Planar Pentacoordinate versus Tetracoordinate Carbons in Ternary

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Planar Pentacoordinate Versus Tetracoordinate Carbons in Ternary CBe4Li4 and CBe4Li4(2-) Clusters Jin-Chang Guo, Lin-Yan Feng, Chuan Dong, and Hua-Jin Zhai J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b08573 • Publication Date (Web): 02 Oct 2018 Downloaded from http://pubs.acs.org on October 3, 2018

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The Journal of Physical Chemistry

Planar Pentacoordinate versus Tetracoordinate Carbons in Ternary CBe4Li4 and CBe4Li42− Clusters Jin-Chang Guo,‡ab Lin-Yan Feng,‡a Chuan Dong*b and Hua-Jin Zhai*a a

Nanocluster Laboratory, Institute of Molecular Science, Shanxi University, Taiyuan 030006, China b

Institute of Environmental Science, Center of Environmental Science and Engineering Research, Shanxi University, Taiyuan 030006, China

E-mail: [email protected], [email protected]

‡ These authors contributed equally to this work.

ABSTRACT 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 C2v CBe4Li4 (1) and D4h 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 2 and 6 delocalization around C center, suggesting that ppC or ptC clusters are governed by double / aromaticity, rather than the 18-electron rule. The outer Be4Li4 ring in 1 and 3 also supports 2 aromaticity, collectively leading to three-fold / aromaticity for these ppC/ptC clusters. Structural transformation from ptC (3) to ppC (1) is discussed, in which 16-electron quasi-ptC CBe4Li4 (2) cluster serves as an intermediate. Cluster 2 as a local

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minimum has severe out-of-plane distortion. Flattening of 2 leads to reorganization of Be4 ring around C center, which offers space for the fifth atom to coordinate and facilitates ppC formation. The latter arrangement optimizes  aromaticity and better manages intramolecular Coulomb repulsion. This work highlights geometric factor (and unconventional electron counting) in the design of planar hypercoordinate carbons.

Keywords: ternary clusters, planar pentacoordinate carbon, planar tetracoordinate carbon, double ( and ) aromaticity, 16-electron counting.

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1. INTRODUCTION For the past 50 years, people have been exploring planar hypercoordinate carbon molecules, 1 − 3 which are primarily motivated by chemical curiosity. Such molecules have unconventional geometries, coordination environments, and chemical bonding.4−28 They are exotic and generally unstable. Success in the field has been limited despite extensive and persistent experimental and theoretical efforts, and only a handful of these molecules are thermodynamically stable and viable to date.1−3 Among them, planar tetracoordinate and pentacoordinate carbons (ptCs and ppCs) dominate, as exemplified by a series of CAl42−,7−14,20,23,25 CAl5+,15,16,21 and CBe54− based19,22,24,27 clusters. The ptC and ppC species are clearly guided by the so-called “18-electron counting”,7,15 either in computational designs or gas-phase experimental works. Nevertheless, it remains unclear why there exists an 18-electron rule for two-dimensional (2D) or quasi-2D clusters. Note that, for example, free-electron 2D nanosystems are governed by a set of revised magic numbers with 6, 8, and 12 electrons, and so on,29 which are in contrast to the 3D shell model.30 In the former case, 18-electron counting is not a magic number. Thus, it is still an open question whether 18-electron counting is a prerequisite for the ptC/ppC molecules. As documented in a review by Keese,2 the electron counting rule for planar hypercoordinate carbons may depend strongly on chemical surrounding. Consequently, deviation from 18-electron counting is of interest for pursuit, which should lead to further ptC/ppC species. Indeed, the current authors28 reported a 16-electron C4v CBe4Au4 cluster. It is well-defined on the potential energy surface as global minimum (GM), by a margin of 14.6 kcal mol−1. However, the C center is moderately out-of-plane and the cluster should be classified only as a quasi-ptC species. Is it possible to tune the structural and bonding properties of a 16-electron CBe4 based cluster? How do peripheral ligands affect bonding in the CBe4 core of a ternary cluster? What would happen if one forces to planarize a quasi-ptC species? Can ptC and ppC structures compete with each other in the same system? To this end, we attempt to computationally design 3



