Structure and Bonding in Planar Hypercoordinate Carbon Compounds

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This entry is adapted from the peer-reviewed paper 10.3390/chemistry4040113

The term hypercoordination refers to the extent of the coordination of an element by its normal value. In the hypercoordination sphere, the element can achieve planar and/or non-planar molecular shape. Hence, planar hypercoordinate carbon species violate two structural rules: (i) The highest coordination number of carbon is four and (ii) the tetrahedral orientation by the connected elements and/or groups. The unusual planar orientations are mostly stabilized by the electronic interactions of the central atom with the surrounding ligands. Primary knowledge of the planar hypercoordinate chemistry will lead to its forthcoming expansion. Experimental and theoretical interests in planar tetracoordinate carbon (ptC), planar pentacoordinate carbon (ppC), and planar hexacoordinate carbon (phC) are continued. The proposed electronic and mechanical strategies are helpful for the designing of the ptC compounds. Moreover, the 18-valence electron rule can guide the design of new ptC clusters computationally as well as experimentally. However, the counting of 18-valence electrons is not a requisite condition to contain a ptC in a cluster. Furthermore, this ptC idea is expanded to the probability of a greater coordination number of carbon in planar orientations. Unfortunately, until now, there are no such logical approaches to designing ppC, phC, or higher-coordinate carbon molecules/ions. There exist a few global minimum structures of phC clusters identified computationally, but none have been detected experimentally. All planar hypercoordinate carbon species in the global minima may be feasible in the gas phase.

anti-van’t Hoff Le Bel planar tetracoordinate carbon planar pentacoordinate carbon planar hexacoordinate carbon

1. Planar Tetracoordinate Carbons (ptCs)

1.1. How to Achieve ptCs

Methane (CH₄) is the simplest hypothetical ptC molecule to think about. The hybridization changes from sp³ to sp² for the planar D_4h configuration. The planar configuration is approximately 130 kcal mol⁻¹ higher in energy compared to the lowest-energy tetrahedral geometry ^[1]. Even the planar structure has higher energy than the C–H bond detachment energy (103 kcal mol⁻¹) ^[2]. After the analysis of the electronic structure of the planar CH₄ molecule, Hoffmann and co-workers suggested a way to stabilize the planar structures. When the tetrahedral structure of methane becomes planar, an extra lone pair is available on the central carbon, which distorts its planar geometry. The other point is the electron-deficient nature of the C–H bonds in the planar form. They suggested that the replacement of hydrogens by σ-donor ligands overcome the electron deficiency problem of the C–H bonds, as the ligands give electrons to the carbon atom. The ligands should have π-acceptor capacity so that they can accept the lone pair on the carbon. So, with the incorporation of simultaneous σ-donor and π-acceptor ligands, a ptC structure can be generated, and this strategy is called the “electronic approach”. Using this approach, many ptC molecules have been theoretically reported ^[3]^[4]^[5]^[6]^[7]^[8]^[9]^[10]^[11]^[12]^[13]^[14]^[15]^[16]^[17]^[18]^[19]^[20]^[21],^[22],^[23],^[24]] and experimentally characterized ^[25]^[26]^[27]^[28]^[29]^[30]^[31]^[32]^[33].

In addition to the electronic approach, ptC structures can be designed by generating enough strain to keep the carbon forcefully in planar orientations, and this method is called the “mechanical strategy”. In this particular approach, to generate sufficient strain, cylindrical cages or tubes, small rings, and annulenes are helpful agents ^[34]^[35]^[36]^[37]^[38]^[39]^[40]. Although some species with ptC were designed theoretically by using this strategy, no experimentally characterized ptC structures based on this strategy have been reported. Following this strategy, some of the computationally predicted ptC species are shown in Figure 1. To achieve ptC structures based on this approach, the fenestrenes and the aromatic unsaturated fenestrenes, rigid 3D cages, such as octaplane, were proposed initially ^[41]^[42]. In 1999, Ding et al. noted that “despite considerable computational efforts no structures with a planar tetracoordinate C(C)₄ substructure have been found” ^[43]. However, Rasmussen et al. computationally reported the first successful ptC structure based on this strategy by adjusting the 1g structure to generate 1h (Figure 1) geometry in which the ptC atom is stabilized in a strained environment ^[37]^[44]. With the use of a similar strategy, Wang and Schleyer reported a set of boron spiroalkanes with a planar C(C)₄ moiety through the replacement of carbon by boron atoms ^[9]^[45].

