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.

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 (C2v, 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 (Cs, 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.

Boron-based Pd3B26 alloy cluster as a nanoscale antifriction bearing system: tubular core-shell structure, double π/σ aromaticity, and dynamic structural fluxionality.

Boron-based nanoclusters show unique geometric structures, nonclassical chemical bonding, and dynamic structural fluxionality. We report here on the theoretical prediction of a binary Pd3B26 cluster, which is composed of a triangular Pd3 core and a tubular double-ring B26 unit in a coaxial fashion, as identified through global structural searches and electronic structure calculations. Molecular dynamics simulations indicate that in the core-shell alloy cluster, the B26 double-ring unit can rotate freely around its Pd3 core at room temperature and beyond. The intramolecular rotation is virtually barrier free, thus giving rise to an antifriction bearing system (or ball bearing) at the nanoscale. The dimension of the dynamic system is only 0.66 nm. Chemical bonding analysis reveals that Pd3B26 cluster possesses double 14π/14σ aromaticity, following the (4n + 2) Hückel rule. Among 54 pairs of valence electrons in the cluster, the overwhelming majority are spatially isolated from each other and situated on either the B26 tube or the Pd3 core. Only one pair of electrons are primarily responsible for chemical bonding between the tube and the core, which greatly weaken the bonding within the Pd3 core and offers structural flexibility. This is a key mechanism that effectively diminishes the intramolecular rotation barrier and facilitates dynamic structural fluxionality of the system. The current work enriches the field of nanorotors and nanomachines.

Chemical Bonding and Dynamic Structural Fluxionality of a Boron-Based Na5B7 Sandwich Cluster.

Doping alkali metals into boron clusters can effectively compensate for the intrinsic electron deficiency of boron and lead to interesting boron-based binary clusters, owing to the small electronegativity of the former elements. We report on the computational design of a three-layered sandwich cluster, Na5B7, on the basis of global-minimum (GM) searches and electronic structure calculations. It is shown that the Na5B7 cluster can be described as a charge-transfer complex: [Na4]2+[B7]3-[Na]+. In this sandwich cluster, the [B7]3- core assumes a molecular wheel in shape and features in-plane hexagonal coordination. The magic 6π/6σ double aromaticity underlies the stability of the [B7]3- molecular wheel, following the (4n + 2) Hückel rule. The tetrahedral Na4 ligand in the sandwich has a [Na4]2+ charge-state, which is the simplest example of three-dimensional aromaticity, spherical aromaticity, or superatom. Its 2σ electron counting renders σ aromaticity for the ligand. Overall, the sandwich cluster has three-fold 6π/6σ/2σ aromaticity. Molecular dynamics simulation shows that the sandwich cluster is dynamically fluxional even at room temperature, with a negligible energy barrier for intramolecular twisting between the B7 wheel and the Na4 ligand. The Na5B7 cluster offers a new example for dynamic structural fluxionality in molecular systems.

Y©B8C4 cluster: a boron-carbon molecular wheel with dodeca-coordination number in plane.

Computational evidence is reported for the largest planar molecular wheel of the Y©B8C4 cluster, featuring an yttrium atom enclosed by a highly symmetric B8C4 ring. The B8C4 ring is viable in the -(BCB)4- form with double 9π/10σ aromaticity. The centered yttrium atom is dodeca-coordinated with the peripheral B8C4 ring, which sets a record coordination number for a planar structure in chemistry heretofore.

Anchoring a bow-shaped boron single chain in binary Be6B7- cluster: hybrid octagonal ring, multifold π/σ aromaticity, and dual electronic transmutation.

