Structure and Bonding in Planar Hypercoordinate Carbon Compounds

Abstract

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. In this review article, we will talk about the current progress in the theoretical prediction of viable planar hypercoordinate carbon compounds. 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.

1. Introduction

The systems containing planar tetracoordinate carbons are seminal examples of non-classical species [1,2,3,4,5,6,7]. The non-classical species have outstanding optical, magnetic, and electronic characteristics and have various potential applications. Most organic molecules are based on two structural rules, (i) the highest coordination number of carbon is four and (ii) the tetrahedral orientation by the connected elements and/or groups [3,8]. However, at that time, it was not considered that the tetracoordinate tetrahedral carbon (ttC) model is valid up to what extent. Therefore, without knowing the beautiful ptC concept, many molecules were characterized. In 1968, the idea of ptC was established by H. J. Monkhorst as a transition state structure of methane in a non-dissociative racemization process [9]. This concept was introduced in the work of Professor Hans Wynberg whose group synthesized the CR₁R₂R₃R₄ hydrocarbons with four non-identical alkyl groups (R₁, R₂, R₃, and R₄) by the chiral routes but did not obtain measurable optical activity [10]. Then, to determine the energy barrier for the possibilities of thermal racemization that causes no optical activity, Professor H. J. Monkhorst began theoretical calculations and ruled out the possibility of planar methane due to its very high relative energy. His intention was not to determine a ptC minimum but rather to conclude that the stereo mutation of methane via a ptC intermediate is quite unfeasible. Later, Roald Hoffmann and co-workers started to explore “how to stabilize a planar geometry so that it could serve as a thermally accessible transition state for a classical racemization experiment” to determine a strategy to lower the ptC stereo mutation energy barriers. They concluded that “it would seem too much to hope for a simple carbon compound to prefer a planar to a tetrahedral structure”. Their 1970 breakthrough was the perspicacious analysis of ptC bonding in a speculative planar CH₄ molecule [11]. Their electronic approach to stabilize ptCs suggested that the σ-donating ligands give electrons to central carbon and, simultaneously, the π-accepting behavior of the ligands takes the lone pair on the carbon atom.

In this review article, we cover the recent advancement in planar hypercoordinate carbon chemistry. Various examples of planar tetracoordinate, pentacoordinate, hexacoordinate, and heptacoordinate molecules, ions, and clusters are included in this article. Some experimentally characterized planar species are also discussed in this article. The electronic and mechanical approaches that are utilized to generate ptCs are discussed. We hope that this review article with various examples will give a primary understanding of planar hypercoordinate carbon, which will lead to its forthcoming expansion.

2. Planar Tetracoordinate Carbons (ptCs)

2.1. 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 [12]. Even the planar structure has higher energy than the C–H bond detachment energy (103 kcal mol⁻¹) [13]. 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 [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31] and experimentally characterized [32,33,34,35,36,37,38,39,40].

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 [41,42,43,44,45,46,47]. 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 [48,49]. In 1999, Ding et al. noted that “despite considerable computational efforts no structures with a planar tetracoordinate C(C)₄ substructure have been found” [50]. 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 [44,51]. 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 [20,52].

2.2. Early Examples of ptCs

With the help of the two suggested strategies, the first example of ptC came from Collins et al. in 1976 [53]. 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. [54]. 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) [55]. 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 [15]. 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 [16]. 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 [16]. 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) [16]. 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 [16]. 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 [16]. 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 [18,40,56].

With the use of Li as ligand atoms, a series of ptC species can be adapted [19]. 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.

