Fluxional Boron Clusters: From Theory to Reality

Ultrathin Boron Growth onto Nanodiamond Surfaces via Electrophilic Boron Precursors

Diamond as a templating substrate is largely unexplored, and the unique properties of diamond, including its large bandgap, thermal conductance, and lack of cytotoxicity, makes it versatile in emergent technologies in medicine and quantum sensing. Surface termination of an inert diamond substrate and its chemical reactivity are key in generating new bonds for nucleation and growth of an overlayer material. Oxidized high-pressure high temperature (HPHT) nanodiamonds (NDs) are largely terminated by alcohols that act as nucleophiles to initiate covalent bond formation when an electrophilic reactant is available. In this work, we demonstrate a templated synthesis of ultrathin boron on ND surfaces using trigonal boron compounds. Boron trichloride (BCl3), boron tribromide (BBr3), and borane (BH3) were found to react with ND substrates at room temperature in inert conditions. BBr3 and BCl3 were highly reactive with the diamond surface, and sheet-like structures were produced and verified with electron microscopy. Surface-sensitive spectroscopies were used to probe the molecular and atomic structure of the ND constructs' surface, and quantification showed the boron shell was less than 1 nm thick after 1-24 h reactions. Observation of the reaction supports a self-terminating mechanism, similar to atomic layer deposition growth, and is likely due to the quenching of alcohols on the diamond surface. X-ray absorption spectroscopy revealed that boron-termination generated midgap electronic states that were originally predicted by density functional theory (DFT) several years ago. DFT also predicted a negative electron surface, which has yet to be confirmed experimentally here. The boron-diamond nanostructures were found to aggregate in dichloromethane and were dispersed in various solvents and characterized with dynamic light scattering for future cell imaging or cancer therapy applications using boron neutron capture therapy (BNCT). The unique templating mechanism based on nucleophilic alcohols and electrophilic trigonal precursors allows for covalent bond formation and will be of interest to researchers using diamond for quantum sensing, additive manufacturing, BNCT, and potentially as an electron emitter.

Probing the Structural and Electronic Properties of the Anionic and Neutral Tellurium-Doped Boron Clusters TeBnq (n = 3-16, q = 0, -1)

In this study, we employ density functional theory along with the artificial bee colony algorithm for cluster global optimization to explore the low-lying structures of TeBnq (n = 3-16, q = 0, -1). The primary focus is on reporting the structural properties of these clusters. The results reveal a consistent doping pattern of the tellurium atom onto the in-plane edges of planar or quasi-planar boron clusters in the most energetically stable isomers. Additionally, we simulate the photoelectron spectra of the cluster anions. Through relative stability analysis, we identify three clusters with magic numbers -TeB7-, TeB10, and TeB12. The aromaticity of these clusters is elucidated using adaptive natural density partitioning (AdNDP) and magnetic properties analysis. Notably, TeB7- exhibits a perfect σ-π doubly aromatic structure, while TeB12 demonstrates strong island aromaticity. These findings significantly contribute to our understanding of the structural and electronic properties of these clusters.

Dynamic Structural Fluxionality in a Planar Tetracoordinate Carbon Cluster Stabilized by Boron Ligands

The design of boron-based molecular rotors stems from boron-carbon binary clusters containing multiple planar hypercoordinate carbons (phCs, such as C2B8). However, the design of boron-coordinated phCs is challenging due to boron's tendency to occupy hypercoordinate centers more than carbon. Although this challenge has been addressed, the designed clusters of interest have not exhibited dynamic fluxionality similar to that of the initial C2B8. To address this issue, we report a σ/π doubly aromatic CB2H5 + cluster, the first global minimum containing a boron-coordinated planar tetracoordinate carbon atom with dynamic fluxionality. Dynamics simulations show that two ligand H atoms exhibit alternate rotation, resulting in an intriguing dynamic fluxionality in this cluster. Electronic structure analysis reveals the flexible bonding positions of the ligand H atoms because they do not participate in π delocalized bonding nor bond to any other non-carbon atom, highlighting this rotational fluxionality. Unprecedentedly, the fluxional process involves not only the usual conversion of the number of bonding atoms, but also the type of bonding (3c π bonds ↔4c σ bonds), which is an uncommon fluxional mechanism. The cluster represents an effort to apply phC species to molecular machines.

A topological path to the formation of a quasi-planar B70 boron cluster and its dianion

In view of the competing assignments regarding the most stable isomer of the B70 boron cluster including the quasi-planar and bilayer structures, we reinvestigated the structural motifs of B70 using a genetic algorithm for structure search (MEGA) in conjunction with density functional theory computations using the PBE functional. The quasi-planar structure was also constructed using the topological leapfrog algorithm. The latter search aimed to give us unique insight into its formation and the growth pattern of boron clusters. Also, the di-anionic state of B70 was explored. Our extensive search suggested a competition between the quasi-planar, tubular and bilayer isomers for the ground state of B70 in both neutral and dianionic states. While the bilayer form is more stable in the neutral state, the quasi-planar counterpart becomes more stable in the dianionic B702-. The stability arises due to the fact that the B702- dianion possesses 50 π electrons that satisfy the disk aromaticity model rule. These results tend to extend the stabilization of the quasi-planar structure upon negative charge addition previously found in small size boron clusters to larger sizes.

Searching for stable copper borozene complexes in CuB7- and CuB8. Phys Chem Chem Phys 2024;26:12928-12938. [PMID: 38456623 DOI: 10.1039/d4cp00296b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Copper has been shown to be an important substrate for the growth of borophenes. Copper-boron binary clusters are ideal platforms to study the interactions between copper and boron, which may provide insight about the underlying growth mechanisms of borophene on copper substrates. Here we report a joint photoelectron spectroscopy and theoretical study on two copper-doped boron clusters, CuB7- and CuB8-. Well resolved photoelectron spectra are obtained for the two clusters at different wavelengths and are used to understand the structures and bonding properties of the two CuBn- clusters. We find that CuB8- is a highly stable borozene complex, which possesses a half-sandwich structure with a Cu+ species interacting with the doubly aromatic η8-B82- borozene. The CuB7- cluster is found to consist of a terminal copper atom bonded to a double-chain B7 motif, but it has a low-lying isomer composed of a half-sandwich structure with a Cu+ species interacting with an open-shell η7-B72- borozene. Both ionic and covalent interactions are found to be possible in the binary Cu-B clusters, resulting in different structures.