Elemental boron clusters do not form linear chain or monocyclic ring structures, which is in contrast to carbon. Based on computer global searches and quantum chemical calculations, we report on the viability of a curved boron single chain in binary Be6B7- cluster. The boron motif assumes a bow shape, being anchored on a Be6 prism. Such a motif, which appears to be highly strained in its free-standing form, is exotic in boron-based clusters and nanostructures. Chemically, the cluster is analogous to a "clam-and-pearl-chain" system at the nanoscale (about 1 nm in size), in which a Be6 clam moderately opens its mouth, except that a B7 pearl chain is too large to be encapsulated inside. The picture differs from a three-layered sandwich. This cluster features a hybrid Be2B7 monocyclic ring, which is octagonal in nature and supports double 10π/6σ aromaticity. The number of π bonds substantially surpasses that in bare boron clusters of similar sizes. Two Be3 rings in the prism are also σ aromatic, albeit with effective 1σ/1σ electron-counting only. The unique multifold 1σ/10π/6σ/1σ aromaticity governs the geometry of the Be6B7- cluster, which can also be rationalized using the concept of dual electronic transmutation.

Boron-based ternary Rb6Be2B6 cluster featuring unique sandwich geometry and a naked hexagonal boron ring.

Computational evidence is reported on a boron-based ternary Rb6Be2B6 cluster as the "Big Mac" sandwich on a subnanoscale with thickness of 0.58 nm. The core hexagonal B6 ring, occurring in the naked form due to double 6π/6σ aromaticity, is capped by two tetrahedral BeRb3 ligands. Such a B6 motif is scarce in boron clusters. The sandwich cluster has four-fold 2σ/6π/6σ/2σ aromaticity and its tetrahedral BeRb3 ligand is the simplest case of three-dimensional aromaticity (or spherical aromaticity). The sandwich can be formulated as a charge-transfer complex, [Rb3Be]3+[B6]6-[BeRb3]3+, whose components are held together by robust electrostatics, facilitating dual-mode dynamic fluxionality.

Ternary 12-electron CBe3X3+ (X = H, Li, Na, Cu, Ag) clusters: planar tetracoordinate carbons and superalkali cations.

Molecules with planar tetracoordinate carbons (ptCs) are exotic in chemical bonding, and they are normally designed according to the 18-electron rule. Here we report on the viability of ptC clusters with as few as 12 valence electrons, which represent the lower limit in terms of electron counting. Specifically, we have computationally designed a class of ternary 12-electron ptC clusters, CBe3X3+ (X = H, Li, Na, Cu, Ag), based on a rhombic CBe32- unit. Computer structural searches reveal that the ptC species are global minima, whose C center is coordinated in-plane by three Be atoms and a terminal X atom via robust C-Be/C-X bonding, either covalent or ionic. The other two X atoms are on the periphery and each bridge two Be atoms. Bonding analyses show that the ptC core is governed by delocalized 2π/6σ bonding, that is, double π/σ aromaticity, which collectively conforms to the 8-electron counting. Additional 4 electrons contribute to peripheral Be-X-Be and Be-Be σ bonding. The delocalized 2π/6σ frameworks appear to be universal for all ptC clusters, ranging from 18-electron down to 12-electron systems. In other words, the ptC species are dictated entirely by the 8-electron counting. Predicted vertical electron affinities of these ptC clusters range from 3.13 to 5.48 eV, indicative of superalkali or pseudoalkali cations.

Boron-based inorganic heterocyclic clusters: electronic structure, chemical bonding, aromaticity, and analogy to hydrocarbons.