a series of ternary C−Be−Li clusters: CBe4Li40/−/2−. These species differ in charge states, with an electron counting from 16 up to 18. Research of C−Be based planar hypercoordinate carbons initiated from GM D5h CAl5+ cluster, which has a ppC.15 Using isoelectronic Be−/Al substitution, a number of ppC clusters were predicted: CAl4Be, CAl3Be2−, CAl2Be32−, and ECBe5− (E = Al, Ga).16,19,21 Although ppC CBe54− pentagon is intrinsically unstable due to Coulomb repulsion, it was stabilized by Li/H/Au ligands, forming a series of ppC clusters: CBe5Linn−4, CBe5Hnn−4 (n = 2−5), and CBe5Au5+.22,24,27 Furthermore, a recent computational study established a quasi-ptC CBe4Au4 cluster, as mentioned above.28 This literature survey indicates that both ppC and ptC species are viable in the C−Be based systems. Therefore, tuning the ligands in a ternary cluster can in principle alter Be−Be bonding and redistribute space around C center, which should facilitate interconversion between ptC and ppC. For the present ternary CBe4Li40/−/2− systems, it turns out that ppC and ptC structures are competing with each other as charge-state varies. The 16-electron CBe4Li4 neutral cluster assumes a C2v ppC geometry, in contrast to a D4h ptC one for 18-electron CBe4Li42− dianion. Both clusters are perfectly planar and the C−Li coordination in the former is close in distance albeit with minimal bonding, which should be viewed as a pseudo-ppC. The observation that charge-state alters the coordination fashion from ptC to ppC, of a specific cluster, is intriguing. Going from neutral to dianion in the CBe4Li40/−/2− series, the ppC isomer systematically loses stability, whereas ptC isomer gains stability. The 16-electron C4v CBe4Li4 isomer contains a quasi-ptC with substantial out-of-plane distortion, which drives the structural transformation from ptC to ppC, making ppC cluster the GM for neutral. This finding highlights the geometric factor, as well as unconventional electron counting, in the design of planar hypercoordinate carbon species.

2. METHODS Machine searches for GM structures of CBe4Li4 and CBe4Li42− clusters were carried out using the Coalescence Kick (CK) algorithm31−33 at the B3LYP/lanl2dz level,34,35 aided with 4


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manual structural constructions. About 3,000 stationary points were probed for the neutral cluster (2,000 singlets versus 1,000 triplets), which indicate that triplet states are generally unimportant for the system. Thus, structural searches for the dianion were primarily focused on singlets, with 1,500 structures being probed. This strategy is further justified because the majority of identified structures have low symmetry. Monoanion CBe4Li4− cluster were not searched independently; they were constructed on the basis of top isomers of CBe4Li4 and CBe4Li42−. Low-lying structures were subsequently re-optimized at PBE0-D3/def2-TZVP level, 36 in which dispersion is included in the functional. Vibrational frequencies were calculated at the same level to ensure that the reported structures are true minima on the potential energy surfaces. To obtain accurate energetics, single-point CCSD(T) calculations37−39 were carried out for top eight isomers at the PBE0-D3/def2-TZVP geometries; that is, at CCSD(T)/def2-TZVP// PBE0-D3/def2-TZVP level. Natural bond orbital (NBO) analyses 40 were performed at PBE0-D3/def2-TZVP to obtain Wiberg bond indices (WBIs) and natural atomic charges. Chemical bonding was elucidated via canonical molecular orbitals (CMOs) and adaptive natural density partitioning (AdNDP).41 Nucleus independent chemical shifts (NICSs)42 were calculated to assess aromaticity. All electronic structure calculations were accomplished using the Gaussian 09 package.43 Molecular structures, CMOs, and AdNDP data were visualized using CYLview and GaussView 5.0.44,45