2.3. Recent Examples of ptCs with 18 Valence Electrons

In 2012, Castro et al. designed CE₄²⁻ (E = Al–Tl) clusters (Figure 4e) with a ptC center in the lowest energy structures [57]. For all the clusters, the other two low-lying isomers have over 20 kcal mol⁻¹ more energy than the ptC isomer. The natural charge analysis shows that the central carbon acts as a simultaneous σ-acceptor and π-donor. The σ-acceptor is confirmed by the high charge density on the carbon atom. The higher occupancies of 2p_x and 2p_y as compared to the 2p_z orbitals are the revelation of the π-back-donation. The authors neutralized one negative charge of the clusters by one Li⁺ ion and the systems are CE₄Li⁻ (E = Al–Tl) [57]. The binding of the Li⁺ ion to the di-anionic system does not significantly disrupt the ptC core. For the CAl₄Li⁻ and CGa₄Li⁻ clusters, the lowest-energy geometries are planar in which the Li⁺ ion bridges the two Al and Ga atoms, respectively (Figure 5). Moreover, the pyramidal geometries of CAl₄Li⁻ and CGa₄Li⁻ clusters are 11.2 and 6.3 kcal mol⁻¹ higher in energy as compared to the lowest-energy isomers, respectively. However, in the case of the CIn₄Li⁻ and CTl₄Li⁻ clusters, the 3D geometries with C_4v symmetry are the lowest-energy structures (Figure 5). The planar structures have 2.5 and 6.8 kcal mol⁻¹ higher energy than the pyramidal geometries for CIn₄Li⁻ and CTl₄Li⁻ clusters, respectively [57].

Merino and coworkers reported the presence of a ptC center in the global minimum geometries of the neutral and 18-valence electronic CAl₃E (E = P, As, Sb, Bi) clusters (Figure 6a) [58]. The closest competitive isomer for all the clusters is more than 14 kcal mol⁻¹ higher energy than the ptC isomers. The energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) decreases drastically from P to Bi, indicating a decrease in the stability following the maximum hardness principle (MHP) [59,60,61]. In these clusters, the π-bonding orbital is mainly located on the C–E bonds unlike the other ptC clusters, and this bond is classified as a double bond. The existence of the C=E bonds is confirmed by the Wiberg bond index (WBI) values [62] and the adaptive natural density partitioning (AdNDP) [63,64] analysis. Additionally, the WBI values for C=E bonds decrease moderately from P to Bi, indicating that the inclusion of the heavier elements causes a decrease in the ability to form C=E bonds. For the CAl₃P and CAl₃As clusters, a remarkable electron shift occurs from the Al atoms to the central carbon. However, in the case of the CAl₃Sb and CAl₃Bi clusters, the electron shift from E and Al atoms to the central carbon is competitive. Simultaneously, the ptC center acts as the π-donor in the clusters. The ptC global minima are kinetically stable enough as predicted by the Born–Oppenheimer molecular dynamics (BOMD) [65] simulations at temperatures of 323 K and 373 K.

Job et al. in 2021 designed an 18-valence electronic CAl₄Mg cluster with a ptC atom in the global minimum energy structure with C_2v symmetry (Figure 6b) [66]. The second-lowest-energy isomer lies at 2.63 kcal mol⁻¹ above the ptC isomer. The ptC structure exhibits σ/π double aromaticity as determined by the nucleus-independent chemical shift (NICS) [67,68,69,70] calculations. The atom-centered density matrix propagation (ADMP) [71,72,73,74,75] simulation at 298 K for 10 ps confirmed the dynamical stability of the ptC isomer. The natural charge analysis showed that the central carbon atom acts as a simultaneous σ-acceptor and π-donor. Electron delocalization within the ptC fragment is well understood from the molecular orbitals, electron localization function (ELF) [76,77], and AdNDP analyses.

Recently, we reported three pentatomic neutral CGa₂Ge₂, CAlGaGe₂, and CSiGa₂Ge (Figure 6c to 6e, respectively) molecules with 18-valence electrons that show a ptC in the minimum-energy structure [78]. The ADMP simulations at 300 K and 500 K show the dynamic stability of the clusters. The natural charge calculations predicted that in all the systems, there is a significant charge transfer (σ-donation) from the surrounding atoms to the middle carbon, and, simultaneously, π-back donation from the carbon to the ligand atoms is also verified. The NICS computations show the σ/π-dual aromaticity of the ptC geometries. The AdNDP analysis shows the 2π/6σ framework of the ptC core in all the systems, which is crucial to maintain the planarity.

