A Spinning Umbrella: Carbon Monoxide and Dinitrogen Bound MB12- Clusters (M = Co, Rh, Ir)

Fluxional Behavior and Stability of the Cu2B8- Cluster: A Copper Borozene with a Freely Rotating Cu2 Dimer

We demonstrate that Cu2B8- exhibits distinct fluxional behavior, akin to that of a functional stirrer, with the Cu2 dimer freely rotating on the B8 molecular wheel. This behavior is confirmed by Born-Oppenheimer molecular dynamics simulations. The initiation of this dynamic motion is facilitated by an ultrasoft vibrational mode (less than 10 cm-1), resulting in a negligible rotational barrier of 0.03 kcal/mol, as calculated at the single-point CCSD(T) level. The high stability of Cu2B8- arises from the strong interlayer electrostatic interaction between Cu2 and B8, due to charge transfer from Cu2 to B8, along with additional covalent interactions from the delocalized π electrons of the B8 wheel to the Cu2 dimer. Notably, the Cu2 dimer in Cu2B8- features a two-center one-electron Cu-Cu single bond, while the B82- moiety displays double aromaticity, characterized by the presence of six delocalized π electrons and six delocalized σ electrons.

Structural Evolution of Small-Sized Phosphorus-Doped Boron Clusters: A Half-Sandwich-Structured PB15 Cluster

The present study is a theoretical investigation into the structural evolution, electronic properties, and photoelectron spectra of phosphorus-doped boron clusters PBn0/- (n = 3-17). The results of this study revealed that the lowest energy structures of PBn- (n = 3-17) clusters, except for PB17-, exhibit planar or quasi-planar structures. The lowest energy structures of PBn (n = 3-17), with the exceptions of PB7, PB9, and PB15, are planar or quasi-planar. The ground state of PB7 has an umbrella-shaped structure, with C6V symmetry. Interestingly, the neutral cluster PB15 has a half-sandwich-like structure, in which the P atom is attached to three B atoms at one end of the sandwich, exhibiting excellent relative and chemical stability due to its higher second-order energy difference and larger HOMO-LUMO energy gap of 4.31 eV. Subsequently, adaptive natural density partitioning (AdNDP) and electron localization function (ELF) analyses demonstrate the bonding characteristics of PB7 and PB15, providing support for the validity of their stability. The calculated photoelectron spectra show distinct characteristic peaks of PBn- (n = 3-17) clusters, thus providing theoretical evidence for the future identification of doped boron clusters. In summary, our work has significant implications for understanding the structural evolution of doped boron clusters PBn0/- (n = 3-17), motivating further experiments regarding doped boron clusters.

Structure, stability, reactivity and bonding in noble gas compounds

Noble gases (Ngs) are recognized as the least reactive elements due to their fully filled valence electronic configuration. Their reluctance to engage in chemical bond formation necessitates extreme conditions such as low temperatures, high pressures, and reagents with high reactivity. In this Perspective, we discuss our endeavours in the theoretical prediction of viable Ng complexes, emphasizing the pursuit of synthesizing them under nearly ambient conditions. Our research encompasses various bonding categories of Ng complexes and our primary aim is to comprehend the bonding mechanisms within these complexes, utilizing state-of-the-art theoretical tools such as natural bond orbital, energy decomposition, and electron density analyses. These complex types manifest distinct bonding scenarios. In the non-insertion type, the donor-acceptor interaction strength hinges on the polarizing ability of the binding atom, drawing the electron density of the Ng towards itself. In certain instances, especially with heavier Ng elements, this interaction reaches a magnitude where it can be considered a covalent bond. Conversely, in most insertion cases, the Ng prefers to share electrons to form a covalent bond on one side while interacting electrostatically on the other side. In rare cases, both bonds may be portrayed as electron-shared covalent bonds. Furthermore, a host cage serves as an excellent platform to explore the limits of achieving Ng-Ng bonds (even for helium), under high pressure.