Figure 1. Schematic presentations of various mechanically stabilized ptC molecules (a–h).

1.2. Early Examples of ptCs

With the help of the two suggested strategies, the first example of ptC came from Collins et al. in 1976 ^[46]. Through a systematic computational investigation, they reported 1,1-dilithiocyclopropane (Figure 2a) and 3,3-dilithiocyclopropene (Figure 2b) systems with ptCs in the energy minimum geometries and the tetrahedral orientations have higher energies than the corresponding planar configurations. One year later, the first experimentally characterized ptC containing compound V₂(2,6-dimethoxyphenyl)₄ (Figure 2c) was published by Cotton et al. ^[47]. This complex contains triple bonds between two vanadium (V) centers and has two ptCs at two ligand rings. However, unfortunately, at that time, the original authors did not realize this beautiful fact. This system has importance in this background as it is the first experimentally predicted ptC-containing compound. Due to the ionic bonding nature of lithium (Li), it prefers bridging positions, and with this concept, Xie et al. in 1991 designed a D_6h symmetric C₆Li₆ system with ptCs (Figure 2d) ^[48]. The simplest molecule with a ptC has only five atoms, and the first example of this category was CAl₂Si₂, which was reported in 1991 by Schleyer and Boldyrev ^[4]. They concluded that cis and trans isomers of CSi₂Al₂ (Figure 3a and 3b, respectively) were local minimum geometries with a ptC, but they did not mention the energy of the tetrahedral-like geometry of this system. They first introduced the 18-valence electron counting concept for the stabilization of planar geometries. After seven years, in 1998, Boldyrev and Simons computed the energies of the planar and tetrahedral-like geometries of the CSi₂Al₂ system, and then they expanded the search for the possibility of a ptC atom in higher analogues such as CSi₂Ga₂ and CGe₂Al₂ species in order to determine the size dependency of the surrounding atoms on the stabilities of these species in planar orientations ^[5]. The optimized structures of CSi₂Al₂ in singlet states are given in Figure 3. The cis and trans isomers of the CSi₂Al₂ system are energy minima based on the theoretical analysis using the B3LYP/6-311+G* method, which is in agreement with the earlier conclusion at the MP2/6-31G* level of theory. However, both these isomers become saddle points in the MP2(full)/6-31+G* and MP2(full)/6-311+G* methods ^[5]. The authors reported that in the case of the CSi₂Al₂ system, the tetrahedral-type geometry is a first-order saddle point in the B3LYP/6-311+G* and MP2(full)/6-311+G* methods and has almost 27−28 kcal mol⁻¹ higher energy than the more stable quasi planar cis and trans isomers 3a and 3b, respectively (Figure 3) ^[5]. Then they studied two 18-valence isoelectronic species, CSi₂Ga₂ and CGe₂Al₂, where the cavities for the carbon center happened to be larger than that in the CSi₂Al₂ system. However, this time they only optimized planar cis and trans and tetrahedral geometries for CSi₂Ga₂ and CGe₂Al₂ systems. In the B3LYP/6-311+G* and MP2(fc)/6-311+G* methods, the planar cis and trans isomers of both these species were reported as energy minima ^[5]. However, the cis isomer (Figure 3c) of CSi₂Ga₂ is less stable than the trans isomer (Figure 3d) by 2 kcal mol⁻¹, while, for the CGe₂Al₂ system, the cis isomer (Figure 3e) has 3 kcal mol⁻¹ lower energy than the trans isomer (Figure 3f). They also reported that the tetrahedral-type geometries have 27 and 25 kcal mol⁻¹ more energy than the most stable isomers for CSi₂Ga₂ and CGe₂Al₂ systems, respectively. The increase in the size of the cavity in the CSi₂Ga₂ and CGe₂Al₂ species permits the incorporation of carbon into it and thus maintains the planar structures. From these analyses, they concluded that pentatomic species with a carbon center and two Al or Ga and two Si or Ge surrounding atoms should have stable planar geometries ^[5]. The planar structures may be preferred over the tetrahedral one when Jahn−Teller distortion makes the tetrahedral geometries unstable and the formation of the maximal carbon–ligand and ligand−ligand bonding by the valence electrons. For this purpose, they compared the occupancy pattern of the valence molecular orbitals (MOs) of the tetrahedral CF₄ molecule with the tetrahedral structures of their systems. The CF₄ molecule is a 32-valence electronic system, and the occupancy pattern of the occupied MOs is 1a₁²1t₂⁶2a₁²2t₂⁶1e⁴3t₂⁶1t₁⁶. They assumed other tetrahedral molecules or nearly tetrahedral structures will follow this occupancy pattern (except for symmetry-imposed degeneracies) and the 18-valence electronic tetrahedral structures show 1a₁²1t₂⁶2a₁²2t₂⁶1e² pattern of occupancy. Due to this partially filled e-orbital, the tetrahedral structures of their systems show Jahn–Teller instability and become distorted to a planar structure. They suggested that the presence of 18-valence electrons is crucial for planar geometries to be stable and preferred over tetrahedral structures. The formation of three σ and one π bonds among the middle carbon and the surrounding atoms and one ligand–ligand bond are the consequences of 18-valence electrons, the appeasement case for planar geometries. It took a long time to encourage experimental researchers to test this prognosis. Nevertheless, the species CAl₄⁻ and CAl₃Si⁻ (isoelectronic to CSi₂Ga₂) were prepared in molecular beams and the planarity of these systems was experimentally confirmed ^[7]^[33]^[49].

