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. 2024 Feb 19;9(9):10913–10928. doi: 10.1021/acsomega.3c10049

In Silico Analysis of the Aromaticity of Some Carbo-Metallabenzenes and Carbo-Dimetallabenzenes (Carbo-mers Proposed from Metallabenzenes)

David Arias-Olivares †,*, Andrés Becerra-Buitrago ‡, Luis Carlos García-Sánchez §, Diego V Moreno ∥, Rafael Islas ⊥,#,*
PMCID: PMC10918654  PMID: 38463261

Abstract

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In the current work, we introduce a novel class of molecules termed carbo-metallabenzenes, and their aromaticity has been comprehensively analyzed. The molecules were strategically designed with the insertion of acetylene (C≡C or C2) units in some selected metallabenzenes. Furthermore, if a second metallic unit is inserted (replacing a sp2 carbon) in the carbo-metallabenzenes rings, a new family of carbo-mers is generated, and this second group has been named as carbo-dimetallabenzenes. The primary objective of this work is to ascertain, through various methodologies, whether these newly proposed molecules retain the aromatic characteristics observed in carbo-benzene. The methodologies employed for bond analysis and aromaticity exploration include the analysis of the molecular orbitals, energy decomposition analysis, electron density of delocalized bonds, magnetically induced current density, and the induced magnetic field (Bind). This study sheds light on that the insertion of the metallic centers reduces the electronic delocalization and their aromaticity is, in some cases, comparable with the electronic delocalization of the inorganic iminobora-borazine and also provides valuable insights into their electronic structure through a multifaceted analysis.

1. Introduction

In 1979, Thorn and Hoffmann proposed the theoretical existence of benzenes with one metal fragment instead one carbon (CH unit).1 This kind of rings are stabilized by aromaticity, where the metal atom participates in the electronic delocalization. This proposal was followed by the synthesis of the first metallacycle in 1982: an osmabenzene.2 Since then, the chemistry of metallacycles presented an enormous expansion and many other rings were synthesized with one metal center replacing a CH unit of benzene.3 The two largest families of these compounds are osmabenzenes and iridabenzenes.4 The electronic delocalization in rings containing metal atoms is catalogued as metallaromaticity5 and, as mentioned before, is one of the mechanisms proposed for the stabilization of the rings.6 The aromaticity of these rings has been computationally evaluated employing several methodologies, some of them based on the energetic stabilization such as isomer stabilization energy (ISE), proposed by Schleyer and Pühlhofer.7 With this methodology, the electronic delocalization was computed in some platinabenzenes by De Proft and Geerlings in 2004.8 Similarly, Lin et al. reported the synthesis and characterization of some rhenabenzenes, reporting the aromatic character of the rings employing ISE calculations.9 Other methodologies dedicated to quantify/qualify the electronic delocalization are the magnetic-based indexes. The most employed index is NICS (nucleus independent chemical shifts) developed by Schleyer et al. in 1996. With NICS, the aromaticity of some metallacycles was analyzed.10−14 Similar to NICS, the induced magnetic field (Bind) has been employed as aromaticity’s descriptor15 and, with the Bind, the diatropic character (associated with aromaticity) was determined in some metallacycles including some fused-cycles,16 metallaborazines,17 and five-membered rings (5MR).18,19 Finally, for a deeper appreciation of the metallacycle chemistry, some reviews are available.3,6,20

Additionally, carbo-mers are extended systems generated from the inclusion of one C≡C unit for each AB bond, forming A–C≡C–B bonds. If the number of the C≡C units, or C2 units, incorporated is equal to the number of bonds, the molecular symmetry is not altered, but the AB length is increased.21−23 With this methodology, the simplest example is acetylene, which is the carbo-mer proposed from the insertion of a C2 unit in the H2 molecule. In this line, the carbo-mer of benzene (C6H6) is called carbo-benzene (C18H6). Computational calculations show that carbo-benzene adopts a symmetric planar ring (D6h), satisfying the structural criterion of aromatic compounds. For confirmation of the aromatic character, the aromaticity of carbo-benzene, carbo-borazine, the inorganic analogue iminobora-borazine, some carbo-cages, and carbo-C42+ (where C42+ is the analogue of the aromatic all-metal Al42–) was studied in terms of the induced magnetic field.24−26 See Figure 1 for carbo-benzene, carbo-borazine, and iminobora-borazine structures’ representation. The aromaticity of other carbo-mers, with fused rings, such as carbo-azulene, has also been analyzed by Poater et al. in 2021.27 Even more, 20 years ago, a set of carbo-mers of heterocycles had been studied, where included the parent system such as pyridine, phosphonine, furan, and pyrrol, among others, demonstrating that the aromaticity from the parent system is conserved after the carbo-merization.28 Besides, aromaticity in carbo-mers is catalogued by Coqc et al. as carbo-aromaticity.29 These types of calculations have inspired experimental chemists to work on its synthesis. Where the first attempts result in carbo-benzenes with various substitution patterns.30,31 An experimental example of other types of extended systems is the germa[N]pericycclyine, reported by Tanimoto et al. in 2017; where the authors synthesized and characterized a macrocycle composed by germanium and butadiyne units.32 These previous works shed light to the theoretical-proposed derivates from carbo-benzenes as highly probable molecules to be studied and analyzed due to the conservation of their symmetry and their stability due to the electronic delocalization (aromatic character).

