Ternary CE2Ba2 (E = As, Sb) Clusters: New Pentaatomic Planar Tetracoordinate Carbon Species with 18 Valence Electrons

18-valence-electron (ve) rule is one important guide for us to design planar tetracoordinate carbon (ptC) species. Using the “polarization of ligands” strategy, the new pentaatomic ptC species CE2Ba2 (E = As, Sb) with 18 ve are designed in this work. Computer structural searches and high-level calculations reveal that the ptC CE2Ba2 (E = As, Sb) species are global minima (GMs) on the potential energy surfaces, whose C center is coordinated by the interspaced E and Ba atoms. CE2Ba2 (E = As, Sb) are also kinetically stable. Chemical bonding analyses reveal that the ptC core is stabilized by two localized C-E σ bonds, one delocalized five-center two-electron (5c-2e) σ bond and one delocalized 5c-2e π bond. One π and three σ bonds collectively conform to the 8-electron counting, which determines the stability of ptC CE2Ba2 (E = As, Sb) species. Interestingly, the delocalized 2π and 2σ electrons render the ptC systems π/σ double aromaticity. Additional 10 electrons contribute to peripheral lone pairs of E and E-Ba bonding.


Introduction
Exploring the bonding capacity of carbon beyond the classical tetrahedral concept, has been a interesting and challenging subject in chemistry for decades. Compared with the tetrahedral configuration, planar tetracoordinate carbon (ptC) structure is unstable with the higher energy in most cases. In 1968, Monkhorst proposed a ptC configuration as transition state in the interconversion of enantiomers [1]. Just 2 years later, Hoffmann et al. put forward the ingenious strategies to stabilize the ptC systems, based on the deep bonding analyses for a hypothetical planar D 4h CH 4 [2]. Since Schleyer and coworkers predicted the first ptC local minimum (1,1-dilithiocyclopropane) in 1976 [3], a variety of ptC, planar pentacoordinate carbon (ppC), and planar hexacoordinate carbon (p6C) species were theoretically designed/predicted or experimentally characterized [4][5][6][7][8][9][10][11][12][13][14][15]. These planar hypercoordinate carbon (phC) species with novel structures and unique bonding are of fundamental significance for enriching our knowledge on chemical bonding. More importantly, they can be used as units to form new materials, which are of fundamental importance to chemistry and materials science [16][17][18][19][20]. For example, the reported ptC-BeC monolayer is a desired semiconductor, which possesses with an indirect band gap of 1.01 eV and ultrahigh room temperature carrier mobilities. It is very important to investigate small phC clusters for designing new phC functional materials.
To design the small ptC clusters, both geometric size match and the number of valence electrons seem to be crucial. The pentaatomic cluster is an ideal probe for understanding the bonding and properties of ptC systems. In 1991, Schleyer and Boldyrev proposed a general strategy to achieve ptC clusters such as pentaatomic cis-CAl 2 Si 2 and trans-CAl 2 Si 2 , which each has 18 valence electrons (ve) [21]. Boldyrev and coworkers reported the ptC CGe 2 Al 2 and CSi 2 Ga 2 clusters in 1998, who pointed out that both three carbon-ligand (C-L) σ bonds and one C-L π bond were crule for the stability of the ptC system [22]. Afterwards, several ptC clusters including CAl 4 − , NaCAl 4 − , CAl 3 Si − , CAl 3 Ge − , CAl 3 C − , and CAl 4 H − were experimentally observed in gaseous phase using anion photoelectron spectroscopy, which each possesses 17 or 18ve [23][24][25][26][27]. According to the isoelectronic principle, the ptC clusters, CE 4 2− (E = Al, Ga, In, Tl), CGa 3 Si − , and CAl 3 E (E = P, As, Sb, Bi), were theoretically predicted [28][29][30]. However, 18ve counting is not a prerequisite. Indeed, several ptC speciess have been reported, which go beyond the 18-electron rule [31][32][33][34][35][36]. Anyway, 18ve counting is still a nice guide to design some new ptC species. Very recently, using the "polarization of ligands" strategy, Merino and coworkers predicted a series of ptC clusters with 18ve, which can be formulated as M m CE 2 p (E = S-Te, M = Li-Cs, m = 2, 3 and p = m-2) [15]. Now, the open