vanadium atom is encapsulated inside a Ge_n cage are predicted to be favored for n ≥ 10. The dopant V atom in the Ge_n clusters has not an immediate effect on the stability of small germanium clusters (n < 6), but it largely contributes to strengthen the stability for n ≥ 7. Our study enhances the large stability of the VGe₁₄ cluster, which presents an O_h symmetry cagelike geometry and a peculiar electronic structure in which the valence electrons of V and Ge atoms are delocalized and exhibit a shell structure associated with the quasi-spherical geometry. Consequently, this cluster is proposed to be a good candidate to be used as the building blocks for developing new materials. The cluster size dependence of the stability, the vertical ionization potentials, and electron affinities of Ge_n+1 and VGe_n are presented. Magnetic properties and the partial density of states of the most stable VGe_n clusters are also discussed.

Transferable tight-binding potential for germanium

We report a new tight-binding potential model for Ge. In this model, the bonding environment around each bond is taken into account. The features of this model are extensively examined using various structures, such as the diamond bulk with point defects, reconstructed surfaces, nanowires and small and medium-sized clusters. The resulting configurations, energies and the phonon dispersion as well as the electronic structures of the tested systems are in agreement with those predicted at the level of density functional theory. This indicates that the new model is able to handle complex Ge-based materials.

A Stochastic Search for the Structures of Small Germanium Clusters and Their Anions: Enhanced Stability by Spherical Aromaticity of the Ge10 and Ge12(2-) Systems

Investigations on germanium clusters in the neutral, anionic, and dianion states Gen(x) (n = 2-12 and x = 0, -1, -2) are performed using quantum chemical calculations with the B3LYP functional and the coupled-cluster singles and doubles [CCSD(T)] methods, in conjunction with the 6-311+G(d) basis set. An improved stochastic method is implemented for searching the low-lying isomers of clusters. Comparison of our results with previous reports on germanium clusters shows the efficiency of the search method. The Ge8 system is presented in detail. The anionic clusters Gen(-/2-) are studied theoretically and systematically for the first time, and their energetics are in good agreement with available experiments. The clusters Ge10, Ge10(2-), and Ge12(2-) are, in their ground state, characterized by large highest occupied molecular orbital-lowest unoccupied molecular orbital gaps, high vertical and adiabatic detachment energies, and substantial average binding energies. The enhanced stability of these magic clusters can consistently be rationalized using the jellium electron shell model and the spherical aromatic character.

Structures of Pb(n) (n = 21-30) clusters from first-principles calculations

Neutral lead clusters Pb(n) (n = 21-30) were studied using a genetic algorithm (GA)/tight-binding (TB) search combined with density functional theory (DFT)-Perdew-Burke-Ernzerhof (PBE) calculations. The calculated results show that the Pb(n) (22 ≤ n ≤ 30) clusters favor endohedral cage structures with two (Pb(22 - 26)) or three (Pb(27 - 30)) endohedral atoms. The binding energies, stabilities, and highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gaps of the Pb(n) clusters were also discussed. The results from our calculations also indicate that Pb(24) and Pb(28) are especially stable clusters compared with their neighbors.

Stabilities and fragmentation energies of Si(n) clusters (n = 2-33)

The structures of Si(n) (n = 2-33) were confirmed by genetic algorithm (GA)/tight binding (TB) search and ab initio calculations at the B3LYP/6- 311++G(2d) and PW91/6-311++G(2d) level, respectively. The fragmentation energies, binding energies, second differences in energy, and highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gaps in the size range 2≤n≤33 were calculated and analyzed systematically. We extended the cluster size involved in the fragmentation analyses up to Si(33), and studied the multi-step fragmentations of Si(n). The calculated result is similar to the fragmentation behavior of small silicon clusters studied previously, showing that Si(6), Si(7), and Si(10) have relatively larger stabilities and appear more frequently in the fragmentation products of large silicon clusters, which is in good agreement with the experimental observations.