Figure 1.

Figure 1

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Structures of carbo-benzene, carbo-borazine, and iminobora-borazine.

In the current work, carbo-mers generated from some selected metallabenzenes are computationally proposed. These new rings are called carbo-metallabenzenes. Also, if a second metallic center is incorporated, the new molecules are carbo-dimetallabenzenes. The aromaticity of carbo-metallabenzenes and carbo-dimetallabenzenes is analyzed as a possible mechanism of their stabilization.

2. Computational Details

The structures proposed for carbo-metallabenzenes were generated considering the incorporation of six C2 units in some metallabenzenes following Scheme 1. In the second step, in the carbo-metallabenzenes proposed, a second metallic center was incorporated (replacing a sp2 carbon of the carbo-metallabenzene), generating a new set of molecules named carbo-dimetallabenzenes (Scheme 2). In this paper, the positions of the metallic centers in carbo-dimetallabenzenes were referred with the prefixes 1,4-, 1,7-, and 1,10-positions, being 1 the position of the first metal atom, and the second number (4, 7, or 10) the position of the second metallic atom as it is depicted in Scheme 2. All the geometries were optimized with the functional PBE033−35 employing the TZVP basis set36 for all atoms, except the metal, where the SARC-ZORA-TZVP basis set37 was used, in the program ORCA 5.038,39 and they were minima on their respective potential energy surfaces (PESs).

Scheme 1. Design of the Carbo-Metallabenzenes.

Scheme 1

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White, gray, and black represent carbon, hydrogen, and metal atoms (including their ligands), respectively.

Scheme 2. Geometries Proposed for Carbo-Dimetallabenzenes; (A) Numbering Positions in the Carbo-Ring; (B) 1,4-Position, (C) 1,7-Position, and (D) 1,10-Position.

Scheme 2

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The white and light-gray atoms represent carbon and hydrogen atoms. Black spheres represent the metallic centers M (where M = metal atoms and their respective ligands).

For EDA, MO construction was based on the ML fragments (metal with its ligands) and the rings (see Scheme 3), which helps to understand the interaction between the fragments through an analysis of bonding energies, combining a fragmented approach to the molecular structure with the decomposition of the interaction energy between fragments according to the Morokuma–Ziegler scheme [energy decomposition analysis (EDA) decomposition scheme]. This interaction between fragments is decomposed as follows

2.

where ΔEPau, ΔEEle, ΔEOrb, and ΔEDis represent the Pauli repulsion, electrostatic interaction, orbital-mixing terms, and dispersion correction, respectively.40,41

Scheme 3. Fragments Considered in EDA Calculations.

Scheme 3

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[M] represent metal atoms and the respective ligands.

The electron density of delocalized bonds (EDDBs) function was implemented following the original methodology by Szczepanik et al.42 The wave function was obtained at the same level of theory as the optimization, except for the metal atom, where the LANL2Z basis set43,44 was used instead of the SARC-ZORA-TZVP in the Gaussian16 Rev. B.01 package.45

The magnetically induced current density (MICD),46 which is related to aromatic response, was calculated using the linear response function47 and the perturbing operator for the magnetic field. The MICD was plotted in the streamline representation of the current density using PyNGL48 and was computed in DIRAC 1749 at the DFT level of theory with the PBE0 functional.35 The four-component Dirac-Coulomb Hamiltonian has been used alongside the unrestricted kinetic balance.50 The cc-pVDZ basis set was employed for all atoms, except for metal atoms.51 For the latter, the uncontracted and special Dyall double-ζ basis set was employed.52

The shielding tensors (σ) were computed in the program Gaussian 16 Rev. B.01 employing the PBE0 functional and def2-TZVP basis set,53 including pseudopotentials for metal atoms.54 The basis set and pseudopotentials were downloaded from Basis Set Exchange Web site.55 The induced magnetic field can be computed following the equation Bind = −σBext, where Bext represents the external magnetic field applied on the perpendicular direction to the molecular plane, and σ represents the shielding tensor (second-rank tensor) computed in any point in the space.15

3. Results and Discussion

3.1. Structural Results

3.1.1. Carbo-Metallabenzenes

For structural comparison, ethane, ethene, ethine, and carbo-benzene geometries were optimized with the same level of theory employed in the optimization of the carbo-rings (Computational Details section). The geometries and the bond length distances are depicted in Scheme 4.

Scheme 4. Bond Lengths of Single, Double, and Triple Carbon–Carbon Bonds.

Scheme 4

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Units are Å.

