Five Bonds to Carbon through Tri-Coordination in Al 3 C − /0 3

: Here, ﬁve bonds to carbon through tri-coordination are theoretically established in the global minimum energy isomers of Al 3 C − 3 anion ( 1a ) and Al 3 C 3 neutral ( 1n ) for the ﬁrst time. Various isomers of Al 3 C − /0 3 are theoretically identiﬁed using density functional theory at the PBE0-D3/def2-TZVP level. Chemical bonding features are thoroughly analyzed for these two isomers ( 1a and 1n ) with different bonding and topological quantum chemical tools, such as adaptive natural density partitioning (AdNDP), Wiberg Bond Indices (WBIs), nucleus-independent chemical shifts (NICS), and atoms in molecules (AIM) analyses. The structure of isomer 1a is planar with C 2v symmetry, whereas its neutral counterpart 1n is non-planar with C 2 symmetry, in which its terminal aluminum atoms are out of the plane. The central allenic carbon atom of isomers 1a and 1n exhibits tri-coordination and thus makes it a case of ﬁve bonds to carbon, which is conﬁrmed through their total bond order as observed in WBI. Both the isomers show σ - and π -aromaticity and are predicted with the NICS and AdNDP analyses. Further, the results of ab initio molecular dynamics simulations reveal their kinetic stability at room temperature; thus, they are experimentally viable systems.