This Perspective article deals with recent computational and experimental findings in boron-based heterocyclic clusters, which focuses on binary B-O and B-S clusters, as well as relevant ternary B-X-H (X = O, S, N) species. Boron is electron-deficient and boron clusters do not form monocyclic rings or linear chains. Boron-based heterocyclic clusters are intuitively even more electron-deficient and feature exotic chemical bonding, which make use of O 2p, S 3p, or N 2p lone-pairs for π delocalization over heterocyclic rings, facilitating new cluster structures and new types of bonding. Rhombic, pentagonal, hexagonal, and polycyclic clusters are discussed herein. Rhombic species are stabilized by four-center four-electron (4c-4e) π bonding, that is, the o-bond. An o-bond cluster differs from a typical 4π antiaromatic system, because it has 4π electrons in an unusual bonding/nonbonding combination, which takes advantage of the empty 2pz atomic orbitals from electron-deficient boron centers. A variety of examples (notably including boronyl boroxine) possess a hexagonal ring, as well as magic 6π electron-counting, making them new members of the inorganic benzene family. Pentagonal clusters bridge rhombic o-bond systems and inorganic benzenes, but they do not necessarily favor 6π electron-counting as in cyclopentadienide anion. In contrast, pentagonal 4π clusters are stable, leading to the concept of pentagonal o-bond. One electron can overturn the potential energy landscape of a system, enabling rhombic-to-hexagonal structural transition, which further reinforces the idea that 4π electron-counting is favorable for rhombic systems and 6π is magic for hexagonal rings. The bonding analogy between heterocyclic clusters and hydrocarbons goes beyond monocyclic species, which allows rational design of boron-based inorganic analogs of polycyclic aromatic hydrocarbons, including s-indacene as a puzzling aromatic/antiaromatic system. Selected linear B-O clusters are also briefly discussed, featuring dual 3c-4e π bonds, that is, ω-hyperbonds. Dual ω-hyperbonds, rhombic or pentagonal o-bond, and inorganic benzenes share a common chemical origin. The field of boron-based heterocyclic clusters is still in its infant stage, and much new chemistry remains to be discovered in forthcoming experimental and theoretical studies.

Sandwich-type Na6B7- and Na8B7+ clusters: charge-transfer complexes, four-fold π/σ aromaticity, and dynamic fluxionality.

Boron-based clusters possess unusual structural and bonding properties owing to boron's electron-deficiency. We report on the theoretical prediction of two binary B-Na clusters, Na6B7- and Na8B7+, which assume unique sandwich geometries, featuring a perfectly planar B7 wheel and two triangular Na3 or quasi-tetrahedral Na4 ligands. Despite distinct electronegativities of B/Na, the B-Na clusters do not form typical salts. Both sandwich species are dynamically fluxional at 300 K and beyond. Two dynamic modes are observed: an in-plane rotation of the B7 wheel versus twisting of the two Na3/Na4 ligands. Their energy barriers are negligibly small. Natural bond orbital calculations show that the clusters are charge-transfer complexes [Na3]+[B7]3-[Na3]+ and [Na4]2+[B7]3-[Na4]2+, respectively. Chemical bonding analyses indicate that the B7 wheel in the clusters has 6π/6σ double aromaticity and the Na3/Na4 ligands are 2σ aromatic, collectively leading to four-fold π/σ aromaticity. The quasi-tetrahedral Na4 ligand is the simplest example of spherical aromaticity and can also be considered a superatom. Interlayer bonding in the sandwiches is greater than 20 eV, due to electrostatics, which should not be confused with weakly bound species. Four-fold π/σ aromaticity and robust interlayer ionic bonding offer uniform and dilute electron clouds over the sandwiches, facilitating their dual-mode dynamic fluxionality. The Na8B7+ cluster is also a superalkali cation.

Ternary CBe4Au4 cluster: a 16-electron system with quasi-planar tetracoordinate carbon.

Planar hypercoordinate carbons as exotic chemical species are dominated by 18-electron counting. We report herein a 16-electron planar tetracoordinate carbon (ptC) cluster, CBe4Au4, which is quasi-planar to be exact, being composed of a C center, a square-planar Be4 ring, and four outer Au bridges. The quasi-ptC cluster is established as a global minimum via computer structural searches, located 14.6 kcal mol-1 below the nearest competitor at the CCSD(T) level. It shows thermodynamic and electronic robustness, with a low electron affinity (1.54 eV at B3LYP) and a large HOMO-LUMO gap (2.21 eV for excitation energy). Bonding analyses reveal 2π and 6σ double aromaticity, in addition to four three-center two-electron (3c-2e) Be-Au-Be σ bonds, confirming that 16-electron counting is perfect for the system. We believe that double (π and σ) aromaticity is a general concept that governs planar or quasi-planar carbons, which overrides the 18-electron rule. Competition between quasi-ptC and tetrahedral carbon (thC) isomers in the CBe4M4 (M = K, Au, H, Cl) series is also examined, which sheds crucial light on factors that govern the ptC clusters. The present findings offer opportunities for further planar and unconventional molecules.

