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

Planar C2v 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.

Are all planar and quasi-planar boron clusters aromatic? Counter examples of island or global π antiaromaticity from chemical bonding analysis.

Boron is an electron-deficient element. The flatland of planar or quasi-planar (2D) boron clusters is believed to possess aromaticity for all members, which remains a fundamental issue in debate in boron chemistry. Using a selected set of D2h B62-, C2h B282-, and C2v B29- clusters as counter examples, we shall present computational evidence for global or island π antiaromaticity in 2D boron clusters. The latter two are flattened for the purpose of clarity, which model their quasi-planar C2 or Cs monoanion clusters observed in prior gas-phase experiments. Chemical bonding in the clusters is elucidated collectively on the basis of canonical molecular orbital (CMO) analysis, adaptive natural density partitioning (AdNDP), electron localization functions (ELFs), and localized molecular orbital (LMO) analysis. These results are complementary to each other and yet highly coherent. As a quantitative indicator, nucleus-independent chemical shifts (NICSs) are calculated at selected specific points in the clusters, which help differentiate between π aromaticity and antiaromaticity. Intriguingly, triangular sites in the same boron cluster can be aromatic, antiaromatic, or nonaromatic, despite the fact that they are physically indistinguishable. The phenomenon is understood in analogy to hydrocarbons and polycyclic aromatic hydrocarbons (PAHs). Even perfect sheet-like boron clusters are convertible to the PAH analogous systems. This work provides compelling examples for global and island π antiaromaticity in the 2D boron clusters.

Nature of Bonding in Bowl-Like B36 Cluster Revisited: Concentric (6π+18π) Double Aromaticity and Reason for the Preference of a Hexagonal Hole in a Central Location.

The bowl-shaped C6v B36 cluster with a central hexagon hole is considered an ideal molecular model for low-dimensional boron-based nanosystems. Owing to the electron deficiency of boron, chemical bonding in the B36 cluster is intriguing, complicated, and has remained elusive despite a couple of papers in the literature. Herein, a bonding analysis is given through canonical molecular orbitals (CMOs) and adaptive natural density partitioning (AdNDP), further aided by natural bond orbital (NBO) analysis and orbital composition calculations. The concerted computational data establish the idea of concentric double π aromaticity for the B36 cluster, with inner 6π and outer 18π electron counting, which both conform to the (4n+2) Hückel rule. The updated bonding picture differs from existing knowledge of the system. A refined bonding model is also proposed for coronene, of which the B36 cluster is an inorganic analogue. It is further shown that concentric double π aromaticity in the B36 cluster is retained and spatially fixed, irrespective of the migration of the hexagonal hole; the latter process changes the system energetically. The hexagonal hole is a destabilizing factor for σ/π CMOs. The central hexagon hole affects substantially fewer CMOs, thus making the bowl-shaped C6v B36 cluster the global minimum.

Chemical Bonding in Transition Metal Nitride Os3N3 + Cluster: 6π Inorganic Benzene and δ2δ*1δ*1 Aromaticity.

Inorganic benzene-like clusters with a planar hexagonal ring are of interest in chemistry, as are new types of aromaticity, multifold aromaticity, and in particular δ aromaticity beyond carbon-based organic systems. Here we report on a computational study of chemical bonding in a binary Os3N3 + D 3h (7A2″) cluster. This transition metal nitride cluster assumes a perfectly planar, heteroatomic, hexagonal geometry. An array of quantum chemistry tools is exploited to elucidate the electronic, structural, and bonding properties of D 3h Os3N3 + cluster, which include canonical molecular orbitals, adaptive natural density partitioning, natural bond orbital analysis, orbital composition calculations, and nucleus-independent chemical shifts. The computational data collectively support the bonding picture of 2-fold π/δ aromaticity: 6π electrons delocalized over all Os/N centers versus an Os-based 4δ framework in the unique δ2δ*1δ*1 configuration. The π sextet renders this heteroatomic cluster an inorganic analog of benzene. Transition metal-based inorganic benzenes are unknown in the literature, to our knowledge. The triplet 4δ electron-counting is a rare case of d-orbital aromaticity and δ-aromaticity, following the reversed 4n Hückel rule for aromaticity in a triplet system. This bonding picture is concrete, differing fundamentally from a recent study on the relevant system.