Introduction
The concept of five bonds to carbon became indispensable since the discovery of methanium ion (CH + 5 ) in the laboratory in 1950 [1]. Recording the infrared spectra of this simple protonated methane molecule was quite challenging, as it took almost five decades from its discovery [2]. The theoretical investigation of lithium carbides such as CLi 5 and CLi 6 [3] and the experimental realization of CLi 6 through mass spectroscopic measurements further motivated the interest in hyper-coordinate carbon molecules [4]. While computational studies on Si 2 (CH 3 ) + 7 [5] and C(CH 3 ) + 5 [6] provided further guidance on hyper-coordinate behavior of group 14 elements, it is the experimental observations such as [CCH 3 ] 2+ 6 , HC[Au(PPh 3 )] + 4 , [(C 6 H 5 ) 3 PAu 5 C] + , [(Ph 3 PAu) 6 C] 2+ , C 6 [CH 3 ] 2+ 6 , etc., that gave chemists the real grandeur of hyper-coordinate carbon molecules [7][8][9][10][11]. Akiba and co-workers have shown penta-and hexa-coordinate anthracene moieties through x-ray crystallography and ab initio calculations [12,13]. The iron-molybdenum nitrogenase cofactor existing in diazotrophs is a clear example of hexa-coordinate carbon in biological systems [14]. From the well-known concept of molecules with a planar tetra-coordinate carbon (ptC) atom [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], the idea was extended to planar penta-coordinate carbon (ppC) [31-40] and planar hexacoordinate carbon (phC) [41][42][43][44]. Hill and coworkers experimentally reported the existence of a penta-coordinate carbon atom in 1981 [45]. The penta-coordinate carbon atom was also theoretically reported by Gleiter and coworkers [46] in the Cp 2 Zr[CH 2 (BH{C 6 F 5 } 2 ) 2 ] complex. In 1996, the experimental proof of the first complex with a hyper-coordinate ylidic carbon atom was also reported by Jones and coworkers [47]. While a gradual amount of progress has been made in these classes of molecules to date, to a larger extent in the literature, the concept of making hyper-coordinate carbon molecules was predominantly Chemistry 2023, 5 1114 focused on making single bonds to the central carbon atom irrespective of whether they are planar or non-planar [48]. However, in this article, the intent is to make five bonds to a carbon atom through tri-coordination instead of penta-coordination, as is normally carried out. To this end, we have theoretically investigated the aluminum-carbon cluster, Al 3 C −/0 3 , in both its anion and neutral forms and established the fact that the global minimum isomers (1a and 1n) contain five bonds to carbon through tri-coordination (see Figures 1 and 2). . While a gradual amount of progress has been made in these classes of molecules to date, to a larger extent in the literature, the concept of making hyper-coordinate carbon molecules was predominantly focused on making single bonds to the central carbon atom irrespective of whether they are planar or non-planar [48]. However, in this article, the intent is to make five bonds to a carbon atom through tri-coordination instead of penta-coordination, as is normally carried out. To this end, we have theoretically investigated the aluminum-carbon cluster, Al C / , in both its anion and neutral forms and established the fact that the global minimum isomers (1a and 1n) contain five bonds to carbon through tri-coordination (see Figures 1 and 2).   coworkers [47]. While a gradual amount of progress has been made in these classes of molecules to date, to a larger extent in the literature, the concept of making hyper-coordinate carbon molecules was predominantly focused on making single bonds to the central carbon atom irrespective of whether they are planar or non-planar [48]. However, in this article, the intent is to make five bonds to a carbon atom through tri-coordination instead of penta-coordination, as is normally carried out. To this end, we have theoretically investigated the aluminum-carbon cluster, Al C / , in both its anion and neutral forms and established the fact that the global minimum isomers (1a and 1n) contain five bonds to carbon through tri-coordination (see Figures 1 and 2).   Various aluminum-carbon clusters have continuously been investigated [16,17,[49][50][51][52] as they have potential applications in energy storage [53] and the production of nanopowders [54,55] and solar cells [56]. Zheng and coworkers theoretically and experimentally explored the Al 4 C −/0 6 system and found that the global minimum isomer in the neutral state contains the planar hexa-coordinate aluminum [57]. In 2022, Kalita et al. reported the planar penta-coordinate Al and Ga centers in Cu 5 Al + 2 and Cu 5 Ga + 2 systems, which were global minimum structures, and found that the stabilizing factor was σ-aromaticity [58].
Recently, Malhan et al. reported the Al 2 C 4 H 2 system with ptC, planar tetra-coordinate aluminum (ptAl), and planar penta-coordinate aluminum (ppAl) atoms with aromatic characteristics [59]. The aforementioned discoveries have also inspired researchers to look for further systems containing hyper-coordinate main group elements, such as group 13 elements. Wang and coworkers reported B − 8 and B − 9 clusters exhibiting planar heptaand octa-coordinate central boron atoms with combined experimental and computational studies [60]. Li et al. reported the global minimum structure of the BCu 5 H − 5 system with planar penta-coordinate boron (ppB) [61]. The global minimum isomer containing the ppB atom in the B 6 H + 5 system with aromatic characteristics was reported by Wu and coworkers. In 2021, Khatun et al. reported BAl 4 Mg −/0/+ [62], in which the global minimum structures were found to have a planar tetra-coordinate boron (ptB) atom in its anionic and cationic forms as well as a ppB atom in the neutral state. In 2022, Das and coworkers explored the potential energy surface of CB 6 Al 0/+ [63] and found that both neutral and cation contain planar hexa-coordinate boron (phB) atoms in their global minima. Thompson et al. experimentally reported the ptAl species [64]. The ptAl species of calix [4] pyrrole aluminate was also experimentally reported by Greb and coworkers in 2019 [65]. In 2023, Merino and coworkers also reported a quasi-ptC atom in the CAl − 11 system [66]. These distinctive bonding arrangements demonstrate not only the fundamental importance of improving our knowledge of chemical bonding but also a completely new class of molecules in the world of chemistry. Herein, the present work reports the Al 3 C −/0 3 system with tri-coordination; that is, five bonds to the central allenic carbon atom via computational quantum chemical modeling. The aluminum and carbon-based molecules have potential applications ranging from cluster assembled materials [67,68], energy storage [69], and two-dimensional donor materials in solar cells [70]. Dong et al. [71] have already reported the isomer 2n of the Al 3 C 3 system with hydrogen storage properties both experimentally and theoretically at MP2/6-311+G* level of theory, which gives us confidence that the Al 3 C −/0 3 system investigated here, has a high chance of synthetic viability in the future.

Computational Methodology
The initial geometries of the Al 3 C −/0 3 system were first generated through chemical intuition, and then, using the in-house Python code, all other possible geometries were explored on these two potential energy surfaces (PESs) using density functional theory (DFT). All geometries were fully optimized using the hybrid functional PBE0 [72] coupled with Grimme's dispersion correction (D3) [73,74] and the def2-TZVP [75,76] basis set. Frequency calculations were carried out at the same level of theory to ensure whether the optimized geometries are true minima or maxima or higher-order saddle points. To get more characteristic features on the chemical bonding of isomers 1a and 1n, the natural bond order (NBO) analysis [77], adaptive natural density partitioning (AdNDP) analysis [78,79], and Wiberg bond indices (WBIs) [80] were performed at the PBE0-D3/def2-TZVP level. The nucleus-independent chemical shift (NICS) [81] calculations for 1a and 1n structures were carried out at the same level to analyze the aromatic behavior of these systems. Atoms in molecules (AIM) analysis [82] of the Laplacian of electron density and electron localization function (ELF) [83] were carried out for isomers 1a and 1n using the wave function file generated by the Gaussian program [84] at the PBE0-D3/def2-TZVP level. The dynamic stabilities of 1a and 1n were evaluated using the atom-centered density matrix propagation (ADMP) [85] at the same level of theory. The AdNDP and ELF were analyzed through the Multiwfn program [86]. All the calculations were performed using the Gaussian 16 package [84].