Electronic Control of the Position of the Pb Atom on the Surface of B8 Borozene in the PbB8 Cluster

Spontaneous symmetry-breaking is common in chemical and physical systems. Here, we show that by adding an electron to the C7v PbB8 cluster, which consists of a planar B8 disk with the Pb atom situated along the C7 axis, the Pb atom spontaneously moves to the off-axis position in the PbB8- anion. Photoelectron spectroscopy of PbB8- reveals a broad ground-state transition and a large energy gap, suggesting a highly stable closed-shell PbB8 borozene complex and a significant geometry change upon electron detachment. Quantum chemistry calculations indicate that the lowest unoccupied molecular orbital of the C7v PbB8 cluster is a degenerate π orbital mainly consisting of the Pb 6px and 6py atomic orbitals. Occupation of one of the 6p orbitals spontaneously break the C7v symmetry in the anion due to the Jahn-Teller effect. The large amplitude of the position change of Pb in PbB8- relative to PbB8 is surprising owing to bonding interactions between the Pb 6p orbital with the π orbital of the B8 borozene.

CBe4H6: a molecular rotor with a built-in on-off switch

It is highly challenging to control (stop and resume as needed) molecular rotors because their intramolecular rotations are electronically enabled by delocalized σ bonding, and the desired control needs to be able to destroy and restore such σ bonding, which usually means difficult chemical manipulation (substitution or doping atom). In this work, we report CBe4H6, a molecular rotor that can be controlled independently of chemical manipulation. This molecule exhibited the uninterrupted free rotation of Be and H atoms around the central carbon in first-principles molecular dynamics simulations at high temperatures (600 and 1000 K), but the rotation cannot be witnessed in the simulation at room temperature (298 K). Specifically, when a C-H bond in the CBe4H6 molecule adopts the equatorial configuration at 298 K, it destroys the central delocalized σ bonding and blocks the intramolecular rotation (the rotor is turned "OFF"); when it can adopt the axial configuration at 600 and 1000 K, the central delocalized σ bonding can be restored and the intramolecular rotation can be resumed (the rotor is turned "ON"). Neutral CBe4H6 is thermodynamically favorable and electronically stable, as reflected by a wide HOMO-LUMO gap of 7.99 eV, a high vertical detachment energy of 9.79 eV, and a positive electron affinity of 0.24 eV, so it may be stable enough for the synthesis, not only in the gas phase, but also in the condensed phase.

Boron-based ternary MgTa2B6 cluster: a turning nanoclock with dynamic structural fluxionality

Boron-based complex clusters are a fertile ground for the exploration of exotic chemical bonding and dynamic structural fluxionality. Here we report on the computational design of a ternary MgTa2B6 cluster via global structural searches and quantum chemical calculations. The cluster turns out to be a new member of the molecular rotor family, closely mimicking a turning clock at the subnanoscale. It is composed of a hexagonal B6 ring with a capping Ta atom at the top and bottom, whereas the Mg atom is linked to one Ta site as a radial Ta-Mg dimer. These components serve as the dial, axis, and hand of a nanoclock, respectively. Chemical bonding analyses reveal that the inverse sandwich Ta2B6 motif in the cluster features 6π/6σ double aromaticity, whose electron counting conforms to the (4n + 2) Hückel rule. The Ta-Mg dimer has a Lewis-type σ bond, and the Mg site has negligible bonding with B6 ring. The ternary cluster can be formulated as an [Mg]0[Ta2B6]0 complex. Molecular dynamics simulations suggest that the cluster is structurally fluxional analogous to a nanoclock, even at a low temperature of 100 K. The Ta-Mg hand turns almost freely around the Ta2 axis and along the B6 dial. The tiny intramolecular rotation barrier is less than 0.3 kcal mol-1, being dictated by the bonding nature of double 6π/6σ aromaticity. The present system offers a new type of molecular rotor in physical chemistry.

CBe2 H5 - : Unprecedented 2σ/2π Double Aromaticity and Dynamic Structural Fluxionality in a Planar Tetracoordinate Carbon Cluster

A 14-electron ternary anionic CBe2 H5 - cluster containing a planar tetracoordinate carbon (ptC) atom is designed herein. Remarkably, it can be stabilized by only two beryllium atoms with both π-acceptor/σ-donor properties and two hydrogen atoms, which means that the conversion from planar methane (transition state) to ptC species (global minimum) requires the substitution of only two hydrogen atoms. Moreover, two ligand H atoms exhibit alternate rotation, giving rise to interesting dynamic fluxionality in this cluster. The electronic structure analysis reveals the flexible bonding positions of ligand H atoms due to C-H localized bonds, highlighting the rotational fluxionality in the cluster, and two CBe2 3c-2e delocalized bonds endow its rare 2σ/2π double aromaticity. Unprecedentedly, the fluxional process exhibits a conversion in the type of bonding (σ bond↔π bond), which is an uncommon fluxional mechanism. The cluster can be seen as an attempt to apply planar hypercoordinate carbon species to molecular motors.

Li6 E5 Li6 : Tetrel Sandwich Complexes with 10-π-Electrons

When (4n +2) π-electrons are located in single planar ring, it conventionally qualifies as aromatic. According Hückel's rule, systems possessing ten π-electrons should be aromatic. Herein we report a series of D5h  Li6 E5 Li6 sandwich structures, representing the first global minima featuring ten π-electrons E5 10- ring (E=Si-Pb). However, these π-electrons localize as five π-lone-pairs rather than delocalized orbitals. The high symmetry structure achieved is a direct consequence of σ-aromaticity, particularly favored in elements from Si to Pb, resulting in a pronounced diatropic ring current flow that contributes to the enhanced stability of these systems.