In the same line, carbo-benzene was optimized with the PBE0 functional and def2-TZVP basis set.53 The bond lengths of (aromatic) carbo-benzene are depicted in Scheme 5. With these references, the first electronic delocalization inspection was possible. The triple bond of the C2 units was not delocalized and shortens the bond length distance similar to the bond length observed in ethine.

Scheme 5. CC Bonds Lengths in Carbo-Benzene.

Scheme 5

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Units are Å.

The geometries of the rings containing one metallic fragment were optimized and they are depicted in Figure 2. On the first examination, the organic part of the carbo-metallabenzenes was compared to carbo-benzene’s bond lengths: there was an alternation between triple and double bond lengths. For all the systems, the C2 units inserted maintained the bond lengths associated with the carbon triple bond; the range observed was 1.227–1.234 Å, very similar to those observed in carbo-benzene (1.231 Å) and larger than methine (1.198 Å). The other C–C bond lengths lied on the range of 1.360–1.371 Å that could be associated with a carbon–carbon double bond (1.324 Å). In few words, these carbo-mers were structurally comparable to carbo-benzene. Additionally, all the optimized structures, except 3 (see Figure 3), were planar rings. This nonplanar ring, adopted a bent structure; this type of geometries (bent rings) has been revised and discussed in metallabenzenes and heterometallabenzenes.56,57 The electronic delocalization of all the planar systems was analyzed (vide infra).

Figure 2.

Figure 2

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Bond lengths of carbo-metallabenzenes (Å). Green and white spheres represent carbon and hydrogen atoms, respectively. Ligands were removed for a better appreciation of the molecular rings. The value charge is the charge of the complete molecule.

Figure 3.

Figure 3

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Dihedral angle formed with C1–C2–C3-Re of 3 is reported in degrees. White, green, and red spheres represent hydrogen, carbon, and oxygen atoms, respectively.

3.1.2. Carbo-Dimetallabenzenes

As mentioned in the Computational Details section, carbo-dimetallabenzenes were proposed after a second CH unit of the carbo-metallabenzenes was replaced by a second metallic center. With this substitution, a new set of molecules were generated and analyzed. For convenience, the prefixes 1,4-, 1,7-, and 1,10- were employed in these rings. Three subgroups were generated based on the orientation of the metallic centers (Scheme 2). Only homodimetallabenzenes were proposed: carbo-diosmabenzene, carbo-dirutheniabenzene, carbo-diiridabenzene, carbo-dirheniumbenzene, carbo-dirhodiumbenzene, and carbo-diplatinabenzene.

The first subgroup, 1,4-carbo-mers were proposed with two metallic centers in nearest-neighbor vertices of the carbo-metallacycles. The system of rhodium and rhenium showed no minima on their respective PESs and, consequently, they were not reported in this section. The other four metallic centers (Ru, Os, Ir, and Pt) are depicted in Figure 4. As per the initial inspection, the presence of the C2 units was visible through the bond lengths in agreement with the original carbo-benzene. However, the planarity was compromised by the vicinity of the voluminous metallic centers that include the metal atom and their respective ligands. For this reason, systems 8, 9, and 10, could be catalogued as quasi-planar rings and this distortion was measured with dihedral angles reported in Figure 5.

Figure 4.

Figure 4

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Bond lengths of 1,4-carbo-dimetallabenzenes. The units are Å. Green and white spheres represent carbon and hydrogen atoms, respectively. Ligands were removed for a better appreciation of the molecular rings. The value charge is the charge of the complete molecule.

Figure 5.

Figure 5

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Some selected dihedral angles (C1–C2–M1–M2, where M1 = M2 = Ru, Os, Ir, and Pt) formed in 7, 8, 9, and 10. The units reported are degrees.

Particularly, the optimized structure of 7 was a highly distorted ring (see Figure 5) and, consequently, electronic delocalization calculations were not realized in this carbomer. The rest of the rings, those that included osmium, iridium, and platinum, were quasi-planar rings. In these rings, bond length alternation was appreciable, but still comparable with carbo-benzene values (Figure 5).

In the second subgroup, the optimized geometries of 1,7-orientation carbo-dimetallabenzenes with ruthenium, rhodium, and rhenium (11, 12, and 13, respectively) were distorted rings. However, osmium, iridium, and platinum systems (14, 15, and 16, respectively) were planar rings, and they are depicted in Figure 6. In Figure 7, lateral views of 11, 12, and 13 are depicted for the appreciation of the distortion of the rings generated by the presence of the metallic centers. In 11, the Ru atom did not form a part of the ring and, for consequently, the organic skeleton was a ring with 16 carbon atoms. In the other rings, the metallic centers were a part of the cyclic structures. The bond lengths of 11 were not different from those measured in 12, 13, 14, 15, and 16; presenting similar lengths observed in carbo-benzene. The only difference of 11 was the C–C bond formed in the place where the C-metal-C bond was placed, forming a 16-carbon ring.

Figure 6.

Figure 6

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Bond lengths of carbo-dimetallabenzenes. The units are Å. Green and white spheres represent carbon and hydrogen atoms, respectively. Ligands were removed for a better appreciation of the molecular rings. The value charge is the charge of the complete molecule.