On the Nature of Bonding in Synthetic Charged Molecular Alloy [P7ZnP7]4- Cluster and Its Relevant [P7]3- Zintl Ion.

Charged molecular alloys and Zintl ions are of interest in synthetic chemistry. However, their chemical bonding has seldom been elucidated using modern quantum chemistry tools. Herein, we report on in-depth chemical bonding analyses for a charged molecular alloy C 2 [P7ZnP7]4- cluster and its relevant Zintl ion C 3v [P7]3- ligand, making use of electronic structure calculations at PBE0/def2-TZVP level, natural bond orbital and orbital composition analyses, canonical molecular orbitals, and adaptive natural density partitioning (AdNDP). The computational data show that C 3v [P7]3- Zintl ion has three isolated, negatively charged, bridging P sites. Such charges are largely P 3p lone-pairs in nature, but they also participate in secondary P-P bonding along the bridging sites. C 2 [P7ZnP7]4- cluster is formulated as [P7]2-[Zn]0[P7]2-, in which [P7]2- ligands maintain the structural and bonding integrity of [P7]3- Zintl ion despite their difference in charge state. Two [P7]2- ligands collectively bind with Zn center via four bridging P sites, resulting in a quasi-tetrahedral ZnP4 core with the eight-electron counting. This bonding picture can alternatively be rationalized using the superatom concept. The Zn-P bonds are weak with a bond order of around 0.5, because the P centers have partial nonbonding 3p character, akin to 3p2 lone-pairs albeit with a lower occupation number.

Chemical Bonding and σ-Aromaticity in Charged Molecular Alloys: [Pd2As14]4- and [Au2Sb14]4- Clusters.

We report a computational study on the structures and bonding of a charged molecular alloy D 2h [Pd2As14]4- (1), as well as a model D 2h [Au2Sb14]4- (2) cluster. Our effort makes use of an array of quantum chemistry tools: canonical molecular orbital analysis, adaptive natural density partitioning, natural bond orbital analysis, orbital composition analysis, and nucleus independent chemical shift calculations. Both clusters consist of two X7 (X = As, Sb) cages, which are interconnected via a M2 (M = Pd, Au) dumbbell, featuring two distorted square-planar MX4 units. Excluding the Pd/As or Au/Sb lone-pairs, clusters 1 and 2 are 50- and 44-electron systems, respectively, of which 32 electrons are for two-center two-electron (2c-2e) As-As or Sb-Sb σ bonds and an additional 16 electrons in 1 for 2c-2e Pd-As σ bonds. No covalent Pd-Pd or Au-Au bond is present in the systems. Cluster 1 is shown to possess two globally delocalized σ electrons, whereas 2 has two σ sextets (each associated with an AuSb4 fragment). Thus, 1 and 2 conform to the (4n + 2) Hückel rule, for n = 0 and 1, respectively, rendering them σ-aromaticity.

Peculiar All-Metal σ-Aromaticity of the [Au2 Sb16 ]4- Anion in the Solid State.

Gas-phase clusters are deemed to be σ-aromatic when they satisfy the 4n+2 rule of aromaticity for delocalized σ electrons and fulfill other requirements known for aromatic systems. While the range of n values was shown to be quite broad when applied to short-lived clusters found in molecular-beam experiments, stability of all-metal cluster-like fragments isolated in condensed phase was previously shown to be mainly ascribed to two electrons (n=0). In this work, the applicability of this concept is extended towards solid-state compounds by demonstrating a unique example of a storable compound, which was isolated as a stable [K([2.2.2]crypt)]+ salt, featuring a [Au2 Sb16 ]4- cluster core possessing two all-metal aromatic AuSb4 fragments with six delocalized σ electrons each (n=1). This discovery pushes the boundaries of the original idea of Kekulé and firmly establishes the usefulness of the σ-aromaticity concept as a general idea for both small clusters and solid-state compounds.

