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Article

CAl4Mg0/−: Global Minima with a Planar Tetracoordinate Carbon Atom

by
Nisha Job
1,
Maya Khatun
2,
Krishnan Thirumoorthy
1,
Sasanka Sankhar Reddy CH
3,
Vijayanand Chandrasekaran
1,
Anakuthil Anoop
2,* and
Venkatesan S. Thimmakondu
4,*
1
Department of Chemistry, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, Tamil Nadu, India
2
Department of Chemistry, Indian Institute of Technology Kharagpur, Kharagpur 721 302, West Bengal, India
3
Department of Electrical and Electronics Engineering, Birla Institute of Technology and Science, Pilani–K K Birla Goa Campus, Goa 403 726, India
4
Department of Chemistry and Biochemistry, San Diego State University, San Diego, CA 92182-1030, USA
*
Authors to whom correspondence should be addressed.
Atoms 2021, 9(2), 24; https://doi.org/10.3390/atoms9020024
Submission received: 16 March 2021 / Revised: 31 March 2021 / Accepted: 7 April 2021 / Published: 9 April 2021
(This article belongs to the Special Issue Planar Tetracoordinate Carbon—Fifty Years and Beyond)
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Abstract

:
Isomers of CAl4Mg and CAl4Mg− 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 CAl4Be 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 CAl4Mg0/− 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 CAl4Mg 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.

1. Introduction

The concept of planar tetracoordinate carbon (ptC) or carbon group elements enthrals both experimentalists [1,2,3,4,5,6,7,8,9,10] and theoreticians [11,12,13,14,15,16,17,18,19] as it is a fundamental deviation from the conventional ideas of tetrahedral tetracoordinate carbon [20,21]. The latter was defined independently by van’t Hoff and Le Bel in 1874. In 1968, Monkhorst first mentioned the idea of ptC as a transition state geometry in a non-dissociative racemization process [22]. In 1970, Hoffmann and co-workers showed ways to stabilize ptC by incorporating appropriate substituents that would act as a good σ -donor/ π -acceptor simultaneously or by embedding the ptC into a (4n + 2) π electron system [11]. In 1976, Schleyer and co-workers computationally identified, for the first time, the real minima (local, not global) in lithium substituted cyclopropane and cyclopropene [12]. Since then, many molecules containing ptC have been characterized in silico [23,24,25,26,27,28,29,30,31,32], and some have been experimentally detected [1,2,3,4,5,6,7,8,9]. Lately, the idea of ptC has been extended to planar hypercoordinate carbon (phC; penta [33,34,35] and hexa [36,37,38,39,40] coordination) as well as to other elements such as B [41,42] or N [43] considering their potential applications in material science [44,45].
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.

2. 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) ω B97XD 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 Figure 2 and Figure 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) ω B97XD/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) ω B97XD/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.

3. Results and Discussion

The optimized geometries of the global minimum structures of CAl 4 Mg (1n) and CAl 4 Mg − (1a) are shown in the top row of Figure 1. Natural atomic charges (q) and Wiberg bond indices are shown in the bottom row of Figure 1. The low-lying isomers of CAl 4 Mg and CAl 4 Mg − are shown in Figure 2 and Figure 3, respectively. ZPVE-corrected relative energies obtained at the ω B97XD/6-311++G(2d,2p) (for neutrals) and U ω B97XD/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 Figure 10 and Figure 11, respectively.

3.1. 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 U ω B97XD/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) ω B97XD/6-311++G(2d,2p) and CBS-QB3 levels, respectively. Therefore, detecting these systems are experimentally feasible.

3.2. 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 CAl 4 H − case, where the H-atom is still connected to the bridge of the Al-Al bond, here, the Mg atom in CAl 4 Mg − binds with the Al-Al bridge through ionic/covalent interactions at the center. WBI for Al-Mg and C-Mg in 1a are 0.21 and 0.02, respectively. The C-Mg distances for neutral and anion are 3.31 and 3.83 Å, respectively. While the neutral molecule broke the valence electron rule in CAl 4 H, here, it is the anion, CAl 4 Mg − , that breaks the rule with 19 valence electrons.

3.3. 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 π -delocalization, 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 2 π /6 σ 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 2 π /6 σ 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.

