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

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 D10h Ta©B10− and Nb©B10− molecular wheels. Here, we report a theoretical study of La©B8C4q (q = +1, 0, −1) clusters with the dodeca-coordinated La atom. The La©B8C4q clusters adopt fascinating molecular wheel structures, showing a La atom enclosed by a perfect B8C4 monocyclic ring. The cationic La©B8C4+ cluster has a C4v 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©B8C4q (q = +1, 0, −1) clusters is unprecedented, which provides a new idea and concept for searching planar hyper-coordinated systems.


Introduction
The electron-deciency of boron results in unconventional geometries in its allotropes and chemical compounds. [1][2][3][4][5][6][7][8][9][10][11][12][13] The bare boron clusters like forming planar or quasi-planar (2D) structures over a wide range of sizes. [4][5][6][9][10][11][12][13][14][15][16][17] The D 7h B 8 2− and D 8h B 9 − 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 (6s + 6p) aromaticity, fullling the 4N s/p + 2 Hückel rule (N s = N p = 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][19][20][21] At present, the highest coordination number in the planar systems has been limited in Ta©B 10 − and Nb©B 10 − . 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 B 8 2− and B 9 − 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©B 8 − (M = Co, Re and Fe) and M©B 9 − (M = Ru, Rh, Ir, Re and Fe) with K = 12. [17][18][19] The deca-coordinated Ta©B 10 − and Nb©B 10 − molecular wheels have a total delocalized electrons of K = 16, possessing 10s and 6p double aromaticity. 21 In the transition-metal centred boron molecular wheels, the partly lled 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-lled d-orbital electrons) don't like to form stable molecular wheel geometries. For instance, the AlB 7 − and AlB 8 − clusters are inclined to form the umbrellashaped geometries. 27 The Au atom with full-lled 5d-orbital electrons in AuB 10 − cluster like forming a covalent B-Au s bond with the corner B atom, serving as H atom. The 5d-orbital electrons, existing in the ve lone pairs, could not effectively participate in bonding with the peripheral boron ring. The Au©B 10 − 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 decacoordinated number in D 10h Ta©B 10 − and Nb©B 10 − molecular wheels, which is realized in the La©B 8

Theoretical methods
We searched the GM structures for cationic and anionic La©B 8 C 4 +/− 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 (DE < 60 kcal mol −1 ) of La©B 8 C 4 +/− and their corresponding neutral structures were reoptimized using B3LYP functional in Gaussian 09 package. 32 The Stuttgart ECP28MWB_ANO basis set with the corresponding energyconsistent 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 ve lowest-lying isomers of La©B 8 C 4 were further rened at the single-point CCSD(T) level using the same basis set combination of B3LYP level. 35 The top isomers of La©B 8 C 4 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©B 8 C 4 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©B 8 C 4 is an openshell system, the AdNDP analysis is performed using the unrestricted AdNDP (UAdNDP) version. The anisotropy of currentinduced 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

Results and discussion
3.1. The geometries and energies of La©B 8 C 4 q (q = +1, 0, −1) The alternative low-lying isomers (sixty-seven structures) of cationic La©B 8 C 4 + 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 ( 1 A 1 ), showing a dodeca-coordinated La atom surrounded by a fascinating -(BCB) 4ring. The central La atom has a little bulge with respect to the peripheral B 8 C 4 ring. Its Cartesian coordinates are given in Table S1 (ESI †). The closest competitor has a symmetry of C s ( 1 A ′ ), being 0.23 and 0.34 eV higher in energy than GM at singlepoint CCSD(T) and B3LYP levels, respectively, whose centered La atom is nona-coordinated with the B 5 C 4 ring. The third and fourth isomers also adopt the molecular wheel structures, albeit with an inferior arrangement of B 8 C 4 ring, which are at least 0.50 eV higher than GM at both levels. In particularly, the h isomer (C 4v , 3 A 1 ) 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 dened on its potential energy surface at the B3LYP and CCSD(T) levels. The GM and low-lying isomers of neutral La©B 8 C 4 cluster are presented in Fig. 1 and S2 (ESI †). All of them possess fascinating molecular wheel geometries. The GM (C 4v , 2 B 1 ) of neutral La©B 8 C 4 cluster adopts the similar architecture with cationic species, whose nearest competitor has a C s ( 2 A ′ ) symmetry, being 0.19 and 0.18 eV higher in energy at the CCSD(T) and B3LYP levels.
As for anionic La©B 8 C 4 − 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©B 8 C 4 − cluster adopts a C s symmetry with the 1 A ′ electronic state, which is identical with that of the closest competitor of neutral La©B 8 C 4 and the fourth isomer of cationic La©B 8 C 4 + . The perfectly planar D 4h ( 1 A 1g ) isomer ( Fig. 1) of La©B 8 C 4 − 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 T 1 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.

