Observation of “Outlaw” Dual Aromaticity in Unexpectedly Stable Open-Shell Metal Clusters Caused by Near-Degenerate Molecular Orbital Coupling

Abstract

Open AccessCCS ChemistryCOMMUNICATION1 Jul 2021Observation of “Outlaw” Dual Aromaticity in Unexpectedly Stable Open-Shell Metal Clusters Caused by Near-Degenerate Molecular Orbital Coupling Jun Li, Jing Wang, Jing Chen, Yu-Xiang Bu and Shi-Bo Cheng Jun Li School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100 Google Scholar More articles by this author , Jing Wang School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100 Google Scholar More articles by this author , Jing Chen School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100 Suzhou Institute of Shandong University, Suzhou 215123 Google Scholar More articles by this author , Yu-Xiang Bu School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100 School of Chemistry and Chemical Engineering, Qufu Normal University, Qufu 273165 Google Scholar More articles by this author and Shi-Bo Cheng *Corresponding author: E-mail Address: [email protected] School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100 Google Scholar More articles by this author https://doi.org/10.31635/ccschem.020.202000364 SectionsSupplemental MaterialAboutAbstractPDF ToolsAdd to favoritesTrack Citations ShareFacebookTwitterLinked InEmail The Hückel’s rule, Baird’s rule, and electronic shell closure model are classical and well-established concepts in chemistry, which have long been employed in rationalizing the aromaticity/antiaromaticity of organic species and stability of inorganic clusters. Thus, the observation of unique species featuring properties out of the fundamental frameworks of these rules is challenging but significant and helps in drawing a complete picture of fascinating concepts in chemistry. Herein, we demonstrated via high-level theory, 59 all-metal clusters possessed not only dual aromaticity in both the ground and excited states but also unexpectedly more stable open-shell geometries, unprecedentedly showing the limitation of these fundamental rules simultaneously. The aromaticity of these clusters was confirmed by various criteria, while the unexpected relative stability of these open-shell clusters was proposed to have originated from the molecular orbital (MO) coupling effect, akin to the hybridization concept in organic chemistry. Our findings have highlighted the exhibition of the diversity of metal clusters in aromaticity and implied that there is considerable room even in well-accepted rules. We wish these findings would stimulate further efforts in acquiring a more comprehensive understanding relative to aromaticity and stability in inorganic metal clusters from both experimental and theoretical estimates. Download figure Download PowerPoint Introduction Aromaticity is one of the most fundamental and fascinating concepts in chemistry, and a term introduced by Kekulé,1 which has been utilized to characterize the properties of special organic compounds with cyclic and conjugated geometries. In this realm, [4n + 2]/[4n] π-electrons Hückel’s rule2 is the most widely used means of probing the ground-state aromaticity/antiaromaticity from the electronic structure perspective. Further extension of this rule to the excited states seems to complete the fundamental understanding of aromaticity. The pioneering work by Baird in 1972,3 namely, Baird’s rule, proposed that the (anti)aromaticity of annulenes in the lowest excited state would be reversed, compared with the Hückel’s rule. That is, annulenes with [4n + 2] π-electrons would possess antiaromaticity, whereas [4n] π-electron systems would show aromatic characteristics in their lowest excited state. Note that Baird’s rule has been verified by a surge of experimental and theoretical studies recently.4–10 Accordingly, although the fundamental argument between these two classical rules is opposite, the deduced consensus is that conjugated species with [4n] or [4n + 2] π-electrons could only have aromaticity in one state, that is, either the ground state or the excited state.11 Whether extraordinary species beyond the prediction of the conventional Hückel’s and Baird’s rules exist or not is a challenging subject. In other words, one might wonder if there is any chance to locate species possessing “outlaw” dual aromaticity in both the ground and excited states that might be beneficial in drawing a complete picture of aromaticity. It is worth mentioning that the original aromaticity concept was advanced successfully to all-metal clusters recently,12–19 fuzzing the boundary between inorganic and organic chemistry. Compared with the traditional aromaticity in organic compounds (mainly the π-aromaticity, as in benzene), the introduction of metals, especially