Figure 7.

Figure 7

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Lateral view of 11, 12, and 13. The distortion of the rings was appreciable. Green and white spheres represent carbon and hydrogen atoms, respectively. Ligands of the metal centers were removed for a better appreciation of the molecular.

The third subgroup, with 1,10-orientation, the rings adopted a planar configuration except for the rhodium system, 18; for this reason, this system was not considered for further analysis. The quasi-planar ring was 17 which presented a small deviation from planarity, adopting a flat boat. Other systems (19, 20, 21, and 22) were completely planar rings. In Figure 8, the geometries and bond length distances are depicted, and in Figure 9, the distorted structure of 18 is shown.

Figure 8.

Figure 8

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Bond lengths of carbo-dimetallabenzenes. The units are Å. Green and white spheres represent carbon and hydrogen atoms, respectively. Ligands were removed for a better appreciation of the molecular rings. The value charge is the charge of the complete molecule.

Figure 9.

Figure 9

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Distortion observed in 18. One of the Ru centers was placed out of the ring and adopted a perpendicular position to the molecular plane.

3.2. Electronic Structure

3.2.1. Molecular orbitals

The analysis of the molecular orbitals (MOs) of all the molecules was realized, showing that not only the classic π-MO participated in the electronic delocalization, but the in-plane orbitals, which are related with triple bonds of acetylene units. In some cases, it was clear the radial nature of specific MOs. Nevertheless, these radial MO were mixed with the π-MO from the ring or the MO of the metal atoms (see Figure 10). This phenomenon was mentioned by Maraval and Chauvin; they explained it with the generation of homoconjugation to adjacent triple bonds (homoaromaticity), generated by the reduced gap between HOMO and LUMO, and this situation could be observed in extended heteroperycyclynes and expanded radialenes.23 An example of homoconjugation is depicted in Figure 10. It is important to highlight that carbo-benzene is aromatic, but it is not homoaromatic.28 Furthermore, it is possible that the dx2–y2 atomic orbitals could favor the electronic delocalization process within the radial orbitals (πin_plane orbitals) of the proposed systems. That situation is also observed in the system herein reported (see Figure 11). Therefore, the HOMO–LUMO gap was measured in our system and reported in Table 1. The computed value for the carbomer is 72.87 kcal/mol. Thus, a reduction in the HOMO–LUMO gap is observed in all systems. The trends appears naturally if the gap is compared with the atomic mass of each metallic center. For the monosubstituted systems, the gap increase as the mass increase for the Ru–Rh–Re triad, as well as for Os–Ir–Pt triad. On the other hand, for the 1,4-substitution, the gaps decrease in the same triads. Even more, for the 1,7- and 1,10-substitution no evident trends arise; nevertheless, the Rh and Ir present the highest gaps for those substitutions, recalling that they belong to the same group in the periodic table.

Figure 10.

Figure 10

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Examples of MOs: (a) HOMO – 24 of 22 represents the out-of-plane MO (π-MO), (b) HOMO – 5 of 6 represents the in-plane MO (radial-MO), (c) HOMO – 6 of 9 represents the orbital generated by the combination of the metal atom with the in-plane triple bond of the C2 unit, (d) HOMO – 7 of 5 represents MOs that could be associated with a Möbius band, and finally, (e) is the HOMO – 19 of 4 and it represents the homoconjugation generated between the metal atom and the in-plane MOs of the adjacent carbon triple bonds.

Figure 11.

Figure 11

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Qualitative MO diagram for carbo-rutheniabenzene. Only π electrons are depicted.

Table 1. Aromatic Character and Relative Energies for the Systems Containing Os, Ir, and Pta.
metal system substitution aromaticity character ΔE (kcal/mol) ΔEL–H (kcal/mol)
Os 4 monosubstituted Hückel aromatic   28.56
8 1,4-carbo-mer Möbius aromatic 0.00 47.03
14 1,7-carbo-mer Double-Twist Möbius aromatic 19.57 31.78
20 1,10-carbo-mer Double-Twist Möbius antiaromatic 26.47 9.77
Ir 5 monosubstituted Huckel aromatic   52.71
9 1,4-carbo-mer Huckel aromatic 7.38 38.28
15 1,7-carbo-mer Huckel aromatic 0.00 55.85
21 1,10-carbo-mer Huckel aromatic 2.95 46.44
Pt 6 monosubstituted Möbius aromatic   48.53
10 1,4-carbo-mer Double-Twist Möbius aromatic 15.23 31.81
16 1,7-carbo-mer Möbius aromatic 0.00 48.08
22 1,10-carbo-mer Double-Twist Möbius aromatic 8.09 29.41
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a

The relative energies were computed at the PBE0/TZVP level as it was reported in the section of Computational Details. The HOMO–LUMO gap is also reported in kcal/mol. The carbomer has a L–H gap of 72.87 kcal/mol.

