CAl 4 Mg 0/ − : Global Minima with a Planar Tetracoordinate Carbon Atom

: Isomers of CAl 4 Mg and CAl 4 Mg − have been theoretically characterized for the ﬁrst time. The most stable isomer for both the neutral and anion contain a planar tetracoordinate carbon (ptC) atom. Unlike the isovalent CAl 4 Be case, which contains a planar pentacoordinate carbon atom as the global minimum geometry, replacing beryllium with magnesium makes the ptC isomer the global minimum due to increased ionic radii of magnesium. However, it is relatively easier to conduct experimental studies for CAl 4 Mg 0/ − as beryllium is toxic. While the neutral molecule containing the ptC atom follows the 18 valence electron rule, the anion breaks the rule with 19 valence electrons. The electron afﬁnity of CAl 4 Mg is in the range of 1.96–2.05 eV. Both the global minima exhibit π / σ double aromaticity. Ab initio molecular dynamics simulations were carried out for both the global minima at 298 K for 10 ps to conﬁrm their kinetic stability.

Perhaps, making molecules containing ptC atoms remains an open challenge to date, although limited amount of success persists experimentally. While the thermodynamic and kinetic stability of these molecules have been greatly emphasized over the years [46,47], the less spoken issue in this endeavor for the purpose of experimental viability is the combination of atoms in achieving the ptC. In the past, many ptC or phC molecules containing beryllium as one constituent elements have been proposed [28,30,39,48]. However, none of them have been experimentally achieved despite their experimental viability. One of the major safety issues in using beryllium is that it can cause the development of chronic beryllium disease [49]. For this reason, beryllium chemistry is somewhat underdeveloped from an experimental perspective [50]. Thus, we aimed to theoretically achieve ptC/phC without using beryllium. Here, the potential energy surfaces (PESs) of CAl 4 Mg 0/− have been characterized computationally using density functional theory and coupled-cluster methods. The global minimum geometries of both the neutral and anion contain a ptC atom (see Figure 1). The isovalent system of the neutral, CAl 4 Be, has been explored elsewhere [30], where the global minimum geometry contains a planar pentacoordinate carbon (ppC). By replacing beryllium with magnesium, one could achieve ptC instead of ppC due to the increased ionic radius of magnesium.  . Bond lengths are given in Å in the top row. The atom numbering scheme used herein is also shown. Natural atomic charges (in |e|; blue color) and Wiberg bond indices (green color) calculated at the (U)ωB97XD/6-311++G(2d,2p) level are given in the bottom row.

Computational Details
Several trial geometries of CAl 4 Mg and CAl 4 Mg − are generated by chemical intuition and the cluster building procedure implemented in PyAR [51,52]. Modeling by intuition was done targeting for ptC and phC based on similar reported molecules. The automated cluster building is done as follows: First, a diatomic molecule is generated from two randomly chosen atoms from C, Al and Mg. To the optimized geometry of these diatomic molecules, another randomly chosen atom is added following the procedure described by Khatun et al. [52] to generate several (N) guess geometries. All these geometries are optimized and unique minima are chosen and further addition of random atoms are continued until the target chemical formula is reached. We performed nine different runs with N = 16 orientations for both the neutral and anionic systems. The trial geometries were optimized using the ORCA program [53] interfaced with PyAR [51,52]. The initial geometry optimizations were carried out using PBE [54] functional with def2-SVP [55] basis set including Grimme's empirical dispersion corrections (D3) [56] with Becke-Johnson (BJ) damping [57,58] and resolution of the identity (RI) approximation. After we filtered all geometries generated from nine different runs, unique geometries were selected for further analysis. Some geometries were reached from both intuitive and stochastic procedures. Overall, for CAl 4 Mg and CAl 4 Mg − , we identified 37 and 33 stationary points, respectively.
The geometries of all CAl 4 Mg 0/− isomers reported here were optimized further using DFT with the (U)ωB97XD hybrid functional [59] and the 6-311++G(2d,2p) basis set [60,61]. Harmonic vibrational frequencies were calculated for each stationary point to confirm whether it is a minimum, transition state, or higher-order saddle-point. The number of imaginary frequencies (NImag) obtained for each stationary point are indicated underneath the geometries (see Figures 2 and 3). To obtain accurate relative energies, calculations were also done using the composite method, CBS-QB3 [62], for all the low-lying isomers lying within 23.06 kcal mol −1 (1 eV). Wavefunction stability analysis was done for both the global minima (1n and 1a) obtained at the (U)ωB97XD/6-311++G(2d,2p) level and no instabilities were found [63]. Nucleus independent chemical shift (NICS) [64] values were calculated to gauge the π/σ dual aromaticity in both the global minima. Chemical bonding in the global minima was analyzed using canonical molecular orbitals (CMOs), adaptive natural density partitioning (AdNDP) [65,66], and natural bond order (NBO) approach [67]. Natural atomic charges (q) and Wiberg bond indices (WBIs) [68] from the NBO analyses were calculated at the (U)ωB97XD/6-311++G(2d,2p) level. To assess the multi-reference character of each molecule, as suggested elsewhere [69], T 1 diagnostic value was calculated. All these calculations were carried out with the Gaussian suite of programs [70].
Topological analysis of electron localization function (ELF) and Laplacian of electron density were carried out for both the neutral and anionic global minima with Multiwfn program [71] using the wave function file generated by Gaussian program [70]. We performed ab initio molecular dynamics (AIMD) simulations using the atom-centered density matrix propagation (ADMP) [72] approach included in Gaussian 16 program [70] for the global minimum structures of CAl 4 Mg and CAl 4 Mg − to check the kinetic stability of these molecules. These simulations were done for 10 ps at 298 K.
For brevity, optimized geometries of high-energy isomers, Cartesian coordinates of all isomers, total energies, zero-point vibrational energies (ZPVEs), net dipole moment and relative energies without and with ZPVE correction are given in the Supplementary Materials.