3.4. 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(rc), potential energy density V(rc), energy density E(rc) or H(rc), -G(rc )/V(rc ) and G(rc)/ ρ (rc) 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 (rc) values and positive ∇ 2 ρ (rc) values suggest there is a closed-shell type of bonding involvement [74]. All the H(rc) with < 0 values confirm a partial covalent interaction [75,76,77]. There is no indication for noncovalent interaction as the ratio -G(rc)/V(rc) lies in between 0.5 and 1 [78]. Some of the G(rc)/ ρ (rc) values (<1) indicate bonding with partial covalent character.

3.5. 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 Figure 10 and Figure 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.

4. 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.

Supplementary Materials

The following are available online at https://www.mdpi.com/article/10.3390/atoms9020024/s1. 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 corrections are given.

Author Contributions

Conceptualization, V.S.T.; methodology, A.A., V.S.T.; software, N.J., M.K., A.A., S.S.R.C., K.T., V.C. and V.S.T.; validation, V.S.T. and A.A.; formal analysis, N.J., M.K., V.S.T., A.A. and K.T.; investigation, V.S.T., K.T. and V.C.; resources, K.T., A.A. and V.S.T.; data curation, S.S.R.C. and V.S.T.; writing—original draft preparation, M.K. and V.S.T.; writing—review and editing, V.S.T. and A.A.; visualization, N.J., M.K., K.T., A.A. and V.S.T.; supervision, V.S.T. and A.A.; and project administration, V.S.T. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding. Computational support provided at the SDSU by DURIP Grant W911NF-10-1-0157 from the U.S. Department of Defense and by NSF CRIF Grant CHE-0947087 is gratefully acknowledged. Additional computational support provided at VIT, Vellore, India, through a research grant (Project. No. YSS/2014/001019) from the Science and Engineering Research Board, Department of Science and Technology, New Delhi, Government of India, is gratefully acknowledged.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data available in article or Supplementary Materials.

Acknowledgments

We acknowledge the resources of the Supercomputing facility at the Indian Institute of Technology Kharagpur established under National Supercomputing Mission (NSM), Government of India and supported by Centre for Development of Advanced Computing (CDAC), Pune. VST thanks Andrew L. Cooksy (SDSU, San Diego) for providing access to the computational resources. We also thank Raviprasad Aduri (BITS Pilani, Goa Campus) for his interest in this work.

Conflicts of Interest

The authors declare no conflict of interest.

Abbreviations

The following abbreviations are used in this manuscript:
ADMPAtom-centered Density Matrix Propagation
AdNDPAdaptive Natural Density Partitioning
CMOsCanonical Molecular Orbitals
DFTDensity Functional Theory
ELFElectron Localization Function
MDMolecular Dynamics
NBONatural Bond Order
NICSNucleus Independent Chemical Shift
ptCPlanar Tetracoordinate Carbon
phCPlanar Hypercoordinate Carbon
ppCPlanar Pentacoordinate Carbon
WBIWiberg Bond Index