Structural Evolution and Electronic Properties of Two Sulfur Atom-Doped Boron Clusters

We present a theoretical study of structural evolution, electronic properties, and photoelectron spectra of two sulfur atom-doped boron clusters S2Bn0/- (n = 2-13), which reveal that the global minima of the S2Bn0/- (n = 2-13) clusters show an evolution from a linear-chain structure to a planar or quasi-planar structure. Some S-doped boron clusters have the skeleton of corresponding pure boron clusters; however, the addition of two sulfur atoms modified and improved some of the pure boron cluster structures. Boron is electron-deficient and boron clusters do not form linear chains. Here, two sulfur atom doping can adjust the pure boron clusters to a linear-chain structure (S2B20/-, S2B30/-, and S2B4-), a quasi-linear-chain structure (S2B6-), single- and double-chain structures (S2B6 and S2B9-), and double-chain structures (S2B5, and S2B9). In particular, the smallest linear-chain boron clusters S2B20/- are shown with an S atom attached to each end of B2. The S2B2 cluster possesses the largest highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap of 5.57 eV and the S2B2- cluster possesses the largest average binding energy Eb of 5.63 eV, which shows the superior chemical stability and relative stability, respectively. Interestingly, two S-atom doping can adjust the quasi-planar pure boron clusters (B7-, B10-, and B120/-) to a perfect planar structure. AdNDP bonding analyses reveal that linear S2B3 and planar SeB11- have π aromaticity and σ antiaromaticity; however, S2B2, planar S2B6, and planar S2B7- clusters have π antiaromaticity and σ aromaticity. Furthermore, AdNDP bonding analyses reveal that planar S2B4, S2B10, and S2B12 clusters are doubly (π and σ) aromatic, whereas S2B5-, S2B8, S2B9-, and S2B13- clusters are doubly (π and σ) antiaromatic. The electron localization function (ELF) analysis shows that S2Bn0/- (n = 2-13) clusters have different electron delocalization characteristics, and the spin density analysis shows that the open-shell clusters have different characteristics of electron spin distribution. The calculated photoelectron spectra indicate that S2Bn- (n = 2-13) have different characteristic peaks that can be compared with future experimental values and provide a theoretical basis for the identification and confirmation of these doped boron clusters. Our work enriches the new database of geometrical structures of doped boron clusters, provides new examples of aromaticity for doped boron clusters, and is promising to offer new ideas for nanomaterials and nanodevices.

Global Optimization: A Soft Computing Perspective

Tackling the problem of global optimization is one of the most important domains that physicists and chemists are working on. The use of soft computing (SC) techniques has made this easier by reducing nonlinearity and instability and making it technologically rich. This Perspective aims at explaining the basic mathematical models of the most efficient and commonly used SC techniques in computational chemistry for finding the global minimum (GM) energy structures of chemical systems. In this Perspective, we discuss the global optimizations of several chemical systems that our group has worked on using CNN, PSO, FA, ABC, BO, and some hybrid techniques, two of which are interfaced to achieve better-quality results.

Structural Evolution and Electronic Properties of Selenium-Doped Boron Clusters SeBn0/- (n = 3-16)

A theoretical research of structural evolution, electronic properties, and photoelectron spectra of selenium-doped boron clusters SeBn0/- (n = 3-16) is performed using particle swarm optimization (CALYPSO) software in combination with density functional theory calculations. The lowest energy structures of SeBn0/- (n = 3-16) clusters tend to form quasi-planar or planar structures. Some selenium-doped boron clusters keep a skeleton of the corresponding pure boron clusters; however, the addition of a Se atom modified and improved some of the pure boron cluster structures. In particular, the Se atoms of SeB7-, SeB8-, SeB10-, and SeB12- are connected to the pure quasi-planar B7-, B8-, B10-, and B12- clusters, which leads to planar SeB7-, SeB8-, SeB10-, and SeB12-, respectively. Interestingly, the lowest energy structure of SeB9- is a three-dimensional mushroom-shaped structure, and the SeB9- cluster displays the largest HOMO-LUMO gap of 5.08 eV, which shows the superior chemical stability. Adaptive natural density partitioning (AdNDP) bonding analysis reveals that SeB8 is doubly aromatic, with 6 delocalized π electrons and 6 delocalized σ electrons, whereas SeB9- is doubly antiaromatic, with 4 delocalized π electrons and 12 delocalized σ electrons. Similarly, quasi-planar SeB12 is doubly aromatic, with 6 delocalized π electrons and 14 delocalized σ electrons. The electron localization function (ELF) analysis shows that SeBn0/- (n = 3-16) clusters have different local electron delocalization and whole electron delocalization effects. The simulated photoelectron spectra of SeBn- (n = 3-16) have different characteristic bands that can identify and confirm SeBn- (n = 3-16) combined with future experimental photoelectron spectra. Our research enriches the geometrical structures of small doped boron clusters and can offer insight for boron-based nanomaterials.

