Persistent Planar Tetracoordinate Carbon in Global Minima Structures of Silicon-Carbon Clusters

Abstract

Recently, we reported a series of global minima whose structures consist of carbon rings decorated with heavier group 14 elements. Interestingly, these structures feature planar tetracoordinate carbons (ptCs) and result from the replacement of five or six protons (H⁺) from the cyclopentadienyl anion (C₅H₅⁻) or the pentalene dianion (C₈H₆²⁻) by three or four E²⁺ dications (E = Si–Pb), respectively. The silicon derivatives of these series are the Si₃C₅ and Si₄C₈ clusters. Here we show that ptC persists in some clusters with an equivalent number of C and Si atoms, i.e., Si₅C₅, Si₈C₈, and Si₉C₉. In all these species, the ptC is embedded in a pentagonal C₅ ring and participates in a three-center, two-electron (3c-2e) Si-ptC-Si σ-bond. Furthermore, these clusters are π-aromatic species according to chemical bonding analysis and magnetic criteria.

1. Introduction

Chemists have a great interest in predicting new chemical entities with exotic non-classical structures. Planar hypercoordinate carbon (phC) atoms, i.e., molecules containing carbon atoms linked to four or more ligands in-plane, are particularly puzzling. The phCs violate the well-established rule of van’t Hoff and Le Bel (regarding the concept of tetrahedral four-coordinate carbon); thus, at the beginning, they were considered experimentally inaccessible. However, in 1968, Monkhorst evaluated, theoretically, methane stereomutation through a planar tetracoordinate carbon (ptC) transition state [1]. Two years later, Hoffmann and co-workers proposed different approaches to stabilize a ptC with the modest purpose of achieving a thermally accessible transition state for a racemization process [2]. These pioneering works inspired different studies that finally allowed the identification of viable ptC compounds [3,4,5,6,7].

In the last 50 years, significant progress has been made in synthesizing and “in silico” proposals of numerous ptC compounds [3,4,5,8,9,10,11]. Even more recently, the chemistry of the family was extended to species in which the carbon coordination number is higher than four (penta [12,13,14,15,16,17,18,19,20,21,22] and hexacoordinate [23,24,25,26]). In many of these systems, the formation of delocalized bonds plays a decisive role in their stability. For instance, the experimentally detected ptC CAl₄²⁻ cluster exhibits doubly σ- and π-aromatic character [10,11].

In 2019, some of the current authors designed a series of ptC global minima composed of carbon and heavier group 14 elements (Si–Pb) [7]. These clusters were obtained by replacing five or six protons (H⁺) from the cyclopentadienyl anion (C₅H₅⁻) or pentalene dianion (C₈H₆²⁻) by three or six E²⁺ dications (E = Si–Pb), respectively. In these clusters, the π-aromatic circuits of the parent aromatic hydrocarbons are preserved. The global minima structures of the clusters Si₃C₅, Ge₃C₅, Si₄C₈, and Ge₄C₈ contain one or two ptCs (see Figure 1). Chemical bonding analysis suggests that these clusters are globally π-aromatic and locally σ-aromatic, where the local aromaticity is due to the E-ptC-E 3c-2e σ-bond. It is important to note that a similar strategy has successfully allowed other aromatic hydrocarbon derivatives with ptCs [6,22,27,28].

The current work highlights that ptCs are more common than one would think in Si-C clusters. For example, in the Si_nC_n combinations, when n = 5, 8, and 9, the global minima contain ptCs. This feature was not perceived in the works that reported these structures [29,30,31], which has motivated us to highlight it here, and analyze these species’ chemical bonding patterns. Remarkably, silicon carbide (SiC) grains are major dust components in carbon-rich stars of the asymptotic giant branch [29]; and there is evidence that combinations of carbon and silicon with suitable stoichiometries favor the formation of two-dimensional materials with the consequent hypercoordination of C and Si [32,33]. Thus, some of these clusters could be involved in these materials’ formation or fragmentation processes. On the other hand, the ptC in the studied clusters is embedded in a pentagonal C₅ ring. This evidence leads us to propose that any polycyclic hydrocarbon, with pentagonal aromatic rings, can be transformed into Si-C clusters favoring the formation of ptCs.