Figure 2. Optimized geometries of (a) 1,1-dilithiocyclopropane and (b) 3,3-dilithiocyclopropene systems. (c) The molecular structure of V₂(2,6-dimethoxyphenyl)₄ features a V≡V triple bond and two planar tetracoordinate carbon (ptC) centers. The H atoms are omitted for clarity. (d) Optimized D_6h symmetric structure of C₆Li₆.

Figure 3. Optimized geometries of (a) cis-CSi₂Al₂, (b) trans-CSi₂Al₂, (c) cis-CSi₂Ga₂, (d) trans-CSi₂Ga₂, (e) cis-CGe₂Al₂, and (f) trans-CGe₂Al₂ systems. Structure (a) has 1.16 kcal mol⁻¹ lower energy than structure (b). Structure (c) has 2.01 kcal mol⁻¹ higher energy than structure (d). Structure (e) has 2.87 kcal mol⁻¹ lower energy than structure (f).

With the use of Li as ligand atoms, a series of ptC species can be adapted ^[8]. For example, the replacement of the CH₂ group in the 1,1-dilithiocyclopropane (Figure 2a) molecule by isoelectronic NH and O generates ptC structures 4a and 4b, respectively (Figure 4). The 4c and 4d ptC structures are also generated by attaching 4a to a heterocyclic system and a benzene ring, respectively. These 4c and 4d species are more viable targets due to the dominance of the aromaticity of imidazole.

Figure 4. Optimized geometries of (a–d) computationally predicted dilithium ptC compounds.

2. Planar Pentacoordinate Carbons (ppCs)

The idea of ptC is expanded to the probability and representation of systems with ppC centers ^[50]. In 1995, Bolton et al. reported the singlet 1,1-dilithioethene molecule (Figure 5a) with the help of the ab initio quantum mechanical methods, which show the ppC local minimum structure having 7.2 kcal mol⁻¹ more energy compared to the lowest-energy isomer with a ptC atom ^[51]. The barrier height for the interconversion between the ppC and the lowest-energy ptC isomers is approximately 0.4 kcal mol⁻¹ indicating that it is impossible to characterize the ppC isomer experimentally.

Figure 5. (a) A C_2v-symmetric ppC-containing isomer of 1,1-dilithioethene contains two bridging Li centers. The computed structures of (b) Cu₅H₅C, (c) Ag₅H₅C, and (d) Au₅H₅C each feature bridging hydrides and a ppC. The global minimum energy structures of (e) CAl₅⁺, (f) CAl₄Be, and (g) CAl₃Be₂⁻ clusters.