the d- and f-block elements, into the aromatic systems could not only form high-spin species but also increased the diversity of aromaticity remarkably, in particular, δ- and hybridized aromaticity.20,21 This fact and our continuous interest in seeking novel properties of clusters22–26 inspired us to explore whether all-metal clusters are appropriate candidates, able to overcome the challenge mentioned above of possessing dual aromaticity in both the ground and the excited states. Thus, in our present communication, we employed multiple aromaticity criteria, including magnetic and electronic indices, to evaluate the aromaticity of a series of metal clusters. Surprisingly, a large number of all-metal clusters (59 cases) were verified to hold dual aromaticity simultaneously in their ground and the lowest excited states, exhibiting the limitation of both the Hückel’s and Baird’s rules. Interestingly, we observed that apart from the aromatic characteristics, all of these metal clusters possessed open-shell ground states, which were more stable than their shell closure counterparts. Such a phenomenon, violating the conventional electronic shell closure model in inorganic metal clusters, was attributable to the intriguing near-degenerate molecular orbital (MO) coupling effect. Our present findings undoubtedly demonstrate the limitation of the classical Hückel’s rule, Baird’s rule, and electronic shell closure model simultaneously, which might further spur more interest in consummating the understanding of these fundamental rules in chemistry. Results and Discussion Considering that conjugated planarity is a key characteristic of aromaticity, four Al2-based triatomic metal clusters with eight valence electrons, namely, Al2Li–, Al2Be, Al2Cu–, and Al2Zn, were adopted initially. Here, we selected clusters consisting of elements from different groups of the periodic chart (IA, IIA, IB, and IIB), along with different charges to explore their potential universality. Notably, the triatomic clusters were adopted with the consideration that most of them featured planar geometries, and thus, more suitable for the exploration of the versatility of aromaticity than four- or five-atomic clusters. To probe their aromaticity and electronic structures, the high-level theoretical calculations (see Supporting Information Computational Details) were performed to optimize their lowest triplet and singlet states (Figure 1). Surprisingly, the ground states of all these clusters were triplets from both density functional theory (DFT) reference calculations (B3LYP) and coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] optimizations, although the energy gaps between the singlet (marked as S1) and triplet (marked as T0) states (ΔEs–t) were different from these two theories. This result indicated that their open-shell structures were more stable than their closed-shell counterparts, which would be discussed further. Note that the T0 term here represented the lowest triplet state, while the S1 term defined the lowest singlet state of the cluster. The subscripts 0 and 1 indicated the energetic order of different spin states of the cluster, which was used to emphasize that the ground states of the studied clusters were all triplets. Figure 1 | Optimized geometries of the lowest T0 and S1 states of four clusters. The values without and with parentheses represent results from B3LYP and CCSD(T) optimizations. The normalized MCI (red), NICS(0) (ppm, green), NICS(1) (ppm, blue), and Δχ (a.u., pink) values are also indicated. CCSD(T), coupled-cluster singles, doubles, and perturbative triples; MCI, multicenter indices; NICS, nucleus-independent chemical shift, S1, singlet; T0, triplet. Download figure Download PowerPoint Having determined the geometries of the four all-metal clusters, we then turned our attention to their aromaticity. Various aromaticity criteria have been proposed theoretically since aromaticity is not a directly measurable quantity. Herein, different criteria demonstrated as effective in probing aromaticity of metal clusters,27–36 including magnetic [nucleus-independent chemical shift (NICS) and magnetic susceptibility anisotropy Δχ] and electronic [multicenter indices (MCI) and localized orbital locator (LOL)] indices were calculated to examine their aromaticity in both the T0 and S1 states. The explanations about other criteria that are not indicated here are listed in Supporting Information Note 1. NICS, originally proposed by Schleyer et al.,37 is one of the most popular tools for probing aromaticity. Species with negative NICS values are aromatic, while positive NICS values indicate antiaromaticity. Obviously, all the clusters examined possessed negative NICS values in both states (Figure 1), manifesting their aromatic