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

Abstract

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.

---

1. Introduction

The electron-deficiency of boron results in unconventional geometries in its allotropes and chemical compounds.^1–13 The bare boron clusters like forming planar or quasi-planar (2D) structures over a wide range of sizes.^4–6,9–17 The D_7h B₈²⁻ and D_8h B₉⁻ clusters are intriguing, adopting the perfect molecular wheel shape with a central hepta- and octacoordinate boron atom,⁶ and get their stability from the double (6σ + 6π) aromaticity, fulfilling the 4N_σ/π + 2 Hückel rule (N_σ = N_π = 1). Numerous transition-metal centred boron molecular wheels M©B_n⁻ with the central hypercoordinate metal atom in plane were designed and characterized according to the principle of double aromaticity.^18–21 At present, the highest coordination number in the planar systems has been limited in Ta©B₁₀⁻ and Nb©B₁₀⁻.^20,22 Recently, the metal-centered monocyclic carbon wheel was theoretically investigated with record coordination number of thirteen.²³ Some main group metal centered boron molecular wheels have also been investigated theoretically.^24,25

In view of the double aromaticity of B₈²⁻ and B₉⁻ molecular wheels, Wang and coworkers have suggested a general electronic design principle (n + x + q = K) for transition-metal centered boron molecular wheels M©B_n^q−,²⁶ where n is the number of delocalized electrons supplied by the peripheral B_n ring, x is the formal valence of central metal atoms, q is the cluster's charge, and K is the total number of delocalized electrons. This electronic design principle is proved to be feasible in M©B₈⁻ (M = Co, Re and Fe) and M©B₉⁻ (M = Ru, Rh, Ir, Re and Fe) with K = 12.^17–19 The deca-coordinated Ta©B₁₀⁻ and Nb©B₁₀⁻ molecular wheels have a total delocalized electrons of K = 16, possessing 10σ and 6π double aromaticity.²¹

In the transition-metal centred boron molecular wheels, the partly filled d-orbitals of transition-metal atoms play a crucial role in describing the interaction between the central metal atom and peripheral ring. In contrast, the metal atoms without d-orbital electrons (or with full-filled d-orbital electrons) don't like to form stable molecular wheel geometries. For instance, the AlB₇⁻ and AlB₈⁻ clusters are inclined to form the umbrella-shaped geometries.²⁷ The Au atom with full-filled 5d-orbital electrons in AuB₁₀⁻ cluster like forming a covalent B–Au σ bond with the corner B atom, serving as H atom. The 5d-orbital electrons, existing in the five lone pairs, could not effectively participate in bonding with the peripheral boron ring. The Au©B₁₀⁻ molecular wheel is an extremely unstable local minimum (LM), being 1.95 eV higher in energy than the global minimum (GM) at B3LYP level.²⁸ Beyond that, the cavity of peripheral ring need match up with the volume of central metal atom in physics. The small cavity cannot accommodate a metal atom. If the cavity is too large, the B–M interaction would be weakened dramatically due to the increased B–M distances. The molecular wheels will fail in competing with the half-sandwich structures.²⁹ Therefore, it is a challenge to push the limit of coordination number in planar structures.

The present paper aims at breaking the record of deca-coordinated number in D_10h Ta©B₁₀⁻ and Nb©B₁₀⁻ molecular wheels, which is realized in the La©B₈C₄^+/0/− clusters. The title clusters have the interesting molecular wheel shapes, showing a central La atom encircled with a closed –(BCB)₄– ring. The La©B₈C₄⁺ and La©B₈C₄ species have the C_4v symmetry with an out-of-plane distortion of La atoms, whereas the La©B₈C₄⁻ is perfectly plane. Thus, sequential reduction reaction in the La©B₈C₄^q (q = +1, 0, −1) results in the structural planarization. The chemical bonding analyses suggest that La©B₈C₄ and La©B₈C₄⁻ molecular wheels have 10σ and 9π/10π delocalized electrons, respectively, faithfully fulfilling the general double aromaticity rule. Whereas, the La©B₈C₄⁺ cluster is a counterexample in planar molecular wheels. It possesses 10σ and 8π delocalized electrons, being the first hypercoordinate molecular wheel with conflicting aromaticity.

