We report the finding of a bowl-shaped quasi-planar structure of a B84 cluster with four hexagonal holes and a three-chain ring all around the edges using ab initio calculations. A large number of other isomers including those explored earlier such as an empty cage, a filled cage, and a disordered structure, have been found to lie in a significantly higher energy band. A tubular structure, however, is only about 0.45 eV higher in energy. Calculations of the infrared and Raman spectra show that the quasi-planar structure is dynamically stable. These results suggest that quasi-planar structures may be among the low energy structures for larger clusters as well. Accordingly we have calculated the optimal quasi-planar structures stabilized with 2, 3, 5, 6, and 7 hexagonal holes also. The stability of quasi-planar structures is discussed in terms of multi-center two-electron bonding and it is shown that with increasing size their binding energy tends to approach the value for an α-boron sheet. This journal is © The Royal Society of Chemistry.

Vijay Kumar

Center for Informatics

Rahane A.B.

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Shiv Nadar University

Nanoscale

The discovery of carbon fullerene cages and their solids opened a new avenue to build materials from stable cage clusters as "artificial atoms"or "superatoms"instead of atoms. However, cage clusters of other elements are generally not stable. In 2001, ab initio calculations showed that endohedral doping of Zr and Ti atoms leads to highly stable Zr@Si16 fullerene and Ti@Si16 Frank-Kasper polyhedral clusters with large HOMO-LUMO gaps. In 2002, Zr@Ge16 was shown to form a Frank-Kasper polyhedron, suggesting the possibility of designing novel clusters by tuning endohedral and cage atoms. These results were subsequently confirmed from experiments. In the past nearly two decades, many experimental and theoretical studies have been carried out on different clusters, and many very stable cage clusters with possibly high abundance have been found by endohedral doping. Indeed in 2017, Ta@Si16 and Ti@Si16 cage clusters have been synthesized in bulk quantity of about 100 mg using a dry-chemistry method, giving rise to a new hope of developing cluster-based materials in macroscopic quantity besides the well-known C60 fullerene solid. Also, wet-chemistry methods have been used to synthesize endohedrally doped clusters as well as ligated clusters and their solids, which auger well for the development of novel nanostructured materials using atomically precise clusters with unique properties. In this comprehensive review, we present results of many such developments in this fast-growing field including (i) endohedrally doped Al, Ga, and In clusters, (ii) small endohedral carbon fullerene cages with ≤ 28 carbon atoms, (iii) metal doped boron cages, (iv) endohedrally doped cages of group 14 elements (Si, Ge, Sn, and Pb), (v) coinage metal (Cu, Ag, Au) cages doped with a transition metal atom as well as their ligated clusters and crystals, (vi) endohedrally doped cages of compound semiconductors, and (vii) multilayer Matryoshka cages and core-shell structures. In a large number of cases, we have performed ab initio calculations to present updated results of the most stable atomic structures and fundamental electronic properties of the endohedrally doped cage clusters. We discuss electronic, magnetic, optical, and catalytic properties in order to shed light on their potential applications. The stability of the doped cage clusters has been correlated to the concept of filling the electronic shells for superatoms such as within a spherical potential model and also using various electron counting rules including Wade-Mingos rules, systems with 18 and 32 electrons, and the spherical aromaticity rule. We also discuss cluster-cluster interaction in cluster dimers and assemblies of some of the promising doped cage clusters in different dimensions. Finally, we give a perspective of this field with a bright future. © 2020 American Chemical Society.

Chemical Reviews

Endohedrally Doped Cage Clusters

We study the stability of drum-shaped transition metal (TM)-doped boron clusters, M@Bn with n = 14 and 16, and M = 3d, 4d, and 5d TM atom using ab initio calculations. Our results show that drum-shaped M@B14 clusters are favored for M = Cr, Mn, Fe, Co, and Ni, while in other cases, open conical or bowl shaped structures become more favorable. The isoelectronic Ni@B14 and Co@B14- clusters have large highest occupied molecular orbital-lowest unoccupied molecular orbital gaps and these are magic clusters. Their stability has been correlated with the occurrence of magic behavior with 24 valence electrons in a disk jellium model, while for Fe@B14 case the drum structure is deformed and the stability occurs at 22 delocalized valence electrons. The bonding nature in these clusters has been studied by analyzing the electron density at bond and ring critical points, the Laplacian distribution of the electron density, the electron localization function, the source function, and electron localization-delocalization indices, all of which suggest two- and three-center σ bonding within and between the two B7 rings, respectively, and hybridization between the TM d orbitals and the π bonded molecular orbitals of the drum. The infrared and Raman spectra of these magic clusters show all real frequencies, suggesting the dynamical stability of the drum-shaped structures. There is a low frequency mode associated with the M atom. Results of the electronic spectra of the anion clusters are also presented that may help to identify these species in future experiments. Further, we discuss the stability of 24 delocalized valence electron systems Mn@B16 anion, Fe@B16, Co@B16 cation, and other related clusters. Assembly of Co@B14 clusters has been shown to stabilize a carbon nanotube-like nanotube of boron with Co atomic nanowire inside while a nanotube of boron with triangular network has been obtained with the assembly of Fe@B16 drum-shaped clusters. Both the nanotubes are metallic. © 2017 American Chemical Society.

Journal of Physical Chemistry C

Electronic Origin of the Stability of Transition-Metal-Doped B14 Drum-Shaped Boron Clusters and Their Assembly into a Nanotube

Boron atomic clusters show several interesting and unusual size-dependent features due to the small covalent radius, electron deficiency, and higher coordination number of boron as compared to carbon. These include aromaticity and a diverse array of structures such as quasi-planar, ring or tubular shaped, and fullerene-like. In the present work, we have analyzed features of the computed electron density distributions of small boron clusters having up to 11 boron atoms, and investigated the effect of doping with C, P, Al, Si, and Zn atoms on their structural and physical properties, in order to understand the bonding characteristics and discern trends in bonding and stability. We find that in general there are covalent bonds as well as delocalized charge distribution in these clusters. We associate the strong stability of some of these planar/quasiplanar disc-type clusters with the electronic shell closing with effectively twelve delocalized valence electrons using a disc-shaped jellium model. B10, B7P, and B8Si, in particular, are found to be exceptional with very large gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, and these are suggested to be magic clusters. © 2016 The Royal Swedish Academy of Sciences.

Physica Scripta

Analysis of the electron density features of small boron clusters and the effects of doping with C, P, Al, Si, and Zn: Magic B7P and B8Si clusters

Journal of the American Chemical Society

The B35Cluster with a Double-Hexagonal Vacancy: A New and More Flexible Structural Motif for Borophene

Nature Communications

Planar hexagonal B36 as a potential basis for extended single-atom layer boron sheets

Accounts of Chemical Research

Understanding Boron through Size-Selected Clusters: Structure, Chemical Bonding, and Fluxionality

Angewandte Chemie International Edition

Cover Picture: Recoding the Genetic Code with Selenocysteine (Angew. Chem. Int. Ed. 1/2014)

B38: an all-boron fullerene analogue

B84: A quasi-planar boron cluster stabilized with hexagonal holes