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Article

Chemical Bonding and Dynamic Structural Fluxionality of a Boron-Based B8Al3+ Cluster

by
Shu-Juan Gao
1,2,* and
Tan-Lai Yu
1,2,*
1
Department of Chemical and Materials Engineering, Lyuliang University, Lishi 033001, China
2
Institute of New Carbon-Based Materials and Zero-Carbon and Negative-Carbon Technology, Lyuliang University, Lishi 033001, China
*
Authors to whom correspondence should be addressed.
Molecules 2024, 29(24), 5961; https://doi.org/10.3390/molecules29245961
Submission received: 26 November 2024 / Revised: 16 December 2024 / Accepted: 17 December 2024 / Published: 17 December 2024
(This article belongs to the Section Computational and Theoretical Chemistry)
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Abstract

:
We studied the boron-based composite cluster B8Al3+ doped with Al atoms. The global minimum structure of the B8Al3+ cluster is a three-layer structure, consisting of three parts: an Al2 unit, a B8 ring and an isolated Al atom. Charge calculations analysis shows that the cluster can be expressed as [Al]+[B8]2−[Al2]2+, has 6π/6σ double aromaticity and follows the (4n+2) Hückel rule. Born–Oppenheimer molecular dynamics (BOMD) simulation shows that the B8Al3+ cluster has dynamic fluxionality properties. Remarkably, at the single-point coupled cluster singles, doubles and triples (CCSD(T)) level, the energy barrier for intramolecular rotation is merely 0.19 kcal mol−1. [B8]2− molecular wheels have magical 6π/6σ double aromaticity properties, providing a continuous cloud of delocalized electrons, which is a key factor in the dynamic fluxionality of the cluster. The B8Al3+ cluster provides a new example of dynamic structural fluxionality in molecular systems.

Graphical Abstract

1. Introduction

Boron, which is positioned nearest to carbon in the periodic table, shares various structural attributes and represents a typical electron-deficient element. Experimental and theoretical investigations of elemental boron clusters have been ongoing since the 1980s [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. Systematic experimental and computational analyses have revealed boron clusters’ propensity to exhibit planar or quasi-planar structures across diverse size scales. Owing to their electron deficiency, boron-based clusters possess a unique electron distribution orbital structure, enabling the formation of distinct chemical bonds. Within these clusters, chemical bonding is influenced by π/σ aromaticity, antiaromaticity, and conflicting aromaticity, necessitating electron delocalization to counterbalance boron’s inherent electronic deficiencies [4,5,6,9]. Additionally, the unusual bonding mode also leads to dynamic structural fluxionality of bare boron clusters and related compound systems.
Metal atoms are introduced into boron clusters to create boron-based alloy clusters. The approach proves effective in exploring structural diversity, adjusting electronic properties, and uncovering new chemical bonds within these clusters [16,17,18,19,20]. Utilizing intramolecular charge transfer allows precise electron counting in alloy clusters, facilitating the deliberate design of new cluster structures and deeper investigation into their bonding and dynamic attributes. Structural fluxionality is an extraordinary attribute inherent in boron clusters, manifesting as dynamic flexibility. Boron tends to form multicenter bonds in both its compounds and at nanoscales, and fluxionality is attributed to the multicenter bonds found in boron clusters [21]. The electron deficiency of boron contributes significantly to this distinct dynamic behavior. Researchers have consistently designed and documented a range of pure boron clusters showcasing dynamic fluxionality, including B11−, B13+, B15+, and B19− [22,23,24,25]. Subsequent research revealed that blending different metals enables the deliberate design of boron-based cluster nanomachines exhibiting dynamic fluxionality. In 2017, Zhai and colleagues identified nearly isoenergetic three-layer and spiral structures within the Be6B11− cluster [26]. The former sandwich structure demonstrates two dynamic rotation/twisting modes, resembling structural fluidity akin to the nanoscale Earth–Moon system. Furthermore, researchers have observed magical dynamic fluxionality in a range of binary boron-based nanoclusters, including Na5B7, V2B7−, and Be3B11− [27,28,29], among others.
To diminish the dynamic energy barrier associated with fluxionality, researchers started incorporating multiple metal atoms to alter the electron distribution within boron clusters. In compass-like clusters MB7X2 and MB8X2 (where X stands for Zn or Cd and M represents Be, Ru, or Os) [30], the X2 needle undergoes rotation along the B8 wheel. The central B6 ring within the boron-based ternary Rb6Be2B6 cluster [31], featuring a distinct sandwich structure, emerges as exposed bare B enclosed by two tetrahedral BeRb3 ligands. The bonding pattern within the vast sandwich cluster encourages distinctive dual-mode dynamic fluxionality. The study aims to examine the structure of the ternary cluster B8Al3+, analyze its structural stability, and determine if it presents novel instances of dynamic structural fluxionality. The GM structure of the B8Al3+ was determined using a CK search. The B8Al3+ cluster exhibits a three-layer structure. Its geometric configuration resembles a “clock”: the middle B8 ring creates the dial, while the two aluminum atoms above it act as pointers, with an Al unit below them. Chemical bonding analysis indicates that the B8Al3+ cluster exhibits 6π/6σ dual aromaticity, with a double delocalized electron cloud facilitating a continuous “orbit,” enabling unrestricted rotation of the Al2 unit above the B8 ring. Charge calculations reveal evident charge transfer among the Al2 unit, the Al atom and the B8 ring, presenting a formal description as a [Al]+[B8]2−[Al2]2+ ion complex.