2. Theoretical methods

We searched the GM structures for cationic and anionic La©B₈C₄^+/− clusters using the Coalescence Kick (CK) algorithm^30,31 at B3LYP/LanL2DZ level, as well as the manual structural constructions. More than 3000 stationary points for each species were probed on their potential energy surfaces. The low-lying isomers (ΔE < 60 kcal mol⁻¹) of La©B₈C₄^+/− and their corresponding neutral structures were reoptimized using B3LYP functional in Gaussian 09 package.³² The Stuttgart ECP28MWB_ANO basis set with the corresponding energy-consistent relativistic pseudopotential ECP28MWB was used for La, and 6-311+G* basis set for boron and carbon.³³ This basis set combination is reasonable for current system according to the literature on transition-metal doped boron clusters.³⁴ The vibrational frequencies were calculated at the same level to verify that the isomers presented are true minima. The relative energies of the top five lowest-lying isomers of La©B₈C₄^+/0/− were further refined at the single-point CCSD(T) level using the same basis set combination of B3LYP level.³⁵ The top isomers of La©B₈C₄^q (q = +1, 0, −1) clusters are independently checked at the PBE0 level as well.

All electronic property calculations were performed at the same theory level with structural optimizations. The Wiberg bond indices (WBIs) and natural atomic charges of La©B₈C₄^q (q = +1, 0, −1) clusters were calculated using the NBO 6.0 program.³⁶ The chemical bonding was elucidated using the canonical molecular orbital (CMO) analyses, the electron localization functions (ELFs)^37,38 and adaptive natural density partitioning (AdNDP).³⁹ Since the neutral La©B₈C₄ is an open-shell system, the AdNDP analysis is performed using the unrestricted AdNDP (UAdNDP) version. The anisotropy of current-induced density (ACID) analyses was carried out using ACID code.⁴⁰ The ring-current images were visualized using the POV-Ray 3.7.⁴¹ and the ELFs and AdNDP data were visualized using Molekel 5.4.0.8.⁴²

3. Results and discussion

3.1. The geometries and energies of La©B₈C₄^q (q = +1, 0, −1)

The alternative low-lying isomers (sixty-seven structures) of cationic La©B₈C₄⁺ cluster are shown in Fig. S1 (ESI†). The GM structure, as shown in Fig. 1 and S1,† adopts an interesting molecular wheel style with a symmetry of C_4v (¹A₁), showing a dodeca-coordinated La atom surrounded by a fascinating –(BCB)₄– ring. The central La atom has a little bulge with respect to the peripheral B₈C₄ ring. Its Cartesian coordinates are given in Table S1 (ESI†). The closest competitor has a symmetry of C_s (¹A′), being 0.23 and 0.34 eV higher in energy than GM at single-point CCSD(T) and B3LYP levels, respectively, whose centered La atom is nona-coordinated with the B₅C₄ ring. The third and fourth isomers also adopt the molecular wheel structures, albeit with an inferior arrangement of B₈C₄ ring, which are at least 0.50 eV higher than GM at both levels. In particularly, the fifth isomer (C_4v, ³A₁) with a triplet ground state, possessing the same geometry with the GM, is 0.89 and 0.70 eV higher than GM at the CCSD(T) and B3LYP levels, respectively. Thus, the GM is clearly defined on its potential energy surface at the B3LYP and CCSD(T) levels.

Fig. 1 Optimized geometry for C_4v (¹A₁) global-minimum (GM) of La©B₈C₄⁺, C_4v (²B₁) GM) of La©B₈C₄ and D_4h (¹A_1g) local-minimum (LM) of La©B₈C₄⁻ clusters at the B3LYP level. The bond distances are shown in Å.

The GM and low-lying isomers of neutral La©B₈C₄ cluster are presented in Fig. 1 and S2 (ESI†). All of them possess fascinating molecular wheel geometries. The GM (C_4v, ²B₁) of neutral La©B₈C₄ cluster adopts the similar architecture with cationic species, whose nearest competitor has a C_s (²A′) symmetry, being 0.19 and 0.18 eV higher in energy at the CCSD(T) and B3LYP levels.

As for anionic La©B₈C₄⁻ cluster, the potential energy surface appears to be more complicated. There are four isomeric geometries within 0.10 eV at the CCSD(T) and B3LYP levels (Fig. S3, ESI†), and the calculated energies are highly consistent at both levels. The GM structure of La©B₈C₄⁻ cluster adopts a C_s symmetry with the ¹A′ electronic state, which is identical with that of the closest competitor of neutral La©B₈C₄ and the fourth isomer of cationic La©B₈C₄⁺. The perfectly planar D_4h (¹A_1g) isomer (Fig. 1) of La©B₈C₄⁻ cluster turns out to be a LM, which is only 0.04 eV higher in energy than GM at both CCSD(T) and B3LYP levels. We mainly focus on the perfect LM structure in this paper. The T₁ diagnostic factors of CCSD(T) for three perfect molecular wheels are 0.022, 0.026 and 0.018, respectively, indicating the reliable CCSD(T) data.