question is: Is there any undiscovered pentaatomic ptC clusters with 18ve? The answer seems to be "yes." Herein, we have tried to find the correct combination towards a ptC system as the global minimum. Based on the "polarization of ligands" strategy, the ptC CE 2 M 2 (E = N-Bi; M = Be-Ba) species can be considered. However, only ptC CE 2 Ba 2 (E = As, Sb) clusters with 18ve are the global mimima at the density functional theory (DFT) level. As we all know, DFT method is reliable for theoretical design [37][38][39][40][41]. CE 2 Ba 2 (E = As, Sb) possess the perfect rhombus structures with D 2h symmetry, whose ptC center is coordinated in-plane by the interspaced E and Ba atoms. The ptC CE 2 Ba 2 (E = As, Sb) clusters are established as the global minima (GMs) via unbiased computer searches. Bonding analyses indicate that the ptC core in cluster 1/2, has one π and three σ bonds, collectively conforming to the "octet rule." The octet rule (eight-electron rule) seems to be universally applicable for the ptC clusters. Peripheral lone pairs (LPs) and E-Ba bonding in cluster 1/2 involves 10 electrons.
The results obtained in this work will complete the series of the pentaatomic ptC species with the 18ve. It is further confirmed that "polarization of ligands" is an effective strategy for expanding ptC clusters.
To get the data of Wiberg bond indices (WBIs) and natural atomic charges of the CE 2 Ba 2 (E = As, Sb) clusters, we performed the natural bond orbital (NBO) [53] analyses at the PBE0-D3/def2-TZVPP level. Canonical molecular orbital (CMO) and adaptive natural density partitioning (AdNDP) [54] analyses were done to explore the bonding characteristics. Nucleus-independent chemical shifts (NICSs) [55] were calculated at PBE0/def2-TZVPP, to quantitatively probe the π and σ aromaticity. The orbital compositions were analyzed by the Multiwfn program [56]. All calculations of electronic structures were done by the Gaussian 09 package [57]. Molecular structures, canonical molecular orbitals (CMOs), and AdNDP bonding patterns were visualized using the CYLview and Molekel programs [58,59].

Design of ptC CE 2 Ba 2 (E = As, Sb)
CAl 4 2− is the most representative pentaatomic cluster with 18ve, which possesses perfect D 4h symmetry. As shown in Scheme 1, using "polarization of ligands" strategy, we can obtain three ptC CE 2 M 2 series, based on different degree of polarization of ligands. Some of ptC CE 2 M 2 (E = C, Si, Ge, Sn, Pb; M = B, Al, Ga. In, Tl) clusters have been reported, such as CSi 2 Al 2 , CGe 2 Al 2 , CSi 2 Ga 2 , and CGe 2 Ga 2 . Very recently, the ptC CE 2 M 2 (E = S, Se, Te; M = Li, Na, K, Rb, Cs) clusters were investigated systematically by Merino et al. [15], which are all true ptC GMs on their potential energy surfaces. It should be noted that the degree of polarization of ligands in (a) is smallest, while that of (c) is biggest. Here, we attempted to stabilize ptC by using a combination of nitrogen group elements and alkaline earth metal atoms as ligands. Thus, an interesting issue arises: Are the ptC CE 2 M 2 (E = N, P, As, Sb, Bi; M = Be, Mg, Ca, Sr, Ba) clusters GMs? To answer above question, two major computational efforts have been made. The first effort is to examine ptC CE 2 M 2 (E = N, P, As, Sb, Bi; M = Be, Mg, Ca, Sr, Ba) clusters, which adopt D 2h and C 2v structures as true minima. As shown in Table S1, there are 12 ptC species are minima without the imaginary frequencies, which include C 2v CN 2

Structures and stability
The optimized GM structures 1, 2 of CE 2 Ba 2 (E = As, Sb) at PBE0-D3/def2-TZVPP level are shown in Fig. 1. The four low-lying isomers (nB-nD) are depicted in Fig. 2, along with their relative energies at the single-point CCSD(T)/ def2-TZVPP level with zero-point energy (ZPE) corrections at PBE0-D3. Cartesian coordinates for top five lowest lying structures are listed in Table S2 (ESI †). The GM clusters 1, 2 are 4.85 and 19.50 kJ·mol −1 more stable than their closest competitors, respectively. In terms of energetics, CSb 2 Ba 2 is particularly well defined on its potential energy surfaces. The GM structures and low-lying isomers contain a tetracoordinate carbon center, except isomer 2E (Fig. 2).