Results and Discussion
The PESs of the Al 3 C −/0 3 are explored, and we found that the global minimum energy geometry (1a and 1n) of both the anion and neutral system contains a carbon atom (C4) with two π bonds and three σ bonds, exhibiting a total of five bonds through tricoordination. The ten low-lying isomers of the anion and the neutral system are given in  Figures S1 and S2, respectively. The Al 3 C − 3 system has a singlet spin state and the Al 3 C 3 system corresponds to a doublet. Isomer 1a is a planar structure with C 2v symmetry, whereas isomer 1n shows C 2 symmetry, in which the terminal aluminum atoms are out of the plane (see Figure 3). The Al 3 C −/0 3 system also has structures that exhibit planar penta-coordinate aluminum (ppAl) and planar tetra-coordinate carbon (ptC) atoms as local minimum energy isomers (8a, 7n; and 3a, 13a, and 8n, respectively) on their PESs. Nevertheless, our focus here is on the global minimum energy isomers, 1a and 1n, which exhibit five bonds to carbon through tri-coordination.

Results and Discussion
The PESs of the Al C / are explored, and we found that the global minimum energy geometry (1a and 1n) of both the anion and neutral system contains a carbon atom (C4) with two π bonds and three σ bonds, exhibiting a total of five bonds through tri-coordination. The ten low-lying isomers of the anion and the neutral system are given in Figures 1 and 2, respectively. All other isomers on the PES of the Al C / system are given in the Supplementary Materials in Figures S1 and S2, respectively. The Al C system has a singlet spin state and the Al C system corresponds to a doublet. Isomer 1a is a planar structure with C2v symmetry, whereas isomer 1n shows C2 symmetry, in which the terminal aluminum atoms are out of the plane (see Figure 3). The Al C / system also has structures that exhibit planar penta-coordinate aluminum (ppAl) and planar tetra-coordinate carbon (ptC) atoms as local minimum energy isomers (8a, 7n; and 3a, 13a, and 8n, respectively) on their PESs. Nevertheless, our focus here is on the global minimum energy isomers, 1a and 1n, which exhibit five bonds to carbon through tri-coordination.

Wiberg Bond Indices
The WBI values obtained from NBO analysis for the allenic carbon (C4) atom in isomers 1a and 1n are critically analyzed. The WBI values and the bond distances are given in Figure 3. The standard covalent bond lengths of C-Al and C=C are 2.01 and 1.34 Å, respectively, which are in close agreement with the obtained values. The C4-Al1 bond length of isomer 1n having 2.11 Å is slightly higher than that of isomer 1a with 2.04 Å.
The WBI values for the C=C bond in isomers 1a and 1n are 1.86 and 1.87, respectively, which confirms the presence of π bonds in both isomers. This further proves that in both cases, the C4 atom makes two π bonds with neighboring atoms. The C4-Al1 bond with WBI values of 0.20 and 0.17 in isomers 1a and 1n suggests the dative bonding nature of the fifth bond. The total bond order of C4 in isomers 1a and 1n is 3.99 and 3.97, respectively. This indicates that the allenic carbon atom, C4, is surrounded by eight electrons but still makes two π bonds with neighboring carbon atoms and also forms an additional dative bond with the central aluminum atom.

Adaptive Natural Density Partitioning (AdNDP) Analysis
To further analyze the bonding scenario, the AdNDP analysis was carried out for the delineation of n-center 2-electron (nc-2e) bonds in the investigated systems. The generated AdNDP orbitals with occupation numbers (ON) for isomers 1a and 1n are shown in Figure 4. As the neutral system is in a doublet state, only alpha orbitals are considered for

