A systematic study of the structural, electronic, and optical properties of cage-like boron clusters, with the number of constituent atoms ranging from 20 to 122, has been carried out within the framework of density-functional theory (DFT), employing the 6-31G(d,p) extended basis set. The dynamic stability of the clusters is analyzed through vibrational frequency analysis, while to study the thermodynamic stability, we computed their binding energies per atom. The results suggest that the 32- and 92-atom cages are the most stable among the small and the large structures, and their stability is analyzed. The optical absorption spectra of these cages are computed using time-dependent density-functional theory (TDDFT), which suggests their applications in optoelectronic devices in a wide range of the spectrum.

In this work, we present large-scale electron-correlated computations on various conformers of B12H12 and B12H6 clusters to understand the reasons behind the high stability of dianion icosahedron (Ih) and cage-like B12H6 geometries. Although the B12 icosahedron is the basic building block in some structures of bulk boron, it is unstable in its free form. Furthermore, its H-passivated entity, i.e., a B12H12 icosahedron, is also unstable in the free form. However, dianion B12H12 has been predicted to be stable as a perfect icosahedron in the free-standing form. To capture the correct picture for the stability of B12H122- and B12H6 clusters, we optimized these structures by employing the coupled-cluster singles and doubles (CCSD) approach and the cc-pVDZ basis set. We also performed the vibrational frequency analysis of the isomers of these clusters using the same level of theory to ensure the stability of the structures. For all of the stable geometries obtained from the vibrational frequency analysis, we additionally computed their optical absorption spectra using the time-dependent density functional theory (TDDFT) approach at the B3LYP/6-31G* level of theory. Our calculated absorption spectra could be probed in future experiments on these clusters.

In this work, we present a large-scale electron-correlated study of various conformers of B12H12 and B12H6 clusters, with the motivation to investigate the reasons behind high stability of di-anion icosahedron (Ih) and cage-like B12H6 geometries. To capture the correct picture of their stability, we optimized all the structures, considered in this work, by employing the coupled-cluster singles-doubles (CCSD) approach, and cc-pVDZ basis set. Furthermore, we also performed vibrational frequency analysis of the isomers of these clusters, using the same level of theory to ensure the stability of the structures. For all the stable geometries obtained from the vibrational frequency analysis, we also computed their optical absorption spectra using the TDDFT approach, at the the B3LYP/6-31G* level of theory. Our calculated absorption spectra could be probed in future experiments on these clusters.

This book presents nanomaterials predicted by computational modelling and numerical simulation tools, then confirmed by modern experimental methods. It discusses atomic clusters and nanostructures, focusing primarily on boron and carbon and their potential applications in nanotechnology.

Clusters and magic numbers were the major research field mid 80s. Many groups around the world worked theoretically and experimentally to find the relationship between the electronic shells and the magic numbers. The structures of the Lithium and Sodium alkali-Metal, as well as Carbon clusters and their electronic properties were the first investigated agglomerates.

Boron and carbon nanotubes and related armchair and zigzag structures are presented and their mechanical, optical and electronic properties and stabilities are discussed. The theoretical and experimental results of both elements in the form of single-, double-, and multi-walled nanotubes are illustrated. The precursors of buckled, $$\alpha $$ - and $$\gamma $$ -sheets rolling up into nanotubes are indicated. The potential applications of these structures are proposed.

Geim and Novoselov synthesized in 2004 single-atom thick carbon sheet graphene and opened the door for research of 2D carbon materials. Graphene and related derivatives called graphynes as well as nanoribbons have unique electronic, optical, and mechanical properties. However, with the prediction of quasi-planar boron clusters and sheets in 1997, I. Boustani also opened the door for the 2D boron sheets research known nowadays as borophene. The synthesis of borophene encouraged researchers to explore the mechanical, optical, magnetic and electronic properties as well as their potential applications in nanotechnology.