2. Computational Details

The potential energy surface of the species Si₅C₅, Si₈C_8, and Si₉C₉ was explored using the AUTOMATON program [34,35]. Geometry optimizations were performed at the PBE0 [36]/def2–TZVP [37] level. Low-lying isomers were reoptimized at the PBE0–D3 [38]/def2–TZVP level, where dispersion is included in the functional, to identify possible effects on the relative energies. Vibrational frequencies were evaluated at the same level to confirm the optimized structures as true minima on their potential energy surface. These computations were performed using the Gaussian16 program [39].

We computed current densities at PBE0/def2-TZVP level using the GIMIC program [40,41], which employs the gauge-including atomic orbital (GIAO) [42] method. The calculations consider a magnetic field directed along the z-axis, i.e., perpendicular to the molecular plane. Note that the unit for current susceptibility is nA·T⁻¹, and the results are, therefore, independent of the magnitude of the magnetic field. We prepared vector plots of the current density in a plane placed 0.5 Å above the molecular plane. In our analysis, diatropic (aromatic) and paratropic (antiaromatic) currents circle clockwise and counterclockwise, respectively. To visualize current pathways, we used Paraview 5.10.0 software [43,44]. The ring current strengths (RCS), a measure of the net current intensity around a molecular ring of interest, were obtained after considering different integration planes. The integration planes correspond to cut-off planes perpendicular to the chosen bonds of the annular moiety and extend horizontally for 3.6 Å along the ring’s plane, with 2.6 Å above and below the ring. For the integration of the current density passing through an integration plane, GIMIC uses the two-dimensional Gauss–Lobatto algorithm [41,45]. For the RCS, positive (diatropic) and negative (paratropic) signs correspond to the aromatic and anti-aromatic molecules, respectively. RCS values close to zero suggest non-aromatic character [46].

To gain insights about chemical bonding, we used different methods: Wiberg bond indices (WBI) [47], natural population analysis (NPA) [48], and the adaptive natural density partitioning (AdNDP) method [49,50]. These approaches are based on the natural bonding orbital (NBO) method and were performed at the PBE0/def2–TZVP level. The WBI and NPA were computed with the NBO 6.0 code [51], and [41] the AdNDP analysis was performed using Multiwfn 3.8 [52]. The molecular structure and AdNDP results were visualized using CYLview 2.0 [53] and VMD 1.9.3 [54], respectively.

3. Results and Discussion

Figure 2 reports the global minima structures of the clusters analyzed in this study: Si₅C₅, Si₈C₈, and Si₉C₉. We can confirm from our searches using the AUTOMATON program that the identified lowest energy structures are the same as those reported in references [29,30,31]. Note that the dispersion inclusion in the calculations, obtained by Grimme’s method (D3), has no significant influence on the relative energy of the lower energy isomers (see Figures S1–S3, and the Cartesian coordinates reported in Table S1). For Si₅C₅, the C atoms form a pentagonal ring resembling the cyclopentadienyl anion. On the other hand, for Si₈C₈ and Si₉C₉, more indene-like carbon structures are formed. Nonetheless, one Si replaces a C for the former to close the six-membered ring.

What about chemical bonding in these species? In general, we are interested in looking at the presence of both the 3c-2e bond of Si-ptC-Si and the π-aromatic circuit around the planar carbonaceous moiety. The NPA analysis predicts a negative partial charge distribution on the C and positive on the Si, agreeing with the differences in C/Si electronegativities. However, the most negative charges (about −0.9 $\left|e\right|$) are on the Si’s surrounding the ptC (see Figure S4). These results agree with the design model for these species, where protons are replaced by Si²⁺ dication.