Wiberg Bond Indices
The WBI values obtained from NBO analysis for the allenic carbon (C4) atom in isomers 1a and 1n are critically analyzed. The WBI values and the bond distances are given in Figure 3. The standard covalent bond lengths of C-Al and C=C are 2.01 and 1.34 Å, respectively, which are in close agreement with the obtained values. The C4-Al1 bond length of isomer 1n having 2.11 Å is slightly higher than that of isomer 1a with 2.04 Å. The WBI values for the C=C bond in isomers 1a and 1n are 1.86 and 1.87, respectively, which confirms the presence of π bonds in both isomers. This further proves that in both cases, the C4 atom makes two π bonds with neighboring atoms. The C4-Al1 bond with WBI values of 0.20 and 0.17 in isomers 1a and 1n suggests the dative bonding nature of the fifth bond. The total bond order of C4 in isomers 1a and 1n is 3.99 and 3.97, respectively. This indicates that the allenic carbon atom, C4, is surrounded by eight electrons but still makes two π bonds with neighboring carbon atoms and also forms an additional dative bond with the central aluminum atom.

Adaptive Natural Density Partitioning (AdNDP) Analysis
To further analyze the bonding scenario, the AdNDP analysis was carried out for the delineation of n-center 2-electron (nc-2e) bonds in the investigated systems. The generated AdNDP orbitals with occupation numbers (ON) for isomers 1a and 1n are shown in Figure 4. As the neutral system is in a doublet state, only alpha orbitals are considered for this analysis. The tri-coordinated C4 atom has two 2c-2e σ and two 2c-2e π bonds with its neighboring carbon atoms, with ON 1.99 |e| and 1.85 |e|, respectively, which confirms the presence of alternating π bonds in the isomer 1a. It also exhibits delocalization of electron densities through 3c-2e σ, 4c-2e σ, 3c-2e π, and 4c-2e π bonds with ON ranging from 1.89 |e| to 2.00 |e, which support the tri-coordination in the structure. The two 2c-2e π bonds in isomer 1n confirm the presence of alternating π bonds which also exhibit delocalization of electron densities through multi-center 2e σ and π bonds, which supports the structural stability. To support the observed AdNDP bonding pattern, the nucleusindependent chemical shift (NICS) values are also calculated for isomers 1a and 1n, which are shown in Figure S3. The negative values of NICS (0) and NICS (1) also confirm the presence σand π-aromatic nature in both the isomers, respectively. two 2c-2e π bonds in isomer 1n confirm the presence of alternating π bonds which also exhibit delocalization of electron densities through multi-center 2e σ and π bonds, which supports the structural stability. To support the observed AdNDP bonding pattern, the nucleus-independent chemical shift (NICS) values are also calculated for isomers 1a and 1n, which are shown in Figure S3. The negative values of NICS (0) and NICS (1) also confirm the presence σ-and π-aromatic nature in both the isomers, respectively.

Atoms in Molecule (AIM) Analysis
The AIM analysis is carried out to gain insight into the bonding characteristic features. The color-filled plots of the electron localization function (ELF) and contour diagram for the Laplacian of electron density (∆ 2 ρ(r)) for isomers 1a and 1n are shown in Figure 5. The ELF plot of isomers 1a indicates the interaction of the C4 atom with its neighboring atoms and supports the delocalization of electron densities within the molecule. Apart from the terminal Al2 and Al3 atoms, which are out of the plane, isomer 1n also supports the delocalization of electron densities around the C4 atom. In 1a, bond critical points (BCPs) between the C4 and its neighboring atoms support the existence of bond paths. Isomer 1n has BCPs between C4 and its adjacent carbon atoms and also has a ring critical point (RCP) which dictates the dominant aromatic characteristics in the structure.
gram for the Laplacian of electron density (∆ 2 ρ(r)) for isomers 1a and 1n are shown in Figure 5. The ELF plot of isomers 1a indicates the interaction of the C4 atom with its neighboring atoms and supports the delocalization of electron densities within the molecule. Apart from the terminal Al2 and Al3 atoms, which are out of the plane, isomer 1n also supports the delocalization of electron densities around the C4 atom. In 1a, bond critical points (BCPs) between the C4 and its neighboring atoms support the existence of bond paths. Isomer 1n has BCPs between C4 and its adjacent carbon atoms and also has a ring critical point (RCP) which dictates the dominant aromatic characteristics in the structure. Figure 5. The color-filled map of ELF (top row) and the Laplacian of electron density (∆ 2 ρ(r)) with bond paths (bottom row) for isomers 1a and 1n at the PBE0-D3/def2-TZVP level.