3.2. The bond distances, Wiberg bond indices and natural atomic charges

The bond distances for GM (C_4v, ¹A₁) of La©B₈C₄⁺ cluster are shown in Fig. 1. The GM has the equivalent B–B (1.57 Å) and B–C (1.38 Å) bond distances. The B–B bonds are distinctly shorter than the standard B–B single bond (1.70 Å),⁴³ and being comparable with the B=B double bond (1.56 Å). The B–C bonds are even shorter than the B=C double bond (1.45 Å), being close to the B≡C triple bond (1.33 Å). The B–La and C–La bond distances are 2.91 and 2.84 Å, respectively. The central La atom is 0.70 Å out of B₈C₄ ring (not shown).

The GM (C_4v, ²B₁) of neutral La©B₈C₄ and LM (D_4h, ¹A_1g) of La©B₈C₄⁻ are almost identical with the GM of La©B₈C₄⁺ species. The B–B and B–C bond distances of La©B₈C₄ are 1.56 and 1.39 Å, and those of La©B₈C₄⁻ are 1.55 and 1.40 Å, respectively, showing slight decrease for B–B bonds and increase for B–C bonds (within 0.01–0.02 Å) compared to La©B₈C₄⁺. Overall, the peripheral B₈C₄ ring enlarges by 0.04 Å for La©B₈C₄ and 0.08 Å for La©B₈C₄⁻ clusters compared with that of La©B₈C₄⁺ cluster. By contrast, the B–La and C–La bond distances shrink markedly (0.05–0.10 Å for the B–La bonds and 0.05–0.07 Å for C–La bonds). The B–La and C–La bond distances in La©B₈C₄ are 2.86 and 2.79 Å, and those in La©B₈C₄⁻ are 2.81 and 2.77 Å. The expansion of B₈C₄ ring and reduction of B–La/C–La links planarize the La©B₈C₄ and La©B₈C₄⁻ clusters. The out-of-plane distortion of central La reduces to 0.46 Å for La©B₈C₄. The La©B₈C₄⁻ turns into a perfectly planar structure.

The above bond distances are rationalized by the calculated WBIs (Fig. S4, ESI†) and natural charge (Fig. S5, ESI†) data from NBO analyses at the B3LYP level. In GM of La©B₈C₄⁺ cluster, the B–B and B–C bonds have the WBIs of 1.19 and 1.62, being distinctly greater than 1.0 (the latter in particular), implying that B₈C₄ ring is controlled by the delocalized σ/π bonds beyond the Lewis B–B/B–C two-center two-electrons (2c–2e) σ single bond. The covalent interaction of B–C bonds are markedly stronger than that of B–B ones, hinting that the delocalized electrons are mainly located at the B–C bonds of peripheral ring. Whereas, the covalent interaction between the central La and peripheral B₈C₄ ring is somewhat weak, with the small WBIs of 0.18 for B–La and 0.23 for C–La links. The WBIs of B–C, B–La and C–La bonds in neutral La©B₈C₄ and anion La©B₈C₄⁻ are consistent with those in La©B₈C₄⁺ cluster (within 0.01). The variations of WBIs among three structures are mainly occurred in B–B bonds, showing a gradual increase by 0.08. It implies that the extra one electron in La©B₈C₄ and two electrons in La©B₈C₄⁻ clusters are primarily dispersed on B–B bonds of B₈C₄ rings (see Section 3.4). Moreover, the total WBIs of centered La atom in La©B₈C₄^+/0/− clusters are 2.34, 2.41 and 2.45, respectively, indicating a negligible increase.

As for the natural charges (Fig. S5, ESI†), in La©B₈C₄⁺ cluster, the C atom carries a plentiful negative charge of −0.92 |e|, whereas the B atom is positively charged by +0.38 |e|, meaning the natural charges are markedly localized at C sites. Overall, the B₈C₄ ring has a collective negative charge of −0.64 |e|. It should be noted that the charge distribution on B₈C₄ ring is in line with their distinct electronegativity of B (2.04) and C (2.55) elements. The central La atom possesses a positive charge of +1.67 |e| with the electronic configuration of [Xe]6s^0.054f^0.105d^1.166p^0.015f^0.016d^0.02, indicating an obvious charge transfer from the La atom to B₈C₄ ring, hinting a robust electrostatic attraction among them. The interaction between the central La and B₈C₄ ring is governed by both electrostatics and covalent interaction. In neutral La©B₈C₄ and anion La©B₈C₄⁻ clusters, the La atoms almost maintain the same positive charge with that in La©B₈C₄⁺. In contrast, the total charges of B₈C₄ rings increase to −1.64 |e| of La©B₈C₄ and −2.64 |e| of La©B₈C₄⁻. Specifically, the carrying charge of C atoms slightly decreases to −0.89 |e| of La©B₈C₄ and −0.86 |e| of La©B₈C₄⁻, and that of B atoms distinctly increases to +0.24 |e| and +0.10 |e|, which are corresponding with the bond distances and WBIs data of B–B/B–C bonds.