Results and Discussion
The optimized geometries of the global minimum structures of CAl 4 Mg (1n) and  Figures 2 and 3, respectively. ZPVE-corrected relative energies obtained at the ωB97XD/6-311++G(2d,2p) (for neutrals) and UωB97XD/6-311++G(2d,2p) (for anions) levels are given for each geometry. The same obtained at the CBS-QB3 level are given in parentheses. Canonical molecular orbitals are shown in Figure 4. The bonding pattern obtained from AdNDP analyses is shown in Figure 5. NICS values calculated at 0 and 1 Å (NICS (0) and NICS (1)) are shown in Figure 6. Color filled map of ELF for 1n and 1a are shown in Figure 7. Gradient lines map of Laplacian of Electron Density (∇ 2 ρ(r)) with bond paths for 1n and 1a are shown in Figure 8. Bond length evolution of 1n and 1a obtained through ab initio MD simulations at 298 K in 10 ps are shown in Figure 9. Energy evolution of 1n and 1a calculated through ab initio MD simulations are shown in Figures 10 and 11, respectively.

Thermal Stability
Isomers with a ptC atom (1n and 1a) turned out to be global minima after our extensive search on the neutral and anion PESs. The second most stable isomer (2n) for the neutral contains a tetrahedral tetracoordinate carbon, which is 2.63 kcal mol −1 above 1n. At CBS-QB3 level, this gap increases to 6.18 kcal mol −1 . In the case of anion, isomer 2a lies 10.13 and 9.37 kcal mol −1 , respectively, above 1a at UωB97XD/6-311++G(2d,2p) and CBS-QB3 levels. This indirectly implies that the formation of 1a is more favorable as there is no other isomer is close by within ∼10 kcal mol −1 . The bonding scenario for the carbon atom in 2a is nearly tetrahedral. The adiabatic electron affinity of 1n is 2.05 and 1.96 eV at the (U)ωB97XD/6-311++G(2d,2p) and CBS-QB3 levels, respectively. Therefore, detecting these systems are experimentally feasible.

Natural Atomic Charge and Wiberg Bond Indices
The atomic charge on the C atom is above −2.70 |e| in both cases. The charge on all Al atoms are positive (0.41 and 0.56 |e| in 1n and 0.17 and 0.44 |e| in 1a). This results in a simultaneous operation of π-accepting and σ-donating effects stabilizing the ptC. As far as electronic structure is concerned, unlike the CAl 4 Be case [30], where ppC atom was established, here, due to increased ionic radii down the group (Be to Mg), the most stable structures exhibit ptC atom. Compared with the experimentally known molecule, CAl 4 H [7], where the H-atom binds with the bridge of the Al-Al bond, here Mg-atom binds on the opposite end where there is a dative Al-Al bond. The Wiberg bond index (WBI) [68] for this dative Al-Al bond is 0.37 and the WBI for C-Mg is negligibly small (0.06). Furthermore, the number of valence electrons in CAl 4 H is 17, and here it is perfectly 18 following the closed-shell valence electron rule suggested elsewhere [4]. Moreover, unlike

Bonding and Aromaticity
The Canonical molecular orbitals (CMOs) of the global minimum geometries of CAl 4 Mg and CAl 4 Mg − are shown in Figure 4. Both the structures containing the ptC atom can be explained using these MOs. In particular, HOMO-4 (CAl 4 Mg) exhibits πdelocalization, whereas HOMO, HOMO-2 and HOMO-5 shown there depict σ-delocalization. Likewise, for CAl 4 Mg − , π-delocalization can be seen in HOMO-5, whereas HOMO, HOMO-1 and HOMO-6 show σ-delocalization. While the Mg atom is directly bonded to the Al atoms in the neutral, it is bound to the Al atoms via ionic/covalent interactions in the anion. HOMO-6 (σ) clearly shows that there is an overlap between the Mg and Al atoms while other σ orbitals in the anion do not show an overlap, which justifies the mixed bonding character.
The overall bonding pattern in 1n and 1a can also be explained from AdNDP analysis, which covers not only Lewis bonding elements but also delocalized multi-center-2e bonds. For brevity, we show only the latter in Figure 5 to account for the 2π/6σ double aromaticity of the ptC in both the systems. Figure 5a,b,d reveals 3c-2e, 4c-2e and 5c-2e σ bonds with occupation numbers (ON) of 1.99, 2.00 and 2.00 |e|, respectively. Figure 5c indicates the 5c-2e π bond with ON of 2.00 |e|. Likewise, for the anion too, AdNDP orbitals ( Figure 5, bottom row) depict the multi-center 2e bonds, which specifies the 2π/6σ double aromaticity of the ptC atom. In both the global minima, the π/σ-dual aromaticity can also be independently confirmed through NICS values. The latter computed at 0 (on the ring) and 1 Å (above the ring) for 1n and 1a are shown in Figure 6. All the values obtained for each triangle are negative in both cases. This implies that both σ-(NICS(0)) and π-aromaticity (NICS(1)) are operatives in these two global minimum geometries containing ptC atom.