[(OB)2-M©B7O7-BO]- (M = Mn, Tc, Re): Chemically Stable and Triply Aromatic Ballet Rotors

Single-molecule nanorotors are generally constructed based on boron atoms to obtain structural fluxionality via possessing the delocalized multicenter bonds. However, the electron-deficient boron atoms are commonly exposed in these nanorotors, which leads to extremely high chemical reactivity, which blocks the synthesis in the condensed phase. In this work, we computationally designed a series of transition-metal-doped boron oxide clusters MB10O10- (in structural configuration of [(OB)2-M©B7O7-BO]-, M = Mn, Tc, Re, © means "centered" in a planar or quasi-planar hypercoordinate environment), which can be vividly named as "ballet rotors" to label their anthropomorphic dynamic rotational behaviors. The rotational fluxionality in ballet rotors originates from the completely delocalized nature of the bonding within their MB10 core moieties. Remarkably, compared with single-molecule nanorotors having bare boron atoms and the narrow HOMO-LUMO gaps (≤4.00 eV) as well as low vertical detachment energies (VDEs, ≤4.46 eV for anions), the ballet rotors possess significantly improved chemical stability, as evidenced sterically by the absence of exposed boron atoms and electronically by much wider HOMO-LUMO gaps (5.66-5.98 eV) as well as obviously higher VDEs between 5.36 and 5.47 eV. Specifically, the ballet rotors are mainly stabilized by the delicately placed peripheral oxygen atoms, which can compensate for all electron-deficient boron atoms via O → B π back bonds and sterically protect them. Simultaneously, they are additionally stabilized by aromatic stabilization effect from possessing the novel S + P + D triple aromaticity. We expect that the proposal of chemically stable ballet rotors in this work can arouse the rational design of nanorotors for experimental realization in the condensed phase.

Photoelectron Spectroscopy and Theoretical Study of Di-Copper-Boron Clusters: Cu2B3- and Cu2B4. J Phys Chem A 2023. [PMID: 37235389 DOI: 10.1021/acs.jpca.3c02417] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Copper has been found to be able to mediate the formation of bilayer borophenes. Copper-boron binary clusters are ideal model systems to probe the copper-boron interactions, which are essential to understand the growth mechanisms of borophenes on copper substrates. Here, we report a joint photoelectron spectroscopy and theoretical study on two di-copper-doped boron clusters: Cu₂B₃^- and Cu₂B₄^-. Well-resolved photoelectron spectra are obtained, revealing the presence of a low-lying isomer in both cases. Theoretical calculations show that the global minimum of Cu₂B₃^- (C_2v, ¹A₁) contains a doubly aromatic B₃^- unit weakly interacting with a Cu₂ dimer, while the low-lying isomer (C_2v, ¹A₁) consists of a B₃ triangle with the two Cu atoms covalently bonded to two B atoms at two vertexes. The global minimum of Cu₂B₄^- (D_2h, ²A_g) is found to consist of a rhombus B₄ unit covalently bonded to the two Cu atoms at two opposite vertexes, whereas in the low-lying isomer (C_s, ²A'), one of the two Cu atoms is bonded to two B atoms.

Two-layer molecular rotors: A zinc dimer rotating over planar hypercoordinate motifs

Multi-layer molecular rotors represent a class of unique combination of topology and bonding, featuring a barrier-free rotation of one layer with respect to other layers. This emerging fluxional behavior has been found in a few doped boron clusters. Herein, we strongly enrich this intriguing family followed by an effective design strategy, summarized as essential factors: i) considerable electrostatic interactions originated from a strong charge transfer between layers; ii) the absence of strong covalent bonds between layers; and iii) fully delocalized σ/π electrons from at least one layer. We found that planar hypercoordinate motifs consisting of monocyclic boron rings and metals with σ + π dual aromaticity can be regarded as one promising layer, which can support the suspended X₂ (X = Zn, Cd, Hg) dimers. By detailed investigations of thermodynamic and kinetic stabilities of 60 species, eventually, MB₇ X₂ ^- and MB₈ X₂ (X = Zn, Cd; M = Be, Ru, Os; Be works only for Zn-based cases) clusters were verified to be the global-minimum two-layer molecular rotors. Especially, their electronic structure analyses vividly confirm the practicability of the electronic structure requirements mentioned above for designing multi-layer molecular rotors.

Dismantlement of ammonia upon interaction with Ben (n ≤ 10) clusters

The interaction of ammonia with Be_n (n < 1-10) clusters has been investigated by density functional theory and ab initio calculations. The main conclusion is that, regardless of the size of the Be cluster, neither the structure of ammonia nor that of the Be clusters are preserved due to a systematic dissociation of its NH bonds and a spontaneous H-shift toward the available Be atoms. This H migration not only leads to rather stable BeH bonds, but dramatically enhances the strength of the BeN bonds as well. Accordingly, the maximum stability is found for the interaction with the beryllium trimer, leading to a complex with three NBe and three BeH bonds. Another maximum in stability, although lower than that reached for n = 3, is found for the Be heptamer, since from n = 6, a new NBe bond is formed, so that complexes from n = 6 to n = 10 are characterized by the formation of a NBe₄ moiety, whose stability reaches a maximum at n = 7. The bonding characteristics of the different species formed are analyzed by means of AIM, NBO, ELF and AdNDP approaches.

Be3B11- cluster: a dynamically fluxional beryllo-borospherene

The beryllium-doped Be₃B₁₁^- cluster has two nearly isoenergetic isomers, adopting the smallest trihedral spherical geometries with a boron single-chain skeleton. The B₁₁ skeleton in the global minimum (C_2v, ¹A₁) comprises three conjoined boron rings (one B₈/two B₇) on the waist, sharing two B₃ equilateral triangles at the top and bottom, respectively. However, the local minimum (C_s, ¹A') has one deformed B₄ pyramid at the top. The drastic structural transformation of B₁₁ skeletons from perfectly planar B₁₁ clusters mainly profited from robust electrostatic interaction between Be atoms and B₁₁ skeletons. The dynamic simulations suggest that two species can interconvert via a novel mechanism, that is "triangle-pyramid-triangle", which facilitates the free migration of boron atoms in the B₁₁ skeleton, thereby showing the fascinating dynamic fluxionality. The chemical bonding analyses reveal that the B₁₁ skeleton is covered by two types of delocalized π bonds in an orthogonal direction, which leads to its spherical aromaticity.