Another most recent work from our group predicted that the mono-anionic 18-valence electronic CSiGaAl₂⁻ and CGeGaAl₂⁻ clusters (Figure 6f and 6g, respectively) have a ptC in the global minimum geometries [79]. The closest competitive isomers for both clusters are more than 8.0 kcal mol⁻¹ higher energy as compared to the ptC isomers. The ptC structures are dynamically stable at 300 K and 500 K temperatures. The simultaneous σ-donation from the surrounding atoms to the carbon and the π-acceptance of the peripheral atoms from the central carbon fulfilled the criteria of the electronic approach to stabilize ptC clusters. The systems are σ/π-dual aromatic. The molecular orbitals along with associated energies for the ptC isomers of both systems are given in Figure 7. In both cases, the HOMO-4 exhibits π-delocalization and HOMO-5 shows the σ-delocalization within the whole clusters. In the HOMO-4 π-delocalized MO of the systems, a significant contribution comes from the perpendicular 2p_z orbital of central carbon. These types of clusters stabilized by the electronic approach, as proposed by Hoffmann and co-workers, have similar σ- and/or π-delocalized MOs, which are responsible for the stability of the clusters in planar forms. For the neutralization of these mono-anionic clusters, Li⁺ ions are used and the systems are denoted as Li@SiGaAl₂ and Li@GeGaAl₂ (Figure 6h and 6i, respectively) in which the most favorable site for the bridging of Li⁺ ion is to the Al–Al bonds [79]. Interestingly, the Li⁺ ion binding on the anionic clusters does not distort the planar geometries. The Li@SiGaAl₂ and Li@GeGaAl₂ clusters also show σ/π-dual aromaticity.

Using group 14 elements (Si and Ge) as the σ-donating and π-accepting ligand atoms, we have reported ptC global minimum structures in the CSi_nGe_4−n²⁺ (n = 1–3) clusters (Figure 8a to 8c, respectively) [80]. The exploration of the potential energy surface (PES) with the help of the ABCluster code [81,82] based on the artificial bee colony algorithm (ABC) shows that the C_2v, D_2h, and C_2v symmetric ptC structures are the lowest-energy isomers for CSiGe₃²⁺, CSi₂Ge₂²⁺, and CSi₃Ge²⁺ clusters, respectively. This algorithm is a swarm-based intelligence method that was put forth by Karaboga et al. in 2005 [83,84]. It is influenced by the foraging behavior of a bee colony, and only three parameters are required to deal with it. These three parameters are (i) employed honeybees, (ii) onlooker bees, and (iii) food sources. In this algorithm, a colony of artificial forager bees (agents) finds rich artificial food sources (good solutions for a given problem). The studied optimization problem is first transformed into the problem of searching for the best parameter vector that minimizes an objective function. Then, the artificial bees arbitrarily find a population of initial solution vectors and iteratively move towards better solutions while discarding the bad solutions. For the CSi₂Ge₂²⁺ cluster, the second stable structure also has a ptC with 0.67 kcal mol⁻¹ higher energy than the lowest energy ptC isomer. The third stable isomer of CSi₂Ge₂²⁺ and the second stable isomers of CSiGe₃²⁺ and CSi₃Ge²⁺ clusters have more than 10 kcal mol⁻¹ higher energy with respect to the lowest-energy ptC structure [80]. All the ptC structures have good kinetic stability against isomerization and decomposition at 300 K and 500 K and 50 ps durations. The systems are σ/π-dual aromatic. The simultaneous σ-donation from the surrounding atoms to the carbon atom and the π-acceptance of the peripheral atoms from the central carbon is predicted from the natural charge analysis [80]. The AdNDP analysis shows the 2π/6σ framework of the ptC core in all the clusters.

2.4. Examples of ptCs without 18 Valence Electrons

We have mentioned previously that the totaling of the 18-valence electrons is not a necessary criterion for molecules/ions to show ptCs. This rule can guide the design of new ptC clusters theoretically as well as experimentally. Hence, various neutral and/or ionic clusters were reported to have a ptC without following this criterion, and the clusters show stability in the planar forms. The global minimum geometry of a 15-valence electronic mono-cationic CB₄⁺ system contains a ptC, which was reported by Merino and co-workers in 2011 (Figure 8d) [85]. They found a planar tetracoordinate boron (ptB) center in the global minimum structure of the CB₄ system, which agrees with the results of Boldyrev and Wang. The lowest-energy ptC isomer is in the doublet state for the CB₄⁺ system and is more stable by 30 kcal mol⁻¹ energy than the quartet states of the cluster. The interesting fact is that Becker and Dietze observed this cluster via laser mass spectrometry of boron carbide in 1988 and the ground state has a ptC structure [86].