Boron-based binary Be6B102- cluster: three-layered aromatic sandwich, electronic transmutation, and dynamic structural fluxionality.

Boron-based nanoclusters have unique structures, bonding, and dynamic properties, which originate from boron's electron-deficiency. We demonstrate here that pouring in extra electrons can alter such systems fundamentally. A coaxial triple-layered Be6B102- sandwich cluster is designed via global structural searches and quantum chemical calculations. It is well defined as the global minimum, which consists of a slightly elongated B10 monocyclic ring and two Be3 rings, the latter forming a Be6 trigonal-prism albeit without interlayer Be-Be bonding. The B10 ring shows structural and chemical integrity with respect to the Be3 rings, and yet it differs markedly from the free B10 cluster and closely resembles the C10 cluster. The present data testify to the idea of electronic transmutation, in which a B- is equivalent to C and a B10 cluster, upon charge-transfer, is converted to and stabilized as a monocyclic ring analogous to C10. Chemical bonding analyses reveal that the B10 ring in the Be6B102- cluster has 10π and 10σ delocalization and each Be3 ring is held together by 2σ electrons, collectively rendering four-fold π/σ aromaticity. The bonding pattern is in line with the formula of [Be3]4+[B10]10-[Be3]4+, suggesting a highly charged electron-transfer complex. Furthermore, the Be6B102- cluster is dynamically fluxional with dual modes of revolution (orbiting) and rotation (twisting), being structurally robust at least up to a temperature of 1500 K.

Planar Pentacoordinate versus Tetracoordinate Carbons in Ternary CBe4Li4 and CBe4Li42- Clusters.

Planar hypercoordinate carbon molecules are exotic species, for which the 18-electron counting has been considered a rule. We report herein computational evidence of perfectly planar C2 v CBe4Li4 (1) and D4 h CBe4Li42- (3) clusters. These ternary species contain 16 and 18 electrons, respectively. The dianion is highly symmetric with a planar tetracoordinate carbon (ptC), whereas the neutral features a planar pentacoordinate carbon (ppC). Thus, charge-state alters the coordination environments of a cluster. Chemical bonding analysis shows that both clusters have 2π and 6σ delocalization around the C center, suggesting that ppC or ptC clusters are governed by double π/σ aromaticity, rather than the 18-electron rule. The outer Be4Li4 ring in 1 and 3 also supports 2σ aromaticity, collectively leading to 3-fold π/σ aromaticity for these ppC/ptC clusters. Structural transformation from ptC (3) to ppC (1) is discussed, in which the 16-electron quasi-ptC CBe4Li4 (2) cluster serves as an intermediate. Cluster 2 as a local minimum has severe out-of-plane distortion. Flattening of 2 leads to reorganization of Be4 ring around the C center, which offers space for the fifth atom to coordinate and facilitates ppC formation. The latter arrangement optimizes π aromaticity and better manages intramolecular Coulomb repulsion. This work highlights the geometric factor (and unconventional electron counting) in the design of planar hypercoordinate carbons.

Star-Like CBe5Au5+ Cluster: Planar Pentacoordinate Carbon, Superalkali Cation, and Multifold (π and σ) Aromaticity.

We report on the computational design of star-like CBe5Au5+ cluster with planar pentacoordinate carbon (ppC), which is also classified as a superalkali cation. Relevant isovalent CBe5Aunn-4 (n = 2-4), BBe5Au5, and NBe5Au52+ clusters with ppC/B/N are studied as well. Global-minimum structures of the clusters are established via computer global searches. The species feature a pentacoordinate pentagonal XBe5 (X = C, B, N) core, with Au occupying outer bridging positions. Molecular dynamics simulations indicate that they are dynamically stable. Bonding analysis reveals 3-fold (π and σ) aromaticity in CBe5Au5+, a key concept that overrides the 18-electron rule and should be applicable for (or help revisit existing models of) other planar hypercoordinate systems. Vertical electron affinities of CBe5Au5+ and its lighter counterparts (CBe5Cu5+ and CBe5Ag5+) are calculated to be unusually low, which are below 3.89 eV, the smallest atomic ionization potential of any element in the periodic table. Thus, these three clusters belong to superalkali cations. The merge of ppC and superalkali characters makes them unique chemical species.