A deeper analysis for the HOMO–LUMO gap was conducted based on the lack of correlation between the energy gap and the aromatic response that some systems have. Unfortunately, the analysis of in-plane HOMO–LUMO as well as the analysis of classical π-HOMO–LUMO gap is not conclusive, i.e., there is not a clear correlation among the (de)stabilization of the metal HOMO (in plane or perpendicular), and the type or lack of aromatic behavior. Nevertheless, the ratio of mixed p/d metal orbitals gives interesting results, if the d orbitals contribute with more than 50%, the molecules present a Hückel aromatic behavior, and on the contrary, if the p orbitals contribute with more than 50%, then the system exhibits a (double) Möbius aromatic character; unfortunately, the information is not enough to differentiate between the traditional Möbius or Double Möbius aromatic character.

Systems 3, 7, 12, 13, and 18 were excluded since they do not meet the planarity criteria. Also 11 was discarded since it does not contain the ML fragments within the ring. For these rings, only π-MO diagrams were analyzed and depicted in the Supporting Information.

For the remaining systems, classic π-MO and radial π-MO diagrams were constructed. Furthermore, the contribution of the dyz and dxz orbitals made by the ML fragments for monosubstituted systems, and by the combination of ML–metalorganic fragments for double-substituted systems was analyzed, generating three types of aromaticity: Hückel, Möbius, and Double-Twisted Möbius (see Figure 12). Due to the construction of atomic orbitals based on symmetry, the 1,10-orientation rings were either Hückel or Double-Twisted Möbius.

Figure 12.

Figure 12

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Types of aromaticity proposed for carbo-metallabenzenes and carbo-dimatellabenzenes.

The π electrons were counted considering the radial orbitals, to identify if the systems fulfill the number of electrons required for each type of aromaticity. It was found that systems 4, 5, 9, 15, and 21 presented Hückel aromaticity (4n + 2) with n = 10 for all of them, except for 5, which has n = 8. Systems 1, 2, 6, 8, and 16 could be associated with Möbius aromaticity (4n) with n = 10, 11, 9, 13, and 11, respectively. Systems 10, 14, 17, 19, and 22 were Double-Twisted Möbius Aromatic with n = 11, 12, 13, 9, and 10, respectively. System 20 was Double-Twisted Möbius antiaromatic since its electron count does not fit with the 4n + 2 rule, proposed for the Double-Twisted Möbius systems,58 as it has 48 π electrons between classic and radial π MO. We have analyzed the stability of the disubstituted isomers through relative energies obtained by single-point energy calculation and the aromatic behavior of each system has been related.

For the Os systems (4, 8, 14, and 20), all of them exhibited a different aromatic character, i.e., system 4 (monosubstituted); system 8 (1,4-carbo-mer); and systems 14 and 20 (1,7- and 1,10-carbo-mer) could be classified as Hückel, Möbius, and Double-Twisted Möbius, respectively. Nevertheless, 20 presented an antiaromatic behavior; even more, all of them showed a low diatropic response. In Table 1, the relative energy of the carbo-dimetallabenzene isomers is also shown, and the least stability (higher ΔE) belongs to system 20. It is in agreement with the electron counting and magnetic responses. The most stable isomer was the 1,4-oriented, being almost 20 kcal/mol more stable than the second most stable isomer.

For the Ir systems (5, 9, 15, and 21), all of them were labeled as Hückel aromatic molecules. The most stable isomer was the 1,7-carbo-mer, but only by 3 kcal/mol.

For the Pt systems (6, 10, 16, and 22), all of them exhibited Möbius or Double-Twisted Möbius aromatic character, i.e., systems 6 (monosubstituted) and 16 (1,7-carbo-mer); and systems 10 and 22 (1,4- and 1,10-carbo-mers) could be classified as Möbius and Double-Twisted Möbius, respectively. In coincidence with the iridium rings, the most stable isomer was the 1,7-carbo-mer.

3.2.2. Energy Decomposition Analysis

The analysis of the interaction of the metallic center with the ring of the proposed structures, were done with EDA, following the partition scheme proposed in computational details section: the interaction analyzed is between one of the metallic centers with the rest of the ring (see Scheme 3 in the Computational Details section).

The values of the EDA calculations are depicted in Table 2. For carbo-metallabenzenes, four out of six rings presented a dominant percentage of the electrostatic contribution to the interaction energy (% ΔEElec); on the other hand, only ruthenium and osmium rings presented a dominant orbital contribution (% ΔEOrb).