The dodeca-coordinated La©B8C4 +/0/- molecular wheels: conflicting aromaticity versus double aromaticity

The transition-metal centered boron molecular wheels have attracted the attention of chemists. The highest deca-coordination number for central metal atoms was observed in D _10h Ta©B₁₀ ^- and Nb©B₁₀ ^- molecular wheels. Here, we report a theoretical study of La©B₈C₄ ^q (q = +1, 0, -1) clusters with the dodeca-coordinated La atom. The La©B₈C₄ ^q clusters adopt fascinating molecular wheel structures, showing a La atom enclosed by a perfect B₈C₄ monocyclic ring. The cationic La©B₈C₄ ⁺ cluster has a C _4v symmetry with the distinctly out-of-plane distortion of the La atom (0.70 Å), which is gradually flattened by the sequential reduction reaction. The distortion of the La atom from the plane in the neutral La©B₈C₄ cluster decreases to 0.46 Å. The La©B₈C₄ ^- species turns out to be perfectly planar. Chemical bonding analyses indicate that the neutral La©B₈C₄ and anionic La©B₈C₄ ^- possess 10σ and 9π/10π double aromaticity, respectively, obeying the principle of double aromaticity. However, the cationic La©B₈C₄ ⁺ has 10σ and 8π conflicting aromaticity, representing a counterexample in planar hyper-coordinated molecular wheels. The dodeca-coordination number in La©B₈C₄ ^q (q = +1, 0, -1) clusters is unprecedented, which provides a new idea and concept for searching planar hyper-coordinated systems.

A plier-shaped binary molecular wheel B7Mg4+ cluster: hybrid in-plane heptacoordination, double π/σ aromaticity, and electronic transmutation

A plier-shaped charge-transfer [Mg2]2+[Mg2B7]− complex cluster exhibits double 6π/6σ aromaticity, whose hybrid molecular wheel structure is rationalized using the concept of electronic transmutation.

Theoretical Investigation of Geometries and Bonding of Indium Hydrides in the In2Hx and In3Hy (x = 0-4,6; y = 0-5) Series

Boron hydrides have been an object of intensive theoretical and experimental investigation for many decades due to their unusual and somewhat unique bonding patterns. Despite boron being a neighboring element to carbon, boron hydrides almost always form non-classical structures with multi-center bonds. However, we expect indium to form its interesting molecules with non-classical patterns, though such molecules still need to be extensively studied theoretically. In this work, we investigated indium hydrides of In₂H_x (x = 0-4,6) and In₃H_y (y = 0-5) series via DFT and ab initio quantum chemistry methods, performing a global minimum search, chemical bonding analysis, and studies of their thermodynamical stability. We found that the bonding pattern of indium hydrides differs from the classical structures composed of 1c-2e lone pairs and 2c-2e bonds and the bonding pattern of earlier investigated boron hydrides of the B_nH_n+2 series. The studied stoichiometries are characterized by multi-center bonds, aromaticity, and the tendency for indium to preserve the 1c-2e lone pair.

B3Al4+: A Three-Dimensional Molecular Reuleaux Triangle

We systematically explore the potential energy surface of the B3Al4+ combination of atoms. The putative global minimum corresponds to a structure formed by an Al4 square facing a B3 triangle. Interestingly, the dynamical behavior can be described as a Reuleaux molecular triangle since it involves the rotation of the B3 triangle at the top of the Al4 square. The molecular dynamics simulations, corroborating with the very small rotational barriers of the B3 triangle, show its nearly free rotation on the Al4 ring, confirming the fluxional character of the cluster. Moreover, while the chemical bonding analysis suggests that the multicenter interaction between the two fragments determines its fluxionality, the magnetic response analysis reveals this cluster as a true and fully three-dimensional aromatic system.

Construction of the Largest Metal-Centered Double-Ring Tubular Boron Clusters Based on Actinide Metal Doping

Metal doping has been considered to be an effective approach to stabilize various boron clusters. In this work, we constructed a series of largest metal-centered double-ring tubular boron clusters An@B₂₄ (An = Th, Pa, Pu, and Am). Extensive global minimum structural searches combined with density functional theory predicted that the global minima of An@B₂₄ (An = Th, Pu, and Am) are double-ring tubular structures. Formation energy analysis indicates that these boron clusters are highly stable, especially for Th@B₂₄ and Pa@B₂₄. Detailed bonding analysis shows that the significant stability of An@B₂₄ is determined by the covalent character of the An-B bonding, which stems from the interactions of An 5f and 6d orbitals and B 2p orbitals. These results show that actinide metal doping is a feasible route to construct stable large metal-centered double-ring tubular boron clusters, offering the possibility to design boron nanomaterials with special physiochemical properties.

The unique sandwich K6Be2B6H6 cluster with a real borozene B6H6 core

Theoretical evidence is reported for a boron-based K₆Be₂B₆H₆ sandwich cluster, showing a perfectly D _6h B₆H₆ ring, being capped by two tetrahedral K₃Be ligands. Due to the comfortable charge transfer, the sandwich is viable in [K₃Be]³⁺[B₆H₆]^6-[BeK₃]³⁺ ionic complex in nature. The [B₆H₆]^6- core with 6π aromaticity vividly imitates the benzene (C₆H₆), occurring as a real borozene. In contrast, the tetrahedral [K₃Be]³⁺ ligand is 2σ three-dimensional aromatic, acting as the simple superatom. Thus, this complex possesses a collectively three-fold 2σ/6π/2σ aromaticity. The interlaminar interaction is governed by the robust electrostatic attraction. The unique chemical bonding gives rise to interesting dynamic fluxionality.

AuB8-: an Au-borozene complex

Photoelectron spectroscopy and quantum chemistry studies are used to investigate the structure and bonding of AuB₈^-. Global minimum sturctural searches show that AuB₈^- possesses a chair-like structure, which can be viewed as Au⁺ bonded to the edge of the doubly-aromatic B₈^2- borozene, Au⁺[η²-B₈^2-]. Chemical bonding analyses reveal that the AuB₈^- is a novel borozene complex with unique Au-borozene bonding.