Vogt-Geisse et al. in 2015 announced a local minimum geometry of two 14-valence electronic Si₂CH₂ and Ge₂CH₂ species with a ptC (Figure 8e and 8f, respectively) [87]. The ptC isomers have 25.1 and 17.2 kcal mol⁻¹ higher energy with respect to the lowest-energy isomer for Si₂CH₂ and Ge₂CH₂ systems, respectively. From the natural bond orbital (NBO) analysis, they proposed the presence of an out-of-plane 3c–2e Si–C–Si and Ge–C–Ge π-bond generated by the delocalization of the lone pair on the central carbon into the empty p-orbitals of silicon and germanium atoms [87]. Additionally, hydrogen-bridged 3c–2e Si–H–C and Ge–H–C bonds exist in the ptC isomers of the Si₂CH₂ and Ge₂CH₂ systems, respectively.

Another interesting work by the group of Hou, Gu, and Li reported the 12-valence electronic ptC species CLi₃E (E = N, P, As, Sb, Bi) and CLi₃E⁺ (E = O, S, Se, Te, Po) (Figure 9) [88]. The PES search shows the C_2v geometries with a ptC are the lowest-energy and most stable in these clusters except for E = N and P. In the global minimum ptC structures, a double bond exists among the carbon and E atoms but the C=E bonds in the CLi₃E cluster are unlike those in the CLi₃E⁺ cluster. In the global minimum structure of the CLi₃E cluster, the π-electron density disperses between C and E, while for the CLi₃E⁺ cluster, it primarily disperses on the E atom. The large energy gap between HOMO and LUMO indicates the stability of both types of complexes in planar orientations [89,90]. Moreover, the CLi₃E⁺ type of complexes has a higher energy gap indicating higher thermodynamic stability than the other types of complexes.

In 2018, Zheng et al. designed CAl₃X (X = Al/Ga/In/Tl) neutral clusters with 16-valence electrons [91]. The exploration of the PES indicated that for CAl₄ (Figure 10a) and CAl₃Ga (Figure 10b) clusters, the global minimum geometries are tetrahedral with 8.70 and 3.66 kcal mol⁻¹ lower energy than the corresponding ptC isomers, respectively. For the CAl₃In cluster (Figure 10c), the tetrahedral isomer is slightly more stable than the ptC isomer by only 0.69 kcal mol⁻¹. Favorably, for the CAl₃Tl cluster (Figure 10d), the ptC global minimum has 1.01 kcal mol⁻¹ lower energy than the tetrahedral isomer. Hence, only for the CAl₃Tl system, the global minimum structure corresponds to the ptC isomer. Moreover, this ptC isomer has 20 kcal mol⁻¹ lower energy than the lowest-energy triplet isomers [91]. Despite the 16-valence electronic cluster, it still shows π-aromaticity. The authors suggested that the ionic [CAl₃⁻]X⁺ plays a major role in the competition between tetrahedral and planar isomers of the clusters.

Neutral 17-valence electronic CSiGaAl₂ and CGeGaAl₂ clusters were reported by us (Figure 10e and 10f, respectively) [79]. The PES shows that the lowest-energy structures contain a ptC center. The kinetic stability of the clusters was verified at 300 K and 500 K temperatures. The NBO analysis confirmed the σ-electron donation from the surrounding atoms to the carbon center and simultaneously π-back donation occurs from the ptC atom to the ligand atoms. The NICS computations predicted the σ/π-dual aromatic nature of the clusters [79].

Merino and co-workers reported in 2018 the presence of a ptC in the 20-valence electronic CE₅⁻ (E=Al–Tl) clusters (Figure 11) [92]. The PES search shows that CAl₅⁻ and CGa₅⁻ clusters have a ptC in the global minimum structure with C_2v symmetry, whereas CIn₅⁻ and CTl₅⁻ clusters have C_4v symmetric 3D structures as the global minima with a pentacoordinate carbon atom. Through the systematic bonding analyses, the authors concluded that the ptC clusters (CAl₅⁻ and CGa₅⁻) can be better represented as the CE₄⁻ fragment collaborates with the E atom. The ptC global minimum structures have both σ and π dual aromaticity with the σ term as the governing term.