Structures, and electronic and spectral properties of single-atom transition metal-doped boron clusters MB24 - (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni)

A theoretical study of geometrical structures, electronic properties, and spectral properties of single-atom transition metal-doped boron clusters MB₂₄ ^- (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) is performed using the CALYPSO approach for the global minimum search, followed by density functional theory calculations. The global minima obtained for the MB₂₄ ^- (M = Sc, Ti, V, and Cr) clusters correspond to cage structures, and the MB₂₄ ^- (M = Mn, Fe, and Co) clusters have similar distorted four-ring tubes with six boron atoms each. Interestingly, the global minima obtained for the NiB₂₄ ^- cluster tend to a quasi-planar structure. Charge population analyses and valence electron density analyses reveal that almost one electron on the transition-metal atoms transfers to the boron atoms. The electron localization function (ELF) of MB₂₄ ^- (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) indicates that the local delocalization of MB₂₄ ^- (M = Sc, Ti, V, Cr, and Ni) is weaker than that of MB₂₄ ^- (M = Mn, Fe, and Co), and there is no obvious covalent bond between doped metal and B atoms. The spin density and spin population analyses reveal that open-shell MB₂₄ ^- (M = Ti, Cr, Fe, and Ni) has different spin characteristics which are expected to lead to interesting magnetic properties and potential applications in molecular devices. The polarizability of MB₂₄ ^- (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) shows that MB₂₄ ^- (M = Mn, Fe, and Co) has larger first hyperpolarizability, indicating that MB₂₄ ^- (M = Mn, Fe, and Co) has a strong nonlinear optical response. Hence, MB₂₄ ^- (M = Mn, Fe, and Co) might be considered as a promising nonlinear optical boron-based nanomaterial. The calculated spectra indicate that MB₂₄ ^- (M = Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) has different and meaningful characteristic peaks that can be compared with future experimental values and provide a theoretical basis for the identification and confirmation of these single-atom transition metal-doped boron clusters. Our work enriches the database of geometrical structures of doped boron clusters and can provide an insight into new doped boron clusters.

Structural transformations in boron clusters induced by metal doping

In the last decades, experimental techniques in conjunction with theoretical analyses have revealed the surprising structural diversity of boron clusters. Although the 2D to 3D transition thresholds are well-established, there is no certainty about the factors that determine the geometry adopted by these systems. The structural transformation induced by doping usually yields a minimum energy structure with a boron skeleton entirely different from that of the bare cluster. This review summarizes those clusters no larger than 40 boron atoms where one or two dopants show a radical transformation of the structure. Although the structures of these systems are not easy to predict, they often adopt familiar shapes such as umbrella-like, wheel, tubular, and cages in various cases.

Highly stable actinide(III) complexes supported by doubly aromatic ligands

Owing to the electron-deficient nature of boron atom, the structures and properties of boron clusters can be enriched by doping various metal atoms, including lanthanide metal atoms. Nevertheless, the viability...

Structural and Electronic Properties of Single-Atom Transition Metal-Doped Boron Clusters MB24 (M = Sc, V, and Mn)

A theoretical study of geometrical structures, electronic properties, and spectral properties of single-atom transition metal-doped boron clusters MB24 (M = Sc, V, and Mn) is performed using the CALYPSO approach for the global minimum search, followed by density functional theory calculations. The global minima obtained for the VB24 and MnB24 clusters correspond to cage structures. Interestingly, the global minima obtained for the ScB24 cluster tend to a three-ring tubular structure. Population analyses and valence electron density analyses reveal that partial electrons on transition-metal atoms transfer to boron atoms. The localized orbital locator of MB24 (M = Sc, V, and Mn) indicates that the electron delocalization of ScB24 is stronger than that of VB24 and MnB24, and there is no obvious covalent bond between doped metals and B atoms. The spin density and spin population analyses reveal that MB24 (M = Sc, V, and Mn) have different spin characteristics which are expected to lead to interesting magnetic properties and potential applications in molecular devices. The calculated spectra indicate that MB24 (M = Sc, V, and Mn) has meaningful characteristic peaks that can be compared with future experimental values and provide a theoretical basis for the identification and confirmation of these single-atom transition metal-doped boron clusters. Our work enriches the database of geometrical structures of doped boron clusters and can provide an insight into new doped boron clusters.