After the detection of the aromatic M₅(μ-H)₅ hydrometal rings (M = Cu, Ag, Au) ^[52]^[53], Li et al. placed one carbon atom at the center of the Cu₅(μ-H)₅ ring and found a perfect D_5h symmetric true local minimum structure with a ppC (Figure 5b) ^[54]. Although the Cu₅(μ-H)₅ ring is aromatic in nature, the inclusion of the carbon causes the nonaromaticity of the ring. Further, the Ag₅H₅C (Figure 5c) and Au₅H₅C (Figure 5d) molecules also have a ppC in their local minimum geometries ^[55].

The first global minimum geometry with a ppC in the CAl₅⁺ system with D_5h symmetry (Figure 5e) was reported based on an extensive potential energy surface (PES) search in 2008 by Zeng and co-workers ^[56]. This ppC geometry is 3.8 kcal mol⁻¹ lower in energy than the second-lowest C_2v isomer of this system. This system is also consistent with the electronic stabilization strategy approach given by Hoffmann and coworkers, and the presence of the back donation from the central carbon to the peripheral atoms is also reported by them. Moreover, the aromaticity analysis based on the nucleus-independent chemical shift (NICS) computations [^[57],^[58],^[59],^[60]] of this ppC system has been carried out by these groups.

After one year, Wang and coworkers substituted the Al atoms with isoelectronic Be atoms to generate neutral CAl₄Be (Figure 5f) and mono-anionic CAl₃Be₂⁻ (Figure 5g) systems containing ppCs in the global minimum structures ^[61]. The aluminum–carbon bond distances are between 2.08 and 2.29 Å, which are somewhat lengthy compared to the value of the normal aluminum–carbon bond distance of 2.00 Å but close to the 2.12 Å values as predicted theoretically for the CAl₅⁺ system. The bonds among the central carbon and the surrounding Be and Al atoms are longer by 0.08 Å to 0.29 Å than the corresponding normal values. The molecular dynamics simulation suggested the dynamic stability of these global minimum ppC isomers. The highly negative charges on the carbon are the consequences of the σ-donation from the surrounding atoms. At the same time, the carbon lone pair is donated to the ligand atoms. Therefore, the central carbon in the global minimum structures acts as the σ-acceptor and π-donor. The energy differences between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are 2.6 eV for both ppC structures indicating the greater stability of these isomers ^[61].

Wu et al., in 2012, reported di-anionic CAl₂Be₃²⁻ (Figure 6a) and its mono-anionic salt complex LiCAl₂Be₃⁻ (Figure 6b) systems by further replacement of Al atoms by Be atoms ^[62]. The PES search shows the global minimum geometry of these clusters has a ppC. The vertical detachment energy (VDE) for the CAl₂Be₃²⁻ cluster is negative (−1.10 eV) indicating that this species is unstable toward electron release. However, the instability of this cluster is resolved by adding one Li⁺ to neutralize one negative charge, and the most preferable binding site of Li⁺ is the Be–Be bond in the LiCAl₂Be₃⁻ cluster. In the LiCAl₂Be₃⁻ system, the first computed VDE is 2.28 eV, indicating that the automatic removal of the additional electron is partially eliminated. Moreover, the energy gap between the HOMO and LUMO increases from 0.94 eV in CAl₂Be₃²⁻ to 1.79 eV in the LiCAl₂Be₃⁻ system. Hence, from these stability comparisons, it is clear that LiCAl₂Be₃⁻ system is more achievable than the CAl₂Be₃²⁻cluster ^[62]. The dynamical stability of the global minimum structures was confirmed at 4 K and 298 K temperatures up to 100 ps simulation time. The natural charge analyses indicate that the addition of Li⁺ to the CAl₂Be₃²⁻ system influences the ionic bonding, but the covalent bonds are not markedly affected.

Figure 6. The global minimum energy structures of (a) CAl₂Be₃²⁻, (b) LiCAl₂Be₃⁻, (c) CBe₅Al⁻, and (d) CBe₅Ga⁻ clusters. The local minimum structures of (e) CBe₅In⁻ and (f) CBe₅Tl⁻ clusters.