3. RESULTS 3.1. Planar pentacoordinate carbon CBe4Li4 cluster Low-lying structures of CBe4Li40/−/2− clusters from the CK global searches are shown in Figure 1, as well as in the supplementary information (Figures S1−S3). Among the reported structures, there are three ppC and three ptC species: 1/4/5 versus 2/3/6. The two-types of isomers are true minima, while their energetics vary and depend sensitively on the charge state. Note that the relative energies are listed in Figures S1−S3 at the single-pint CCSD(T) level, 5



with zero-point energy (ZPE) corrections at PBE0. These are considered to be the ultimate energetics data in this study. Neutral GM CBe4Li4 cluster assumes a perfectly planar geometry: 1 (C2v, 1A1) (Figure 1). The C center is coordinated in the first shell by four Be atoms plus one Li atom, constituting a ppC species. The remaining three Li atoms are coordinated to Be sites in a bridging fashion, which form a second shell. Bond distances for C−Li links are 2.08 versus 3.67/3.71 Å, which differ fundamentally. Moreover, bond angles around C center are 75.8 for LiCBe versus 69.9/68.6 for BeCBe, which are roughly comparable, suggesting that five Be/Li sites are spatially equivalent in terms of coordination to C. Indeed, the Li site appears to be even slightly more spacious than the Be ones. While C/Be/Li differ in electronegativity (2.55/1.57/0.98), the recommended covalent radii by Pyykkö46 can still guide the understanding of bonding in cluster 1, according to which single C−Be and Be−Be bonds have an upper bound of 1.77 and 2.04 Å, respectively. Gas-phase Be2 dimer is van der Waals type (2.45 Å)47 and Be2+ has a half bond (2.21 Å).48 Thus, C−Be links in 1 (1.67/1.76 Å) are consistent with strong bonding (WBIs: 0.70/0.64; Figure 2). The Be−Be distances of 1.97/1.99 Å also indicate strong bonding (WBIs: 0.68/0.83).49 The C−Li link of 2.08 Å falls in the regime of single bond (2.08 Å),46 but the calculated WBI is rather small (0.08; Figure 2), which may be partly attributed to the ionic nature. This is an unusual situation: short distance and weak bonding (vide infra). The Be−Li links span from 2.33 to 2.54 Å, which correspond to WBIs of 0.19−0.26, hinting for delocalized bonding in the periphery. The nearest isomeric structure of CBe4Li4 is in triplet (Figure S1), being 2.28 kcal mol−1 above cluster 1 at single-point CCSD(T). It contains a quasi-ppC. An isomer with ptC, 2 (C4v, 1

A1), turns to be 11.17 kcal mol−1 above cluster 1. The former deviates markedly from planarity.

3.2. Planar tetracoordinate carbon CBe4Li42− cluster The CBe4Li42− dianion cluster has a better defined GM, 3 (D4h, 1A1g) (Figure 1). It is 6


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perfectly planar with a ptC, being at least ~5 kcal mol−1 more stable than alternative isomers (Figure S2). The ppC counterpart, 4 (Cs, 1A), is quasi-planar at 5.57 kcal mol−1. The C−Be links in 3 (1.64 Å; Figure 1) are shortened relative to ppC cluster 1 (1.67/1.76 Å). The former bonds have WBIs of 0.62 (Figure 2), which are substantial and yet they turn out to be slightly smaller than those in 1.49 In contrast, peripheral Be−Be links in 3 (2.31 Å) are markedly elongated with respect to 1 (1.97−1.99 Å), resulting in reduced WBIs of 0.41 in 3. The Be−Li distances in 3 are comparable to those in 1, but their WBIs are boosted to 0.45.49

3.3. Monoanion CBe4Li4− cluster For monoanion CBe4Li4− cluster (Figure S3), the ppC and ptC isomers are the second and third lowest in energy, respectively: 5 (C2v, 2A1) and 6 (C4v, 2A1). Again, the ptC species is quasi-planar. GM structure, Cs (2A), is 3D in shape. Here the C center is coordinated to four Be atoms, as well as a vertically oriented Li2 dimer, collectively leading to hexacoordination. It is interesting to follow charge-state dependence of ppC versus ptC structures along the CBe4Li40/−/2− series. For neutral cluster, ppC CBe4Li4 (1) is clearly advantageous than ptC CBe4Li4 (2), by a large margin of 11.17 kcal mol−1. In contrast, the dianion favors ptC CBe4Li42− (3) over ppC CBe4Li42− (4) by 5.57 kcal mol−1. For the monoanion, ppC CBe4Li4− (5) and ptC CBe4Li4− (6) are quite close in energy (within 1 kcal mol−1).