Another 12-valence electronic system, CBe₃X₃⁺ (X = H, Li, Na, Cu, Ag) (Figure 12), was predicted by Guo et al. in 2019 [93]. The PES search shows that the ptC structures are global minima, in which the central carbon is connected to three in-plane beryllium (Be) atoms and a terminal X center. The remaining two X atoms are present at the perimeter and each bridge with two beryllium atoms. The second most stable geometries for CBe₃X₃⁺ (X = H, Li, Na, Cu, Ag) have 3.66, 3.98, 1.90, 7.91, and 5.92 kcal mol⁻¹ higher energies as compared to the corresponding lowest energy ptC isomers, respectively [93]. The bonding analyses predicted that the eight electrons are used for delocalized 2π/6σ bonding on the ptC moiety and the remaining four electrons are used for the surrounding Be–X–Be and Be–Be σ–bonding. The global minimum ptC isomers have π/σ dual aromaticity. The molecular dynamics simulations at 300 K for 50 ps suggest that the ptC structures are kinetically stable enough against isomerization and decomposition.

Furthermore, Wu et al. recently designed 14- and 16-valence electronic CLi₂AlE and CLiAl₂E (E = P, As, Sb, Bi) clusters (Figure 13), respectively [94]. The PES exploration indicated the global minimum structures have a ptC except for the CLiAl₂P cluster. In these species, the formation of the C=E bonds is crucial to stabilizing the clusters in planar orientations. The systematic bonding analyses of the clusters show the appearance of three σ and one π bonds among the carbon and surrounding ligand atoms. The ptC geometries have good kinetic stability at 298 K temperature. The NICS computations predicted the σ/π-dual aromaticity of the ptC structures, which are in support of the stability of the clusters.

In 2021, Job et al. designed a 19-valence electronic CAl₄Mg⁻ system (Figure 6b) with a ptC atom in the global minimum energy structure [66]. The second-lowest isomer has 10.13 kcal mol⁻¹ higher energy than the ptC isomer. The ptC structure exhibits σ/π double aromaticity as confirmed by the NICS calculations. The natural charge analysis shows that the central carbon behaves as simultaneous σ-acceptor and π-donor.

In 2021, Leyva-Parra et al. designed and explored the PES of M_mCE₂^p (E=S−Te, M=Li−Cs, m=2, 3 and p=m − 2) and M_nCE₃^q (E=S−Te, M=Li−Cs, n=1, 2 and q=n − 2) systems (Figure 14) [95]. They found that among 38 global minima, 24 are ptCs and 14 are ppCs species. All of the ptCs and ppCs that have been recognized as potential global minima with C_2v (M₂CE₃, MCE₃⁻, and M₃CE₂⁺) or C_s (M₂CE₂) geometries have C–E bond lengths between single and double bonds. In all of these systems, covalent connections between carbon and chalcogens and favorable electrostatic attractions between carbon and alkali metals are confirmed by chemical bonding analyses. Thus, all of these systems satisfy the geometric and electronic requirements for classification as systems with planar hypercoordinate carbon atoms. Furthermore, the detected systems are dynamically stable, suggesting that their experimental validation at room temperature is feasible.

2.5. Examples of ptCs Using New Principles

In 2017, Merino and co-workers proposed stable ptC-containing compounds embedded in aromatic hydrocarbons [96]. They used such types of ligands that have empty orbitals and do not change the sp² hybridization of the aromatic carbons. With the use of the empty orbitals that are perpendicular to the aromatic rings, the ligands take part in the aromatic π-electronic delocalization. Under these two situations, the ligands encourage the formation of a three-centered-two-electron σ-bond with the ptC atom. The authors found a ptC global minimum for the Si₂C₅H₂ cluster (Figure 15a) for which the next lowest-energy isomer has 24.6 kcal mol⁻¹ higher energy than the ptC isomer. Moreover, Ge₂C₅H₂, Ge₂C₆H₃⁺, Sn₂C₅H₂, Sn₂C₆H₃⁺, Pb₂C₅H₂, Pb₂C₆H₃⁺, and Si₂C₆H₃⁺ clusters also have a ptC in the global minimum structures (Figure 15) [96].

The presence of the ptC center in the allene-type structures was reported by the group of Merino and co-workers in 2021. They explored the PES of the CE₂M₂ (E = Si–Pb; M = Li and Na) clusters (Figure 16a) [97]. In the case of CE₂Li₂ clusters, the global minima and also the second lowest structures have a ptC. However, for the CE₂Na₂, except for CPb₂Na₂, all other clusters have a ptC in the global minimum geometries with D_2h symmetry. For the CPb₂Na₂ cluster, the ptC geometry has 1.0 kcal mol⁻¹ higher energy than the most stable tricoordinate carbon structure. The design, based on a π-localization strategy, appeared in a ptC with two double bonds to establish a linear or bent allene-type E═C═E fragment. The magnetic response study shows the σ-delocalization by the bent allene-type E═C═E moiety, which has a crucial role in maintaining the stability of the clusters. Through the bonding analyses, the authors concluded the ionic nature of the C–M bonds and the covalent nature of the C–E bonds.