Planar Tricyclic B8O8 and B8O8- Clusters: Boron Oxide Analogues of s-Indacene C12H8.

Boron clusters and their oxides are electron-deficient species with (π and σ) aromaticity and antiaromaticity, enabling a structural and bonding analogy between them and the aromatic hydrocarbons. s-Indacene C12H8 is normally considered as a border system between the classes of aromatic and antiaromatic hydrocarbons. We show herein, via computer global-minimum searches and B3LYP and single-point CCSD(T) calculations, that boron oxide clusters D2h B8O8 (1, 1Ag) and D2h B8O8- (2, 2B2g) adopt planar tricyclic structures, which feature fused heterocyclic B3O2/B4O2/B3O2 rings and two boronyl (BO) terminals, a structural pattern analogous to the C5/C6/C5 rings in s-indacene. Bonding analyses indicate that B8O8 (1) is a formally antiaromatic 12π system, the molecular orbitals of which are largely similar to those of s-indacene. Infrared and ultraviolet-visible spectra of B8O8 (1) neutral, as well as the photoelectron spectrum of B8O8- (2) anion, are predicted computationally. The latter spectrum shows a sizable energy gap of 3.5 eV for 2, demonstrating the electronic robustness of 1. Our bonding analyses also shed critical light on the nature of bonding in s-indacene.

Wheel-like, elongated, circular, and linear geometries in boron-based CnB7-n (n = 0-7) clusters: structural transitions and aromaticity.

We report a quantum chemical study on the structural and bonding properties of a series of boron-carbon mixed clusters with seven atoms: CnB7-n (n = 0-7). Global-minimum structures were searched using the Coalescence Kick (CK) method, followed by B3LYP/6-311+G(d) calculations for full optimizations and energetics. Top candidate structures were further benchmarked at the single-point CCSD(T) level. Structural transitions were revealed to occur successively between wheel-like, elongated, circular, and linear geometries upon the increase of C contents in the clusters. Chemical bonding was elucidated via canonical molecular orbital (CMO) analyses and adaptive natural density partitioning (AdNDP). The number of delocalized electrons (σ plus π) in the clusters was shown to vary by one at a time from 5σ to 7σ, as well as from 3π to 6π, which allows aromaticity, antiaromaticity, and conflicting aromaticity to be precisely tuned according to the (4n + 2) and 4n Hückel rules. Delocalized π and σ bonds and their electron counting appear to dictate the cluster structures of the whole series. Aromaticity in the systems was independently confirmed using nucleus-independent chemical shifts (NICSs). The monocyclic B2C5 cluster was shown to possess the greatest NICS values, consistent with its 6π plus 6σ electron countings for double aromaticity. Our analyses also shed light on the reason why C in the filled-hexagonal B6C cluster occupies a peripheral site rather than the center and why C avoids hypercoordination in B-C binary clusters. A similar argument should be valid for other B-C clusters in prior reports, such as B6C2-, B7C-, and B8C.

Pentagonal five-center four-electron π bond in ternary B3N2H5 cluster: an extension of the concept of three-center four-electron ω bond.

Boron-based heteroatomic rings can have exotic chemical bonding, in which the p lone-pairs of heteroatoms manage to participate in delocalized π bonding, compensating for boron's electron-deficiency. We explore herein the bonding properties of ternary B-N-H systems with a pentagonal ring, using the B3N2H50/-/2- clusters as examples. Computational structural searches lead to perfectly planar C2v B3N2H5 (1, 1A1) and C2v B3N2H5- (2, 2B1) as global minima for the neutral species and monoanion, which feature a pentagonal B3N2 ring. The corresponding dianion C2v B3N2H52- (3, 1A1) is a local minimum, whose global minimum adopts a chain-like open structure. Bonding analyses reveal a five-center four-electron (5c-4e) π system in 1, dubbed the 5c-4e o-bond. It is a 4π system in the bonding/nonbonding combination, originating from two N 2p lone-pairs, which can be considered as an extension of the concept of 3c-4e ω-bond. The extra electrons in 2 and 3 occupy a markedly destabilized π orbital. Thus, a 4π configuration, rather than a π sextet according to the (4n + 2) Hückel rule, is electronically robust for the B3N2H50/-/2- system. Infrared and photoelectron spectra are predicted for 1 and 2, respectively. Structural evolution of ring-like and chain-like isomers with charge-state in B3N2H50/-/2- is elucidated. B3N2H5- (2) is used as ligand for sandwich-type complexes: C2h [(B3N2H5)2Fe]2- and C2h [(B3N2H5)2Fe]Li2.