2. Results

2.1. Global Minimum of B8Al3+ Cluster

Figure 1a shows the GM C1 (1A) structure of the B8Al3+ cluster. The relative energies of the top 20 low-lying isomers, including zero-point energy correction (ZPE), are provided in Figure S1. The B8Al3+ cluster exhibits C1 symmetry, signifying the global minimum on the potential energy surface. Initial computations using PBE0/def2-TZVP on the top 20 structures revealed the GM cluster to be 1.01 kcal mol−1 lower in energy than its nearest competitor. It is worth noting that within the DFT method, the PBE0 and B3LYP functionals are widely acknowledged for their complementarity in molecular systems. To ensure computational consistency across density functionals concerning geometry and energetics, we completed a comparison at the B3LYP/def2-TZVP method level, revealing the GM cluster to be 7.71 kcal mol−1 lower in energy than its closest competitor. Subsequent calculations conducted at the CCSD(T)/def2-TZVP//PBE0/def2-TZVP and complementary CCSD(T)/def2-TZVP//B3LYP/def2-TZVP levels indicated energy advantages of 5.61 kcal mol−1 and 4.65 kcal mol−1, respectively, for the GM structure. Hence, based on the aforementioned data, the GM C1 (1A) structure of B8Al3+ cluster is confirmed to be a really minimal structure on the potential energy surface.
Figure 1a displays the top and side views of the GM B8Al3+ cluster, representing a closed-shell electronic system. The GM B8Al3+ cluster comprises three layers, resembling a clock: the middle B8 ring creates the dial, while the two aluminum atoms above it act as pointers, with an Al unit below it. Figure 1b demonstrates the similarity between the TS structure and the GM structure, where the Al–Al pointer rotates approximately 25.7° to achieve the TS structure. Currently, the Al–Al pointer is positioned between the two B atoms on the dial. The cartesian coordinates of GM cluster and TS structure at PBE0/def2-TZVP are presented in Table S1.