Metallocene: multi-layered molecular rotors

The electronic and structural prerequisites for a multi-layered molecular rotor have been demonstrated herein in terms of nine 18-valence-electron metallocene sandwich complexes. First, the lack of strong covalent bonds between layers is a key issue to obtain a barrier-free rotation of one layer relative to other layers, where the considerable energetic but unidirectional (such as electrostatic interactions) interactions are needed between layers to keep the structural integrity against fragment separation and structural distortion in a rotation process. Second, one or more layers should possess continuous and delocalized π electron clouds to provide a driving force for the barrier-free rotation. More importantly, besides a negligible rotation barrier, the reasonable rotational period associated with the ultra-soft rotation mode is a critical point for the observability of dynamical behavior in multi-layered molecular rotors.

Atomic Clusters: Structure, Reactivity, Bonding, and Dynamics

Atomic clusters lie somewhere in between isolated atoms and extended solids with distinctly different reactivity patterns. They are known to be useful as catalysts facilitating several reactions of industrial importance. Various machine learning based techniques have been adopted in generating their global minimum energy structures. Bond-stretch isomerism, aromatic stabilization, Rener-Teller effect, improved superhalogen/superalkali properties, and electride characteristics are some of the hallmarks of these clusters. Different all-metal and nonmetal clusters exhibit a variety of aromatic characteristics. Some of these clusters are dynamically stable as exemplified through their fluxional behavior. Several of these cluster cavitands are found to be agents for effective confinement. The confined media cause drastic changes in bonding, reactivity, and other properties, for example, bonding between two noble gas atoms, and remarkable acceleration in the rate of a chemical reaction under confinement. They have potential to be good hydrogen storage materials and also to activate small molecules for various purposes. Many atomic clusters show exceptional opto-electronic, magnetic, and nonlinear optical properties. In this Review article, we intend to highlight all these aspects.

Possible effects of fluxionality of a cavitand on its catalytic activity through confinement

The discovery of fullerenes was a huge milestone in the scientific community, and with it came the urge to discover and analyze various small and large atomic and molecular clusters having a cavity. These cavitands of varied shapes and sizes have wide applications in the encapsulation of rare gas atoms to induce bond formation between them, storage of hydrogen and hydrocarbons to be used as alternative sources of fuel, catalyzation of otherwise slow reactions without using a catalyst, activation of small gas molecules, etc. Various cavitands like fullerenes, [ExBox]4+, cucurbit[n]urils, borospherenes, octa acid, etc. have been used for this purpose. Some clusters including cavitands exhibit fluxional behaviour. Systems in a confined environment often manifest interesting variations in their properties and behaviour, compared to their unconfined counterparts, facilitating the aforementioned applications. In this perspective article, we explore the possibility of making use of this extra degree of freedom, viz., the fluxionality, in changing the catalytic activity of the cavitand.

Transition-metal-like bonding behaviors of a boron atom in a boron-cluster boronyl complex [(η7-B7)-B-BO]. Chem Sci 2021;12:8157-8164. [PMID: 34194706 PMCID: PMC8208299 DOI: 10.1039/d1sc00534k]

Boron displays many unusual structural and bonding properties due to its electron deficiency. Here we show that a boron atom in a boron monoxide cluster (B₉O⁻) exhibits transition-metal-like properties. Temperature-dependent photoelectron spectroscopy provided evidence of the existence of two isomers for B₉O⁻: the main isomer has an adiabatic detachment energy (ADE) of 4.19 eV and a higher energy isomer with an ADE of 3.59 eV. The global minimum of B₉O⁻ is found surprisingly to be an umbrella-like structure (C_6v, ¹A₁) and its simulated spectrum agrees well with that of the main isomer observed. A low-lying isomer (C_s, ¹A′) consisting of a BO unit bonded to a disk-like B₈ cluster agrees well with the 3.59 eV ADE species. The unexpected umbrella-like global minimum of B₉O⁻ can be viewed as a central boron atom coordinated by a η⁷-B₇ ligand on one side and a BO ligand on the other side, [(η⁷-B₇)-B-BO]⁻. The central B atom is found to share its valence electrons with the B₇ unit to fulfill double aromaticity, similar to that in half-sandwich [(η⁷-B₇)-Zn-CO]⁻ or [(η⁷-B₇)-Fe(CO)₃]⁻ transition-metal complexes. The ability of boron to form a half-sandwich complex with an aromatic ligand, a prototypical property of transition metals, brings out new metallomimetic properties of boron.