Further, the complete substitution of Al atoms was performed by Castro et al., in which they generated heptaatomic anionic clusters CBe₅E⁻ (E = Al, Ga, In, Tl) and searched the PES of the designed systems ^[63]. For CBe₅Al⁻ (Figure 6c) and CBe₅Ga⁻ (Figure 6d) clusters, the ppC structures are the global minima. However, for CBe₅In⁻ (Figure 6e) and Cbe₅Tl⁻ (Figure 6f) clusters, the ppC local minima have only 1.2 kcal mol⁻¹ and 1.8 kcal mol⁻¹ higher energy compared to the lowest-energy isomers, respectively. The geometries show that the ppC atom is present in the middle of the Be₄E ring, and an extra Be atom is bonded to one Be–Be bond in the plane. In the case of the CBe₅Al⁻ geometry, the aluminum–carbon bond distance is 2.233 Å, which is somewhat lengthier than the normal aluminum–carbon bond length of 2.00 Å and the 2.12 Å values theoretically predicted for the CAl₅⁺ system. The highly negative charges on the carbon are the consequences of the σ-donation from the surrounding atoms. From the valence electronic configuration of the carbon atom, they concluded that the carbon lone pair is donated to the ligand atoms, which assists in stabilizing the planar geometries ^[63]. The authors found that the planar global minimum geometries are σ- and π-aromatic.

In 2008, Qiong et al. designed CBe₅ and CBe₅⁴⁻ systems having a ppC atom in their stable local minimum structures (Figure 7a) ^[64]. The Be₅ ring assists as a σ-donor and a π-acceptor in the D_5h structure of CBe₅ and CBe₅⁴⁻ systems, respectively. The NICS calculations predicted that in the D_5h structure of CBe₅ and CBe₅⁴⁻ systems, σ-aromaticity and π-aromaticity, respectively, are dominant. Although the CBe₅⁴⁻ cluster has a ppC, the greater charge density makes it unstable. However, the instability of this cluster is resolved by adding Li⁺ ions to neutralize the negative charges and the resulting species are CBe₅Li_nⁿ⁻⁴ (n = 1 to 5) (Figure 7b to 7f, respectively) ^[65]. In these clusters, the ppC cores are preserved when Li⁺ ions are bonded with their corresponding anions. The central carbon in the global minimum structures acts as the σ-acceptor and π-donor. The electron delocalization within the CBe₅Li_nⁿ⁻⁴ (n = 1 to 5) clusters is predicted from the induced magnetic field analysis. The energy gap between the HOMO and LUMO increases moderately upon increasing the counter ions from CBe₅Li₃⁻ (3.47 eV) to CBe₅Li₅⁺ (7.11 eV), suggesting increased stability following the maximum hardness principle (MHP) [^[66],^[67]]. The molecular dynamics simulations of the systems at 1000 K for 20 ps show that the CBe₅ pentagon remains intact during the entire simulation. The negative charge density on the CBe₅⁴⁻ cluster is also decreased by capping H⁺ ions to the system, just as in the case of Li⁺ ions, and the species are CBe₅H_nⁿ⁻⁴ (n = 2–5) ^[68]. In the case of CBe₅H₂²⁻ (Figure 8a) and CBe₅H₃⁻ (Figure 8b) clusters, the ppC structures are the lowest-energy C_2v point group of symmetry. For the CBe₅H₄ cluster (Figure 8c), a quasi-planar geometry has 1.8 kcal mol⁻¹ more energy compared to the tetrahedral global minimum structure. Moreover, the CBe₅H₅⁺ cluster (Figure 8d) has a quasi-planar ppC structure as the global minimum. The stability of the ppC- or quasi-ppC-containing geometries is governed by the presence of the peripheral three-centered-two-electron Be–H–Be bonds, the origination of the stable eight-electron shell structure, and the presence of the 6σ and 2π dual aromaticity. The excess charge density on the CBe₅⁴⁻ system is also reduced by complexing with halogen cations (F⁺, Cl⁺, and Br⁺) or alkali metal cations (Li⁺, Na⁺, and K⁺) to generate CBe₅X₅⁺ systems ^[69]. The PES search shows that the global minima of the clusters are either in ppC or quasi-ppC forms. The global minima of CBe₅F₅⁺, CBe₅Li₅⁺, CBe₅Na₅⁺, and CBe₅K₅⁺ clusters have excellently planar and extremely symmetric D_5h geometries, whereas CBe₅Cl₅⁺ and CBe₅Br₅⁺ clusters experience slight non-planar contortion as C₂ geometries. Again, in these systems, the three-centered-two-electron Be–X–Be bonds provide stability in planar forms. The NICS analysis proved the double aromatic character (σ- and π-aromaticity) of the systems is in agreement with the adaptive natural density partitioning (AdNDP) analyses [^[70],^[1]]. The molecular dynamics simulations suggested that the ppC-containing CBe₅ ring in the minimum energy structures is well conserved throughout the whole simulation, indicating that the geometries are rigid against isomerization and decomposition.