2.2. Bond Distances, Wiberg Bond Indices, and Natural Atomic Charges

Figure 2a displays the bond distances and bond orders for the GM B8Al3+ cluster. The boron ring’s peripheral bond distances are 1.54–1.55 Å, below the upper bound of 1.70 Å for B–B single bonds. This suggests that there is a force between the B atoms involving both covalent single bonds and delocalized electrons. The bond orders of the B8 ring are greater than 1, which also illustrates this essence. Radial B–B links are much longer (1.74–1.85 Å); the links are in line with delocalized π/σ bonding, and are weaker than a single bond. Indeed, their calculated WBIs amount to 0.50–0.67. The distance between the two Al atoms, 2.89 Å, is close to the upper limit of the Al–Al single bond (2.52 Å), and the corresponding Al–Al bond order is 0.42, indicating the presence of an Al–Al single bond.
The natural atomic charges were calculated by natural bond orbital (NBO) analysis, as shown in Figure 3. The Al9 atom below the B ring carries a positive charge of +0.91 |e|. These natural atomic charge data indicate that one electron is transferred from the Al atom to the B8 ring. The rightmost B6 atom near the pointer Al2 carries a charge of −0.31 |e|, indicating an electrostatic interaction between the B and Al atoms (Figure 3a). The B atoms are negatively charged from −0.03 to −0.40 |e| in GM and from −0.01 to −0.74 |e| in TS. The charge carried by Al2 unit is +1.47 |e|, which can be regarded as transferring approximately two electrons to the B8 ring. The bond distances and bond order of TS and GM are similar. Due to the deflection of the Al needle, the natural atomic charge changes slightly. Overall, the charge transfer case is identical. The similarity in structure and chemical bonding of GM and TS implies that there is a lower energy barrier between them. Thus, both the GM and TS structures of B8Al3+ cluster are essential charge transfer complexes of [Al]+[B8]2−[Al2]2+.

3. Discussion

3.1. Dynamic Structural Fluxionality

Vibration frequency analysis was conducted on the GM and TS structures of B8Al3+ cluster at PBE0 level, as illustrated in Figure S2. The GM B8Al3+ cluster exhibits a vibration soft mode at 30.43 cm−1, corresponding to the tangential reverse motion involving the Al2 unit and the B8 ring. The movement along the vibration soft mode vector leads to the formation of the corresponding TS structure. The TS structure’s vibration soft mode is 29.48i cm−1. Both exhibit similar rotation modes that facilitate the relative rotation of the Al2 unit above the B8 ring. These soft vibrational modes are perfectly in line with dynamic structural fluxionality of the system as a molecular rotor.
To vividly demonstrate the dynamic fluxionality of the B8Al3+ cluster, we have run a BOMD simulation at a selected set of temperatures of 300 K for a time span of 50 ps. In the BOMD simulation, we take the GM structure as the initial structure and simulate the dynamic evolution process. The coordinates of the whole molecular dynamics process can be obtained at the set temperature, and the analysis of the results can be performed to obtain the corresponding dynamic properties. The system dynamics trajectories were obtained by taking GM structure as the initial coordinate at PBE0 level. The BOMD data are visualized using GaussView 6.0, which vividly shows that the present ternary cluster behaves similarly to a functioning compass at the subnanoscale. The BOMD simulation results vividly illustrate the dynamic fluxionality process within the B8Al3+ cluster: the Al−Al unit rotates above the B8 ring, resembling the motion of a clock hands. Throughout the BOMD simulation, the B8Al3+ cluster consistently retained geometric stability without noticeable deformation. A short video is extracted from the simulation and presented in the ESI. The animation approximately lasts for 12 ps.
Figure 4 displays the dynamic evolution process of B8Al3+ cluster. The rotation energy barrier for B8Al3+ cluster is 0.32 kcal mol−1 at PBE0 level, refined to 0.19 kcal mol−1 at the CCSD(T) level. The Al−Al unit, resembling a pointer, is suspended above the B8 ring. Starting from GM1 as the initial configuration, it rotates clockwise with the B8 ring’s center as the axis. As the Al−Al pointer rotates 25.7° clockwise, surpassing the rotation energy barrier, it reaches the first transition state, TS1-2, while the Al−Al pointer is perpendicular to the B-B bond of the two adjacent B atoms below at this stage. Upon rotating the Al–Al dimer by another 25.7° clockwise, one recovers the GM geometry (GM2). Subsequently, it continues to rotate clockwise, always exceeding the reaction energy barrier. After completing the above process using six TS configurations and five GM configurations, all atoms in the B8Al3+ cluster eventually return to their initial positions.