Coaxial Triple-Layered versus Helical Be6 B11- Clusters: Dual Structural Fluxionality and Multifold Aromaticity.

Two low-lying structures are unveiled for the Be6 B11- nanocluster system that are virtually isoenergetic. The first, triple-layered cluster has a peripheral B11 ring as central layer, being sandwiched by two Be3 rings in a coaxial fashion, albeit with no discernible interlayer Be-Be bonding. The B11 ring revolves like a flexible chain even at room temperature, gliding freely around the Be6 prism. At elevated temperatures (1000 K), the Be6 core itself also rotates; that is, two Be3 rings undergo relative rotation or twisting with respect to each other. Bonding analyses suggest four-fold (π and σ) aromaticity, offering a dilute and fluxional electron cloud that lubricates the dynamics. The second, helix-type cluster contains a B11 helical skeleton encompassing a distorted Be6 prism. It is chiral and is the first nanosystem with a boron helix. Molecular dynamics also shows that at high temperature the helix cluster readily converts into the triple-layered one.

Concentric dual π aromaticity in bowl-like B30 cluster: an all-boron analogue of corannulene.

A chemical bonding model is presented for the bowl-like C5v B30 global-minimum cluster with a central pentagonal hole. The B30 cluster is composed of three concentric boron rings: first B5, second B10, and third B15. The first and second B rings constitute an inner double-chain ribbon and support a delocalized π sextet. The second and third rings form an outer double-chain ribbon, where 14π delocalized electrons are situated. The unique π systems lead to concentric dual π aromaticity for B30, a concept established from concerted computational data on the bases of canonical molecular orbital (CMO) analysis, adaptive natural density partitioning (AdNDP), nucleus-independent chemical shifts (NICS), and natural charge calculations. A proposal is put forward that the bowl-like B30 cluster is an exact all-boron analogue of corannulene (C20H10), a fragment of C60 fullerene. The bonding nature of corannulene is revisited and fully elucidated herein. A comparison of the bonding patterns in bowl-like C5v B30 cluster and two other structural isomers (Cs and C1) unravels the mechanism as to why the defective hole prefers to be positioned at the center.

Chemical bonding and dynamic fluxionality of a B15(+) cluster: a nanoscale double-axle tank tread.

A planar, elongated B15(+) cationic cluster is shown to be structurally fluxional and functions as a nanoscale tank tread on the basis of electronic structure calculations, bonding analyses, and molecular dynamics simulations. The outer B11 peripheral ring behaves like a flexible chain gliding around an inner B4 rhombus core, almost freely at the temperature of 500 K. The rotational energy barrier is only 1.37 kcal mol(-1) (0.06 eV) at the PBE0/6-311+G* level, further refined to 1.66 kcal mol(-1) (0.07 eV) at the single-point CCSD(T)/6-311G*//CCSD/6-311G* level. Two soft vibrational modes of 166.3 and 258.3 cm(-1) are associated with the rotation, serving as double engines for the system. Bonding analysis suggests that the "island" electron clouds, both σ and π, between the peripheral ring and inner core flow and shift continuously during the intramolecular rotation, facilitating the dynamic fluxionality of the system with a small rotational barrier. The B15(+) cluster, roughly 0.6 nm in dimension, is the first double-axle nanoscale tank tread equipped with two engines, which expands the concepts of molecular wheels, Wankel motors, and molecular tanks.