The global minimum of the B₉O⁻ cluster is found to have an umbrella-like structure, where the central B atom exhibits transition-metal-like bonding properties, coordinated by a η⁷-B₇ ligand on one side and a BO ligand on the other.

The teetotum cluster Li2FeB14 and its possible use for constructing boron nanowires

Systematic density functional theory (DFT) calculations using the TPSSh functional and the def2-TZVP basis set were carried out to identify the global energy minimum structure of the Li2FeB14 cluster. Keeping the double ring tubular shape of FeB14, capping of two Li atoms leads to a teetotum form at a low spin state, in which the Fe atom is endohedrally covered by two B7 strings, and both Li atoms are attached to Fe along the C7 axis at both sides. Calculated results show that strong electrostatic interactions between 2Li+ and Fe2- arising from Li electron transfer upon doping particularly provide a key driving force for stabilizing this charge-transfer structure. The bonding pattern of the teetotum can be understood from the hollow cylinder model (HCM). TD-DFT calculations demonstrate that this cluster can also be regarded as a useful material for transparent optoelectronic devices. Furthermore, the Li2FeB14 superatom can be used as a building block for making boron-based nanowires with metallic character. Replacement of Li atoms by Mg atoms was also found to lead to nanowires.

LiB13: A New Member of Tetrahedral-Typed B13 Ligand Half-Surround Cluster

It will get entirely unusual derivatives with gratifying chemical bonding schemes for boron clusters by doping with lithium, the lightest alkalis. The geometric structures and electronic properties of the LiBn0/- (n = 10-20) clusters have been studied through Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) structural search approach along with the density functional theory (DFT) calculations. The low-lying candidates of LiBn0/- (n = 10-20) are reoptimized at the B3LYP functional in conjunction with 6-311 + G(d) basis set. Three forms of geometric configurations are identified for the ground-state structures of LiBn0/- clusters: half-sandwich-type, quasi-planar and drum-type structures. The photoelectron spectra (PES) of the LiBn- clusters have been calculated through time-dependent density functional theory (TD-DFT). A promising LiB13 with tetrahedral-typed B13 ligand half-surround cluster and robust stability is uncovered. The molecular orbital and adaptive natural density partitioning (AdNDP) analysis show that B-B bonds in the B13 moiety combined with the interaction between the B13 shell and Li atom stabilize the C2v LiB13 cluster. Our results advance the fundamental understanding about the alkali metal doped boron clusters.

Intriguing structural, bonding and reactivity features in some beryllium containing complexes

We highlighted our contributions to Be chemistry which include bond-stretch isomerism in Be₃²⁻ species, Be complexes bound with noble gas, CO, and N₂, Be based nanorotors, and intriguing bonding situations in some Be complexes.