Figure 7. (a) The symmetric structures CBe₅ and CBe₅⁴⁻ are ppC species. The neutral and tetraanionic forms have the same shape but different bond lengths. The global minimum structures of (b) CBe₅Li³⁻, (c) CBe₅Li₂²⁻, (d) CBe₅Li₃⁻, (e) CBe₅Li₄, and (f) CBe₅Li₅⁺ clusters.

Figure 8. The global minimum structures of (a) CBe₅H₂²⁻ and (b) CBe₅H₃⁻ clusters with a perfect ppC. The local and global minimum structures of (c) CBe₅H₄ and (d) CBe₅H₅⁺ clusters, respectively, with a quasi-ppC.

In 2018, Zhao et al. reported various ppC systems by adding hydrogen atoms to the CAl₄Be, CAl₃Be₂⁻, CAl₂Be₃²⁻, and CAlBe₄³⁻ parent molecules ^[71]. They reported nine new planar and quasi-planar ppC clusters of CAl_nBe_mH_x^q (n + m = 5, q = 0, ±1, x = q + m − 1) (Figure 9). The ppC core remains unchanged geometrically and electronically with the gradual introduction of hydrogen atoms. Interestingly, the energy gap between the HOMO and LUMO increases in the studied clusters as compared to the parent anionic clusters. The presence of the three-centered-two-electron Be–H–Be or Be–H–Al π bonds is responsible for the stabilization of the ppC geometries ^[71]. Remarkably, among the nine studied clusters, seven molecules show ppC in the global minimum structures. Again, among the global minimum geometries, only CAl₃Be₂H, CAl₂Be₃H⁻, CAl₂Be₃H₂, and CAlBe₄H₄⁺ clusters are dynamically stable enough. For the CAl₄BeH₄⁺ and CAl₃Be₂H₂⁺ clusters, the ppC isomers have 10.7 and 3.8 kcal mol⁻¹ higher energy, respectively, with respect to the lowest-energy structures. However, the closest isomers of the CAl₃Be₂H, CAl₂Be₃H⁻, CAl₂Be₃H₂, CAl₂Be₃H₃⁺, CAlBe₄H₂⁻, CAlBe₄H₃, and CAlBe₄H₄⁺ clusters have 4.6, 3.1, 4.6, 3.6, 3.7, 2.8, and 15.0 kcal mol⁻¹ higher energies, respectively, with respect to the global minimum structures ^[71]. The NICS calculations predicted that the considered clusters are σ- and π-dual aromatic. The natural bond orbital (NBO) computations predicted that there is a significant contribution of the ionic and covalent bonding toward the stabilization of the ppC structures.

Figure 9. Optimized structures of (a) CAl₄BeH₄⁺, (b) CAl₃Be₂H, (c) CAl₃Be₂H₂⁺, (d) CAl₂Be₃H⁻, (e) CAl₂Be₃H₂, (f) CAl₂Be₃H₃⁺, (g) CAlBe₄H₂⁻, (h) CAlBe₄H₃, and (i) CAlBe₄H₄⁺ clusters.