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Atoms 09 00024 g001 550
Figure 1. Global minimum structures of CAl 4 Mg (1n) and CAl 4 Mg − (1a). 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) ω B97XD/6-311++G(2d,2p) level are given in the bottom row.
Figure 1. Global minimum structures of CAl 4 Mg (1n) and CAl 4 Mg − (1a). 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) ω B97XD/6-311++G(2d,2p) level are given in the bottom row.
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Atoms 09 00024 g002 550
Figure 2. Low-lying isomers of CAl 4 Mg on the singlet PES. Relative energies including ZPVE correction (in kcal mol − 1 ) are calculated at the ω B97XD/6-311++G(2d,2p) level. Relative energies obtained at the CBS-QB3 level are shown in parentheses. Number of imaginary frequencies (NImag) obtained for each stationary point are indicated underneath the geometries.
Figure 2. Low-lying isomers of CAl 4 Mg on the singlet PES. Relative energies including ZPVE correction (in kcal mol − 1 ) are calculated at the ω B97XD/6-311++G(2d,2p) level. Relative energies obtained at the CBS-QB3 level are shown in parentheses. Number of imaginary frequencies (NImag) obtained for each stationary point are indicated underneath the geometries.
Atoms 09 00024 g002
Atoms 09 00024 g003 550
Figure 3. Low-lying isomers of CAl 4 Mg − on the doublet PES. Relative energies including ZPVE correction (in kcal mol − 1 ) are calculated at the U ω B97XD/6-311++G(2d,2p) level. Relative energies obtained at the CBS-QB3 level are shown in parentheses. The number of imaginary frequencies (NImag) obtained for each stationary point are indicated underneath the geometries.
Figure 3. Low-lying isomers of CAl 4 Mg − on the doublet PES. Relative energies including ZPVE correction (in kcal mol − 1 ) are calculated at the U ω B97XD/6-311++G(2d,2p) level. Relative energies obtained at the CBS-QB3 level are shown in parentheses. The number of imaginary frequencies (NImag) obtained for each stationary point are indicated underneath the geometries.
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Atoms 09 00024 g004 550
Figure 4. Canonical molecular orbitals (CMOs) of CAl 4 Mg (1n) and CAl 4 Mg − (1a) obtained at the (U) ω B97XD/6-311++G(2d,2p) level.
Figure 4. Canonical molecular orbitals (CMOs) of CAl 4 Mg (1n) and CAl 4 Mg − (1a) obtained at the (U) ω B97XD/6-311++G(2d,2p) level.
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Figure 5. AdNDP bonding patterns of CAl 4 Mg (1n) and CAl 4 Mg − (1a) obtained at the (U) ω B97XD/6-311++G(2d,2p) level.
Figure 5. AdNDP bonding patterns of CAl 4 Mg (1n) and CAl 4 Mg − (1a) obtained at the (U) ω B97XD/6-311++G(2d,2p) level.
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Figure 6. Nucleus independent chemical shifts (NICSs; in ppm) for CAl 4 Mg (1n) and CAl 4 Mg − (1a) calculated at the (U) ω B97XD/6-311++G(2d,2p) level. NICS (1) (green color) is calculated at 1 Å above the ring, whereas NICS(0) (blue color) refers to on the plane values.
Figure 6. Nucleus independent chemical shifts (NICSs; in ppm) for CAl 4 Mg (1n) and CAl 4 Mg − (1a) calculated at the (U) ω B97XD/6-311++G(2d,2p) level. NICS (1) (green color) is calculated at 1 Å above the ring, whereas NICS(0) (blue color) refers to on the plane values.
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Atoms 09 00024 g007 550
Figure 7. Color filled map of ELF for CAl 4 Mg (1n) and CAl 4 Mg − (1a) calculated at the (U) ω B97XD/6-311++G(2d,2p) level. Relative geometric distances are shown in the abscissal and longitudinal coordinates. For clarity, the atomic label and index are added nearby the position of the corresponding atom.
Figure 7. Color filled map of ELF for CAl 4 Mg (1n) and CAl 4 Mg − (1a) calculated at the (U) ω B97XD/6-311++G(2d,2p) level. Relative geometric distances are shown in the abscissal and longitudinal coordinates. For clarity, the atomic label and index are added nearby the position of the corresponding atom.
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Atoms 09 00024 g008 550
Figure 8. Contour map of the Laplacian of Electron Density (∇ 2 ρ (r)) with the bond paths for CAl 4 Mg (1n) and CAl 4 Mg − (1a) calculated at the (U) ω B97XD/6-311++G(2d,2p) level. The blue lines show areas of charge concentration ∇ 2 ρ (r) ≤ 0, whereas the red lines show areas of charge depletion δ 2 ρ (r) ≥ 0. The brown dots represent the nucleus critical point or NCP. The brown lines connect NCP and bond critical points (BCP). The green line connecting RCP (ring critical point, orange dot) shows the inter-basin path. For clarity, the atomic label and index are added nearby the position of the corresponding atom.