Table 2. EDA Values Computed in All the Proposed Ringsa.
  system metal net charge ML charge ΔEPauli ΔEElec % ΔEElec ΔEOrb % ΔEOrb ΔEDis ΔETot
carbo-metallabenzenes 1 Ru 1 0 15.86 –9.03 37.06 –15.33 62.94 –0.25 –8.76
2 Rh 0 1 15.66 –16.90 61.26 –10.69 38.74 –0.30 –12.22
3 Re 0 1 13.07 –15.97 63.24 –9.28 36.76 –0.22 –11.95
4 Os 1 0 19.23 –11.44 38.77 –18.07 61.23 –0.27 –10.55
5 Ir 0 1 18.13 –19.08 61.46 –11.96 38.54 –0.25 –13.17
6 Pt 0 1 18.24 –19.97 62.12 –12.18 37.88 –0.17 –14.09
1,4-carbo-bimetallic 7 Ru 2 0 36.90 –18.10 39.82 –27.30 60.18 –0.50 –9.03
8 Os 2 0 21.60 –14.50 43.50 –18.80 56.50 –0.30 –12.00
9 Ir 0 1 24.20 –20.30 53.99 –17.30 46.01 –0.30 –13.70
10 Pt 0 1 17.30 –16.10 51.41 –15.20 48.59 –0.20 –14.20
1,7-carbo-bimetallic 11 Ru 2 0 14.40 –7.00 39.13 –10.89 60.87 –0.35 –3.84
12 Rh 0 1 15.62 –15.57 58.31 –11.13 41.69 –0.31 –11.39
13 Re 0 1 12.20 –14.50 60.99 –9.28 39.01 –0.20 –11.80
14 Os 2 0 18.10 –10.10 37.92 –16.50 62.08 –0.30 –8.75
15 Ir 0 1 17.90 –18.50 60.01 –12.30 39.99 –0.30 –13.10
16 Pt 0 1 26.00 –22.80 56.93 –17.20 43.07 –0.20 –14.20
1,10-carbo-bimetallic 17 Ru 2 0 16.20 –11.90 43.88 –15.20 56.12 –0.20 –11.10
18 Rh 0 1 15.60 –16.50 60.60 –10.70 39.40 –0.30 –8.59
19 Re 0 1 12.80 –15.40 62.61 –9.18 37.39 –0.20 –11.90
20 Os 2 0 19.40 –14.20 45.05 –17.30 54.95 –0.30 –12.30
21 Ir 0 1 20.00 –19.80 58.26 –14.20 41.74 –0.20 –14.20
22 Pt 0 1 18.20 –20.00 60.09 –13.30 39.91 –0.20 –15.30
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Energies are collected in eV.

Also, in Table 2, two different sets of Eint are observed, one who presented bigger orbital energy contribution which is related with covalent interaction and, the other one, with bigger electrostatic energy contribution which is related with ionic interaction. The former includes the systems 1, 4, 8, 14, 20, and 17 which were taken into account for aromaticity studies, while the systems 7 and 11 were outside of the analysis due to lack of planarity. In this way, systems 1, 4, and 14 presented bigger orbital contributions (>60%), in agreement with the Bind calculations (vide infra) that showed that these systems were the least diatropic. The latter were the systems 2, 19, 5, 6, 9, 10, 15, 16, 21, and 22 with higher diatropic response in comparison with those that presented a higher orbital interaction; a possible explanation for this behavior was the diminished σ interaction between the metal and the nearest carbon but a higher electrostatic interaction among the axial p–d interaction through the long bond distances as observed in previous EDA analysis between metals and light atoms.17 Furthermore, the interaction between the metal center and the ring was always in the range of −8.5 and −15.3 eV/mol. The highest interaction consistently remained in the Pt and Ir centers. Systems 3, 12, 18, and 13, have been outside of this analysis based on the planarity criteria.

3.2.3. Electron Density of Delocalized Bonds

Analyzing the ring and its delocalization, the EDDBP (electrons delocalized along a selected pathway) was used instead of the global descriptor (EDDBG) or the description avoiding hydrogen atoms (EDDBH). The inclusion of the ligands from the metal fragment introduced electron density around the metal and this expanded the visualized isosurface of EDDB, giving rise to misinterpretations over the electrons delocalized and their electron counting (Figure 13). This led to a different π-electron counting compared with the EDA analysis. Thus, for system 6, the population of delocalized electrons in the EDDBG was 22.47e (1.79e from Pt), in the EDDBH was 20.92e (1.76e from Pt), and finally for EDDBP was 11.46e (0.37e from Pt).

Figure 13.

Figure 13

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Electron delocalization for system 6 in the (left) EDDBG function and (right) EDDBP function. Isovalue = 0.01.

Analogue to benzene, the carbo-benzene showed a fully delocalized bond over the system (Figure 14A). In most of the systems, similar delocalization was observed over the organic fragments, and it slightly vanished close to the metal. As an example, the platinum systems were shown alongside carbo-benzene (Figure 14). This lack of homogeneous delocalization played an important role over the induced magnetic field avoiding a fully delocalized nature of the electron density but an induced current density in parts of the ring. Platinum always showed an electron contribution of d-like orbitals to the ring. Nevertheless, the contribution was not high enough to be fully delocalized. All EDDB plots are presented in ESI. While the carbo-benzene had a uniformly delocalized electron nature of 0.78e per atom (total 14.09e), all the proposed carbo-metallabenzenes contributed with less than 0.5e for metal atoms and the contribution per carbon atom was significatively reduced. Except for osmium systems 4 and 20 with metal contributions of 0.58e and 0.83e, respectively.