Planar Networks of Boron Triangles: Analogies to Benzene and Other Planar Aromatic Hydrocarbons

The lowest energy structures for B_n species (n = 6 to 23 except for 20) observed experimentally in the gas phase with a mass spectrometer are planar networks of boron triangles. Such networks are considered to consist of trigonal planar sp²-hybridized boron atoms having perpendicular p orbitals similar to the carbon atoms in benzene and other planar aromatic hydrocarbons. Electron bookkeeping for reasonable chemical bonding topologies of wheel-like structures such as B@B_n-1 (n = 6-9) leads to two π-electrons for B₆ and B₇⁺ similar to the cyclopropenyl cation and six π-electrons for B₈^2- and B₉^- similar to benzene. Related chemical bonding topology analyses for low-energy oval B₁₀ and B₁₁^- structures as well as for larger planar boron triangle networks with 12, 13, and 14 boron atoms suggest six π-electrons in such structures. Planar networks of boron triangles having 16-19 boron atoms are shown to be systems with 10 π-electrons similar to naphthalene. Similarly, low-energy planar B₂₂ and B₂₃^- structures are shown to be 4 π-electron systems 1analogous to linear anthracene and angular phenanthrene, respectively. Intermediate B₁₅^- and B₂₁^- systems are shown to be systems with 4k rather than 4k + 2 π-electrons with 8 and 12 π-electrons, respectively. Structures based on planar networks of boron triangles are strongly energetically disfavored for B₂₀ relative to a nonplanar decagonal antiprism structure with ideal D_10d symmetry.

Probing the Nature of the Transition-Metal-Boron Bonds and Novel Aromaticity in Small Metal-Doped Boron Clusters Using Photoelectron Spectroscopy

Photoelectron spectroscopy combined with quantum chemistry has been a powerful approach to elucidate the structures and bonding of size-selected boron clusters (B_n^-), revealing a prevalent planar world that laid the foundation for borophenes. Investigations of metal-doped boron clusters not only lead to novel structures but also provide important information about the metal-boron bonds that are critical to understanding the properties of boride materials. The current review focuses on recent advances in transition-metal-doped boron clusters, including the discoveries of metal-boron multiple bonds and metal-doped novel aromatic boron clusters. The study of the RhB^- and RhB₂O^- clusters led to the discovery of the first quadruple bond between boron and a transition-metal atom, whereas a metal-boron triple bond was found in ReB₂O^- and IrB₂O^-. The ReB₄^- cluster was shown to be the first metallaborocycle with Möbius aromaticity, and the planar ReB₆^- cluster was found to exhibit aromaticity analogous to metallabenzenes. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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...

From a Möbius-aromatic interlocked Mn2B10H10 wheel to the metal-doped boranaphthalenes M2@B10H8 and M2B5 2D-sheets (M = Mn and Fe): a molecules to materials continuum using DFT studies

The design of (1) Möbius aromatic interlocked boron wheel Mn2B10H10, (2) Hückel aromatic boron analogs of naphthalene (M2@B10H8; M = Mn and Fe), and (3) metal boride monolayers (FeB5 and Fe2B5), creating a molecules to materials continuum.

KEu2In3B12S13: A Novel Type of Thioborate Featuring B12S12 Cluster and Unique In6S6 12-membered Ring

Both borates and sulfides are important inorganic multifunctional materials. Encouraged by this background, thioborates attract broad interest. However, their investigations are highly hindered by the available ones’ scarcity and new...

Theoretical probing of twenty-coordinate actinide-centered boron molecular drums

The exploration of metal-doped boron clusters has a great significance in the design of high coordination number (CN) compounds. Actinide-doped boron clusters are probable candidates for achieving high CNs. In this work, we systematically explored a series of actinide metal atom (U, Np, and Pu) doped B₂₀ boron clusters An@B₂₀ (An = U, Np, and Pu) by global minimum structural searches and density functional theory (DFT). Each An@B₂₀ cluster is confirmed to be a twenty-coordinate complex, which is the highest CN obtained in the chemistry of actinide-doped boron clusters so far. The predicted global minima of An@B₂₀ are tubular structures with actinide atoms as centers, which can be considered as boron molecular drums. In An@B₂₀, U@B₂₀ has a relatively high symmetry of C₂, while both Np@B₂₀ and Pu@B₂₀ exhibit C₁ symmetry. Extensive bonding analysis demonstrates that An@B₂₀ has σ and π delocalized bonding, and the U-B bonds possess a relatively higher covalency than the Np-B and Pu-B bonds, resulting in the higher formation energy of U@B₂₀. Therefore, the covalent character of An-B bonding may be crucial for the formation of these high CN actinide-centered boron clusters. These results deepen our understanding of actinide metal doped boron clusters and provide new clues for developing stable high CN boron-based nanomaterials.

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.

Theoretical Design of Novel Boron-Based Nanowires via Inverse Sandwich Clusters

Borophene has important application value, boron nanomaterials doped with transition metal have wondrous structures and chemical bonding. However, little attention was paid to the boron nanowires (NWs). Inspired by the novel metal boron clusters Ln₂B_n⁻ (Ln = La, Pr, Tb, n = 7–9) adopting inverse sandwich configuration, we examined Sc₂B₈ and Y₂B₈ clusters in such novel structure and found that they are the global minima and show good stability. Thus, based on the novel structural moiety and first-principles calculations, we connected the inverse sandwich clusters into one-dimensional (1D) nanowires by sharing B−B bridges between adjacent clusters, and the 1D-Sc₄B₂₄ and 1D-Y₂B₁₂ were reached after structural relaxation. The two nanowires were identified to be stable in thermodynamical, dynamical and thermal aspects. Both nanowires are nonmagnetic, the 1D-Sc₄B₂₄ NW is a direct-bandgap semiconductor, while the 1D-Y₂B₁₂ NW shows metallic feature. Our theoretical results revealed that the inverse sandwich structure is the most energy-favored configuration for transition metal borides Sc₂B₈ and Y₂B₈, and the inverse sandwich motif can be extended to 1D nanowires, providing useful guidance for designing novel boron-based nanowires with diverse electronic properties.