Figure 8. Contour map of the Laplacian of Electron Density (∇ 2 ρ (r)) with the bond paths for CAl 4 Mg (1n) and CAl 4 Mg − (1a) calculated at the (U) ω B97XD/6-311++G(2d,2p) level. The blue lines show areas of charge concentration ∇ 2 ρ (r) ≤ 0, whereas the red lines show areas of charge depletion δ 2 ρ (r) ≥ 0. The brown dots represent the nucleus critical point or NCP. The brown lines connect NCP and bond critical points (BCP). The green line connecting RCP (ring critical point, orange dot) shows the inter-basin path. For clarity, the atomic label and index are added nearby the position of the corresponding atom.
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Figure 9. Bond length (C-Mg) evolution of CAl 4 Mg (1n) and CAl 4 Mg − (1a) at 298 K in 10 ps ab initio MD simulations calculated at the (U) ω B97XD/6-311++G(2d,2p) level.
Figure 9. Bond length (C-Mg) evolution of CAl 4 Mg (1n) and CAl 4 Mg − (1a) at 298 K in 10 ps ab initio MD simulations calculated at the (U) ω B97XD/6-311++G(2d,2p) level.
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Figure 10. Energy evolution of CAl 4 Mg (1n) at 298 K in 10 ps ab initio MD simulations calculated at the ω B97XD/6-311++G(2d,2p) level.
Figure 10. Energy evolution of CAl 4 Mg (1n) at 298 K in 10 ps ab initio MD simulations calculated at the ω B97XD/6-311++G(2d,2p) level.
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Figure 11. Energy evolution of CAl 4 Mg − (1a) at 298 K in 10 ps ab initio MD simulations calculated at the U ω B97XD/6-311++G(2d,2p) level.
Figure 11. Energy evolution of CAl 4 Mg − (1a) at 298 K in 10 ps ab initio MD simulations calculated at the U ω B97XD/6-311++G(2d,2p) level.
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Table
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) ω B97XD/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(rc), potential energy density V(rc), energy density E(rc) or H(rc), -G(rc )/V(rc ) and G(rc)/ ρ (rc) at the critical points are also given.
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) ω B97XD/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(rc), potential energy density V(rc), energy density E(rc) or H(rc), -G(rc )/V(rc ) and G(rc)/ ρ (rc) at the critical points are also given.
SystemsBCP & RCP ρ (rc) δ 2 ρ (rc)G(rc)V(rc)H(rc)ELF-G(rc)/V(rc)G(rc)/ ρ (rc)
CAl4MgAl4-Mg20.02630.00290.0076−0.0144−0.00680.43700.52600.2880
C1-Al40.08320.31000.1050−0.1330−0.02770.15700.78901.2620
Al6-C10.06720.22400.0766−0.0972−0.02060.14800.78801.1390
C1-Mg20.01990.01040.0057−0.0088−0.00310.35000.64700.2870
Al3-Mg20.02630.00290.0076−0.0144−0.00680.43700.52600.2870
C1-Al30.08320.31000.1050−0.1330−0.02770.15700.78901.2620
Al5-C10.06720.22400.0766−0.0972−0.02060.14800.78801.1390
CAl4Mg−Al4-Mg20.02350.00560.0069−0.0124−0.00550.39200.55600.2930
C1-Al40.08080.31600.1040−0.1300−0.02540.14700.80001.2870
C1-Mg20.0227−0.00340.0039−0.0088−0.00480.63700.45100.1740
Al6-C10.07230.26500.0880−0.1100−0.02180.14400.80001.2170
Al3-Mg20.02350.00560.0069−0.0124−0.00550.39200.55600.2940
C1-Al30.08080.31600.1040−0.1300−0.02540.14700.80001.2870
Al5-C10.07230.26500.0880−0.1100−0.02180.14400.80001.2170
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Job, N.; Khatun, M.; Thirumoorthy, K.; CH, S.S.R.; Chandrasekaran, V.; Anoop, A.; Thimmakondu, V.S. CAl4Mg0/−: Global Minima with a Planar Tetracoordinate Carbon Atom. Atoms 2021, 9, 24. https://doi.org/10.3390/atoms9020024

AMA Style

Job N, Khatun M, Thirumoorthy K, CH SSR, Chandrasekaran V, Anoop A, Thimmakondu VS. CAl4Mg0/−: Global Minima with a Planar Tetracoordinate Carbon Atom. Atoms. 2021; 9(2):24. https://doi.org/10.3390/atoms9020024

Chicago/Turabian Style

Job, Nisha, Maya Khatun, Krishnan Thirumoorthy, Sasanka Sankhar Reddy CH, Vijayanand Chandrasekaran, Anakuthil Anoop, and Venkatesan S. Thimmakondu. 2021. "CAl4Mg0/−: Global Minima with a Planar Tetracoordinate Carbon Atom" Atoms 9, no. 2: 24. https://doi.org/10.3390/atoms9020024

APA Style

Job, N., Khatun, M., Thirumoorthy, K., CH, S. S. R., Chandrasekaran, V., Anoop, A., & Thimmakondu, V. S. (2021). CAl4Mg0/−: Global Minima with a Planar Tetracoordinate Carbon Atom. Atoms, 9(2), 24. https://doi.org/10.3390/atoms9020024

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