4. DISCUSSION 4.1. D4h CBe4Li42− (3) cluster: an 18-electron ptC system Cluster D4h CBe4Li42− (3) is perfectly planar (Figure 1). It is highly symmetric with a ptC center. It also conforms to the 18-electron counting, which has been considered a magic rule for planar hypercoordinate molecules.7,15,16,19−25,27 These features make cluster 3 a natural starting point for our discussion. As an 18-electron system, valence electrons of 3 occupy nine CMOs as depicted in Figure 3. The CMOs are sorted to four subsets on the basis of atomic orbitals (AOs) of which a specific CMO is composed; see Tables S1 and S2 (ESI†) for detailed data of orbital 7



compositions for 1 and 3. Subset (a) consists of four  CMOs that are located on four Li−Be−Li edges of outer Be4Li4 ring. The CMOs are dominated by Be s/p AOs (56−76%; Table S2, ESI†), with complementary Li s/p components (24−35%). Electron cloud is clearly centered on the Be sites. Specifically, HOMO−3 is completely bonding between four Li−Be−Li edges, the degenerate HOMO−2 pair partially bonding/nonbonding, and HOMO antibonding between four Li−Be−Li edges. Note that all four CMOs are bonding within each of the Li−Be−Li edges. This pattern strictly follows the building principles for CMOs, which are readily recombined as three-center two-electron (3c-2e) Li−Be−Li  bonds, one on each of the four edges. It is stressed that this is overall an 8c-8e  subsystem, which is islanded as four 3c-2e bonds, but not 2c-2e Lewis bonds. In other words, this  subsystem cannot be localized completely. Subset (b) has only one CMO: HOMO−1. It is  in nature, derived from Be p AOs (81%) and oriented tangentially to the Be4 ring. This CMO is completely delocalized and complete bonding (rather than antibonding). It cannot be transformed to Lewis elements, thus rendering the cluster  aromaticity according to the (4n + 2) Hückel rule. The inner CBe4 core supports four CMOs. For subset (c), HOMO−4 is a delocalized  bond, which is completely bonding on CBe4 core, with 70% contribution from C p AO and 29% from Be p AOs. The 2 electron counting also conforms to the Hückel rule for aromaticity. Lastly, subset (d) consists of three  CMOs, clouding also on inner CBe4 core (with 67−78% contributions from C s or p AO). This  sextet closely resembles the prototypical  sextet in benzene in terms of spatial shapes, rendering  aromaticity for cluster 3. In short, among four mutually independent and orthogonal bonding subsystems50 in cluster 3, only subsystem (a) can be reduced to linear 3c-2e Li−Be−Li  bonds. The remaining three subsystems are intrinsically delocalized in nature, whose 2/2/6 electron counting renders three-fold / aromaticity to 3. Calculated NICS data at PBE0/6-311+G(d) level confirm the assessment of aromaticity; see Table 1. The above bonding picture is perfectly borne out from AdNDP analysis (Figure 4). Note 8


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that four bonding subsystems are spatially separated from each other, so that the outer Be4Li4 ring has four 3c-2e island  bonds and one delocalized  bond. For these five CMOs, the C center has relatively minor contributions. In contrast, inner 2/6 subsystems are exclusively clouded on the CBe4 core. Thus, while cluster 3 is an 18-electron system, the ptC center is bound actually by eight electrons only, hinting that the key mechanism behind a ptC species is probably not the 18-electron counting. Rather, 2/6 double aromaticity underlies a ptC cluster. We believe this concept is crucial in rational design of planar hypercoordinate molecules.