Figure 14.

Figure 14

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EDDBP for (a) carbo-benzene, (b) system 6, (c) system 10, (d) system 16, and (e) system 22. Isovalue = 0.01.

While all systems presented a partially delocalized electron nature, some of them could be potentially aromatic based on the low change in the population per carbon atom (systems 3 and 6), and the total electron population delocalization. If the total delocalized electron population was applied to the Hückel’s rule, then, the carbo-benzene would be an aromatic system with n = 3, while if n = 2 is considered (total electrons equals 10), then system 2 with a total population of 10.39e, system 5 with 9.45e, system 10 with 9.83e, system 13 with 9.57e, and system 16 with 9.76e were potentially aromatic systems. Alongside system 15 with n = 1 (total electrons equals 6) and a total population of 5.95e, system 20 with 6.31e.

3.3. Electronic Delocalization

3.3.1. Magnetically Induced Current Density

The four-component Dirac Hamiltonian was used to compute the induced current density. The relativistic current density is plotted at the molecular plane, and at the planes at 1a0 and 2a0 above the ring. As a reference, the carbomer molecule is plotted (Figure 15). The delocalized nature of the carbomer system was more evident at 1a0 and 2a0 over the molecular plane. Diatropic current densities were induced in a counterclockwise direction over the carbons, and in the inner part of the ring, a paratropic current density was sustained. This behavior was analogous to the benzene molecule and then it could be categorized as aromatic16 based on this magnetic criterion.

Figure 15.

Figure 15

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MICD with four-component Dirac Hamiltonian for carbo-benzene system. (A) At the molecular plane, (B) at 1a0 above the molecular plane, and (C) 2a0 above the molecular plane. Counterclockwise direction represents diatropic current (aromatic).

This behavior was also found in some system proposed here. Systems 2, 3, 5, 6, 9, 10, 16, 15, and 22 could be considered aromatic, they could sustain diatropic currents at different levels. Figure 16 shows the plots where the diatropic current is highlighted in the possible aromatic systems. Blue arrows represent total diatropic current, while the green arrow represents local diatropic currents. The integration of the current densities was not calculated due to important statements: (i) the local diatropic response contributes to the total diatropic response. This contribution influences the integration of the current density possibly overestimating the total diatropic current density. (ii) The integration is path-dependent and there was not a common integration plane. The closer to a nucleus the path is, the bigger the integrated value will result. This also occur if the plane contains a considerable amount of local current densities. (iii) The lack of symmetry of the system results of different values if it is integrated in different directions, i.e., above or below the molecular plane.

Figure 16.

Figure 16

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MICD for aromatic systems. Blue arrows belong to total current density and the green arrow to local current density.

3.3.2. Induced Magnetic Field, Bind

The Bind is a vector that represents the magnetic response of the molecules exposed to an external magnetic field (Bext). The z-component of this vector is labeled as Bindz, and it is equivalent to the negative of the zz-component of the shielding tensor (and also equivalent to NICSzz). Bindz is a scalar value and it was calculated in several points placed perpendicular to the molecular ring (Scheme 6).59,60 This induced field is characteristic for antiaromatic and aromatic molecules and, the more negative is the value of Bindz, more diatropic the system is. For a better reference, the Bindz of carbo-benzene and iminobora-borazine were also computed. Only planar or quasi-planar molecules were analyzed with this methodology.

Scheme 6. Orientation of the Profile Computed in the Carbo-Cycles.

Scheme 6

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The shielding tensors were computed perpendicular to the molecular plane and parallel to the z-axis.

The first group analyzed was the monosubstituted and the magnetic response of 1, 2, and 4 was similar to the response of iminobora-borazine (see Figure 17). For this reason, they could be catalogued as no-aromatic. However, the diatropic responses of 5 and 6 were less intense than carbo-benzene but they could be catalogued as aromatic.

Figure 17.

Figure 17

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Profile of the Bindz computed on carbo-metallabenzenes, including carbo-benzene and iminobora-borazine as reference.

Compounds with a double metallic center were separated in the 1,4-, 1,7-, and 1,10-carbo-mer groups (Figure 18). Following this order, the first analyzed group was the 1,4-carbo-mers. For this group, 7 was not analyzed due its nonplanar geometry. The magnetic response of 8 is similar in distribution and magnitude to the response calculated in the iminobora-borazine. The other two rings, 9 and 10, presented a diatropic response. The magnetic responses of the rings with 1,7-orientation, 14, 15, and 16, showed a no-aromatic character due to the weak diatropic response. In particular, the response of 14 was equivalent to the iminobora-borazine. Finally, the set conformed by the 1,10-carbo-mer rings, 20 could be catalogued as no-aromatic; and 19, 21 and 22 could be considered as aromatic compounds, but not comparable with the diatropic response of the carbo-benzene.

Figure 18.