Topological Analysis
Two color filled map of ELF for CAl 4 Mg (1n) and CAl 4 Mg − (1a) is given in Figure 7. The ELF plot shows the delocalization of electron density within the molecule. The analysis further confirms that the interaction between the central C atom and four Al atoms is strong and the interaction between C and Mg atoms are much weaker. While the delocalization of electron density between Als and Mg are stronger, the delocalization between C and Mg are weaker in the neutral 1n compared to anionic 1a. This indicates that the addition of negative charge increases the interaction between the center (C atom) of the ptC system and the distant Mg atom.
We further analyzed the topology of electron density (ρ(r)) for the ptC geometries based on the Quantum Theory of Atoms In Molecules (QTAIM) [73]. The contour plots of the Laplacian of electron density (∇ 2 ρ(r)) along with bond paths and critical points for 1n and 1a are given in Figure 8. The topological parameters such as Lagrangian kinetic energy G(r c ), potential energy density V(r c ), energy density E(r c ) or H(r c ), -G(r c )/V(r c ) and G(r c )/ρ(r c ) at the critical points are given in Table 1. The bond paths indicate the bond between the central C atom with the four Al atoms. The electron density is found to be more between central C and Mg in the anionic 1a. The low ρ(r c ) values and positive ∇ 2 ρ(r c ) values suggest there is a closed-shell type of bonding involvement [74]. All the H(r c ) with < 0 values confirm a partial covalent interaction [75][76][77]. There is no indication for noncovalent interaction as the ratio -G(r c )/V(r c ) lies in between 0.5 and 1 [78]. Some of the G(r c )/ρ(r c ) values (<1) indicate bonding with partial covalent character. Table 1. Electron density descriptors (in a.u.) at the (3, −1) bond critical points (BCP) and ring critical point (RCP, C1-Mg2) obtained from the (U)ωB97XD/6-311++G(2d,2p) level for CAl 4 Mg (1n) and CAl 4 Mg − (1a). The topological parameters such as Lagrangian kinetic energy G(r c ), potential energy density V(r c ), energy density E(r c ) or H(r c ), -G(r c )/V(r c ) and G(r c )/ρ(r c ) at the critical points are also given.

Kinetic Stability
We carried out ab initio MD simulations using ADMP approach to evaluate the kinetic stability of 1n and 1a. We analyzed the changes in the structure and bond length between C and Mg, as well as changes in the energy. The time evolution of the bond length of 1n and 1a is shown in Figure 9. We checked the snapshots during the simulation from 0 to 10 ps at 298 K at intervals of 1 ps. The characteristic bond length (C-Mg) changes from 2.93 to 3.49 Å for neutral CAl 4 Mg. For anionic CAl 4 Mg − , the range of fluctuation in bond length is 3.46-3.85 Å. In Figures 10 and 11, the evolution of energy (in a.u.) is shown up to 10 ps of simulation time at temperature 298 K for CAl 4 Mg (1n) and CAl 4 Mg − (1a). A few geometries at different snapshots are given to show the structural changes during the simulation. The changes in energy (in a.u.) with time (in ps) shows the oscillation in energy for both cases (1n and 1a). The range of oscillation of energy is comparatively higher for an anionic system (1a). The steady fluctuations in energy and consistency in the geometry suggest the kinetic stability of these molecules. For anion, the range is higher, which may be attributed to the extra negative charge present within the system. However, we note that the EA value obtained for the neutral is in the range of 1.96-2.05 eV.

Conclusions
Molecules with a ptC atom have been theoretically characterized for the first time in both CAl 4 Mg (1n) and CAl 4 Mg − (1a). Their electronic structures reveal that the Mg atom makes a bond with Al atoms at a non-bridging position in the neutral, whereas it is bound to the Al atoms with a mixture of ionic/covalent interactions in the anion. The neutral molecule obeys the 18 valence electron rule but the anion breaks the rule with 19 valence electrons in total. However, both are stabilized by π/σ double aromaticity. More than the valence electron, it is the double aromaticity factor that governs the stabilization of these molecules. Topological analysis through ELF and the electron density plot confirm that both the systems contain a ptC atom. Ab initio MD simulations carried out at 298 K for 10 ps revealed that these molecules are kinetically stable. Considering the electron affinity values of 1.96-2.05 eV for the neutral, it is believed that the rule-breaking anion and then the rule-abiding neutral could be identified in the laboratory.