Kinetic Stability
The ab initio molecular dynamics (AIMD) simulations are carried out for 3000 fs at 298 K and 1 atm pressure using the ADMP approach to explore the kinetic stability of the investigated structures. The time evolution of energy plots for isomers 1a and 1n are given in Figure 6. Slight structural deformation occurs during the simulation, which causes an increase in nuclear kinetic energy. However, the present data reveal that the overall geometry is not completely destroyed, which indicates that these molecules are kinetically stable apart from their thermodynamic stability. As expected, for both isomers 1a and 1n, the five bonds to the C4 atom remain the same throughout the simulation pe- Figure 5. The color-filled map of ELF (top row) and the Laplacian of electron density (∆ 2 ρ(r)) with bond paths (bottom row) for isomers 1a and 1n at the PBE0-D3/def2-TZVP level.

Kinetic Stability
The ab initio molecular dynamics (AIMD) simulations are carried out for 3000 fs at 298 K and 1 atm pressure using the ADMP approach to explore the kinetic stability of the investigated structures. The time evolution of energy plots for isomers 1a and 1n are given in Figure 6. Slight structural deformation occurs during the simulation, which causes an increase in nuclear kinetic energy. However, the present data reveal that the overall geometry is not completely destroyed, which indicates that these molecules are kinetically stable apart from their thermodynamic stability. As expected, for both isomers 1a and 1n, the five bonds to the C4 atom remain the same throughout the simulation period. The structural stability of these isomers is well maintained during the simulation, and no isomerization or other structural modifications occur in these molecules, suggesting that they are indeed kinetically stable. riod. The structural stability of these isomers is well maintained during the simulation, and no isomerization or other structural modifications occur in these molecules, suggesting that they are indeed kinetically stable.

Conclusions
Using density functional theory, various isomers of the Al C / system were explored first by chemical intuition, and other possible isomers are then identified with the help of the in-house Python code. The global minimum isomers 1a and 1n exhibit five bonds to carbon through tri-coordination. The present work reports for the first time five bonds to carbon through tri-coordination in the Al C / system as observed in isomers 1a and 1n, respectively. Isomer 1a is a planar structure with C2v symmetry, whereas isomer 1n shows C2 symmetry with the terminal aluminum atoms out of the plane. WBI analysis indicates that the central allenic carbon atom in both the isomers (1a and 1n) forms five bonds through tri-coordination and also obeys the octet rule simultaneously. The BCPs from AIM analysis confirm the presence of bond paths between allenic carbon and its adjacent atoms. The aromatic nature that stabilizes both the isomers 1a and 1n is well supported by AdNDP, ELF, and NICS analyses. Both the isomers are kinetically stable as

Conclusions
Using density functional theory, various isomers of the Al 3 C −/0 3 system were explored first by chemical intuition, and other possible isomers are then identified with the help of the in-house Python code. The global minimum isomers 1a and 1n exhibit five bonds to carbon through tri-coordination. The present work reports for the first time five bonds to carbon through tri-coordination in the Al 3 C −/0 3 system as observed in isomers 1a and 1n, respectively. Isomer 1a is a planar structure with C 2v symmetry, whereas isomer 1n shows C 2 symmetry with the terminal aluminum atoms out of the plane. WBI analysis indicates that the central allenic carbon atom in both the isomers (1a and 1n) forms five bonds through tri-coordination and also obeys the octet rule simultaneously. The BCPs from AIM analysis confirm the presence of bond paths between allenic carbon and its adjacent atoms. The aromatic nature that stabilizes both the isomers 1a and 1n is well supported by AdNDP, ELF, and NICS analyses. Both the isomers are kinetically stable as inferred from the ab initio molecular dynamics simulations at 1 atm pressure and 298 K temperature up to 3000 fs of time. The obtained results on the Al 3 C −/0 Supplementary Materials: The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/chemistry5020076/s1, The optimized geometries of all Al 3 C − 3 and Al 3 C 3 isomers are given in Figures S1 and S2, respectively, NICSs in ppm for the isomers 1a and 1n are given in Figure S3, AdNDP bonding patterns with occupation numbers (ONs) for isomers 1a and 1n are given in Figures S4 and S5, respectively, total energies (in a.u), Zero-point vibrational energies (ZPVEs; in a.u), ZPVE corrected total energies (E+ZPVE; in a.u), relative energies (∆E+ZPVE; in kcal mol −1 ), and the number of imaginary frequencies (NImag) of all Al 3 C − 3 and Al 3 C 3 isomers at PBE0-D3/def2-TZVP level are given in Tables S1 and S2, respectively, and Cartesian coordinates of all Al 3 C − 3 and Al 3 C 3 isomers at the PBE0-D3/def2-TZVP level are given in Tables S3 and S4,