3.2. Chemical Bonding

To understand the unique geometries, stability, and dynamic fluxionality of GM B8Al3+ cluster, it is essential to elucidate their chemical bonding. For this purpose, CMOs and AdNDP analyses are fundamental. The GM B8Al3+ cluster is a closed-shell cluster with 32 valence electrons. Its 16 occupied CMOs are sorted to five subsets based on their constituent atomic orbitals (AOs), as shown in Figure 5. The two CMOs in subset (a) are composed mainly of 3s/3p AOs from two aluminum atoms, in their constructive versus destructive combinations. According to the CMO construction principles, these two CMOs can be localized as the lone pairs of Al 3s2. HOMO–3 in subset (b) is responsible for an interlayer Al–Al σ single bond, which originates from 3s AOs of two Al atoms. Meanwhile, the 14 orbital electrons in subset (c) are derived mainly from the 2s and 2p atomic orbitals of the B8 ring.
There are seven CMOs in subset (c) containing HOMO–15, HOMO–14, HOMO–13, HOMO–12, HOMO–10, HOMO–8 and HOMO–7, which constitute a complete series with 0–3 nodal planes (sequentially from left to right), including 2 degenerate pairs. Upon recombination, these seven orbitals can form seven two-center two-electron (2c–2e) bonds, thereby being localized as seven B–B σ bonds. These Lewis-type bonds constitute the cluster’s structural framework, utilizing a total of 14 electrons. Figure 6a shows the AdNDP bonding scheme, affirming the alignment between seven CMOs and the seven 2c–2e single bonds on the B8 ring. The occupation numbers (ONs) are 1.90–1.93 |e|, which are generally close to the ideal value of 2.00 |e|. Subset (d) is the cluster’s delocalized π framework, which is primarily sourced from the 2s/2p orbitals of B atoms (Table S2). The corresponding AdNDP bonding scheme allocates three delocalized π orbitals into three 11c–2e bonds, with an occupation value of 2.00 |e|. Three CMOs in subset (e) constitute a delocalized 6σ subsystem, situated on the eight B atoms. Subsets (d) and (e) each comprise three orbitals and six delocalized electrons, satisfying the (4n+2) Hückel rule (n = 1), establishing the cluster’s π/σ dual aromaticity. In subset (b), an Al–Al σ orbital aligns with AdNDP bonding principles, corresponding to the AdNDP scheme in Figure 6a (right). In the TS structure, the CMOs, AdNDP scheme and orbital compositions remain virtually unaltered (Figures S3 and S4, ESI†), which explains why the dynamic fluxionality process has no energy barrier.
In summary, the chemical bonding of the B8Al3+ cluster consists of the lone pairs of two Al atoms, a covalent Al–Al single bond, seven 2c–2e Lewis single bonds within the B8 ring, three 11-center delocalized σ and three 11-center delocalized π bonds, which establishes their two-fold 6π/6σ aromaticity. This dual aromaticity collectively underlies the unique dynamic fluxionality of the cluster.
To more intuitively observe the dual 6π/6σ aromaticity, the color-filled maps of ICSSzz of B8Al3+ cluster at 0 (ICSSzz(0)) and 1 Å (ICSSzz(1)) above the B8 ring plane are plotted in Figure 7. The green areas in (a) and (b) within the molecular wheel, in which the shielding effect is primarily concentrated, are in line with σ and π aromaticity of the cluster, respectively. Obviously, the [B8]2− unit is doubly 6π/6σ aromatic, which is the key factor that causes the ground state to stabilize. In essence, 6π/6σ double aromaticity of [B8]2− is based on its charge transfer, as described previously. Nucleus-independent chemical shifts, NICS and NICSzz, are calculated for the GM B8Al3+ cluster as additional criteria for aromaticity (Table S3, ESI). The large negative values are consistent with the assessment of π and σ double aromaticity. The NICS and NICSzz values at the center of a B3 triangle are actually helpful for understanding the aromaticity of GM B8Al3+, whereas those at 1 Å below the plane probe π aromaticity. The electron clouds over the system are uniform and dilute facilitate dynamic fluxionality; these effects are based on two-fold magic 6π/6σ aromaticity.