characteristics in both the triplet and the singlet states. For comparison, the NICS(0) and NICS(1) of benzene were −8.07 and −10.03 ppm, respectively, calculated at the same theoretical level. This result demonstrated that the studied clusters had strong aromaticity in their T0 and S1 states. Moreover, compared with other locations, the NICS(1) was more effective in evaluating π-aromaticity. Apparently, all the clusters had larger negative values than that of benzene, indicating their strong π-aromaticity. Besides the NICS, Δχ is another valid descriptor for diagnosing aromaticity, where the aromatic species possessed negative Δχ. All theoretical Δχ values for these clusters were negative (Figure 1), further confirming their aromaticity in both states. MCI, proposed by Giambiagi et al.,38 is also an effective indicator for examining aromaticity according to the molecular electronic structure. Higher MCI values correspond to stronger aromaticity, and normalization could aid in a direct comparison of MCI values with different center numbers.39 All normalized MCI values for both the T0 and S1 states of the examined metal clusters were within 0.5052–0.8038 (Figure 1), comparable or even larger than those of the well-defined aromatic Al42− (0.4486) and benzene (0.693) calculated at the same theoretical level.12 This fact further supported the aromatic properties of the clusters in both states. Furthermore, topological analysis of LOL-π is also a criterion for evaluating π-aromaticity.40 To understand the electron delocalization path, the LOL-π plane maps above 1 Å of the metal clusters were drawn (Figure 2 and Supporting Information Figure S1), providing visualized pictures that showed their π-aromaticity. Their high LOL-π distributions undoubtedly exhibited a favorable delocalization path and unveiled the three-center π bond, confirming further their π-aromaticity in both states. Also, to better understand the difference between the clusters with and without π-aromaticity, the LOL-π maps of well-defined π-aromatic (1Al42− and 1Al3−) and non-π-aromatic (1Mg3 and 1Mg2Li2) clusters are included (Figure 2).12,18,41,42 Figure 2 | Color-filled maps of LOL-π above 1 Å of the triplet and singlet states of the Al2Li– and Al2Be cluster planes. For comparison, the LOL-π images of the π-aromatic 1Al42– and 1Al3– together with the non-π-aromatic 1Mg3 and 1Mg2Li2 are also included. LOL, localized orbital locator. Download figure Download PowerPoint As mentioned earlier, it sounds incredible for molecular species to exhibit dual aromaticity in both the ground and excited states simultaneously according to the basic statements of classical Hückel’s and Baird’s rules. However, the observation made in the four inorganic clusters studied and further extensions (see below) revealed the breakdown of these rules in some inorganic systems, indicated by various aromaticity criteria employed. These findings confirmed the simultaneous existence of “outlaw” dual aromaticity in both the T0 and S1 states of these 8e all-metal clusters, thereby, unveiling the limitation of the classical Hückel’s and Baird’s rules. Besides the evidenced dual aromaticity, another unexpected result regarding the relative stability of the clusters also captured our attention. In cluster science, it is well-known that the electronic shell closure model is probably the most widely used tool in rationalizing the exceptional stability of metal clusters. In this model, like atoms, the quantum states in the metal clusters group into shells, and clusters containing 2, 8, 18, 20, 34, 40 electrons, and so on, possess closed shell, along with enhanced stability. A famous example is the “magic” Al13− with 40e.43 Thus, one concern is whether this model is applicable to our studied singlet 8e clusters, which existed in the metastable states based on our theoretical calculations since 8e is a magic number. We addressed this consideration by calculating the clusters’ one-electron energy levels and their corresponding MOs (Figure 3 and Supporting Information Figure S2). Taking 1Al2Li– as an example (Figure 3a), all eight valence electrons occupied the highest four occupied MOs, where the lowest MO could be regarded as a typical 1S shell with delocalized orbital, well spread over the whole cluster. Subsequently, the upper three occupied MOs represented the P-type states, followed by the unoccupied MOs. The lowest unoccupied MO (LUMO) was almost symmetric, which could be viewed as a 2S shell. MOs above such 2S shell are typical 1D-type MOs. Accordingly, the electronic configuration of 1Al2Li– is 1S21P62S01D0 satisfied the shell closure model, which exhibited the superatom characteristics. Similar shell arrangements are also observed in other singlet clusters (Figure 3c and Supporting