The unified quantum mechanical structure of tubular molecular rotors with multiple equivalent global minimum structures: the 18*C2h → D9d case of La-[B2@B18]-La

La-[B₂@B₁₈]-La demonstrates decisive changes of the properties of molecular rotors, from multiple (here 18) equivalent individual global minimum structures to a quantum mechanical unified structure. This affects their geometries, their symmetries (18*C_2h → D_9d), the generation of energy bands, and high-resolution spectroscopy.

Photoelectron Spectroscopy of Size-Selected Bismuth-Boron Clusters: BiBn- (n = 6-8)

Because of its low toxicity, bismuth is considered to be a "green metal" and has received increasing attention in chemistry and materials science. To understand the chemical bonding of bismuth, here we report a joint experimental and theoretical study on a series of bismuth-doped boron clusters, BiB_n^- (n = 6-8). Well-resolved photoelectron spectra are obtained and are used to understand the structures and bonding of BiB_n^- in conjunction with theoretical calculations. Global minimum searches find that all three BiB_n^- clusters have planar structures with the Bi atom bonded to the edge of the planar B_n moiety via two Bi-B σ bonds as well as π bonding by the 6p_z orbital. BiB₆^- is found to consist of a double-chain B₆ with a terminal Bi atom. Both BiB₇^- and BiB₈^- are composed of a Bi atom bonded to the planar global minima of the B₇^- and B₈^- clusters. Chemical bonding analyses reveal that BiB₆^- is doubly antiaromatic, whereas BiB₇^- and BiB₈^- are doubly aromatic. In the neutral BiB_n (n = 6-8) clusters, except BiB₆ which has a planar structure similar to the anion, the global minima of both BiB₇ and BiB₈ are found to be half-sandwich-type structures due to the high stability of the doubly aromatic B₇^3- and B₈^2- molecular wheel ligands.

Electronic Structure of Superoxidized Radical Cationic Dodecaborate-Based Clusters

The expanding field of boron clusters has attracted continuous theoretical efforts to understand their diverse structures and unique bonding. We recently discovered a new reversible redox event of B₁₂(O-3-methylbutyl)₁₂ in which the superoxidized radical cationic form [B₁₂(O-3-methylbutyl)₁₂]^•+ was identified and isolated for the first time. Herein, comprehensive (TD-)DFT studies in tandem with electrochemical experiments were employed to demonstrate the generality of the reported behavior across perfunctionalized B₁₂(OR)₁₂ clusters (R = aryl or alkyl). While the spin density of radical cationic clusters is delocalized in the core region, the oxidation brings about notable gains of positive partial charges on the supporting groups whose electronics can readily tune the redox potential of the 0/•+ couple. The underlying changes of frontier orbitals were elucidated, and the resulting [B₁₂(OR)₁₂]^•+ species manifest a general diagnostic absorption as a consequence of mixed local/charge-transfer excitations.

Magic-Sized Stoichiometric II-VI Nanoclusters

Metal chalcogenide nanomaterials have gained widespread interest in the past two decades for their potential optoelectronic, energy, and catalytic applications. The colloidal growth of various forms of these materials, such as nanowires, platelets, and lamellar assemblies, proceeds through certain thermodynamically stable, ultrasmall (<2 nm) intermediates called magic-sized nanoclusters (MSCs). Due to quantum confinement and its resultant intriguing properties, isolation or direct synthesis of MSCs and their structure characterization, which is very much challenging, are current topics of fundamental and applied scientific research. By comprehensive understanding of the structure-activity relationships in MSCs, the nucleation and growth processes can be manipulated, resulting in the synthesis of novel metal chalcogenide materials for various applications. This review focuses on recent advances in the chemical synthesis, characterization, and theoretical calculations of CdSe and its related II-VI nanoclusters. It highlights the studies of photophysical and magneto-optical properties as well as heteroatom doping of MSCs followed by their chemical transformation to high-dimensional nanostructures. At the end of the review, future directions and possible ways to overcome the challenges in the research of semiconductor MSCs are also presented.

Theoretical Prediction of Structures, Vibrational Circular Dichroism, and Infrared Spectra of Chiral Be4B8 Cluster at Different Temperatures

Lowest-energy structures, the distribution of isomers, and their molecular properties depend significantly on geometry and temperature. Total energy computations using DFT methodology are typically carried out at a temperature of zero K; thereby, entropic contributions to the total energy are neglected, even though functional materials work at finite temperatures. In the present study, the probability of the occurrence of one particular Be4B8 isomer at temperature T is estimated by employing Gibbs free energy computed within the framework of quantum statistical mechanics and nanothermodynamics. To identify a list of all possible low-energy chiral and achiral structures, an exhaustive and efficient exploration of the potential/free energy surfaces is carried out using a multi-level multistep global genetic algorithm search coupled with DFT. In addition, we discuss the energetic ordering of structures computed at the DFT level against single-point energy calculations at the CCSD(T) level of theory. The total VCD/IR spectra as a function of temperature are computed using each isomer's probability of occurrence in a Boltzmann-weighted superposition of each isomer's spectrum. Additionally, we present chemical bonding analysis using the adaptive natural density partitioning method in the chiral putative global minimum. The transition state structures and the enantiomer-enantiomer and enantiomer-achiral activation energies as a function of temperature evidence that a change from an endergonic to an exergonic type of reaction occurs at a temperature of 739 K.