4. Methods

The global minimum (GM) structure and low-lying isomers of the B8Al3+ cluster were determined through a Coalescence Kick (CK) search and more than 5000 stationary points (3000 singlet and 2000 triplet) were detected on the potential energy surface with the help of artificial structure construction [32,33]. The candidate low-lying structures were subsequently reoptimized at the PBE0/def2-TZVP level [34,35]. Frequency calculations were carried out at the same level to ensure that the reported structures are true minima. To check for the computational consistency of different functionals in structures and energetics, the zero-point correction energy was also calculated at the B3LYP/PBE0/def2-TZVP. In order to benchmark the relative energies, the top five low-lying isomers were further assessed at the single-point CCSD(T)/def2-TZVP level on the basis of their PBE0/def2-TZVP and B3LYP/def2-TZVP geometries [36,37,38].
At the PBE0/def2-TZVP level, orbital composition analysis was completed through NAO calculations, and Wiberg bond indices (WBIs) and natural atomic charges were obtained through natural bond orbital (NBO) calculations [39]. Chemical bonds were elucidated using canonical molecular orbital (CMO) analysis and adaptive natural density partitioning (AdNDP) [40]. Nucleus-independent chemical shifts (NICSs) and iso-chemical shielding surfaces (ICSSs) were calculated to evaluate π/σ aromaticity [41,42]. AdNDP analysis and ICSSs calculations were performed using the Multifwn program [43]. We performed Born–Oppenheimer molecular dynamics (BOMD) simulations at a temperature of 300 K to study the dynamic properties of the clusters [44]. All the above calculations were performed using the Gaussian 09 software package [45]. The visualization of the calculation results was completed through GaussView 6.0, CYLview 1.0 and VMD 1.9.4 programs [46,47,48].

5. Conclusions

In summary, we have designed a cationic ternary boron-based binary B–Al cluster, B8Al3+, which adopted a three-layered structure in a subnanoscale clock shape with a quasi-planar B8 wheel. The Al2 pointer is above the wheel and there is another aluminum atom under it. It features dynamic structural fluxionality at 300 K. Charge calculations suggest that the cluster can be described as a charge transfer ion complex and formulated as [Al]+[B8]2−[Al2]2+, whose three charged layers are bound via quite strong electrostatic forces. BOMD simulation indicates that the Al–Al pointer can freely rotate on the dial below, requiring an energy barrier of 0.19 kcal mol−1 to facilitate its rotation. Chemical bonding analyses indicate the magic 6π/6σ double aromaticity of the B8Al3+ cluster. The dual delocalized electron clouds create a fluid “orbital” that allows the Al2 unit above the B8 ring to rotate freely, thus imparting dynamism to the cluster. The balance of electrostatic traction and repulsion between layers is critical to the dynamic fluxionality of the cluster. The stability of molecular wheels and molecular motors is contingent upon the cluster structure, size, bonding mode, and charge state. A deeper understanding of how delocalized electrons change and flow during the rotation of a molecular motor, and of the factors determining the level of rotational energy barriers, would be beneficial. Similarly, further insight into the interaction mechanism between a molecular motor and an electron beam, and its effect on rotational energy barriers, would be valuable. Subsequently, doping strategies or electron compensation strategies may be employed to transform rigid boron radicals into structurally rheological boron radicals. It will be possible to initiate or terminate the operation of molecular motors by adjusting the temperature, electric field, magnetic field, and so forth. Based on this, it will be possible to further develop valuable functionalized molecular machines. Examples include nano cars, nano trucks, one-wheeled nano cars and walking robots.