Information Figures S2a and S2c). Consequently, all these singlet clusters presented closed-shell species. Figure 3 | One-electron energy levels of (a) 1Al2Li–, (b) 3Al2Li–, (c) 1Al2Zn, and (d) 3Al2Zn. The continuous and dashed lines indicate the occupied and unoccupied states, respectively. The majority and minority spin states are represented by the up and down arrows, respectively. The isosurfaces are equal to 0.008 a.u., while energy is in eV units. Download figure Download PowerPoint Unexpectedly, these closed-shell clusters were less stable than their open-shell counterparts (Figure 1). We then asked, what effect is responsible for this extraordinary phenomenon? A careful inspection of the MOs of Al2Li– (Figures 3a and 3b) revealed that one 1Pz (minority) MO of 3Al2Li− lifted to a higher energy level as the LUMO, while its nearly symmetric 2S (majority) MO44 went down and became the highest occupied MO (HOMO). Such change dramatically increased the HOMO–LUMO (H–L) gap of the open-shell cluster, promoting its energetic stability. Intriguingly, the energy gaps between the S-type HOMO and P-type HOMO-1 of these triplet clusters were minimal (0.11 eV) in 3Al2Li– (Figure 3b), which might have induced MO coupling between them. Similar situations also exist in other triplet clusters (Figure 3d and Supporting Information Figures S2b and S2d). Next, we considered drawing an analogy between such near-degenerate MO coupling in inorganic clusters and the s–p hybridization in organic carbon chemistry. It is well-established that, in some cases, the s and p orbitals of C prefer to hybridize because hybridized orbitals tend to have lower energy than their unhybridized counterparts, thereby assisting in the stabilization of such compounds. Analogously, the present near-degenerate MO coupling could stabilize the occupied MO energies considerably along with the splitting of the HOMO and LUMO levels, forming the stable open-shell 3Al2Li–. Similar situations also existed in the other three clusters examined (Figure 3 and Supporting Information Figure S2), providing further evidence about the existence of such a coupling effect. To gain more insight into the impact of such coupling, the dependence of the H–L gap on the MO coupling was calculated (Figures 4a–4d). By changing the Al-M (M = Li, Be, Cu, Zn) bond lengths gradually, we observed that the smaller orbital spacing (stronger MO coupling) corresponded to the larger H–L gap. Thus, an plain correlation was evidenced in these two variables, confirming the effect of such a coupling mechanism on the stability of open-shell metal clusters. Figure 4 | (a–d) The relationship between the MO spacings (gray triangle) and H–L gaps (cyan circle) of four triplet clusters. Energy is in eV units. MO, molecular orbital; H–L, HOMO–LOMO. Download figure Download PowerPoint Having rationalized the existence of such a coupling effect, we then turned our attention to its influence on the cluster stability. Two criteria, H–L gap and the second energy difference, Δ2E, were employed to examine the relative stability between these open-shell clusters and their neighbors. The optimized geometries of AlnLi–, AlnBe, AlnCu–, and AlnZn (n = 1–5) were calculated to obtain their H-L gaps and Δ2E ( Supporting Information Figure S3). It has been established from a previous report that a large H-L gap was indicative of enhanced stability.45 We found that the H–L gaps of these 8e open-shell clusters were in the range of 1.63–1.69 eV ( Supporting Information Figure S4a), comparable with the values of C60 (1.70 eV) and Al13– (1.87 eV), which implied their relative high stability.43,46 In addition, the thermodynamic stability was probed by their Δ2E ( Supporting Information Figure S4b). The positive Δ2E values obtained for these 8e open-shell metal clusters revealed their higher stability than their neighboring clusters. Thus, it was evident that the H–L gaps and the Δ2E both exhibited oscillatory behavior in the corresponding cluster series, with the 8e open-shell clusters being the local maxima, signifying their relative high stability. Since our present findings show the existence of “outlaw” dual aromaticity in different states, and the MO coupling promoted stability enhancement in all-metal clusters, implying the limitation of the classical rules, we were curious about knowing if this discovery could be extended to more inorganic clusters. By conducting an isovalent substitution, the structures of other 54 metal clusters featuring 8e planar geometries were optimized ( Supporting Information Figure S5). Identical criteria, namely NICS, Δχ, MCI, and LOL-π ( Supporting Information Table S2 and Figure S6), were all employed to examine their aromaticity, which yielded similar results, demonstrating that all of these