The bond distances, Wiberg bond indices and natural atomic charges
The bond distances for GM (C 4v , 1 A 1 ) of La©B 8 C 4 + cluster are shown in Fig. 1  La height relative to the B 8 C 4 rings, we performed the potential energy scanning as the La atoms move along with their C 4 axes, prescribed by the La/B 8 C 4 angle q, as shown in Fig. 2. The perfect D 4h structure of La©B 8 C 4 + 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©B 8 C 4 + . In essence, the D 4h structure is the transition state (TS) structure for the La atom traversing the B 8 C 4 ring. The C 4v GM of La©B 8 C 4 + has the q value of ±14.19°, being corresponding to a La height of 0.70 Å above the center of B 8 C 4 ring. The potential energy curve of La©B 8 C 4 is atter than that of La©B 8 C 4 + , 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©B 8 C 4 , which is attribute to its enlarged B 8 C 4 ring and reduced B-La/C-La bond distances. The potential energy curve of La©B 8 C 4 − indicates that the D 4h structure is the true minimum.

Chemical bonding
In leading to its 8p antiaromaticity in view of (4N p ) Hückel rule (N p = 2). Overall, La©B 8 C 4 + molecular wheel is a system of 10s and 8p conicting aromaticity. Following Boldyrev, the term con-icting 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 p CMOs can be appropriately recombined four three-center twoelectrons (3c-2e) -BCBisland p bonds (see the ELFs and AdNDP analyses), being in line with its C 4v symmetry.
The La©B 8 C 4 − cluster is a system with 44 valence electrons, occupying 22 CMOs (Fig. S7, ESI †). It has one more full-lled p CMO (HOMO) than La©B 8  The coordination interactions of d-p s CMOs with the relatively large orbital component of La 5d AOs are a little bit stronger than those of d-p p CMOs. Quantitively, the HOMO and HOMO-2 in La©B 8 C 4 + (Fig. S6, ESI †) have a 19.89% La 5d x 2 −y 2 and 10.39% La 5d xy AOs contribution, respectively. In La©B 8 C 4 − , the La 5d x 2 −y 2 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 p CMOs, the La 5d xz /5d yz AOs contributes merely by 6.72% in HOMO-4/4 ′ of La©B 8 C 4 + , and 8.11% in HOMO-5/5 ′ of The CMOs bonding images of La©B 8 C 4 +/− molecular wheels are faithfully conrmed by the ELFs analyses. As shown in Fig. 4, the ELF s patterns of La©B 8 C 4 + and La©B 8 C 4 − clusters are almost identical, showing twelve localized 2c-2e B-B/B-C s bonds (le panels) and strong global delocalized s electron density (middle panels). Obviously, two molecular wheels mainly differ in ELF p patterns. The p electron density of La©B 8 C 4 + is clearly segmented into four -BCBislands (right panels), but that of La©B 8 C 4 − is continuous, and being smoothly distributed on the whole B 8 C 4 ring, which rmly supports the above assessments of 8p antiaromaticity for La©B 8     where, the B 8 C 4 (LM, D 4h , 1 A 1g ) has a square geometry, a true local minimum on its potential surface. Rather, the B 8 C 4 (frozen, D 4h , 1 A 1g ) represents the frozen fragment form La©B 8 C 4 molecular wheel, which is a second-order saddle point. The B 8 C 4 (LM, D 4h , 1 A 1g ) and B 8 C 4 (frozen, D 4h , 1 A 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, conrming the stabilization of dodeca-coordinated La©B 8 C 4 molecular wheel. The energy difference between the BDE and inherent interaction energy describes the isomerization energy of B 8 C 4 motif from the square geometry to a circular one in nature (Fig. S11, ESI †). The fascinating transition-metal centered boron molecular wheels M©B n q− is controlled by the double (s and p) aromaticity, following the electronic design principle (n + x + q = K) proposed by Wang and coworkers. 26 In intriguing La©B 8 C 4 +/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 m C 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©B 8 C 4 +/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©B 8 C 4 − molecular wheel has (10s + 10p) double aromaticity, following (4N s/p + 2) Hückel rule with N s = N p = 2, respectively. The neutral La©B 8 C 4 molecular wheel is an openshell system with a single occupied p orbital, possessing the 10s and 9p double aromaticity. Interestingly, the cationic La©B 8 C 4 + cluster is a conicting aromatic system of with 10s and 8p delocalized electrons (K = 18), obeying the (4N s + 2) and (4N p ) Hückel rule with N s = N p = 2, respectively. Thus, La©B 8 C 4 + represents a counterexample for double aromaticity in planar hypercoordinate molecular wheels.

Conclusions
In summary, we have theoretically predicated three dodecacoordinated La©B 8 C 4 +/0/− molecular wheels, featuring a central La atom enclosed by a perfectly planar B 8 C 4 ring, which is viable in the -(BCB) 4   principle of double aromaticity, whereas, the La©B 8 C 4 + molecular wheel is a counterexample, which has the conicting aromaticity with 10s and 8p delocalized electrons. The La©B 8 C 4 +/0/− molecular wheels with dodeca-coordination number are unprecedented for a planar system in coordination chemistry.

Conflicts of interest
There are no conicts to declare.