4.2. C2v CBe4Li4 (1) cluster: a 16-electron ppC system On the basis of CMO analysis for ptC D4h CBe4Li42− (3), it is relatively easy to rationalize the bonding in ppC C2v CBe4Li4 (1) cluster. Cluster 1 differs from 3 by two electrons, leading to a 16-electron system, which is less common in planar hypercoordinate molecules.28 Despite the fact that 1 and 3 features a ppC and ptC center, respectively, their CMOs are closely similar. The CMOs of cluster 1 are sorted to four subsets as shown in Figure 5. For subsets (b)−(d), the CMOs show strict one-to-one correspondence to those of 3, except for degeneracy lift in the former due to lower symmetry. For subset (a) of cluster 1, HOMO−3 and HOMO are completely bonding and completely antibonding (two nodal planes), respectively, whereas HOMO−1 is partially bonding (with one nodal plane). The three CMOs constitute an incomplete combination for  bonding in outer Be4Li4 ring. This observation is associated to the lowering symmetry of 1 with respect to 3, which lifts the degeneracy of a pair of partially bonding CMOs with one nodal plane, so that one of them is elevated in energy to above the “antibonding” HOMO. In other words, the  framework for peripheral Be4Li4 ring in 1 is incomplete and cannot be islanded as four 3c-2e Li−Be−Li  bonds (as in 3; Figure 4), because only six electrons are available. Nonetheless, the lower symmetry of 1 distorts the four CMOs in subsets (a) and (b), making them more localized and spatially complementary with each other. Effectively, these four CMOs may be approximated as 3c-2e Be−Li−Be island  bonds. AdNDP data confirm this 9



understanding. Two AdNDP schemes are presented for cluster 1: A more delocalized one (Figure 6) versus an island one (Figure S4). We prefer the former AdNDP scheme because it is closer to the truth of bonding in the system. In summary, cluster 1 possesses three-fold / aromaticity, as well as a distorted and incomplete outer Be4Li4  framework. It is interesting to compare the bonding pattern of ppC C2v CBe4Li4 (1) with its isovalent C4v CBe4Au4 counterpart.28 While both are 16-electron systems, they differ markedly. First, C4v CBe4Au4 cluster assumes a quasi-ptC geometry, compared to ppC for 1. Second, C4v CBe4Au4 cluster has a complete 3c-2e  framework for the periphery (with 8 electrons), whereas cluster 1 has an incomplete Be4Li4  framework (6 electrons only; Figure 5(a)). Third, C4v CBe4Au4 cluster features 2/6 double aromaticity, in contrast to three-fold / aromaticity for 1. We believe the key to the above differences is charge distributions. In C4v CBe4Au4 cluster, outer Au4 sites are neutral and positive charges are located on Be4 ring. The opposite is true for cluster 1: outer Li4 sites are positively charged and inner Be4 sites have little charges. The consequence51 is much larger WBIs for Be−Be links in 1 (0.68−0.83; Figure 2) relative to 0.23 in C4v CBe4Au4,28 which in turn shortens the Be−Be distances in 1 and offers potential for an extra coordinate site around C center (vide infra). Remarkably, in ternary clusters 1 and 3, the C−Be/C−Li/Be−Be/Be−Li interactions interplay closely so that the C−Be/C−Li/Be−Be distances are entangled and can alter, depending on coordination environment, type of ligands, and charge state, which offers opportunities for novel planar clusters. We shall comment on the nature of Li coordination to C in ppC cluster 1. As described in Section 3.1, bond angles LiCBe (75.8) around C center are comparable to and even slightly greater than BeCBe (69.9/68.6), which indicate that the Li site is more spacious than Be ones, justifying the Li center as the fifth coordination to C. The corresponding C−Li link (2.08 Å) is also far shorter than the rest (3.67/3.71 Å). Overall, the ppC nature of cluster 1 is physically solid. One peculiar aspect is that, despite closeness in distance, the C−Li bond order is small (WBI: 0.08; Figure 2) relative to the C−Be links (0.64−0.70). One may argue that the tiny WBI is due to polar nature of C−Li bonding, because C/Li have quite different electronegativities: 10


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2.55 versus 0.98. However, this is not the complete truth. For comparison, we also calculated a simple Td CLi4 cluster (Figure S5, ESI†), whose C−Li links can reach 1.87 Å with WBIs of 0.54. Therefore, we should conclude that cluster 1 is only a pseudo-ppC species. Note that in a ternary CBe4Li4 (1) cluster, this C−Li distance appears to be controlled by neighboring Be−Li bonds, which have larger WBI values. Thus C−Li bonding is not necessarily optimal. Born-Oppenheimer molecular dynamics (BOMD) simulations52 show that the Li site coordinated to C is quite fragile. It frequently moves upon and down the ppC plane, or even migrates on the plane to other Be sites, whereas the remaining CBe4Li3 fragment maintains intact. Intriguingly, these movements occur even at room temperature (298 K; Figure 7).