Recently, Pan et al. reported a family of systems with ppC based on the next heaviest analogue of the CAl₅⁺ system ^[72]. As the size of the Ga atom is larger than that of the Al, no ppC isomer is found as a global and/or local minimum for the CGa₅⁺ system. Hence, with the use of the smaller-sized beryllium (Be) atoms, the isoelectronic substitution of Ga atoms generated CGa₄Be, CGa₃Be₂⁻, CGa₂Be₃²⁻, and CGaBe₄³⁻ clusters with ppC in the global minimum structures (Figure 10). For the neutralization of the anionic clusters, one, two, and three Li⁺ ions were used for CGa₃Be₂⁻, CGa₂Be₃²⁻, and CGaBe₄³⁻ clusters, respectively, to generate CGa₃Be₂Li, CGa₂Be₃Li₂, and CGaBe₄Li₃ clusters (Figure 10). Although the anionic systems have ppC in the global minimum structures, the first ionization potential of CGa₂Be₃²⁻ and CGaBe₄³⁻ clusters are negative (−2.91 and −6.45 eV, respectively) suggesting the spontaneous loss of an electron from the clusters ^[72]. However, the first ionization potential of the CGa₃Be₂⁻ cluster is positive (1.20 eV) indicating its stability towards the spontaneous loss of an electron. The central carbon in the global minimum structures acts as the σ-acceptor and π-donor. Moreover, the extent of π-back-bonding from the 2p_z orbital of the central carbon also increases by increasing the number of counter-ions. The electron delocalization within the system is well understood from the molecular orbitals and their magnetic responses studies. The magnetic responses indicated the σ- and π-aromaticity of the global minimum structures, and the σ-contribution is the governing one ^[72].

Figure 10. The lowest-energy ppC forms for (a) CGa₄Be, (b) CGa₃Be₂⁻, (c) CGa₂Be₃²⁻, (d) CGaBe₄³⁻, (e) CGa₃Be₂Li, (f) CGa₂Be₃Li₂, and (g) CGaBe₄Li₃ clusters.

Using silicon (Si) as the surrounding atoms, Zdetsis et al. in 2011 designed Si₅C²⁻ and Si₅C⁻ clusters (Figure 11a) with the help of the DFT and the coupled-cluster theory that predicted planar structures of the clusters stabilized by the C–Si bonds ^[73]. These local minimum structures have 12.9 and 22.8 kcal mol⁻¹ higher energy compared to the three-dimensional-type global minimum for Si₅C²⁻ and Si₅C⁻ clusters, respectively. For the Si₅C⁻ cluster, the authors reported two planar structures with D_5h and C_s point groups of symmetries that are related by Jahn–Teller distortions. However, these two geometries differ by only 8 kcal mol⁻¹ of energy.

Figure 11. (a) The symmetric structures Si₅C²⁻ and Si₅C⁻ clusters are ppC species. The monoanionic and dianionic forms have the same shape but different bond lengths. The lowest-energy isomers of (b) CAl₄MX₂ clusters and (c) CAl₄M(C₅H₅)₂ clusters. The global minimum structure of (d) CB₅S₅⁺ cluster with a ppC.

Merino and co-workers used transition metals along with the main group elements to design a ppC in the global minimum structure. They reported CAl₄MX₂ clusters (M = Zr and Hf; X = F–I and C₅H₅) with a ppC connected to a transition metal and attached to a metallocene skeleton (Figure 11b,c) ^[74]. The natural charge analysis suggested that a significant amount of electron transfer occurs from the surrounding atoms to the central carbon atom and the values are in the range of −2.21 to −2.37 |e|. The BOMD simulations assist the kinetic stability of the Zr systems at 700 K.

Very recently, Sun et al. designed a sulfur-surrounded boron wheel CB₅S₅⁺ cluster with a ppC in the global minimum structure (Figure 11d) ^[75]. In this cluster, the presence of the strong π back-donation from the five-bridged sulfur atoms to the boron atoms lowers the electron-deficient nature of the boron centers. The second-lowest isomer with a ptC atom has 1.1 kcal mol⁻¹ higher energy than the lowest-energy ppC isomer. The structure with planar pentacoordinate boron (ppB) has 61.2 kcal mol⁻¹ higher energy than the ppC structure. The BOMD simulation suggested that at 4 K, the global minimum is dynamically very rigid. Moreover, the planarity of the cluster is well conserved at 298 K, 500 K, and 1000 K temperatures. The considered cluster has a 7.47 eV energy gap between HOMO and LUMO, a high VDE value of 13.22 eV, and a low vertical electron affinity (VEA) of 4.31 eV, indicating an electronically robust structure ^[75]. The NICS computations show the σ + π double aromaticity in the CB₅S₅⁺ cluster.