3.3. The stabilities of La©B₈C₄^+/0/− along with out-of-plane distortion of La atom

The B₈C₄ rings of La©B₈C₄⁺ and La©B₈C₄ are slightly small, cannot accommodate the large La atom, leading to a tiny hump of central La atom. In order to quantitatively evaluate the relative stabilities of La©B₈C₄^+/0/− molecular wheels with different La height relative to the B₈C₄ rings, we performed the potential energy scanning as the La atoms move along with their C₄ axes, prescribed by the La⋯B₈C₄ angle θ, as shown in Fig. 2. The perfect D_4h structure of La©B₈C₄⁺ is a one-order saddle point with the imaginary frequency of 73.93i cm⁻¹, which is 0.17 eV above the C_4v GM La©B₈C₄⁺. In essence, the D_4h structure is the transition state (TS) structure for the La atom traversing the B₈C₄ ring. The C_4v GM of La©B₈C₄⁺ has the θ value of ±14.19°, being corresponding to a La height of 0.70 Å above the center of B₈C₄ ring. The potential energy curve of La©B₈C₄ is flatter than that of La©B₈C₄⁺, whose D_4h structure (with a small imaginary frequency of 49.82i cm⁻¹) is only 0.03 eV higher in energy than C_4v GM of La©B₈C₄, which is attribute to its enlarged B₈C₄ ring and reduced B–La/C–La bond distances. The potential energy curve of La©B₈C₄⁻ indicates that the D_4h structure is the true minimum.

Fig. 2 The potential energy curves of C_4v (¹A₁) GM La©B₈C₄, C_4v (²B₁) GM La©B₈C₄, and D_4h (¹A_1g) LM La©B₈C₄⁻ clusters along with the out-of-plane distortion central La atom.

3.4. Chemical bonding

In view of the similar molecular wheel structures of La©B₈C₄^+/0/− clusters, the chemical bonding analyses are mainly focused on the close-shelled La©B₈C₄⁺ and La©B₈C₄⁻ species. The La©B₈C₄⁺ cluster has 42 valence electrons, occupying 21 valence CMOs (Fig. S6, ESI†). These occupied CMOs are divided into three subsets based on their constituent atomic orbitals (AOs). The twelve CMOs in subset (a) are primarily composed of 2s and tangential 2p AOs of B/C, which can be reasonably localized into eight 2c–2e B–C and four 2c–2e B–B Lewis σ bonds in B₈C₄ ring. The five delocalized σ CMOs in subset (b) are composed of the radial 2p AOs of B/C and 5d AOs of La (d_x²−y² in HOMO and d_xy in HOMO-2). It should be noted that the HOMO and HOMO-2 σ CMOs are formally degenerated. These five CMOs constitute the delocalized σ framework, resulting in the 10σ aromaticity of La©B₈C₄⁺, according to (4N_σ + 2) Hückel rule (N_σ = 2). There are four delocalized π CMOs in subset (c), being composed of the vertical 2p AOs of B/C and 5d AOs of La (d_xz in HOMO-4 and d_yz in HOMO-4′), constructing the π framework of La©B₈C₄⁺, and leading to its 8π antiaromaticity in view of (4N_π) Hückel rule (N_π = 2). Overall, La©B₈C₄⁺ molecular wheel is a system of 10σ and 8π conflicting aromaticity. Following Boldyrev, the term conflicting aromaticity refers to the systems with simultaneous presence of aromaticity and antiaromaticity in orthogonal planes, there is aromaticity in one plane and anti-aromaticity in the plane orthogonal to it.^14,44 In nature, the four delocalized π CMOs can be appropriately recombined four three-center two-electrons (3c–2e) –BCB– island π bonds (see the ELFs and AdNDP analyses), being in line with its C_4v symmetry.

The La©B₈C₄⁻ cluster is a system with 44 valence electrons, occupying 22 CMOs (Fig. S7, ESI†). It has one more full-filled π CMO (HOMO) than La©B₈C₄⁺. The five delocalized π CMOs in subset (c) are one-to-one corresponding with the σ CMOs in subset (b), following the same spatial distribution. Thus, La©B₈C₄⁻ cluster is double aromatic with 10σ and 10π delocalized electrons. The σ CMOs (HOMO-1/HOMO-4) and π CMOs (HOMO/HOMO-2) also are formally degenerated, being similar to the σ CMOs (HOMO/HOMO-2) of La©B₈C₄⁺ in Fig. S6(b) (ESI†). The energy gap between the HOMO and HOMO-2 is 1.83 eV, which hints the out-of-plane distortion of central La atom in neutral La©B₈C₄ and cationic La©B₈C₄⁺ molecular wheels is not due to the Jahn–Teller effect. The electron density of HOMO is mainly dispersed on four B–B bonds, which leads to decrease of bond distances by 0.02 Å (Fig. 1) and increase of WBIs by 0.16 compared with those in La©B₈C₄⁺ wheel (Fig. S4, ESI†).