4.3. On the mechanism of structural transformation between ptC and ppC clusters Having established the GM structures of ptC D4h CBe4Li42− (3) and ppC C2v CBe4Li4 (1), it is natural to ask a fundamental question: why dianion and neutral clusters assume different geometries? To address this critical issue, it is instructive to analyze the 16-electron ptC or quasi-ptC CBe4Li4 cluster, whose optimized structure is C4v CBe4Li4 (2) (Figure 8; Figure S1). It is a true local minimum (LM), being quasi-planar and ~11 kcal mol−1 above GM 1. Comparing the geometries of ptC 3 (dianion; Figure 1) and quasi-ptC 2 (neutral; Figure 8), a major difference is the shrink of Be−Be bonds from 2.31 Å in 3 to 2.09 Å in 2, which leads to substantial constraints for the ptC core in 2. A side-view of 2 is also illustrated in Figure 8. It has a diagonal Li−Li distance of 5.98 Å versus a height of 1.94 Å from C to Li. Bond angle BeCBe is 80.4, which deviates markedly from 90 for a perfectly planar geometry. Out-of-plane distortion is clearly a con for the ptC species. We mention two reasons. First, the  framework in cluster 2 is highly distorted (Figure S6(c)). Second, due out-of-plane distortion, Li−Li distances in 2 (4.23 Å) are markedly shorter than those in 3 (4.79 Å), which is not ideal for management of electrostatics, particularly in light of increased positive charges53 on Li sites in 2 (+0.65 e). The same reasons drive the structural transformation from ptC to ppC in neutral CBe4Li4 cluster. Pushing cluster 2 to planarity expands and breaks the Be4 ring, 11



in which Be−Be links reoptimize, leaving room for the fifth atom to coordinate to C center. This transformation can proceed straightforwardly and leads naturally to ppC cluster 1. Such a process not only strengthens the  framework, but also helps better manage electrostatics, which collectively govern the stability of ppC cluster 1. Note that the Li−Li distances expand from 4.23 Å in 2 to 4.38/4.73 Å in 1. One reviewer is curious about the possible AdNDP pattern of cluster 2. We comment here that, as established throughout this paper for a series of clusters and specifically in Figure S6, cluster 2 is four-fold / delocalized for the periphery as well as for the ptC core, so that none of the CMOs can be reduced to Lewis elements, or even island Li−Be−Li 3c-2e bonds (due to an incomplete skeleton  framework; Figure S6(a)). Therefore, a correct AdNDP scheme is to reproduce each and every CMO in Figure S6. Such an AdNDP scheme does not offer new insight beyond the CMO analysis.

5. CONCLUSIONS We have computationally designed two ternary C−Be−Li clusters, C2v CBe4Li4 and D4h CBe4Li42−. They are perfectly planar, featuring planar pentacoordinate and tetracoordiate carbons (ppC and ptC), respectively. Both species show 2 and 6 delocalization around the C center, suggesting that double / aromaticity (rather than the 18-electron rule) governs such exotic ppC or ptC clusters. The outer Be4Li4 ring also supports 2 aromaticity. In short, ppC C2v CBe4Li4 and ptC D4h CBe4Li42− clusters possess three-fold / aromaticity. Deviation from 18-electron counting is allowed in the design of ppC/ptC clusters, which in this case leads to a 16-electron ppC species. Geometric constraints are revealed for a 16-electron ptC or quasi-ptC CBe4Li4 cluster, which suffers from out-of-plane distortion, driving structural transformation from ptC to ppC. This process not only optimizes the  aromaticity, but also better manages intramolecular Coulomb repulsion, which collectively govern ppC C2v CBe4Li4 cluster.

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Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.xxxxxxx. Orbital compositions of C2v CBe4Li4 (1) and D4h CBe4Li42− (3) clusters, Cartesian coordinates for optimized structures of CBe4Li4 (1), CBe4Li42− (3), and C4v CBe4Li4 (2) clusters at PBE0-D3/def2-TZVP level, alternative low-lying structures of CBe4Li4, CBe4Li4−, and CBe4Li42− clusters at PBE0-D3, an alternative AdNDP scheme for CBe4Li4 (1), optimized structure of CLi4 (Td, 1A1) at PBE0-D3, and CMOs of CBe4Li4 (2).