All the above-mentioned global and/or local minimum structures contain one ppC. In 2005, Schleyer and coworkers reported certain fluxional wheel-like species, namely, C₂B₈, C₃B₉³⁺, and C₅B₁₁⁺, in which the interior C₂, C₃, and C₅ fragments revolve within the boron rings, respectively (Figure 12) ^[76]. In C₂B₈, C₃B₉³⁺, and C₅B₁₁⁺ species, there are two, three, and five ppC centers that coexist in the energy minimum geometries, respectively. The NICS computations predict the π-aromaticity of these species with more than one ppC atom. These unusual planar clusters are stable when the constituent elements are suited nicely, both geometrically and electronically.

Figure 12. The boron–carbon clusters (a) C₂B₈, (b) C₃B₉³⁺, and (c) C₅B₁₁⁺ are local minimum structures that include conformationally dynamic C₂, C₃, and C₅ units, respectively, within boron rings.

3. Planar Hexacoordinate Carbons (phCs)

The possibility of the ptC and ppC molecules and/or ions are discussed in the previous two sections. Now the question arises of whether it is feasible to obtain a planar hexacoordinate carbon (phC) or a planar heptacoordinate carbon, or a planar octacoordinate carbon. In the case of the main group of components, the existence of planar hexacoordination is limited. Despite various species with hexacoordinate carbon being described, they have 3D geometries (Figure 13) ^[77]^[78]^[79]. In 2000, the first example with a phC is the CB₆²⁻ di-anionic system (Figure 14a), studied by Exner et al. using DFT and high-level ab initio calculations ^[80]. This system has a D_6h point group of symmetry. The reported structure is not the lowest-energy isomer, rather it is a local minimum with 143.9 kJ mol⁻¹ more energy compared to the lowest-energy structure. This cluster shows benzene-like HOMOs and is aromatic in nature.

Figure 13. Some compounds with hexacoordinate carbons have three-dimensional structures.

Figure 14. Local minimum structures of (a) CB₆²⁻ and (b) CN₃Be₃⁺ clusters with a phC. Global minimum structures of (c) CO₃Li₃⁺ and (d) CE₃M₃⁺ (E = S–Te, and M = Li–Cs) clusters.

In 2012, Wu et al. used a CB₆²⁻ unit and executed isoelectronic replacement on it to compose unipositive CN₃Be₃⁺ and CO₃Li₃⁺ clusters (Figure 14b and 14c, respectively) ^[81]. Both clusters in their phC structures correspond to the D_3h symmetry. The CN₃Be₃⁺ cluster is a local minimum with 25.5 kJ mol⁻¹ more energy with respect to the global minimum geometry. However, the CO₃Li₃⁺ cluster is a putative global minimum with a phC center. The authors mentioned that the three bridging Li⁺ ions stabilized the CO₃²⁻ ion electrostatically. Later, Leyva-Parra et al. studied the charges on the middle carbon and the bridging Li centers, and the values are 0.87 |e| and 0.97 |e|, respectively ^[82]. Hence, the positive charges on both carbon and lithium atoms imply electrostatic repulsion between them. Due to this repulsion and the nonappearance of any remarkable orbital overlap between them, this hexacoordinate environment is ambiguous. Because of the different electronegativity values of carbon and oxygen atoms, positive charges on the phC are expected. Therefore, Leyva-Parra et al. substituted the oxygen atoms with the least electronegative sulphur atoms to obtain a true phC atom in the global minimum structures ^[82]. The fifteen possible CE₃M₃⁺ (E=S–Te, and M=Li–Cs) combinations are to be identified as phC clusters (Figure 14d). The natural charge analysis shows negative charges on the phC and positive charges on the bridging metal atoms suggesting electrostatic attractions between the partially negative central carbon atom and partially positive bridged metal atoms. These phC clusters were designed following the so-called “proper polarization of ligand” approach ^[82]. Through systematic bonding analyses, the authors stated the covalent nature of the C–E bonds and the ionic nature of the C–M bonds.

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