Aromaticity of Singlet and Triplet Boron Disk-like Clusters: A Test for Electron Counting Aromaticity Rules

Boron clusters are polyhedral boron-containing structures that have unique features and properties. The disk-like boron clusters are among the most fascinating boron cluster forms. These clusters have a molecular orbital (MO) distribution similar to the one derived from the simple particle-on-a-disk model. In this model, the MOs come in pairs except for m = 0. Disk-like boron clusters in their singlet ground state are aromatic when they reach a closed-shell structure. One could expect that disk-like aromatic boron clusters in the singlet state, when acquiring or releasing two electrons, may also be aromatic in the lowest-lying triplet state. We use magnetically induced current densities and bond current strengths to analyze the aromatic character of a series of disk-like boron clusters. Our results show that, with the exception of triplet ³B₁₉^-, the disk-like boron clusters follow Hückel and Baird's rules if one considers the different MOs grouped by their symmetry. We also found that if the lowest-lying triplet state in disk-like boron clusters is aromatic, this triplet state is the ground state for this species.

Boron Silicon B2Si3q and B3Si2p Clusters: The Smallest Aromatic Ribbons

The small binary boron silicon clusters B₂Si₃^q with q going from -2 to +2 and B₃Si₂^p with p varying from -3 to +1 were reinvestigated using quantum chemical methods. The thermodynamic stability of these smallest ribbon structures is governed by both Hückel and ribbon models for aromaticity. The more negative the cluster charge, the more ribbon character is shown. In contrast, the more positive the charge state, the more pronounced the Hückel character becomes. The ribbon aromaticity character can also be classified into ribbon aromatic, semiaromatic, antiaromatic, and triplet aromatic when the electron configuration of a ribbon structure is described as [...π²⁽ⁿ⁺¹⁾σ²ⁿ], [...π²ⁿ⁺¹σ²ⁿ], [...π²ⁿσ²ⁿ], and [...π²ⁿ⁺¹σ^2n-1], respectively. Geometry optimizations of the B₂Si₃ lowest-energy structure by some density functional theory (DFT) functionals result in a nonplanar shape because it possesses an antiaromatic ribbon character. However, its π aromaticity assigned by the Hückel rule is stronger in such a way that several other DFT and coupled-cluster theory CCSD(T) calculations show that B₂Si₃ is indeed stable in a planar form (C_s). A new global equilibrium structure for the anion B₂Si₃^2-, which is a ribbon semiaromatic species, was identified. Some benchmark tests were also carried out to evaluate the performance of popular methods for the treatment of binary B-Si clusters. At odds with some previous studies, we found that with reference to the high accuracy CCSD(T)/CBS method, the hybrid TPSSh functional is reliable for a structure search, whereas the hybrid B3LYP functional is more suitable for simulations of some experimental spectroscopic results.

Electronic structure, stability, and aromaticity of M2B6 (M = Mg, Ca, Sr, and Ba): an interplay between spin pairing and electron delocalization

It has been shown in previous studies that the Be₂B₆ complex exhibits a triplet ground state with double aromaticity. In this work, the stability, electronic structure, and aromaticity of the homologous series M₂B₆ (M = Mg, Ca, Sr and Ba) were examined and compared to those of Be₂B₆. At the CCSD(T)/def2-TZVP//B3LYP/def2-TZVP level of theory, the target molecules were found to be more stable in the singlet than in the triplet spin state. Magnetically induced current densities and multicentre delocalization index (MCI) were employed to assess the aromatic character of the studied complexes. Both employed methods agree that M₂B₆ (M = Mg, Ca, Sr and Ba) are π aromatic and σ nonaromatic in the singlet ground state, and double aromatic in the triplet state. It was demonstrated that the electron counting rules of aromaticity cannot be used to correctly predict the aromaticity and relative stability of the examined molecules in different spin states.

Spatial and electronic structures of BeB8 and MgB8. How far the analogy goes?

Doping of boron clusters with Be and its heavier alkaline-earth congener, Mg usually leads to complexes of different geometry and electronic structure. In this work we showed that both neutral BeB 8 and MgB 8 exhibit a singlet ground state umbrella-like form. In addition, the stability, electronic structure, and aromaticity of the target molecules were compared. The magnetically induced current densities showed that BeB 8 and MgB 8 are double aromatic systems: π and σ electrons induce strong diatropic currents. The current densities induced in the studied complexes are of very similar intensity, but with a different spatial distribution. The found differences between the current density patterns in BeB 8 and MgB 8 arise from the very nature of the bonding interactions between the M atom and B 8 fragment, as demonstrated through the energy decomposition analysis (EDA).