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected]. *E-mail: [email protected]. Author Contributions §

J.-C.G., L.-Y.F.: These authors contributed equally to this work.

Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS This work was supported by the National Natural Science Foundation of China (21873058, 21573138), the China Postdoctoral Science Foundation (2017M611193), and the Sanjin Scholar Distinguished Professors Program.

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(26) Cui, Z. H.; Vassilev-Galindo,V.; Cabellos, J. L.; Osorio, E.; Orozco, M.; Pan, S.; Ding, Y. H.; Merino, G. Planar pentacoordinate carbon atoms embedded in a metallocene framework. Chem. Commun. 2017, 53, 138–141. (27) Guo, J. C.; Feng, L. Y.; Zhang, X. Y.; Zhai, H. J. Star-Like CBe5Au5+ Cluster: Planar pentacoordinate carbon, superalkali cation, and multifold (π and σ) aromaticity. J. Phys. Chem. A 2018, 122, 1138–1145. (28) Guo, J. C.; Feng, L. Y.; Zhai, H. J. Ternary CBe4Au4 cluster: a 16-electron system with quasi-planar tetracoordinate carbon. Phys. Chem. Chem. Phys. 2018, 20, 6299–6306. (29) Janssens, E.; Tanaka, H.; Neukermans, S.; Silverans, R. E.; Lievens, P. Two-dimensional magic numbers in mass abundances of photofragmented bimetallic clusters. New J. Phys. 2003, 5, 46. (30) Knight, W. D.; Clemenger, K.; de Heer, W. A.; Saunders, W. A.; Chou, M. Y.; Cohen, M. L. Electronic shell structure and abundances of sodium clusters. Phys. Rev. Lett. 1984, 52, 2141– 2143. (31) Sergeeva, A. P.; Averkiev, B. B.; Zhai, H. J.; Boldyrev, A. I.; Wang, L. S. All-boron analogues of aromatic hydrocarbons: B17− and B18−. J. Chem. Phys. 2011, 134, 224304. (32) Saunders, M. Stochastic search for isomers on a quantum mechanical surface. J. Comput. Chem. 2004, 25, 621–626. (33) Bera, P. P.; Sattelmeyer, K. W.; Saunders, M.; Schaefer III, H. F.; Schleyer, P. v. R. Mindless chemistry. J. Phys. Chem. A 2006, 110, 4287–4290. (34) Hay, P. J.; Wadt, W. R. Ab Initio effective core potentials for molecular calculations. Potentials for the transition metal atoms Sc to Hg. J. Chem. Phys. 1985, 82, 270–283. (35) Hay, P. J.; Wadt, W. R. Ab initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core orbitals. J. Chem. Phys. 1985, 82, 299–310. (36) Adamo, C.; Barone, V. Toward reliable density functional methods without adjustable parameters: The PBE0 model. J. Chem. Phys. 1999, 110, 6158–6170. (37) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. Quadratic configuration interaction. A general technique for determining electron correlation energies. J. Chem. Phys. 1987, 87, 5968–5975. (38) Scuseria, G. E.; Janssen, C. L.; Schaefer III, H. F. An efficient reformulation of the closed-shell

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Kalemos, A. The nature of the chemical bond in Be2+, Be2, Be2−, and Be3. J. Chem. Phys. 2016, 145, 214302.

(48) Antonov, I. O.; Barker, B. J.; Bondybey, V. E.; Heaven, M. C. Spectroscopic characterization of Be2+ X 2u+ and the ionization energy of Be2. J. Chem. Phys. 2010, 133, 074309. (49) For such ternary C−Be−Li clusters, WBI does not necessarily anticorrelate to bond distance. Charge state, ionicity versus covalency, charge distributions, and coordination environments all sensitively affect this relationship. (50) Mercero, J. M.; Boldyrev, A. I.; Merino, G.; Ugalde, J. M. Recent developments and future