Figure 18

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Profiles of the Bindz computed on carbo-dimetallabenzenes, including carbo-benzene and iminobora-borazine as reference.

In general, the inclusion of the metallic centers in the carbo-benzene ring generated a diminished intensity of the diatropic character. Also, the nonfully delocalized compounds (8, 14, and 20) presented a similar magnetic response to iminobora-borazine, for this reason, they could be catalogued as no-aromatic.

When the profiles were grouped by element instead of oriented-substitution, it was possible to observe that osmium’s carbo-mers presented a paratropic values with values around 4 ppm around the ring’s center, except for 4 which was around −4 ppm in the same zone. The carbomers formed with iridium and platinum could be catalogued as (slightly) diatropic compounds based on their magnetic response. The carbo-mers of ruthenium and rhenium were not analyzed in all the conformations. Plots formed by the profiles of Bindz grouped by element are depicted in the Supporting Information.

In Figure 19, isolines maps and isosurfaces of the Bindz calculated in carbo-benzene, iminobora-borazine, and the platinum rings (6, 10, 16, and 22) are depicted (isolines maps of all the rings are reported in the Supporting Information). Compared with carbo-benzene, the rest of the rings presented a smaller diatropic response or, in other words, they were less aromatic. As expected, the electronic delocalization in iminobora-borazine was interrupted by the difference of the electronegativities of the boron and nitrogen atoms, generating strong diatropic zones around the nitrogen atoms, generating a characteristic response associated to a no-aromatic molecule.

Figure 19.

Figure 19

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Isolines maps and isosurfaces of the Bindz calculated in carbo-benzene, iminobora-borazine, and platinum rings. Isolines maps are placed.

4. Conclusions

The configurations of carbo-metallabenzenes and carbo-dimatellabenzenes generally maintained carbon–carbon bond lengths akin to those observed in carbo-benzene. Despite a discernible reduction in electronic delocalization resulting from the introduction of metallic centers, the distribution pattern of their impact within the ring structure exhibited no consistent trend. Notably, the specific metallic atoms selected played a decisive role in influencing electronic delocalization, with platinum and iridium compounds demonstrating the highest degree of delocalization. Osmium-containing rings exhibited responses comparable to those observed in iminobora-borazine.

In terms of the most stable isomer, only osmium, iridium, and platinum exhibited comparability, as they were the sole elements yielding planar (or quasi-planar) rings across all three proposed orientations for carbo-dimatellabenzenes. Remarkably, the 1,10-carbo-mers rings did not emerge as the most stable or aromatic. For iridium and platinum, the 1,7-carbo-mers configurations proved to be the most stable, deviating from the anticipated trend. However, only 1,7-carbo-diiridiumbenzene adhered to the expectation that the most aromatic isomer corresponds to the most stable. Finally, a comprehensive summary of the aromaticity analysis results is presented in Table 3.

Table 3. Final Summary of the Analysis of Aromaticity.

system metal charge EDDB MICD Bindz
1 Ru 1 delocalizeda no delocalized low diatropicd
2 Rh 0 delocalizeda low delocalized low diatropicd
3 Re 0 delocalizeda half delocalized no analyzedb
4 Os 1 delocalizeda no delocalized low diatropicd
5 Ir 0 delocalizeda delocalized diatropicc
6 Pt 0 delocalizeda delocalized diatropicc
7 Ru 2 half delocalizeda half delocalized no analyzedb
8 Os 2 half delocalizeda half delocalized low diatropicd
9 Ir 0 half delocalizeda delocalized diatropicc
10 Pt 0 half delocalizeda delocalized diatropicc
11 Ru 2 half delocalized half delocalized no analyzedb
12 Rh 0 half delocalizeda half delocalized no analyzedb
13 Re 0 delocalizeda not analyzeda no analyzedb
14 Os 2 delocalizede no delocalized low diatropicd
15 Ir 0 half delocalizeda delocalized low diatropic
16 Pt 0 delocalizeda delocalized low diatropic
17 Ru 2 half delocalizeda no delocalized low diatropicd
18 Rh 0 half delocalizeda half delocalized no analyzedb
19 Re 0 delocalizeda not analyzed low diatropic
20 Os 2 half delocalizeda no delocalized low diatropicd
21 Ir 0 half delocalizeda not analyzede low diatropic
22 Pt 0 delocalizeda delocalized diatropicc
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a

Observations: the ring is delocalized except for the metallic center.

b

No planar ring.

c

Less diatropic than carbo-benzene.

d

Magnetic response similar to inorganic iminobora-borazine. Associated to the nonaromatic response.

e

Unstable obtained wave function.

Acknowledgments

L.C.G.-S. and A.B.-B. acknowledge the CECAD-UD for the Computing Facility and CIDC for the financial support under the project 4-50-598-19.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.3c10049.

  • MO diagrams of the complete series of systems, EDDB figures, MICD figures separated by a metallic center, Bindz profiles grouped by the metallic center, and Bindz isolines of all the proposed molecules (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao3c10049_si_001.pdf (10.3MB, pdf)

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