“Everything we see around us is made of atoms, the tiny elemental building blocks of matter. From stone, to copper, to bronze, iron, steel, and now silicon, the major technological ages of humankind have been defined by what these atoms can do in huge aggregates, trillions upon trillions of atoms at a time, molded, shaped, and refined as macroscopic objects. Even in our vaunted microelectronics of 1999, in our highest-tech silicon computer chip the smallest feature is a mountain compared to the size of a single atom. The resultant technology of our 20th century is fantastic, but it pales when compared to what will be possible when we learn to build things at the ultimate level of control, one atom at a time.”

Beyond the conventional allotrope of carbon, graphite, diamond and related compounds, the structures of small carbon clusters were investigated in order to understand their transition to nanoclusters and nanostructures, like fullerenes and graphenes. The alternation between even and odd carbon clusters was also studied. In addition, the transition from 1D to 2D and to 3D structures is explained and at at which cluster size can occur.

The spherical cages of boron and carbon, known as fullerenes, were investigated theoretically and experimentally by many research groups around the world. Theoretically, different first-principles methods and molecular dynamics simulations were used to investigate the fullerene’s structures and related electronic properties. Experimentally, the scientists developed different methods to fabricate a large quantity of fullerenes, the new allotrope of carbon, and of boron clusters, nanotubes and sheets (borophene).

Besides the conventional allotrope of the p-block non-metal element boron, like $$\alpha $$ -rhombohedral, $$\beta $$ -rhombohedral, and $$\gamma $$ -orthorhombic solids, and of the p-block non-metal element carbon, like graphite, diamond of many of organic structures, there are a lot of boron and carbon non-conventional structures in the form of clusters, nanotubes, nanocages and nanosheets. These nanostructures present the nanomaterials of both boron and carbon atoms.

In this work we undertake a comprehensive numerical study of the ground state structures and optical absorption spectra of isomers of B12 cluster. Geometry optimization was performed at the coupled-cluster-singles-doubles (CCSD) level of theory, employing cc-pVDZ extended basis sets. Once the geometry of a given isomer was optimized, its ground state energy was calculated more accurately at the coupled-cluster-singles-doubles along with perturbative treatment of triples (CCSD(T)) level of theory, employing larger cc-pVTZ basis sets. Thus, our computed values of binding energies of various isomers are expected to be quite accurate. Our geometry optimization reveals eleven distinct isomers, along with their point group, and electronic ground state symmetries. We also performed vibrational frequency analysis on the three lowest energy isomers, and found them to be stable. Therefore, we computed the linear optical absorption spectra of these isomers of B12, employing large-scale multi-reference singles-doubles configuration-interaction (MRSDCI) approach, and found a strong structure-property relationship. This implies that the spectral fingerprints of the geometries can be utilized for optical detection, and characterization, of various isomers of B12. We also explored the stability of the isomer with the structure of a perfect icosahedron, with Ih symmetry. In bulk boron icosahedron is the basic structural unit, but, our vibrational frequency analysis reveals that it is unstable in the isolated form. We speculate that this instability could be due to Jahn-Teller distortion because five-fold degenerate HOMO orbitals in Ih structure are unfilled.

In this work we undertake a comprehensive numerical study of the ground state structures and optical absorption spectra of isomers of B$_{12}$ cluster. Geometry optimization was performed at the coupled-cluster-singles-doubles (CCSD) level of theory, employing cc-pVDZ extended basis sets. Once the geometry of a given isomer was optimized, its ground state energy was calculated more accurately at the coupled-cluster-singles-doubles along with perturbative treatment of triples (CCSD(T)) level of theory, employing larger cc-pVTZ basis sets. Thus, our computed values of binding energies of various isomers are expected to be quite accurate. Our geometry optimization reveals ten distinct isomers, along with their point group, and electronic ground state symmetries. We also performed vibrational frequency analysis on the three lowest energy isomers, and found them to be stable. Therefore, we computed the linear optical absorption spectra of these isomers of Btextsubscript{12}, employing large-scale multi-reference singles-doubles configuration-interaction (MRSDCI) approach, and found a strong structure-property relationship. This implies that the spectral fingerprints of the geometries can be utilized for optical detection, and characterization, of various isomers of B$_{12}$. While, in bulk boron, icosahedron is the basic structural unit, but, in the isolated form, we demonstrate it to be unstable. We argue that the disc-like lowest-energy structure of B$_{12}$ cluster can be seen as a consequence of the Jahn-Teller distortion of its icosohedral isomer.