Formation of the quasi-planar B56 boron cluster: topological path from B12 and disk aromaticity

Formation and stability of the B56 boron cluster were investigated using a topological approach and the disk aromaticity model. An extensive global energy minimum search for the B56 system which...

Ground and Electronically Excited States of Main-Group-Metal-Doped B20 Double Rings

Ab initio coupled-cluster, electron propagator, and Møller-Plesset second-order perturbation theory calculations are utilized to analyze the low-lying electronic states of several metal-doped B₂₀. In the ground state, the presently focused AB₂₀/EB₂₀ (A = Li, Na, and K; E = Mg and Ca) consist of charge-separated A⁺B₂₀^-/E²⁺B₂₀^2- frameworks. The excited electronic states of AB₂₀ and EB₂₀⁺ were analyzed by computing the vertical electron attachment energies (VEAEs) of AB₂₀⁺ and EB₂₀²⁺. In several excited states, the radical electron is predominantly localized on the B₂₀ frames, which are counterparts of the low-lying states of bare B₂₀^-. A variety of basis sets were tested on obtaining VEAEs, and the aug-cc-pVDZ/_A,E d-aug-cc-pVDZ/_B combination provided the best accuracy-efficiency compromise on them. Furthermore, this work analyzes the Rydberg-like excited states of AB₂₀ and EB₂₀⁺ and will serve as a guide for future studies on similar metal-doped boron systems.

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.

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.

Topological population analysis and pairing/unpairing electron distribution evolution: Atomic B3+ cluster bending mode, a case study

Local and non-local topological treatment of electronic distributions are applied to a simple out of equilibrium case of an electron-deficient three-atom cluster, B3⁺. The bending movement is described in detail through the onset and disappearance of critical points defining two kinds of molecular structures, characterizing a transition state (TS) and predicting two stable equilibrium geometries. All points in this rich evolution and the structural change in the out of equilibrium conformations has been featured and distinguished by the behavior of the population magnitudes and of the paired and unpaired electron densities within the non-local and local points of view of the topological formalism. The unpaired or electron hole density appears as relevant in both versions, the non-local or integrated one, in which it is sometimes called free-valence and also for its complementary counterpart, the local one, to describe and to quantify the interatomic interactions. The stability of the cluster B₃⁺ is characterized in terms of a topologically defined ring structure and the highest total two- and three-center populations, thus showing the role of the geometry, the covalence, and the complex patterns. Consideration of the electron correlation effects constitutes the basement of the results gathered, thus displaying their influence in the formation and breaking of boron bonding interactions.

Structure and bonding of molecular stirrers with formula B7M2- and B8M2 (M = Zn, Cd, Hg)

In this work, we systematically explored clusters with formula B₇M₂^- and B₈M₂ (M = Zn, Cd, Hg). The putative global minima are formed by an M₂ dimer and a disk-shaped boron wheel. Moreover, the chemical bonding analysis revealed that charge transfer from the metal atoms to the boron motifs resulted in (B₇)^3-(M₂)²⁺ and (B₈)^2-(M₂)²⁺ complexes with double (σ + π) aromatic boron wheels and a single bond for the metallic dimer. Above all, the computed rotational barriers of the M-M fragment with respect to the boron disk and molecular dynamics simulations indicate a virtually barrierless spin, resembling a magnetic stirrer on a baseplate.

Singlet and triplet states of the sandwich-type Be2B6 and Be2B7+ clusters. A test for the electron counting rules of aromaticity

The studied complexes exhibit double aromaticity in their triplet states in line with the predictions of Hückel and Baird's rules.

Formation of the M2B18q Teetotum Boron Clusters with 4d and 5d Transition Metals M = Rh, Pd, Ir, and Pt

In the present theoretical study using DFT computations, we successfully designed a series of boron clusters possessing a teetotum shape stabilized upon metal doping. The resulting M₂B₁₈ teetotum geometry emerges as a general structural motif for the B₁₈ boron cluster doped by either two 4d and 5d transition metal atoms. Doping of two different metal atoms also conserves the teetotum motif such as in the mixed RhPdB₁₈⁺ and IrPtB₁₈⁺ clusters. A bonding analysis points out that each dimeric metal unit enjoys several stabilizing orbital interactions with an idealized B₁₈ tubular moiety and thereby establish a bimetallic configuration of [σ(σ_5s-B₁₈)]² [π(π_4d-B₁₈)]⁴ [σ(σ_4d-B₁₈)]² [δ(δ_4d-B₁₈)]⁴ [σ*(σ_4d-B₁₈)]² [π*_4d]⁴ [σ(σ*_4d-B₁₈)]² [δ*_4d]⁴ for 4d metals and of [σ(σ_6s-B₁₈)]² [π(π_5d-B₁₈)]⁴ [σ(σ_5d-B₁₈)]² [δ(δ_5d-B₁₈)]⁴ [σ*(σ_5d-B₁₈)]² [π*_5d]⁴ [σ(σ*_5d-B₁₈)]² [δ*_5d]⁴ for 5d metal atoms for 24 electrons. All the M₂B₁₈^q teetotum structures considered behave as aromatic compounds whose character is indicated by the strongly diatropic current density.