Fluxional Boron Clusters: From Theory to Reality

Isolated boron clusters exhibit many intriguing properties, which have only recently been unfolding with the hand-in-hand advancement of state-of-the-art experimental and theoretical methods for the analyses of their electronic structure, chemical reactivity, and nuclear dynamics. A fascinating property that a number of these clusters display is fluxionality, a dynamical phenomenon associated with the delocalized nature of the chemical bonding and related to the continuous exchange between interatomic neighbors. The electron-deficient nature of boron is the driving force behind its extraordinary ability to form multicenter bonds, and this in turn leads to fluxional behavior only when an appropriate combination of topology and bonding is present. The first instance of fluxionality in boron clusters, the quasi-planar anion B₁₉^-, was reported in 2010. The rotational barrier of the inner B₆ unit spinning within the peripheral B₁₃ ring can be overcome even at low temperature, mimicking the characteristic motion of a rotary internal combustion engine, and hence, B₁₉^- was entitled a boron-based molecular Wankel engine. Shortly after that, it was found that other quasi-planar boron clusters, like B₁₃⁺ and B₁₈^2-, also exhibit an almost barrier-free rotation of internal planar moieties. The case of the B₁₃⁺ cation is special because, on the one hand, it was chosen to examine the way to initiate, control, and direct the internal rotation using circularly polarized laser radiation, and on the other hand, the experimental manifestation of fluxionality was first established for this system through infrared experiments. Nevertheless, fluxional behavior is not limited to planar or pure boron clusters. Larger boron clusters, such as the fullerene-analogue borospherenes B₄₀ and B₃₉^-, are also predicted to show pronounced dynamical behavior that is related to the interconversion between six- and seven-membered rings. Be₆B₁₁^-, a triple-layer cluster, is another particularly interesting system since it exhibits multifold fluxionality consisting of the revolution of the outer boron ring around the Be₆ core and the spinning of the two Be₃ rings with respect to each other. The essential criteria for dynamical behavior in boron clusters are (1) the absence of a localized two-center, two-electron (2c-2e) bond between two molecular regions that tend to rotate with respect to each other, (2) the absence of steric hindrances for rotation and reorganization, and (3) retention of the delocalized electronic structure throughout the rotation/reorganization process. The fulfillment of the above three conditions ensures that low energy barriers will be associated with the rotation or reorganization of molecular moieties. The first two points can be illustrated from the facts that a single localized C-B σ bond in CB₁₈ raises the rotational barrier by 27.0 kcal·mol^-1 and the expansion of the outer ring by a single boron atom in moving from B₁₂⁺ to B₁₃⁺ lowers the rotational barrier by 7.5 kcal·mol^-1. Alternatively, it is also possible to make a rigid boron cluster fluxional through doping, where the geometric and electronic changes caused by a suitable dopant, as in MB₁₂^- (M = Co, Rh, Ir) and B₁₀Ca, reduce the corresponding rotational barriers enough to achieve fluxionality. At present, there are 13 pure boron clusters (B₁₁^-/0/+, B₁₃^+/0/-, B₁₅^+/0/-, B₁₈^2-, B₁₉^-, and B₂₀^-/2-) and eight metal-doped boron clusters (B₁₀Ca, NiB₁₁^-, [B₂-Ta@B₁₈]^-, Be₆B₁₁^-, Be₆B₁₀^2-, and MB₁₈^- (M = K, Rb, Cs)) that have sufficiently small rotational barriers (less than ∼1.5 kcal·mol^-1) to exhibit fluxional behavior at low temperature. Some of the other reported boron clusters show more sizable barriers, and their dynamical behavior is manifested only at elevated temperatures. The research on such systems is driven by the notion that it ultimately will pave the way for the development of light-harvesting boron-based nanomotors/machines and robots, a reality that may not be that far away!

How Far Can One Push the Noble Gases Towards Bonding?: A Personal Account

Noble gases (Ngs) are the least reactive elements in the periodic table towards chemical bond formation when compared with other elements because of their completely filled valence electronic configuration. Very often, extreme conditions like low temperatures, high pressures and very reactive reagents are required for them to form meaningful chemical bonds with other elements. In this personal account, we summarize our works to date on Ng complexes where we attempted to theoretically predict viable Ng complexes having strong bonding to synthesize them under close to ambient conditions. Our works cover three different types of Ng complexes, viz., non-insertion of NgXY type, insertion of XNgY type and Ng encapsulated cage complexes where X and Y can represent any atom or group of atoms. While the first category of Ng complexes can be thermochemically stable at a certain temperature depending on the strength of the Ng-X bond, the latter two categories are kinetically stable, and therefore, their viability and the corresponding conditions depend on the size of the activation barrier associated with the release of Ng atom(s). Our major focus was devoted to understand the bonding situation in these complexes by employing the available state-of-the-art theoretic tools like natural bond orbital, electron density, and energy decomposition analyses in combination with the natural orbital for chemical valence theory. Intriguingly, these three types of complexes represent three different types of bonding scenarios. In NgXY, the strength of the donor-acceptor Ng→XY interaction depends on the polarizing power of binding the X center to draw the rather rigid electron density of Ng towards itself, and sometimes involvement of such orbitals becomes large enough, particularly for heavier Ng elements, to consider them as covalent bonds. On the other hand, in most of the XNgY cases, Ng forms an electron-shared covalent bond with X while interacting electrostatically with Y representing itself as [XNg]+Y-. Nevertheless, in some of the rare cases like NCNgNSi, both the C-Ng and Ng-N bonds can be represented as electron-shared covalent bonds. On the other hand, a cage host is an excellent moiety to examine the limits that can be pushed to attain bonding between two Ng atoms (even for He) at high pressure. The confinement effect by a small cage-like B12N12 can even induce some covalent interaction within two He atoms in the He2@B12N12 complex.

NbB12−: a new member of half-sandwich type doped boron clusters with high stability

The global minimum structure of a NbB₁₂⁻ cluster of half-sandwich type.

Exhaustive exploration of MgBn (n = 10–20) clusters and their anions

An unexpected tubular-shaped MgB₁₈ cluster is identified for the first time in alkaline-earth metal-doped boron clusters.