The CMOs bonding pattern of La©B₈C₄ cluster (Fig. S8, ESI†) is similar to that of La©B₈C₄⁻ cluster, albeit possessing a single occupied π molecular orbital (that is the SOMO). Thus, La©B₈C₄ molecular wheel is dominated by 10σ and 9π double aromaticity. The delocalized π frameworks in La©B₈C₄^+/0/− clusters are compared with the D_4h B₈C₄⁴⁻ ring and planar aromatic D_10h C₁₀H₁₀ (annulene) model molecule (see Fig. 3). Note that the D_4h B₈C₄⁴⁻ ring and D_10h C₁₀H₁₀ are not the true minimums.⁴⁵ The delocalized π CMOs in La©B₈C₄ and La©B₈C₄⁻ clusters are one to one corresponding to those in D_4h B₈C₄⁴⁻ ring and D_10h C₁₀H₁₀ model. Importantly, the SOMO in La©B₈C₄ and HOMO in La©B₈C₄⁻ facilitate the π electron delocalization on B₈C₄ ring and enhance the interaction of B–La links, which would obviously shorten the B–La bond distances, and make the molecular wheels planarization.

Fig. 3 Comparison of the delocalized canonical molecular orbitals (CMOs) between (a) C_4v (¹A₁) GM La©B₈C₄, (b) C_4v (²B₁) GM La©B₈C₄, (c) D_4h (¹A_1g) LM La©B₈C₄⁻ clusters, (d) D_4h (¹A_1g) B₈C₄⁴⁻ and (e) D_10h C₁₀H₁₀ (annulene) model molecule.

It should be pointed out that the coordination interaction between the La atom and B₈C₄ ring is mainly attributed to the d–p (La 5d_x²−y²/5d_xy AOs and B/C radial 2p AOs) σ CMOs (HOMO/HOMO-2 in La©B₈C₄⁺ and HOMO-1/HOMO-4 in La©B₈C₄⁻) and d–p (La 5d_xz/5d_yz AOs and B/C vertical 2p AOs) π CMOs (HOMO-4/4′ in La©B₈C₄⁺ and HOMO-5/5′ in La©B₈C₄⁻). The coordination interactions of d–p σ CMOs with the relatively large orbital component of La 5d AOs are a little bit stronger than those of d–p π CMOs. Quantitively, the HOMO and HOMO-2 in La©B₈C₄⁺ (Fig. S6, ESI†) have a 19.89% La 5d_x²−y² and 10.39% La 5d_xy AOs contribution, respectively. In La©B₈C₄⁻, the La 5d_x²−y² AO contributes by 14.58% to HOMO-1, and La 5d_xy AO contributes by 8.42% to HOMO-4 (Fig. S7, ESI†). For the d–p π CMOs, the La 5d_xz/5d_yz AOs contributes merely by 6.72% in HOMO-4/4′ of La©B₈C₄⁺, and 8.11% in HOMO-5/5′ of La©B₈C₄⁻.

The CMOs bonding images of La©B₈C₄^+/− molecular wheels are faithfully confirmed by the ELFs analyses. As shown in Fig. 4, the ELF_σ patterns of La©B₈C₄⁺ and La©B₈C₄⁻ clusters are almost identical, showing twelve localized 2c–2e B–B/B–C σ bonds (left panels) and strong global delocalized σ electron density (middle panels). Obviously, two molecular wheels mainly differ in ELF_π patterns. The π electron density of La©B₈C₄⁺ is clearly segmented into four –BCB– islands (right panels), but that of La©B₈C₄⁻ is continuous, and being smoothly distributed on the whole B₈C₄ ring, which firmly supports the above assessments of 8π antiaromaticity for La©B₈C₄⁺ and 10π aromaticity for La©B₈C₄⁻.

Fig. 4 Electron localization functions (ELFs) for (a) the C_4v (¹A₁) GM of La©B₈C₄⁺ and (b) the D_4h (¹A_1g) LM of La©B₈C₄⁻ clusters.