Very recently, Inostroza et al. explored the PES of E₆C₁₅ (E = Si–Pb) polycyclic aromatic compounds and reported the presence of three ptCs in the putative global minimum structures of Si₆C₁₅ (Figure 16b) and Ge₆C₁₅ (Figure 16c) systems with D_3h symmetry [98]. However, in the case of Sn₆C₁₅ (Figure 16d) and Pb₆C₁₅ systems (Figure 16e), due to the large size of Sn and Pb atoms, the global minimum is a bowl-shaped geometry with three quasi-ptCs. Three ptCs are also present in the second stable isomers of Si₆C₁₅ and Ge₆C₁₅ systems, which are 8.2 and 2.8 kcal mol⁻¹ higher in energy compared to the global minimum geometries, respectively. All four lowest-energy isomers have higher HOMO–LUMO energy gaps between 2.13 and 4.03 eV. The C–C bond lengths are within the range of single and double bonds (1.41–1.47 Å), supporting the delocalized character of the bonding. Three delocalized E-ptC-E three-centered-two-electron (3c–2e) σ-bonds and nine delocalized π-bonds are found in the chemical bonding study, supporting an aromatic nature in accordance with Huckel’s 4n + 2 rule. The authors show that without disrupting ptC units, these systems may also be employed as a partner to create supramolecular complexes with coronene or [12] cycloparaphenylene ([12] CPPs).

2.6. Examples of Experimentally Predicted ptC Compounds

Interestingly, 17-valence electronic pentatomic CAl₄⁻ and CAl₃E (E = Si, Ge) systems and 18-valence electronic CAl₃E⁻ (E = Si, Ge) were detected in a photoelectron spectroscopy experiment and ab initio calculations by Wang as early as 1999 [18,56]. The 16-valence electronic CAl₄ molecule has a tetrahedral geometry and the CAl₄⁻ system has a planar geometry with D_4h symmetry (Figure 17a). The experimental vertical detachment energy (VDE) of CAl₄⁻ is approximately 2.65 ± 0.06 eV, which is in good agreement with the computed value of 2.71 eV. The authors stated that the tetrahedral CAl₄ molecule should have a 1a₁²1t₂⁶2a₁²2t₂⁶1e⁰ electronic arrangement, which represents four σ bonds (1a₁ and 1t₂) and four lone-pair bonds (2a₁ and 2t₂). Adding one extra electron to the 1e LUMO gives the 1a₁²1t₂⁶2a₁²2t₂⁶1e¹ electronic arrangement for the CAl₄⁻ cluster. As the 1e orbital is unsymmetrically filled, it is expected to show Jahn–Teller distortion to give a D_4h symmetric planar structure (Figure 17a). The planarity in the CAl₄⁻ cluster is accomplished by the ligand–ligand bonding relationships in the HOMO. For the CAl₃Si system, the authors predicted two planar low-lying C_2v-I (Figure 17b) and C_2v-II (Figure 17c) structures, but the C_2v-I isomer has 2.5 kcal mol⁻¹ lower energy than the C_2v-II isomer. Moreover, the C_2v-I isomer has 7.8 kcal mol⁻¹ lower energy than the tricoordinate C_s isomer. Hence, they mentioned that in the case of the CAl₃Si cluster, the C_2v-I isomer is the global minimum structure [56]. Similar to the CAl₃Si cluster, the CAl₃Ge system has two minima C_2v-I (Figure 17b) and C_2v-II (Figure 17c) [56]. In the case of the CAl₃Si⁻ and CAl₃Ge⁻ systems, the C_2v symmetric ptC structures (Figure 17b) were reported as the lowest-energy isomers. In all these clusters, the appearance of a four-center bond was discovered to be crucial for the stability of the ptC isomers.