Figure 3 shows the chemical bonding interpretation for the Si₅C₅ cluster according to AdNDP analysis. There are five lone pairs (one on each Si), five 2c-2e C-C σ-bonds connecting the C₅ ring (similar to the cyclopentadienyl anion C₅H₅⁻). The Si’s on the plane are connected to two C’s (ptC neighbors) of the C₅ ring by 2c-2e C-Si σ-bonds and participate in a 3c-2e Si-ptC-Si σ-bond. It also recovered three π-bonds distributed on the planar C₅Si₂ fragment, suggesting the possibility of aromaticity according to Hückel’s rule. The out-of-plane Si₃ fragment shares one edge of the C₅ pentagon; it exhibits three 3c-2e σ-bonds and one 2c-2e π-bond. These results show that Si₅C₅ retains much of the C₅H₅^– π-aromatic features. It also exhibits the multicentric Si-ptC-Si 3c-2e σ-bond, a feature highlighted as a local aromaticity and stabilizing factor in these species [2,6,7,22]. This chemical bonding picture entirely agrees with the Wiberg bond indexes (WBI) analysis. Figure S4 shows that five C-C single bonds (with some contribution of double bonds) join the C₅ ring with WBI values between 1.02 and 1.33 (higher than a single bond), the lowest being for the C-C bonded to the out-of-plane Si₃ fragment. The in-plane Si-C and Si-ptC bonds have a WBI value of 1.03 and 0.51, in complete agreement with the single and multicentric bonds recovered by AdNDP analysis.

In the case of Si₈C₈ and Si₉C₉ (Figure 4 and Figure 5), AdNDP predicts that both have a pentagonal C₅ ring connected by 2c-2e C-C σ-bonds. The C₅ pentagon of Si₈C₈ is connected to the chain -C-C-Si-C- by two neighboring vertices. Where 2c-2e σ-bonds link carbons, the Si of this chain forms multicentric bonds with the out-of-plane Si₄ fragment and the neighboring C’s. In the case of Si₉C₉, the pentagonal ring is connected to a C₄ chain, forming a bicycle analogous to the indene, where 2c-2e σ-bonds connect this bicycle. In both systems, two in-plane Si’s are coordinating the ptC (embedded in the C₅ pentagon), forming part of a 3c-2e Si-ptC-Si σ-bond, in addition to 2c-2e σ-bonds with the C’s neighboring the ptC. In addition, Si₉C₉ has one of its Si as a bridge (single) on one side of the C₆ hexagon, linked to the C’s by Si-C 2c-2e σ-bonds. All in-plane bridged silicon have a lone pair of electrons, in agreement with the design criteria for these species [2,6,7,22]. Both clusters also exhibit π-bonds, six in both cases, which could be associated with an aromatic character. Interestingly, as in Si₅C₅, the π orbitals are located around the SiC₂ fragments (bridged silicon). This bonding feature is also in complete agreement with the initial design strategy of these systems, where it is advisable to use ligands that can receive electrons in their p_z orbitals, and thus participate in the π-circuit and aromaticity when it is favored [2,6,7,22]. As with the Si₅C₅ cluster, the chemical bonding description provided by AdNDP is in complete agreement with the WBI analysis (see Figure S4). WBI predicts bond orders for the C-C bonds slightly higher than the single bonds (higher than 1.15). For Si₈C₈, the Si that closes the hexagonal ring and which is annealed to the pentagonal ring, has a bond order of 0.82 and 0.84, agreeing with the detection of multicentric bonds according to AdNDP. Besides, Si’s bridged on the hexagonal C₆ ring of Si₉C₉ have Si-C bond orders of 0.75 and 0.81 in agreement with the detection of two S-C single bonds by AdNDP.

We will now analyze the magnetic response to an external magnetic field applied perpendicular to the Cn plane. This analysis aims to identify patterns related to the (anti) aromaticity phenomenon, i.e., the presence of (diatropic) paratropic ring currents, and to evaluate their intensity (ring current strength, RCS). For reference, the ring current circuits of benzene have been analyzed at the level used in this work. As can be seen from the results (Figure S5), benzene has a paratropic ring current of medium intensity (−3.5 nA.T⁻¹) inside the C₆ ring (from σ-electrons). In addition, there is an intense diatropic ring current (15.3 nA.T⁻¹) around the C₆ ring, giving an appreciable diatropic resultant of 11.8 nA.T⁻¹, characterizing this aromatic molecule par excellence [40,55,56,57,58].