The chemical bonding patterns in both La©B₈C₄^+/− molecular wheels are accurately elucidated by the AdNDP analyses. The AdNDP results for La©B₈C₄⁺ (Fig. 5) reveal eight localized 2c–2e B–C σ bonds and four localized 2c–2e B–B σ bonds in peripheral B₈C₄ ring, which are related to the CMOs in Fig. S6(a) (ESI†). There are four 3c–2e –BCB– island σ bonds and one thirteen-center two-electrons (13c–2e) σ bond in B₈C₄ ring, supporting its 10σ aromaticity. Meanwhile, the four 3c–2e –BCB– island π bonds are in line with 8π antiaromaticity. The island version for four 3c–2e σ and π bonds are fully supported by the ELFs analyses. The AdNDP results for La©B₈C₄⁻ (Fig. 6) show the identically localized B–B/B–C σ bonds and delocalized σ framework on B₈C₄ ring with La©B₈C₄⁺. Differently, it has one more fully delocalized 13c–2e π bond except for four 3c–2e –BCB– island π bonds, firmly confirmed its 10π aromaticity. It should be noted that the occupation numbers (ON) of the 3c–2e –BCB– σ and π bonds in both La©B₈C₄⁺ and La©B₈C₄⁻ clusters (1.88/1.87 versus 1.85) are less than 2, hinting a small degree of covalent interaction between the B₈C₄ ring and the central La atom, which is consistent with the small WBIs of B–La/C–La links. The AdNDP data of La©B₈C₄ cluster (obtained from UAdNDP version) are indicated in Fig. S9 (ESI†), showing one global delocalized 13c–1e π bond. In addition, the AdNDP chemical bonding images (four 3c–2e island σ/π bonds plus one 13c–2e delocalized σ/π bond) of La©B₈C₄^+/− molecular wheels are reasonable, which is in line with the structural data, and rationalizes the delocalized σ and π frameworks as well.

Fig. 5 Chemical bonding pattern of the C_4v (¹A₁) GM La©B₈C₄⁺ cluster based on the adaptive natural density partitioning (AdNDP) analysis. Occupation numbers (ONs) are indicated.

Fig. 6 Chemical bonding pattern of the D_4h (¹A_1g) LM La©B₈C₄⁻ cluster based on the AdNDP analysis. The ONs are indicated.

The anisotropy of current-induced density (ACID) analyses was performed to probe the ring currents of La©B₈C₄⁺ and La©B₈C₄⁻ clusters, induced by an external magnetic field being vertical to molecular wheels. The decomposed σ and π-ring current images with a high-resolution are depicted in Fig. S10 (ESI†). The La©B₈C₄⁺ molecular wheel shows the robust σ-ring current (Fig. S10(a)†) on whole B₈C₄ peripheral ring. In contrast, its π-ring current is clearly localized on four –BCB– units, showing local circulation for vector of induced current density. The direction of π-ring current is opposite to that of σ-ring currents, supporting the 10σ and 8π conflicting aromaticity. The La©B₈C₄⁻ molecular wheel shows the robust σ and π-ring current (Fig. S10(b)†), perfectly elucidating the 10σ and 10π double aromaticity.

The thermal stabilization for La©B₈C₄^+/0/− molecular wheels is mainly attributed to the cyclic electron delocalization in peripheral B₈C₄ ring, albeit the La©B₈C₄⁺ cluster possesses 8π antiaromaticity. Furthermore, we calculated the bond dissociation energy (BDE) and inherent interaction energy of La©B₈C₄ between the central La atom and B₈C₄ motif according to the below formulas.

La©B₈C₄ (C_4v, ²B₁) = B₈C₄ (LM, D_4h, ¹A_1g) + La

La©B₈C₄ (C_4v, ²B₁) = B₈C₄ (frozen, D_4h, ¹A_1g) + La

where, the B₈C₄ (LM, D_4h, ¹A_1g) has a square geometry, a true local minimum on its potential surface. Rather, the B₈C₄ (frozen, D_4h, ¹A_1g) represents the frozen fragment form La©B₈C₄ molecular wheel, which is a second-order saddle point. The B₈C₄ (LM, D_4h, ¹A_1g) and B₈C₄ (frozen, D_4h, ¹A_1g) are calculated at B3LYP/6-311+G* level, the La atom is done at B3LYP/ECP28MWB_ANO level, respectively. The BDE and inherent interaction energies are as high as −178.99 and −208.59 kcal mol⁻¹, respectively, confirming the stabilization of dodeca-coordinated La©B₈C₄ molecular wheel. The energy difference between the BDE and inherent interaction energy describes the isomerization energy of B₈C₄ motif from the square geometry to a circular one in nature (Fig. S11, ESI†).