[Sb4Au4Sb4](2-): A designer all-metal aromatic sandwich.

We report on the computational design of an all-metal aromatic sandwich, [Sb4Au4Sb4](2-). The triple-layered, square-prismatic sandwich complex is the global minimum of the system from Coalescence Kick and Minima Hopping structural searches. Following a standard, qualitative chemical bonding analysis via canonical molecular orbitals, the sandwich complex can be formally described as [Sb4](+)[Au4](4-)[Sb4](+), showing ionic bonding characters with electron transfers in between the Sb4/Au4/Sb4 layers. For an in-depth understanding of the system, one needs to go beyond the above picture. Significant Sb → Au donation and Sb ← Au back-donation occur, redistributing electrons from the Sb4/Au4/Sb4 layers to the interlayer Sb-Au-Sb edges, which effectively lead to four Sb-Au-Sb three-center two-electron bonds. The complex is a system with 30 valence electrons, excluding the Sb 5s and Au 5d lone-pairs. The two [Sb4](+) ligands constitute an unusual three-fold (π and σ) aromatic system with all 22 electrons being delocalized. An energy gap of ∼1.6 eV is predicted for this all-metal sandwich. The complex is a rare example for rational design of cluster compounds and invites forth-coming synthetic efforts.

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.

On the nature of chemical bonding in the all-metal aromatic [Sb3Au3Sb3](3-) sandwich complex.

In a recent communication, an all-metal aromatic sandwich [Sb3Au3Sb3](3-) was synthesized and characterized. We report herein a density-functional theory (DFT) study on the chemical bonding of this unique cluster, which makes use of a number of computational tools, including the canonical molecular orbital (CMO), adaptive natural density partitioning (AdNDP), Wiberg bond index, and orbital composition analyses. The 24-electron, triangular prismatic sandwich is intrinsically electron-deficient, being held together via six Sb-Sb, three Au-Au, and six Sb-Au links. A standard, qualitative bonding analysis suggests that all CMOs are primarily located on the three Sb3/Au3/Sb3 layers, three Au 6s based CMOs are fully occupied, and the three extra charges are equally shared by the two cyclo-Sb3 ligands. This bonding picture is referred to as the zeroth order model, in which the cluster can be formally formulated as [Sb3(1.5+)Au3(3-)Sb3(1.5+)](3-) or [Sb3(0)Au3(3-)Sb3(0)]. However, the system is far more complex and covalent than the above picture. Seventeen CMOs out of 33 in total involve remarkable Sb → Au electron donation and Sb ← Au back-donation, which are characteristic of covalent bonding and effectively redistribute electrons from the Sb3 and Au3 layers to the interlayer edges. This effect collectively leads to three Sb-Au-Sb three-center two-electron (3c-2e) σ bonds as revealed in the AdNDP analyses, despite the fact that not a single such bond can be identified from the CMOs. Orbital composition analyses for the 17 CMOs allow a quantitative understanding of how electron donation and back-donation redistribute the charges within the system from the formal Sb3(0)/Au3(3-) charge states in the zeroth order model to the effective Sb3(1.5-)/Au3(0) charge states, the latter being revealed from the natural bond orbital analysis.

Observation and characterization of the smallest borospherene, B28(-) and B28.

Free-standing boron nanocages or borospherenes have been observed recently for B40(-) and B40. There is evidence that a family of borospherenes may exist. However, the smallest borospherene is still not known. Here, we report experimental and computational evidence of a seashell-like borospherene cage for B28(-) and B28. Photoelectron spectrum of B28(-) indicated contributions from different isomers. Theoretical calculations showed that the seashell-like B28(-) borospherene is competing for the global minimum with a planar isomer and it is shown to be present in the cluster beam, contributing to the observed photoelectron spectrum. The seashell structure is found to be the global minimum for neutral B28 and the B28(-) cage represents the smallest borospherene observed to date. It is composed of two triangular close-packed B15 sheets, interconnected via the three corners by sharing two boron atoms. The B28 borospherene was found to obey the 2(n + 1)(2) electron-counting rule for spherical aromaticity.