In this study, the RCS has been evaluated using integration planes for this purpose, placed bisecting different bonds. In addition, profiles of these integration planes have been analyzed to facilitate the dissection of the different contributions: local, semi local, and global. The analysis used to identify the different ring current circuits has been performed according to the strategy initially proposed in references [46,59], which consists of establishing equations that account for the couplings of the different current flows. Note that this strategy has been used satisfactorily in our group in different recent works [60,61]. The integration planes used and the RCS values (total and partial: profiles) are reported in Figures S3–S5 in the Supplementary Material. From the results (summarized in Figure 6), we wish to highlight first the presence of a moderately intense local diatropic current around the ptC, of 4.2, 4.8, and 5.6 nAT⁻¹, for Si₅C₅, Si₈C₈, and Si₉C₉, respectively. The presence of this ring current agrees with the AdNDP analysis, which detects a multicentric Si–ptC–Si σ-bond, thus providing support for the presence of a stabilizing local aromatic contribution. Next, all local C₅ and C₆ rings have a low-intensity inner paratropic current (between −5.4 and −1.3 nA.T⁻¹), which would be σ in nature, analogous to that exhibited by aromatic hydrocarbons (see the case of benzene mentioned above). Si₅C₅ exhibits a diatropic current involving the C₂-ptC-Si₂ fragment, but not the entire C₅ pentagon. This arises from the π-electron cloud involving the Si bridged to the C₅ ring.

Si₈C₈ exhibits a local current around the pentagonal C₅ ring, which would result from the π bonds in this fragment. A horseshoe-shaped diatropic current circuit is also evident around the C₃–ptC–C₂ fragment. In addition, there is a semi-local diatropic current that does not close the SiC₅ hexagonal circuit; however, it does surround the C₅ ring. This is related to the delocalized π-bonds distributed throughout the system. Si₉C₉ exhibits a local diatropic current around the C₅ ring (3.2 nA.T⁻¹) with participation of the π-orbitals. In addition, an intense global diatropic current (13.9 nA.T⁻¹) is evident, which is mainly delocalized around the C₉ ring. To summarize (Figure 6), Si₅C₅, Si₈C₈, and Si₉C₉ exhibit local aromaticity (σ and π), with the participation of bridged Si and ptC and semi-local aromaticity (in the first two), and global aromaticity in the case of Si₉C₉, as a consequence of the π-electron cloud.

4. Conclusions

Here, we highlight that the global minima of the Si₅C₅, Si₈C₈, and Si₉C₉ clusters comprise a planar tetracoordinate carbon (ptC), a feature unnoticed in previous works. Chemical bonding analysis allows us to establish that C_n rings are formed, monocyclic in the case of Si₅C₅, and bicyclic in the other two (in the case of Si₈C₈, a Si atom close one of the rings). A pentagonal C₅ ring is present in the latter, similar to what happens in the former. The ptC is embedded in this pentagonal ring in all cases, in which two Si form a 3c–2e Si–ptC–Si σ-bond. In addition, several delocalized π-bonds are detected. Therefore, the bonding analysis suggests the possibility of both local (σ) and semi-local or global (π) aromaticity. The latter is corroborated by the analysis of induced current density by an external magnetic field; i.e., the presence of local, semi-local, and global diatropic rings—a characteristic of aromatic compounds—is confirmed. In particular, in all cases, a local ring current is detected between the Si–ptC–Si fragment, which confirms this local aromatic σ-contribution. The other contributions would be of the π-type. These findings open up the possibility of identifying other Si–C combinations in which conditions are provided to favor the presence of ptCs; that is, to favor local, semi-local and global aromaticity in these species.