3.5. The electronic counting rule in La©B₈C₄^q molecular wheels

The fascinating transition-metal centered boron molecular wheels M©B_n^q− is controlled by the double (σ and π) aromaticity, following the electronic design principle (n + x + q = K) proposed by Wang and coworkers.²⁶ In intriguing La©B₈C₄^+/0/− boron–carbon molecular wheels, each C atom can provide two delocalized electrons, one more than B atom. Thus, an update version of electronic design principle for M©B_mC_n^q− molecular wheels is proposed, that is m + 2n + x ± q = K, where the m and n is the number of peripheral B and C atoms, x is the formal valence of central metal atoms, q is the cluster's charge. The La©B₈C₄^+/0/− molecular wheels are unprecedent with the highest dodeca-coordination number in plane, following m + 2n + x ± q = 18, 19 and 20 electronic counting principles, respectively. The anionic La©B₈C₄⁻ molecular wheel has (10σ + 10π) double aromaticity, following (4N_σ/π + 2) Hückel rule with N_σ = N_π = 2, respectively. The neutral La©B₈C₄ molecular wheel is an open-shell system with a single occupied π orbital, possessing the 10σ and 9π double aromaticity. Interestingly, the cationic La©B₈C₄⁺ cluster is a conflicting aromatic system of with 10σ and 8π delocalized electrons (K = 18), obeying the (4N_σ + 2) and (4N_π) Hückel rule with N_σ = N_π = 2, respectively. Thus, La©B₈C₄⁺ represents a counterexample for double aromaticity in planar hypercoordinate molecular wheels.

4. Conclusions

In summary, we have theoretically predicated three dodeca-coordinated La©B₈C₄^+/0/− molecular wheels, featuring a central La atom enclosed by a perfectly planar B₈C₄ ring, which is viable in the –(BCB)₄– form. The La©B₈C₄⁺ and La©B₈C₄ molecular wheels have the C_4v symmetry with a slightly out-of-plane distortion of La atom. The La©B₈C₄⁻ molecular wheel is perfectly planar. The stabilizations of La©B₈C₄^+/0/− molecular wheels are benefit from their unique chemical bonding. The La©B₈C₄ and La©B₈C₄⁻ molecular wheels have 10σ and 9π/10π delocalized electrons, obeying the universal principle of double aromaticity, whereas, the La©B₈C₄⁺ molecular wheel is a counterexample, which has the conflicting aromaticity with 10σ and 8π delocalized electrons. The La©B₈C₄^+/0/− molecular wheels with dodeca-coordination number are unprecedented for a planar system in coordination chemistry.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the Natural Science Foundation of Shanxi Province (2018103), and the Innovation and Entrepreneurship Training Program for College students of Shanxi Province (20220931).