As depictured in Fig. 1, the C-As bond distance in 1 is 1.84 Å, while the C-Ba distance is 2.49 Å. Although C-As/C-Ba bonding is polar, the C-As/C-Ba single bond has an upper bound of 1.96/2.71 Å based on covalent atomic radii [60]. Therefore, the C-As bonding in 1 is quite strong, probably greater than single bond. Interestingly, the As-Ba bonding is also substantial and being close to a half bond. Wiberg bond indices (WBIs) and natural population analysis (NPA) charges offer valuable bonding information. The WBI data for clusters 1, 2 are also shown in Fig. 1. For CE 2 Ba 2 (1), the C center has robust bonding with its coordinating As ligands (WBIs: 1.34), which possesses the partial double bond properties. The C-Ba link has relatively small WBIs (0.36). For the periphery, 1 has substantial E-Ba bonding (WBIs: 0.48), which is close to  Root-mean-square deviations (RMSDs) of GM clusters 1, 2 of CE 2 Ba 2 (E = As, Sb) during the Born-Oppenheimer molecular dynamics (BOMD) simulations at 300 K half a bond. In terms of NPA charges, the C center carries a negative charge of − 1.54 |e| for 1, while the Ba, As ligands possess the charge of + 1.16 and − 0.39 |e|, respectively, due to the difference of electronegativity. The WBIs and NPA charges in 2 are similar with those of 1, there are only a few minor differences.
Global searches of the potential energy surfaces of CE 2 Ba 2 (E = As, Sb) indicate that ptC structures 1 and 2 as the GM structures have good thermodynamic stabilities (Fig. 2). For experimental characterization, the dynamic stability of clusters is as important as the thermodynamic stability. To probe the dynamic stability of CE 2 Ba 2 (E = As, Sb) (1 and 2), Born-Oppenheimer molecular dynamics (BOMD) simulations [61] were performed at the PBE0/def2-SVP level, for 50 ps at room temperature (300 K). The root-mean-square deviations (RMSDs) during these BOMD simulations are the reliable evaluation indicators for the kinetic stability. As depictured in Fig. 3, the average RMSDs of clusters 1, 2 are relatively small (0.31 and 0.20 Å), suggesting that the ptC CE 2 Ba 2 (E = As, Sb) clusters possess good kinetic stabilities, being robust against decomposition or isomerization.