Boron Nanowheels with Axles Containing Noble Gas Atoms: Viable Noble Gas Bound M©B10- Clusters (M=Nb, Ta)

The viability of noble gas axled boron nanowheels Ng_n M©B₁₀^- (Ng=Ar-Rn; M=Nb, Ta; n=1, 2) is explored by ab initio computations. In the resulting Ng₂ -M complexes, the Ng-M-Ng nanorod passes through the center of the B₁₀^- ring, providing them with an inverse sandwich-like structure. While in the singly Ng bound analogue, the Ng binding enthalpy H_b at 298 K ranges from 2.5 to 10.6 kcal mol^-1 , in doubly Ng bound cases it becomes very low for the Ng₂ M©B₁₀^- →Ng+NgM©B₁₀^- dissociation channel, except for the case of Rn, for which the corresponding H_b values are 3.4 (Nb) and 4.0 kcal mol^-1 (Ta). For a given Ng, Ta has slightly higher Ng-binding ability than Nb. The corresponding free-energy changes indicate that these systems, particularly the Xe and Rn complexes, are good candidates for experimental realization in a low-temperature matrix. The Ng-M bonds were found to be covalent in nature, as reflected in their large Wiberg bond indices, formation of a 2c-2e σ orbital between Ng and M centers in natural bond orbital and adaptive natural density partitioning (AdNDP) analyses, and the short Ng-M distances. Energy decomposition analysis and a study on the natural orbitals for chemical valence show that the Ng-M contact is supported mainly by the orbital and electrostatic interactions, with almost equal contributions. Although both the Ng→M σ donation and Ng←M π backdonation play roles in the origin of orbital interaction, the former is significantly dominant over the latter. Further, AdNDP analysis indicates that the doubly aromatic character (both σ and π) in MB₁₀^- clusters is not perturbed by the interaction with Ng atoms.

Noble gas encapsulated B40 cage

The efficacy of B₄₀ borospherene to act as a host for noble gas atoms is explored via density functional theory based computations. Although the Ng@B₄₀ complexes are thermochemically unstable with respect to dissociation into free Ng and B₄₀, it does not rule out their viability as all the systems possess a high activation free energy barrier (84.7-206.3 kcal mol^-1). Therefore, once they are formed, it is hard to take out the Ng atom. Two Ng atoms can also be incorporated within B₄₀ for the lighter Ng atoms (He and Ne). In fact, the destabilization offered by the encapsulation of one and two He atoms and one Ne atom inside B₄₀ is significantly less than that in experimentally synthesized He@C₂₀H₂₀, highlighting their greater possibility for synthesis. Although Ar₂ and Kr₂ encapsulated B₄₀ systems are very much destabilized by the repulsive interaction between Ng₂ and B₄₀, an inspection of the bonding situation reveals that the confinement can even induce some degree of covalent interaction between two otherwise non-bonded Ng atoms. Ng atoms transfer electrons towards B₄₀ which is smaller for lighter Ng atoms and gradually increases along He to Rn. Even if the electrostatic interaction between Ng and B₄₀ is the most predominant term in these systems, the extent of the orbital interaction is also considerable. However, the very large Pauli repulsion counterbalances the attractive interaction, eventually turning the interaction repulsive in nature. Ng@B₄₀ also shows dynamical behaviour involving continuous exchange between hexagonal and heptagonal holes, similar to the host cage, as understood from the very little variation in the activation barrier because of the Ng encapsulation. Furthermore, sandwich complexes like [(η⁵-C₅Me₅)Fe(η⁶-B₄₀)]⁺ and [(η⁵-C₅Me₅)Fe(η⁷-B₄₀)]⁺ are noted to be viable with the latter being slightly more stable than the former. The encapsulation of Xe slightly improves the dissociation energy associated with the decomposition into Xe@B₄₀ and [Fe(η⁵-C₅Me₅)]⁺ compared to that in the bare one.

Probing the structural and electronic properties of zirconium doped boron clusters: Zr distorted B12 ligand framework

The lowest-energy structure ZrB₁₂ shows that the dopant Zr atom breaks the triangle B₃ present in other M@B₁₂ clusters (M = Co, Rh, Ir) to form a quasi-linear B₃ unit in the B₁₂ motif and induce strong Zr–B interactions that enhance the stability of the neutral half-sandwich ZrB₁₂ cluster.