In 2017, Xu et al. reported a combined experimental and theoretical study of CAl₄H and CAl₄H⁻ clusters based on anion photoelectron spectroscopic and quantum mechanical methods [99]. The authors showed that the most preferable binding site of H is bridging to the Al−Al bond instead to bind with one Al atom in both these clusters (Figure 17d). The neutral and mono-anionic species have 17- and 18-valence electrons, respectively. For the CAl₄H cluster, the experimental electron affinity (EA) value is 2.6 eV. In the case of the CAl₄H⁻ cluster, the experimental VDE is 2.88 eV, in good agreement with the computed VDE of 2.75 eV indicating its high stability [99]. The PES search shows the ptC isomers with a bridging H as global minimum structures for both these clusters. The molecular orbital analysis predicts the delocalized π orbitals, which play an important role in maintaining the planar structure of the clusters, and the species show aromatic character. The acceptable agreement between experimental and computational studies concludes that the ground state of CAl₄H^−/0 clusters have ptC.

3. Planar Pentacoordinate Carbons (ppCs)

The idea of ptC is expanded to the probability and representation of systems with ppC centers [100]. In 1995, Bolton et al. reported the singlet 1,1-dilithioethene molecule (Figure 18a) 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 [101]. 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.

Wang and Schleyer suggested the design principles of “hyparenes” and reported a family of systems with ppC using density functional theory (DFT)-based computations [102]. They predicted that it is possible to construct “hyparenes” with the replacement of the –(CH)₃– groups in aromatic and/or antiaromatic hydrocarbons by three borocarbon units with ppCs –C₃B₃– (Type I), –C₂B₄– (Type II), and –CB₅– (Type III) (Figure 19). The uncommon geometries of the hyparenes can offer unique characteristics that are of use to compose new materials. The hyparenes correspond to the low-lying local minima with normal C–B, B–B, and C–C bond distances. The partial σ and partial π bonds to the planar pentacoordinate carbons contributed to the multicenter bonding in the hyparenes. After the detection of the aromatic M₅(μ-H)₅ hydrometal rings (M = Cu, Ag, Au) [103,104], 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 18b) [105]. 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 18c) and Au₅H₅C (Figure 18d) molecules also have a ppC in their local minimum geometries [106].

The first global minimum geometry with a ppC in the CAl₅⁺ system with D_5h symmetry (Figure 18e) was reported based on an extensive PES search in 2008 by Zeng and co-workers [107]. 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 NICS computations 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 18f) and mono-anionic CAl₃Be₂⁻ (Figure 18g) systems containing ppCs in the global minimum structures [108]. 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 HOMO and LUMO are 2.6 eV for both ppC structures indicating the greater stability of these isomers [108].

Wu et al., in 2012, reported di-anionic CAl₂Be₃²⁻ (Figure 20a) and its mono-anionic salt complex LiCAl₂Be₃⁻ (Figure 20b) systems by further replacement of Al atoms by Be atoms [109]. The PES search shows the global minimum geometry of these clusters has a ppC. The 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 [109]. 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.

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 [110]. For CBe₅Al⁻ (Figure 20c) and CBe₅Ga⁻ (Figure 20d) clusters, the ppC structures are the global minima. However, for CBe₅In⁻ (Figure 20e) and Cbe₅Tl⁻ (Figure 20f) 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 [110]. 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 21a) [111]. 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 21b to 21f, respectively) [112]. 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 MHP. 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) [113]. In the case of CBe₅H₂²⁻ (Figure 22a) and CBe₅H₃⁻ (Figure 22b) clusters, the ppC structures are the lowest-energy C_2v point group of symmetry. For the CBe₅H₄ cluster (Figure 22c), a quasi-planar geometry has 1.8 kcal mol⁻¹ more energy compared to the tetrahedral global minimum structure. Moreover, the CBe₅H₅⁺ cluster (Figure 22d) 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 [114]. 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 (Figure 23) have excellently planar and extremely symmetric D_5h geometries, whereas CBe₅Cl₅⁺ and CBe₅Br₅⁺ clusters experience slight non-planar contortion as C₂ geometries (Figure 23). 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 AdNDP analyses. 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.

In 2018, Zhao et al. reported various ppC systems by adding hydrogen atoms to the CAl₄Be, CAl₃Be₂⁻, CAl₂Be₃²⁻, and CAlBe₄³⁻ parent molecules [115]. 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 24). 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 [115]. 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 [115]. The NICS calculations predicted that the considered clusters are σ- and π-dual aromatic. The NBO computations predicted that there is a significant contribution of the ionic and covalent bonding toward the stabilization of the ppC structures.