Concentric Inner 2π/6σ and Outer 10π/14σ Aromaticity Underlies the Dynamic Structural Fluxionality of Planar B19- Wankel Motor Cluster

Planar C_2v B₁₉^- global-minimum (GM) cluster is known as a molecular Wankel motor, featuring unique chemical bonding and structural fluxionality. While the geometry, bonding, and molecular dynamics of the cluster are documented in the literature, it remains warranted to fully understand its bonding nature and unravel the mechanism behind the structural dynamics. We shall offer herein an updated bonding model on the bases of canonical molecular orbital (CMO) analysis and adaptive natural density partitioning (AdNDP), further aided by natural bond orbital (NBO) analysis and orbital composition calculations. The computational data indicate that the B₁₉^- cluster has inner 2π/6σ and outer 10π/14σ concentric 4-fold π/σ aromaticity. Being spatially isolated from each other, the inner B₆ disk supports 2π and 6σ subsystems, whereas the outer B₁₈ double-ring ribbon has 10π and 14σ subsystems. All 4-fold π/σ subsystems are intrinsically delocalized and conform to the (4n + 2) Hückel rule for aromaticity. The change of Wiberg bond index (WBI) from GM to transition-state (TS) for radial B-B links is minimal and uniform, which offers a semiquantitative measure of structural dynamics and underlies the low energy barrier.

Cooperativity and Anticooperativity in Ion-Water Interactions: Implications for the Aqueous Solvation of Ions

Non-additive effects in hydrogen bonds (HB) take place as a consequence of electronic charge transfers. Therefore, it is natural to expect cooperativity and anticooperativity in ion-water interactions. Nevertheless, investigations on this matter are scarce. This paper addresses the interactions of (i) the cations Li⁺ , Na⁺ , K⁺ , Be²⁺ , Mg²⁺ , and Ca²⁺ together with (ii) the anions F^- , Cl^- , Br^- , NO₃ ^- and SO₄ ^2- with water clusters (H₂ O)_n , n=1-8, and the effects of these ions on the HBs within the complete molecular adducts. We used quantum chemical topology tools, specifically the quantum theory of atoms in molecules and the interacting quantum atoms energy partition to investigate non-additive effects among the interactions studied herein. Our results show a decrease on the interaction energy between ions and the first neighbouring water molecules with an increment of the coordination number. We also found strong cooperative effects in the interplay between HBs and ion-dipole interactions within the studied systems. Such cooperativity affects considerably the interactions among ions with their first and second solvation shells in aqueous environments. Overall, we believe this article provides valuable information about how ion-dipole contacts interact with each other and how they relate to other interactions, such as HBs, in the framework of non-additive effects in aqueous media.

Strong Binding of Noble Gases to [B12X11]-: A Theoretical Study

We systematically explore the stability and properties of [B₁₂X₁₁NG]^- adducts resulting from the binding of noble gas atoms to anionic [B₁₂X₁₁]^- clusters in the gas phase of mass spectrometers. [B₁₂X₁₁]^- can be obtained by stripping one X^- off the icosahedral closo-dodecaborate dianion [B₁₂X₁₂]^2-. We study the binding of the noble gas atoms He, Ne, Ar, Kr, and Xe to [B₁₂X₁₁]^- with substituents X = F, Cl, Br, I, and CN. While He cannot be captured by these clusters and Ne only binds at low temperatures, the complexes with the heavier noble gas atoms Ar, Kr, and Xe show appreciable complexation energies and exceed 1 eV at room temperature in the case of [B₁₂(CN)₁₁Xe]^-. The predicted B-NG equilibrium distance in the complexes with Ar, Kr, and Xe is only 0.10-0.25 Å longer than the sum of the covalent radii of the two corresponding atoms, and a significant charge transfer from the noble gas atom to the icosahedral B₁₂ cage is observed.

Double σ-Aromaticity in a Planar Zinc-Doped Gold Cluster: Au9Zn. J Phys Chem A 2021;125:4606-4613. [PMID: 34014680 DOI: 10.1021/acs.jpca.1c02954]

The strong relativistic effects result in many interesting chemical and physical properties for gold and gold compounds. One of the most surprising findings has been that small gold clusters prefer planar structures. Dopants can be used to tune the electronic and structural properties of gold nanoclusters. Here we report an experimental and theoretical investigation of a Zn-doped gold cluster, Au₉Zn^-. Photoelectron spectroscopy reveals that Au₉Zn^- is a highly stable electronic system with an electron binding energy of 4.27 eV. Quantum chemical studies show that the global minimum of Au₉Zn^- has a D_3h structure with a closed-shell electron configuration (¹A₁'), which can be viewed as replacing the central Au atom by Zn in the open-shell parent Au₁₀^- cluster. The high electronic stability of Au₉Zn^- is corroborated by its extremely large HOMO-LUMO gap of 3.3 eV. Chemical bonding analyses revealed that the D_3h Au₉Zn^- are bonded by two sets of delocalized σ bonds, giving rise to double σ aromaticity and its remarkable stability. Two planar low-lying isomers are also observed, corresponding to a similar triangular structure with the Zn atom on the edge and another one with one of the corner Au atoms moved to the edge of the triangle.

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.

Expanded Inverse-Sandwich Complexes of Lanthanum Borides: La2B10- and La2B11. J Phys Chem A 2021;125:2622-2630. [PMID: 33739102 DOI: 10.1021/acs.jpca.1c01149]

Inverse-sandwich structures have been observed recently for dilanthanide boride clusters, in which two Ln atoms sandwich a monocyclic B_x ring for x = 7-9. An interesting question is if larger B_x rings are possible to form such inverse-sandwich clusters. Here we address this question by investigating La₂B₁₀^- and La₂B₁₁^- using photoelectron spectroscopy and ab initio quantum chemical calculations. Photoelectron spectra of La₂B₁₀^- and La₂B₁₁^- show complicated, but well-resolved, spectral features that are used to compare with theoretical calculations. We have found that global minimum structures of the two clusters are based on the octa-boron ring. The global minimum of La₂B₁₀^- consists of two chiral enantiomers with C₁ symmetry, which can be viewed as adding a B₂ unit off-plane to the B₈ ring, whereas that of La₂B₁₁^- can be viewed as adding a B₃ unit in-plane to the B₈ ring in a second coordination shell. Chemical bonding analyses reveal localized B-B bonds on the edge of the clusters and delocalized bonds in the expanded boron frameworks. The interactions between the La atoms and the boron frameworks include the unique (d-p)δ bonding, which was found to be the key for inverse-sandwich complexes with monocyclic boron rings. The current study confirms that the largest monocyclic boron ring to form the inverse-sandwich structures is B₉ and provide insights into the structural evolutions of larger lanthanide boride clusters.