Formation of the quasi-planar B50 boron cluster: topological path from B10 and disk aromaticity

The lowest-lying isomer of the B50 boron cluster is confirmed to have a quasi-planar shape with two hexagonal holes. By applying a topological (leap-frog) dual operation followed by boron capping, we demonstrated that such a quasi-planar structure actually comes from the smallest elongated B102-, and its high thermodynamic stability is due to its inherent disk aromaticity arising from its 32 valent π electrons that fully occupy a disk configuration of [(1σ)2(1π)4(1δ)4(2σ)2(1φ)4(2π)4(1γ)4(2δ)4(1η)4]. The aromatic character of the quasi-planar B50 is further supported by a strong diatropic magnetic current flow. The sudden appearance of a quasi-planar B50 again points out that the growth pattern of pure boron clusters is still far from being completely understood.

Magnetically induced current density in triple-layered beryllium–boron clusters

Magnetically induced current densities reveal the double aromatic character of the examined Be–B clusters.

Boron Teetotum: Metallic [Ti(B6C xN y)] q and Bimetallic [Ti2(B6C xN y)] q Nine-Membered Heterocycles with x + y = 3 and -1 ≤ q ≤ 3

We investigated the geometry, stability, and aromaticity of a series of singly and doubly titanium-doped boron clusters. Ti dopants bring in planar cyclic form with a nine-membered boron ring B₉^- and B₉^3- and C and N isoelectronic derivatives where perfectly planar B₆N₃, B₆CN₂, B₆C₂N, and B₆C₃ heterorings are coordinated with one and two Ti atoms. The presence of both C and N atoms induces bimetallic heterocycles while Ti₂B₉^q clusters are not stable in cyclic form. Doubly Ti doped clusters have the shape of a teetotum toy. High thermodynamic stability of these bimetallic boron heterocycles, that are global equilibrium structures of corresponding systems, can be understood as the result of a stabilizing overlap between bonding and antibonding MOs of Ti₂ with different eigenstates of B₆C _xN _y cycles. Both C and N elements, which are more electronegative than the B atom, also enjoy the formation of planar nine-membered ring via classical 2c-2e bonding, rather than occupancy of high coordination position. A double aromaticity feature which comprises both σ and π aromaticity is supported by magnetic responses of electron density within a planar cycle. Such an aromatic character is also in line with the classical electron count for both sets of delocalized σ and π electron systems.

B3@Si12+: strong stabilizing effects of a triatomic cyclic boron unit on tubular silicon clusters

Remarkably strong effects of the aromatic B₃ cycle in stabilizing tubular silicon clusters were observed for the first time. The doped cluster B₃@Si₁₂⁺ presents a novel structural motif for silicon clusters in which a B₃ cycle is encapsulated into a (6 × 2) Si₁₂ prism giving rise to a high symmetry stable tubular structure (D_3h). A large amount of electron density is transferred to the boron cycle, and the B₃^δ- unit not only retains a delocalized bonding pattern within the Si₁₂ prism but also enables a two-fold aromaticity for the resulting silicon double ring. This double ring can be used as a building block to make longer nanotubes.

Formation of a bi-rhodium boron tube Rh2B18 and its great CO2 capture ability

The geometries, bonding and abilities for CO₂ capture of the doubly rhodium-doped boron cluster Rh₂B₁₈ are presented.

Planarization of B20 clusters by Si and C atom substitution

An optimization strategy combining a global semi-empirical quantum mechanical search and all-electron density functional theory was adopted to determine the lowest energy structures of B₁₉Si and B₁₉C clusters. The planarization of a B₂₀ cluster by Si and C atom substitution was observed. The structural transition was from the double-ring tubular B₂₀ to an almost perfect planar B₁₉Si and a quasi-planar bowl B₁₉C. B₁₉Si possessed a geometry with a central B atom surrounded by a six-membered ring and a 13-atom outer ring. B₁₉C adopted a geometry with a B₅C six-membered hole. Both Si and C atoms occupied peripheral positions. The observed planarization may be attributed to sp² hybridization, changes in the peripheral bonding, and structural mechanics. Some properties, including the HOMO-LUMO gaps, on-site charge on Si and C atoms, and deformed charge distribution, were discussed.