Supplementary Materials

The following supporting information can be downloaded at https://www.mdpi.com/article/10.3390/molecules29245961/s1. Table S1: Cartesian coordinates for optimized global minimum (GM) and transition state (TS) structures of the B8Al3+ cluster at the PBE0/def2-TZVP level; Table S2: Orbital composition analyses of occupied canonical molecular orbitals (CMOs) of GM (C1, 1A) B8Al3+ cluster; Table S3: Calculated NICSzz and NICS (shown in italics in brackets) of GM B8Al3+ cluster at the PBE0/def2-TZVP level. These values are calculated at the center of the B3 triangle, as well as at 1 Å above the center; Table S4: Vibrational frequencies of the B8Al3+ cluster at the PBE0/def2-TZVP level; Figure S1: Alternative optimized structures for the B8Al3+ cluster at the PBE0/def2-TZVP level including zero-point energy (ZPE) corrections, along with their relative energies. Relative energies are also presented for top five lowest-energy isomers at the single-point CCSD(T)/def2-TZVP//PBE0/def2-TZVP (in parentheses) and for the top two lowest-energy isomers at the B3LYP/def2-TZVP (in square brackets, with ZPE corrections), and single-point CCSD(T)/def2-TZVP//B3LYP/def2-TZVP (in curly brackets) levels of theory. All energies are shown in kcal mol−1; Figure S2: Displacement vectors of the vibrational modes of (a) GM and (b) TS structures of the B8Al3+ cluster at the PBE0/def2-TZVP level; Figure S3: Pictures of occupied canonical molecular orbitals (CMOs) of TS B8Al3+ cluster. (a) Lone pairs. (b) Lewis-type Al–Al σ bond. (c) Seven CMOs for Lewis B–B σ single bonds along the periphery of disk B8 motif. (d) Three delocalized π CMOs. (e) Three delocalized σ CMOs; Figure S4: AdNDP bonding scheme for TS (C1, 1A) B8Al3+ cluster. Occupation numbers (ONs) are shown.

Author Contributions

Conceptualization, S.-J.G.; methodology, S.-J.G.; validation, S.-J.G. and T.-L.Y.; investigation, S.-J.G.; writing—original draft preparation, S.-J.G.; writing—review and editing, S.-J.G. and T.-L.Y. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the National Natural Science Foundation of China (22173053), the Natural Science Foundation of Shanxi Province (201801D121103, 202103021224318 and 202303021212289), the Shanxi “1331” Project, and Lyuliang City High-Level Scientific and Technological Talents Project (2023RC14).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article and Supplementary Materials.

Conflicts of Interest

The authors declare no conflicts of interest.