References

1. W. N. Lipscomb, Science, 1977, 96, 1047.
2. J. Barroso, D. Pan and G. Merino, Chem. Soc. Rev., 2022, 51, 1098.
3. Q. Q. Yan, T. Zhang, Y. Y. Ma, Q. Chen, Y. W. Mu and S. D. Li, Nanoscale, 2022, 14, 11443.
4. J. E. Fowler and J. M. Ugalde, J. Phys. Chem. A, 2000, 104, 397.
5. H. J. Zhai, B. Kiran, J. Li and L. S. Wang, Nat. Mater., 2003, 2, 827.
6. H. J. Zhai, A. N. Alexandrova, K. A. Birch, A. I. Boldyrev and L. S. Wang, Angew. Chem., Int. Ed., 2003, 42, 6004.
7. B. Kiran, S. Bulusu, H. J. Zhai, S. Yoo, X. C. Zeng and L. S. Wang, Proc. Natl. Acad. Sci. U. S. A., 2005, 102, 961.
8. E. Oger, N. R. M. Crawford, R. Kelting, P. Weis, M. M. Kappes and R. Ahlrichs, Angew. Chem., Int. Ed., 2007, 46, 8503.
9. W. Huang, A. P. Sergeeva, H. J. Zhai, B. B. Averkiev, L. S. Wang and A. I. Boldyrev, Nat. Chem., 2010, 2, 202.
10. H. J. Zhai, Y. F. Zhao, W. L. Li, Q. Chen, H. Bai, H. S. Hu, Z. A. Piazza, W. J. Tian, H. G. Lu, Y. B. Wu, Y. W. Mu, G. F. Wei, Z. P. Liu, J. Li, S. D. Li and L. S. Wang, Nat. Chem., 2014, 6, 727.
11. Z. A. Piazza, H. S. Hu, W. L. Li, Y. F. Zhao, J. Li and L. S. Wang, Nat. Commun., 2014, 5, 3113.
12. Y. J. Wang, Y. F. Zhao, W. L. Li, T. Jian, Q. Chen, X. R. You, T. Ou, X. Y. Zhao, H. J. Zhai, S. D. Li, J. Li and L. S. Wang, J. Chem. Phys., 2016, 144, 064307.
13. S. Pan, J. Barroso, S. Jalife, T. Heine, K. R. Asmis and G. Merino, Acc. Chem. Res., 2019, 52, 2732.
14. A. N. Alexandrova, A. I. Boldyrev, H. J. Zhai and L. S. Wang, Coord. Chem. Rev., 2006, 250, 2811.
15. A. P. Sergeeva, D. Y. Zubarev, H. J. Zhai, A. I. Boldyrev and L. S. Wang, J. Am. Chem. Soc., 2008, 130, 7244.
16. A. P. Sergeeva, Z. A. Piazza, C. Romanescu, W. L. Li, A. I. Boldyrev and L. S. Wang, J. Am. Chem. Soc., 2012, 134, 18065.
17. A. P. Sergeeva, I. A. Popov, Z. A. Piazza, W. L. Li, C. Romanescu, L. S. Wang and A. I. Boldyrev, Acc. Chem. Res., 2014, 47, 1349.
18. C. Romanescu, T. R. Galeev, W. L. Li, A. I. Boldyrev and L. S. Wang, Angew. Chem., Int. Ed., 2011, 50, 9334.
19. W. L. Li, C. Romanescu, T. R. Galeev, Z. A. Piazza, A. I. Boldyrev and L. S. Wang, J. Am. Chem. Soc., 2012, 134, 165.
20. C. Romanescu, T. R. Galeev, A. P. Sergeeva, W. L. Li, L. S. Wang and A. I. Boldyrev, J. Organomet. Chem., 2012, 721–722, 148.
21. T. R. Galeev, C. Romanescu, W. L. Li, L. S. Wang and A. I. Boldyrev, Angew. Chem., Int. Ed., 2012, 51, 2101.
22. T. Heine and G. Merino, Angew. Chem., Int. Ed., 2012, 51, 4275.
23. X. Q. Lu, H. G. Lu and S. D. Li, RSC Adv., 2021, 11, 27193.
24. J. C. Guo, W. Z. Yao, Z. Li and S. D. Li, Sci. China, Ser. B: Chem., 2009, 52, 566.
25. R. Islas, T. Heine, K. Ito, P. v. R. Schleyer and G. Merino, J. Am. Chem. Soc., 2007, 129, 14767.
26. C. Romanescu, T. R. Galeev, W. L. Li, A. I. Boldyrev and L. S. Wang, Acc. Chem. Res., 2013, 46, 350.
27. T. R. Galeev, C. Romanescu, W. L. Li, L. S. Wang and A. I. Boldyrev, J. Chem. Phys., 2011, 135, 104301.
28. H. J. Zhai, C. Q. Miao, S. D. Li and L. S. Wang, J. Phys. Chem. A, 2010, 114, 12155.
29. I. A. Popov, W. L. Li, Z. A. Piazza, A. I. Boldyrev and L. S. Wang, J. Phys. Chem. A, 2014, 118, 8098.
30. M. Saunders, J. Comput. Chem., 2004, 25, 621.
31. P. P. Bera, K. W. Sattelmeyer, M. Saunders, H. F. Schaefer III and P. v. R. Schleyer, J. Phys. Chem. A, 2006, 110, 4287.
32. M. J. Frisch, et al., Gaussian 09, revision D.01, Gaussian Inc., Wallingford, Connecticut, 2009.
33. C. Adamo and V. Barone, J. Chem. Phys., 1999, 110, 6158.
34. Z. Y. Jiang, T. T. Chen, W. J. Chen, W. L. Li, J. Li and L. S. Wang, J. Phys. Chem. A, 2021, 125, 2622.
35. R. J. Bartlett and M. Musial, Rev. Mod. Phys., 2007, 79, 291.
36. E. D. Glendening, C. Landis and F. Weinhold, NBO 6.0, Theoretical Chemistry Institute, University of Wisconsin, Madison, 2013.
37. B. Silvi and A. Savin, Nature, 1994, 371, 683.
38. T. Lu and F. W. Chen, J. Comput. Chem., 2012, 33, 580.
39. D. Y. Zubarev and A. I. Boldyrev, Phys. Chem. Chem. Phys., 2008, 10, 5207.
40. D. Geuenich, K. Hess, F. Kohler and R. Herges, Chem. Rev., 2005, 105, 3758.
41. Povray, Persistence of vision raytracer, POV-Ray 3.7, 2013, https://www.povray.org.
42. U. Varetto, Molekel 5.4.0.8, Swiss National Supercomputing Center, Manno, Switzerland, 2009.
43. P. Pyykkö, J. Phys. Chem. A, 2015, 119, 2326.
44. A. I. Boldyrev and L. S. Wang, Chem. Rev., 2005, 105, 3716.
45. S. Masamune, K. Hojo, K. H. G. Bigam and D. L. Rabenstein, J. Am. Chem. Soc., 1971, 93, 4966.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d2ra07155j

---