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prospects of all-metal aromatic compounds. Chem. Soc. Rev. 2015, 44, 6519–6534. (51) Note also that peripheral Be4Au4 ring in quasi-ptC C4v CBe4Au4 appears to be far more robust (WBIs: 0.58),28 compared to 0.19−0.26 for ppC cluster 1 (Figure 2). This justifies the ptC geometry for CBe4Au4. (52) VandeVondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. Comput. Phys. Commun. 2005, 167, 103–128. (53) Two neutral structures 1 and 2, despite their difference in coordination environments, show similar charge distributions: the C enter is negatively charged with around −2 e, the Be sites are moderately charged (by −0.7 e in total), and the outer Li sites are highly positively charged (by +2.6 to +2.8 e in total). For dianion cluster 3, the charges from inner out are −2.3, −0.8, and +1.1 e, respectively, suggesting that two extra charges primarily affect outer Be4Li4 ring. Therefore, intramolecular Coulomb repulsion seems to be more severe in neutral clusters 1 and 2 than in dianion 3.

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Table 1.

Nucleus-independent chemical shifts (NICSs) of CBe4Li4 (1, C2v, 1A1) and CBe4Li42− (3, D4h, 1A1g) clusters, calculated at a distance R (in Å) above ppC/ptC centers at PBE0/6-311+G(d) level. NICS data of C6H6 are also listed for comparison.

R

CBe4Li42− (3)

CBe4Li4 (1)

C6H6

NICS

NICSzz

NICS

NICSzz

NICS

NICSzz

1.0

−10.51

−7.88

−48.22

−118.50

−10.34

−29.61

2.0

−2.04

−8.14

−17.07

−53.53

−4.88

−17.57

19



Figure Captions

Figure 1.

Optimized global-minimum (GM) structures at PBE0-D3/def2-TZVP level for CBe4Li4 (1, C2v, 1A1) and CBe4Li42− (3, D4h, 1A1g) clusters. Bond distances (in Å) are labeled. Carbon atom is shown in gray, Be in gold, and Li in purple.

Figure 2.

Wiberg bond indices (WBIs; in blue color) and natural charges (in e; red color) for CBe4Li4 (1) and CBe4Li42− (3), calculated at PBE0-D3/def2-TZVP level.

Figure 3.

Canonical molecular orbitals (CMOs) of 18-electron ptC D4h CBe4Li42− (3) cluster. (a) Four  CMOs based on Be s/p and Li s/p atomic orbitals (AOs); these can be transformed to four Li−Be−Li three-center two-electron (3c-2e)  bonds. (b) One delocalized, completely bonding  CMO composed of tangential Be p AOs. (c) One delocalized  CMO on the CBe4 core. (d) Three  CMOs (that is,  sextet) on the CBe4 core.

Figure 4.

Bonding pattern for 18-electron ptC D4h CBe4Li4 (3) cluster, as revealed from adaptive natural density partitioning (AdNDP). Occupation numbers (ONs) are indicated.

Figure 5.

CMOs of 16-electron ppC C2v CBe4Li4 (1) cluster. (a) Three  CMOs based on Be s/p and Li s/p AOs. (b) One delocalized, completely bonding  CMO, which is composed of tangential Be p AOs and located on outer Be4Li4 ring. (c) One delocalized  CMO on the CBe4 core. (d) Three  CMOs on the CBe4 core.

Figure 6.

AdNDP bonding pattern for 16-electron ppC C2v CBe4Li 4 (1) cluster. ONs are shown. An alternative “island” version is presented in Figure S4.

Figure 7.

Root-mean-square deviations (RMSD) of ppC C2v CBe4Li4 (1) cluster during Born-Oppenheimer molecular dynamics (BOMD) simulations at 298 and 398 K.

Figure 8.

(a) Optimized local-minimum (LM) structure of CBe4Li4 (2, C4v, 1A1) at PBE0-D3/def2-TZVP level. Bond distances are shown in Å. (b) WBIs (in blue color) and natural charges (in e; red color). 20


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Figure 1.

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Figure 2.

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Figure 3.

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Figure 4.

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Figure 5.

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Figure 6.

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Figure 7.

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Figure 8.

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Table of Contents:

29


Planar Pentacoordinate versus Tetracoordinate Carbons in Ternary

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