Spontaneous bond dissociation cascades induced by Ben clusters (n = 2,4)

High-level single and multireference ab initio calculations show that the Be₄ cluster behaves as a very efficient Lewis acid when interacting with conventional Lewis bases such as ammonia, water or hydrogen fluoride, to the point that the corresponding acid-base interaction triggers a sequential dissociation of all the bonds of the Lewis base. Notably, this behavior is already found for the simplest beryllium cluster, the Be₂ dimer. However, whereas for Be₂ the first dissociation process involves a low activation barrier which is above the reactants, for Be₄ all the bond dissociation processes involve barriers below the entrance channel leading to a cascade of successive exothermic processes, which end up spontaneously in a global minimum in which the bonding patterns of both the base and the Lewis acid are completely destroyed. Indeed, the global minimum, in all cases, is stabilized by three-center Be-H-Be bonds and covalent interactions between the Be atoms and the basic center of the base, which replace the initial metallic bond stabilizing the Be₄ cluster. As a consequence, in the global minimum the basic atoms (N, O and F) behave as hyper-coordinated centers. Also importantly, the Be₄ cluster and its complexes present RHF-UHF instabilities (not reported before for Be₄), which require the use of multireference methods to correctly describe them.

B48-: a bilayer boron cluster

Size-selected negatively-charged boron clusters (B_n^-) have been found to be planar or quasi-planar in a wide size range. Even though cage structures emerged as the global minimum at B₃₉^-, the global minimum of B₄₀^- was in fact planar. Only in the neutral form did the B₄₀ borospherene become the global minimum. How the structures of larger boron clusters evolve is of immense interest. Here we report the observation of a bilayer B₄₈^- cluster using photoelectron spectroscopy and first-principles calculations. The photoelectron spectra of B₄₈^- exhibit two well-resolved features at low binding energies, which are used as electronic signatures to compare with theoretical calculations. Global minimum searches and theoretical calculations indicate that both the B₄₈^- anion and the B₄₈ neutral possess a bilayer-type structure with D_2h symmetry. The simulated spectrum of the D_2h B₄₈^- agrees well with the experimental spectral features, confirming the bilayer global minimum structure. The bilayer B₄₈^-/0 clusters are found to be highly stable with strong interlayer covalent bonding, revealing a new structural type for size-selected boron clusters. The current study shows the structural diversity of boron nanoclusters and provides experimental evidence for the viability of bilayer borophenes.

Structure, stability and bonding of the leapfrog B24 0 ,±1,±2

Two new structural motifs of the B₂₄ clusters are constructed by use of the leapfrog transformation. The resulting leapfrog B₂₄ has either a bowl shape with a square vacancy or a quasi-planar 2D close-packed triangular boron sheet. The neutral and ionic forms of the latter are found to be more stable than their homologous leapfrog bowl clusters, with the exception of the dicationic B₂₄ ⁺² . While the leapfrog isomer is less stable than the tubular double ring in the neutral state, it becomes competitive in some ionic states. The nucleus independent chemical shift, electron localization function, ring current maps and the electronic structure of leapfrog B₂₄ clusters reveal them to behave as aromatics.

Vibrational band-structures caused by internal rotations of the boron Wankel rotor B11. RSC Adv 2021;11:3613-3621. [PMID: 35424268 PMCID: PMC8694174 DOI: 10.1039/d0ra08821h]

Nuclear quantum effects are often neglected for systems without hydrogen atoms. However some planar boron rotors turn out to exhibit remarkable nuclear quantum effects. Recent experiment on infrared spectroscopy of B₁₃⁺ shows unexpected spectral broadening which still awaits physical explanation. Here we present quantitative investigations of the vibrational energy levels of B₁₁⁻ up to full dimension. A harmonic-bath averaged Hamiltonian suitable for planar boron rotors is constructed and used to predict typical types of vibrational states of B₁₁⁻. Band structures caused by internal rotations are found for all the investigated vibrational states. The experimental phenomenon of spectral broadening is thus due to the band structures of the corresponding vibrational levels. The detailed information of the relevant vibrational states reported in the present work may provide valuable references for future investigations of high resolution spectroscopy of B₁₁⁻.

The band structures of the vibrational energy levels of B₁₁⁻ lead to corresponding spectral broadening. The vibrational band-structures of planar boron rotors are caused by internal rotations.

Boron-based Be2B5+/0/− alloy clusters: inverse sandwiches with pentagonal boron ring and reduction-induced structural transformation to molecular wheel structure

Boron-based Be₂B₅^+/0/− alloy clusters feature inverse sandwich versus molecular wheel structures, which sensitively depend on their charge states and show distinct π/σ aromaticity.

Exploration of Free Energy Surface and Thermal Effects on Relative Population and Infrared Spectrum of the Be6B11- Flux-Ional Cluster

The starting point to understanding cluster properties is the putative global minimum and all the nearby local energy minima; however, locating them is computationally expensive and difficult. The relative populations and spectroscopic properties that are a function of temperature can be approximately computed by employing statistical thermodynamics. Here, we investigate entropy-driven isomers distribution on Be₆B₁₁⁻ clusters and the effect of temperature on their infrared spectroscopy and relative populations. We identify the vibration modes possessed by the cluster that significantly contribute to the zero-point energy. A couple of steps are considered for computing the temperature-dependent relative population: First, using a genetic algorithm coupled to density functional theory, we performed an extensive and systematic exploration of the potential/free energy surface of Be₆B₁₁⁻ clusters to locate the putative global minimum and elucidate the low-energy structures. Second, the relative populations’ temperature effects are determined by considering the thermodynamic properties and Boltzmann factors. The temperature-dependent relative populations show that the entropies and temperature are essential for determining the global minimum. We compute the temperature-dependent total infrared spectra employing the Boltzmann factor weighted sums of each isomer’s infrared spectrum and find that at finite temperature, the total infrared spectrum is composed of an admixture of infrared spectra that corresponds to the spectra of the lowest-energy structure and its isomers located at higher energies. The methodology and results describe the thermal effects in the relative population and the infrared spectra.