On the structure and bonding in the B4O4(+) cluster: a boron oxide analogue of the 3,5-dehydrophenyl cation with π and σ double aromaticity.

Boron oxide clusters offer intriguing molecular models for the electron-deficient system, in which the boronyl (BO) group plays a key role and the interplay between the localized BO triple bond and the multicenter electron delocalization dominates the chemical bonding. Here we report the structural, electronic, and bonding properties of the B4O4(+) cationic cluster on the basis of unbiased Coalescence Kick global-minimum searches and first-principles electronic structural calculations at the B3LYP and single-point CCSD(T) levels. The B4O4(+) cluster is shown to possess a Cs (1, (2)A') global minimum. It represents the smallest boron oxide species with a hexagonal boroxol (B3O3) ring as the core, terminated by a boronyl group. Chemical bonding analyses reveal double (π and σ) aromaticity in Cs B4O4(+), which closely mimics that in the 3,5-dehydrophenyl cation C6H3(+) (D3h, (1)A1'), a prototypical molecule with double aromaticity. Alternative D2h (2, (2)B3g) and C2v (3, (2)A1) isomeric structures of B4O4(+) are also analyzed, which are relevant to the global minima of B4O4 neutral and B4O4(-) anion, respectively. These three structural motifs vary drastically in terms of energetics upon changing the charge state, demonstrating an interesting case in which every electron counts. The calculated ionization potentials and electron affinities of the three corresponding neutral isomers are highly uneven, which underlie the conformational changes in the B4O4(+/0/-) series. The current work presents the smallest boron oxide species with a boroxol ring, establishes an analogy between boron oxides and the 3,5-dehydrophenyl cation, and enriches the chemistry of boron oxides and boronyls.

A first-principles study on the B5O5 (+/0) and B5O5 (-) clusters: The boron oxide analogs of C6H5 (+/0) and CH3Cl.

The concept of boronyl (BO) and the BO/H isolobal analogy build an interesting structural link between boron oxide clusters and hydrocarbons. Based upon global-minimum searches and first-principles electronic structural calculations, we present here the perfectly planar C2v B5O5 (+) (1, (1)A1), C2v B5O5 (2, (2)A1), and tetrahedral Cs B5O5 (-) (3, (1)A') clusters, which are the global minima of the systems. Structural and molecular orbital analyses indicate that C2v B5O5 (+) (1) [B3O3(BO)2 (+)] and C2v B5O5 (2) [B3O3(BO)2] feature an aromatic six-membered boroxol (B3O3) ring as the core with two equivalent boronyl terminals, similar to the recently reported boronyl boroxine D3h B6O6 [B3O3(BO)3]; whereas Cs B5O5 (-) (3) [B(BO)3(OBO)(-)] is characterized with a tetrahedral B(-) center, terminated with three BO groups and one OBO unit, similar to the previously predicted boronyl methane Td B5O4 (-) [B(BO)4 (-)]. Alternatively, the 1-3 clusters can be viewed as the boron oxide analogs of phenyl cation C6H5 (+), phenyl radical C6H5, and chloromethane CH3Cl, respectively. Chemical bonding analyses also reveal a dual three-center four-electron (3c-4e) π hyperbond in Cs B5O5 (-) (3). The infrared absorption spectra of B5O5 (+) (1), B5O5 (2), and B5O5 (-) (3) and anion photoelectron spectrum of B5O5 (-) (3) are predicted to facilitate their forthcoming experimental characterizations. The present work completes the BnOn (+/0/-) series for n = 1-6 and enriches the analogous relationship between boron oxides and hydrocarbons.