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Molecules 29 05961 g001
Figure 1. Optimized (a) C1 global minimum (GM) and (b) C1 transition state (TS) structures of B8Al3+ cluster at the PBE0/def2-TZVP level. Presented in top and side views. The B and Al atoms are in pink and blue, respectively. The same below.
Figure 1. Optimized (a) C1 global minimum (GM) and (b) C1 transition state (TS) structures of B8Al3+ cluster at the PBE0/def2-TZVP level. Presented in top and side views. The B and Al atoms are in pink and blue, respectively. The same below.
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Figure 2. Calculated bond distances (in Å, black color) and Wiberg bond indices (WBIs, in red color) for (a) C1 (1A) GM and (b) C1 (1A) TS structures of B8Al3+ cluster at the PBE0/def2-TZVP level. The WBIs are obtained from the natural bond orbital (NBO) analysis at PBE0/def2-TZVP.
Figure 2. Calculated bond distances (in Å, black color) and Wiberg bond indices (WBIs, in red color) for (a) C1 (1A) GM and (b) C1 (1A) TS structures of B8Al3+ cluster at the PBE0/def2-TZVP level. The WBIs are obtained from the natural bond orbital (NBO) analysis at PBE0/def2-TZVP.
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Figure 3. Natural atomic charges (in |e|) for (a) C1 (1A) GM and (b) C1 (1A) TS structures of B8Al3+ cluster. The data are obtained from the NBO analyses at PBE0/def2-TZVP.
Figure 3. Natural atomic charges (in |e|) for (a) C1 (1A) GM and (b) C1 (1A) TS structures of B8Al3+ cluster. The data are obtained from the NBO analyses at PBE0/def2-TZVP.
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Figure 4. Structural evolution of B8Al3+ cluster during intramolecular dynamic rotation of the Al–Al dimer with respect to B8 molecular wheel.
Figure 4. Structural evolution of B8Al3+ cluster during intramolecular dynamic rotation of the Al–Al dimer with respect to B8 molecular wheel.
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Figure 5. Pictures of occupied canonical molecular orbitals (CMOs) of GM B8Al3+ cluster. (a) Lone pairs. (b) Lewis-type Al–Al σ bond. (c) Seven CMOs for Lewis B–B σ single bonds along the periphery of disk B8 motif. (d) Three delocalized π CMOs. (e) Three delocalized σ CMOs.
Figure 5. Pictures of occupied canonical molecular orbitals (CMOs) of GM B8Al3+ cluster. (a) Lone pairs. (b) Lewis-type Al–Al σ bond. (c) Seven CMOs for Lewis B–B σ single bonds along the periphery of disk B8 motif. (d) Three delocalized π CMOs. (e) Three delocalized σ CMOs.
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Figure 6. AdNDP bonding scheme for GM (C1, 1A) B8Al3+ cluster. (a) Seven quasi-Lewis-type 2c-2e B–B σ bonds along the periphery and a Al–Al σ bond. (b) Two lone pairs of Al. (c) Global π sextet. (d) Global σ sextet. Occupation numbers (ONs) are shown.
Figure 6. AdNDP bonding scheme for GM (C1, 1A) B8Al3+ cluster. (a) Seven quasi-Lewis-type 2c-2e B–B σ bonds along the periphery and a Al–Al σ bond. (b) Two lone pairs of Al. (c) Global π sextet. (d) Global σ sextet. Occupation numbers (ONs) are shown.
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Figure 7. The iso-chemical shielding surfaces (ICSSs) of GM B8Al3+ cluster. (a) ICSSzz(0) at the B8 disk plane. (b) ICSSzz(1) at 1.0 Å below the disk plane. For ICSSs, a positive value indicates aromaticity, and vice versa.
Figure 7. The iso-chemical shielding surfaces (ICSSs) of GM B8Al3+ cluster. (a) ICSSzz(0) at the B8 disk plane. (b) ICSSzz(1) at 1.0 Å below the disk plane. For ICSSs, a positive value indicates aromaticity, and vice versa.
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Gao, S.-J.; Yu, T.-L. Chemical Bonding and Dynamic Structural Fluxionality of a Boron-Based B8Al3+ Cluster. Molecules 2024, 29, 5961. https://doi.org/10.3390/molecules29245961

AMA Style

Gao S-J, Yu T-L. Chemical Bonding and Dynamic Structural Fluxionality of a Boron-Based B8Al3+ Cluster. Molecules. 2024; 29(24):5961. https://doi.org/10.3390/molecules29245961

Chicago/Turabian Style

Gao, Shu-Juan, and Tan-Lai Yu. 2024. "Chemical Bonding and Dynamic Structural Fluxionality of a Boron-Based B8Al3+ Cluster" Molecules 29, no. 24: 5961. https://doi.org/10.3390/molecules29245961

APA Style

Gao, S.-J., & Yu, T.-L. (2024). Chemical Bonding and Dynamic Structural Fluxionality of a Boron-Based B8Al3+ Cluster. Molecules, 29(24), 5961. https://doi.org/10.3390/molecules29245961

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