Chemical bonding and aromaticity
To elucidate the stability of ptC CE 2 Ba 2 (E = As, Sb) clusters, it is essential to perform chemical bonding analyses. Since the essence of bonding is similar in ptC CE 2 Ba 2 (E = As, Sb) species (1, 2), herein, we only use 1 as an example. The CAs 2 Ba 2 cluster has 18 valence electrons. All the occupied CMOs and their compositions of CE 2 Ba 2 (E = As, Sb) are shown in Table S3-S4. AdNDP is an important analysis approach for chemical bonding, which is an ingenious extension of NBO method. AdNDP analyses recovers typical Lewis bonding elements (LPs and two-center two-electron (2c-2e) bonds) and novel delocalized nc-2e (n ≥ 3) bonds. As shown in Fig. 4, the AdNDP analyses provide a relatively simple and intuitive bonding picture for the ptC CAs 2 Ba 2 cluster. Figure 4(a) shows that there are two lone pairs (LPs) of two As atoms. As Fig. 4(b) shown, there is one three-center two-electron (3c-2e) As-C-As π bond, with ON = 1.80 |e|, which is one non-bonding orbital in nature, because there is no contributions of C. In other words, it contributes little to the stability of the system. On the periphery of the cluster, Fig. 4 AdNDP bonding schemes of the ptC cluster CAs 2 Ba 2 (1) with 18ve. Two lone pairs (LPs) of two As atoms (a). One three-center two-electron (3c-2e) As-C-As π bond, with ON = 1.80 |e| (b). Two Ba-As-Ba (3c-2e) σ bonds, with ON = 2.00 |e| (c). Two localized C-As (2c-2e) σ bonds and one delocalized 5c-2e σ bond (d) there are two Ba-As-Ba (3c-2e) σ bonds, with ON = 2.00 |e| (Fig. 4(c)). The ptC CAs 2 Ba 2 (1) cluster has a relatively rigid peripheral E 2 Ba 2 ring, which is interconnected via two 3c-2e Ba-E-Ba σ bonds. As a comparison, there is only one delocalized 4c-2e σ bond for the peripheral Al 4 ring in CAl 4 2− . As shown in Fig. 4(d), there are two localized C-As (2c-2e) σ bonds and one delocalized 5c-2e σ bond. In addition, there is one 5c-2e π bond, with ON = 2.00 |e|, as shwon in Fig. 4(e). Interestingly, the Ba atoms participate in global π framework via their 5d AOs (by 4%). Although the most important contribution is from As-C-As, the contribution of two Ba atoms seems to be cannot be neglected. Thus, one delocalized π bond together with one σ bond rendered the ptC clusters 2π/2σ double aromaticity, following the (4n + 2) Hückel rule. As shown in Fig.S2, cluster 2 has similar bonding patterns with 1, three σ and one π bonds around the ptC core.
As depictured in Fig. 5, the π/σ double aromaticity of ptC clusters 1, 2 is independently confirmed via the NICS calculations. Systems with negative NICS values are considered aromatic. All NICS(1) (from − 7.06 to − 15.50 ppm) and NICS(0) (− 6.53 and − 9.18 ppm) are negative at PBE0/ def2-TZVPP, which are calculated at 1 Å above the ptC center, and above 1/0 Å of the center of a C-E-Ba triangle.
The NICS values suggest that ptC clusters 1, 2 truly possess π and σ double aromaticity, in line with bonding analyses.
In order to facilitate future experimental characterization, the IR spectrums of the ptC clusters 1 and 2 were simulated theoretically at the PBE0-D3/def2-TZVPP level (see Fig. S3). As shown in Fig. S3, the absorption peak at 493 cm −1 of CAs 2 Ba 2 (1), mainly originates from C-Ba anti-symmetry stretching vibration. The peak at 989 cm −1 originates from its anti-symmetry C-As stretching vibration. The other absorption peaks are mainly generated by coupled vibrations. The calculated IR spectra of CSb 2 Ba 2 turned out to be similar with CAs 2 Ba 2 . All absorption peaks of CSb 2 Ba 2 are redshifted slightly, due to the large mass number of Sb.

Conclusions
We have designed two planar tetracoordinate carbon (ptC) clusters, CE 2 Ba 2 (E = As, Sb), which are GMs via unbiased structural searches and high-level quantum chemical calculations. Chemical bonding analyses suggest that the ptC CE 2 Ba 2 (E = As, Sb) clusters have one π and three σ bonds around the ptC core, which make the carbon center conform to the octet rule. Additional ten electrons contribute to peripheral lone pairs of E and E-Ba bonding. One delocalized π bond together with one delocalized σ bond endow the 2π and 2σ double aromaticity. The bonding pattern is ideal for these ternary ptC clusters, justifying their 18-electron counting.