Recently, Pan et al. reported a family of systems with ppC based on the next heaviest analogue of the CAl₅⁺ system [116]. 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 25). 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 25). 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 [116]. 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 [116].

Using silicon (Si) as the surrounding atoms, Zdetsis et al. in 2011 designed Si₅C²⁻ and Si₅C⁻ clusters (Figure 26a) with the help of the DFT and the coupled-cluster theory that predicted planar structures of the clusters stabilized by the C–Si bonds [117]. 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.

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 26b,c) [118]. 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 26d) [119]. 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 [119]. 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 27) [120]. 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.

4. 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 28) [121,122,123]. In 2000, the first example with a phC is the CB₆²⁻ di-anionic system (Figure 29a), studied by Exner et al. using DFT and high-level ab initio calculations [124]. 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 30 contains the proposed phC species by Ito et al. utilizing CB₆²⁻ as the building block [125].

In 2012, Wu et al. used a CB₆²⁻ unit and executed isoelectronic replacement on it to compose unipositive CN₃Be₃⁺ and CO₃Li₃⁺ clusters (Figure 29b and 29c, respectively) [126]. 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 [127]. 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 [127]. The fifteen possible CE₃M₃⁺ (E=S–Te, and M=Li–Cs) combinations are to be identified as phC clusters (Figure 29d). 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 [127]. Through systematic bonding analyses, the authors stated the covalent nature of the C–E bonds and the ionic nature of the C–M bonds.

5. Higher Coordinate Carbons

The exploration for planar hypercoordinate carbon is not restricted to phC species. Boron rings are broadly utilized to generate planar hypercoordinate carbon species, but the size of the carbon is pivotal for producing the planar structures. For the first time, Minyaev et al. proposed the B₇C⁻ cluster with a planar heptacoordinate carbon in the local minimum D_7h structure (Figure 29e) [128] with 63.9 kcal mol⁻¹ higher energy than the corresponding lowest-energy planar heptacoordinate boron isomer. The authors stated that the B₇C⁻ system can be considered a substitute for the central B⁻ ion with a carbon atom in the B₈²⁻ cluster, which contains a heptacoordinate boron atom in the lowest-energy isomer [129]. The magnificent agreement between the experiment and the theory predicted the C_2v symmetric global minimum with planar heptacoordinate boron for the B₇C⁻ system. Hence, from this combined study, the authors concluded that the appearance of the heptacoordinate carbon in the carbon and boron clusters is exceptionally unfavorable. It is hoped that a planar octacoordinate carbon structure will be generated by placing carbon at the center of the B₈ ring. Unfortunately, the smaller size of carbon is the factor that prevents octacoordination in this system. Hence, the planar D_8h structure of the B₈C cluster is in a transition state and is converted to a stable ppC cluster with C_2v geometry (Figure 29f).

6. Conclusions

This present review documented the recent advancement in the planar hypercoordinate carbon species. These species disobey the primary and most broadly utilized structural rules in organic chemistry and biochemistry. The ttC model proposed by van’t Hoff and Le Bel are disobeyed by the theoretically designed and/or experimentally characterized planar orientations of four or more groups in a carbon. These species might have numerous main-group elements and transition-metal atoms as the surrounding ligand atoms. The proposed electronic and mechanical strategies are helpful in designing the ptC compounds. Moreover, the 18-valence electron rule can guide the design of new ptC clusters theoretically as well as experimentally. The formation of three σ and one π bonds among the middle carbon and the surrounding atoms are the consequences of 18-valence electrons. However, the counting of 18-valence electrons is not a prerequisite to have a ptC in a cluster. Various species are described in this review article, in which the 18-valence electrons counting is not followed. Furthermore, this ptC idea is expanded to the probability of a greater coordination number of carbon in planar orientations. Unfortunately, until now, there has been no such logical approach to design ppC, phC, or higher-coordinate carbon molecules/ions.

The experimental validation of the computationally designed planar hypercoordinate carbon molecules/ions is difficult. The species can be feasible in the gas phase if they show enough thermodynamic stability, and interestingly, some ptC species were detected in the gas phase. All planar hypercoordinate carbon species in the global minima may be feasible in the gas phase. These unusual clusters provide unique properties and have opened new vistas in the allied research fields.