Applying ab initio quantum chemical methods, molecular wheels composed of metal and light atoms were investigated. High quality basis sets 6-31G*, TZPV, and cc-pVTZ as well as exchange and non-local correlation functionals B3LYP, BP86 and B3P86 were used. The ground-state energy and structures of cyclic planar and pyramidal clusters TiBn (for n = 3-10) were computed. In addition, the relative stability and electronic structures of molecular wheels TiBxNyCz (for x, y, z = 0-10) and MBnC10-n (for n = 2 to 5 and M = Sc to Zn) were determined. This paper sustains a follow-up study to the previous one of Boustani and Pandey [Solid State Sci. 14 (2012) 1591], in which the calculations were carried out at the HF-SCF/STO3G/6-31G level of theory to determine the initial stability and properties. The results show that there is a competition between the 2D planar and the 3D pyramidal TiBn clusters (for n = 3-8). Different isomers of TiB10 clusters were also studied and a structural transition of 3D-isomer into 2D-wheel is presented. Substitution boron in TiBio by carbon or/and nitrogen atoms enhances the stability and leads toward the most stable wheel TiB3C7. Furthermore, the computations show that Sc, Ti and V at the center of the molecular wheels are energetically favored over other transition metal atoms of the first row. (C) 2013 Elsevier Masson SAS. All rights reserved.

Applying ab initio quantum chemical methods, molecular wheels composed of metal and light atoms were investigated. High quality basis sets 6-31G*, TZPV, and cc-pVTZ as well as exchange and non-local correlation functionals B3LYP, BP86 and B3P86 were used. The ground-state energy and structures of cyclic planar and pyramidal clusters TiBn (for n 1⁄4 3e10) were computed. In addition, the relative stability and electronic structures of molecular wheels TiBxNyCz (for x, y, z 1⁄4 0e10) and MBnC10 n (for n 1⁄4 2 to 5 and M 1⁄4 Sc to Zn) were determined. This paper sustains a follow-up study to the previous one of Boustani and Pandey [Solid State Sci. 14 (2012) 1591], in which the calculations were carried out at the HF-SCF/STO3G/6-31G level of theory to determine the initial stability and properties. The results show that there is a competition between the 2D planar and the 3D pyramidal TiBn clusters (for n 1⁄4 3e8). Different isomers of TiB10 clusters were also studied and a structural transition of 3D-isomer into 2Dwheel is presented. Substitution boron in TiB10 by carbon or/and nitrogen atoms enhances the stability and leads toward the most stable wheel TiB3C7. Furthermore, the computations show that Sc, Ti and V at the center of the molecular wheels are energetically favored over other transition metal atoms of the first

We extensively study the fragmentation and Coulomb explosion of multiply charged small boron clusters B-n (n = 2-13), where n is the cluster size. Our calculations are based on ab initio quantum-chemistry methods. Highly charged unstable clusters dissociate spontaneously into several neutral or charged fragments, and large amounts of energy are produced, depending on the charge of the parent cluster. We argue that this mechanism makes boron clusters a clean, safe, and cheap energetic material.

By means of ab initio quantum chemical methods we have determined the energies and electronic structures of molecular wheels TiBn, TiBnN10-n, TiCnN10-n and TiCnB10-n (for n = 0-10). The ground state energies and the corresponding spin states of each atom, cluster and molecular wheel were calculated first in the framework of Hartree-Fock self-consistent-field (HF-SCF) using minimal and more accurate basis sets STO-3G and 6-31G. Computations at higher level and accuracy are processing in a follow-up study. The most stable wheel system is TiCnB10-n (for n = 5-10). Thereof particularly highly stable is the TiC5B5 molecular wheel followed by the TiC6B4. At the HF-SCF/6-31G level, however, we have calculated the wheel system MeC5B5 considering for Me, the first row of transition metal atoms Me = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn. The molecular wheel MeC5B5 favours Sc atom at the centre, but also Ti and Fe are the next favoured atoms. (C) 2012 Elsevier Masson SAS. All rights reserved.