clusters possessed dual aromaticity in both the T0 and S1 states. Moreover, our theoretical calculations showed that all the clusters possessed triplet open-shell ground states and more stable than their closed-shell counterparts ( Supporting Information Figure S5). Meanwhile, calculations about the H–L gaps and near-degenerate orbital spacings of different states of these clusters further supported their all ground triplet states due to their possession of small MO spacings, corresponding to larger H–L gaps than those of their singlet counterparts ( Supporting Information Figure S7). These findings convinced us that such intriguing dual aromaticity and coupling effects might exist widely in inorganic, all-metal clusters. Moreover, it was evident that the NICS(1) values of the singlet states of the studied metal clusters were more negative than those of their triplet counterparts (Figure 1 and Supporting Information Table S2), indicating that the closed-shell clusters (singlet) were more aromatic than the open-shell ones. It is well-accepted that the electron configuration is one of the factors governing the cluster stability, and aromaticity is associated with the delocalized electron configuration, which reinforces the stability of metal clusters. However, our results showed that the calculated open-shell configurations with weaker aromaticity were verified to be the ground states of these metal clusters, which further confirmed the significance and power of the proposed coupling effect in enhancing the cluster stability. Besides, although the large number of triatomic clusters studied here could well present the potential universality of such an “outlaw” phenomenon in inorganic metal clusters, more detailed research that would consider more doping elements is still urgently needed to aid in gaining more and complete understanding about such striking phenomena. The exploration of the possible involvement of the partially filled d or f electrons, the existence of the strong relativistic effect, as well as the degree of the electron delocalization, and others, might be all beneficial for this objective. Apart from the anionic and neutral clusters discussed earlier, one more cation Al3+ cluster was also investigated to demonstrate further the potential universality of the findings highlighted here. The geometries of the lowest T0 and S1 of Al3+ were optimized ( Supporting Information Figure S8). Indeed, similar to the above mentioned anionic and neutral systems, all the normalized MCI, NICS(0), NICS(1), and Δχ values disclosed dual aromaticity of Al3+ in both the T0 and S1 states. Furthermore, the theoretical triplet open-shell geometry of 3Al3+ was 0.41 eV more stable than its closed-shell counterpart with the 1S21P62S01D0 electronic configuration ( Supporting Information Figure S9a). In addition, the one-electron energy level ( Supporting Information Figure S9b) and the dependence between the H–L gap and the orbital spacing ( Supporting Information Figure S10) of 3Al3+ were also examined, which undoubtedly showed the existence and power of the coupling effect in promoting the energetic stability. Hence, it seems that the striking phenomena (dual aromaticity and coupling effect) observed here might exist broadly among metal clusters, independent of the cluster charges. Conclusion We have demonstrated that 59 all-metal clusters possessed dual aromaticity in both the T0 and S1 states with unexpectedly stable open-shell geometries induced by the near-degenerate MO coupling effect, showing the limitation of conventional Hückel’s rule, Baird’s rule, and electronic shell closure model simultaneously. Specifically, various aromaticity criteria conjointly confirmed their aromaticity in both states, while the existence of stable open-shell metal clusters was attributable to the intriguing near-degenerate MO coupling, akin to the s–p hybridization in organic chemistry. Interestingly, other coupling effects in inorganic metal clusters, involving different shells were also observed in our group, which would be discussed further in a separate report. Furthermore, one significance of the findings of our current communication is the verification of the dual aromaticity and the coupling effect that facilitated energetic stability among a large number of metal cluster species. This question the universality of the conventional aromaticity rules proposed originally in organic chemistry for the precise understanding of aromaticity of inorganic metal clusters embraced in this field previously with much success. We believe that these findings could spur more efforts in exploring new mechanisms, which would be beneficial for obtaining a complete picture on these classical concepts, including aromaticity and cluster stability. Supporting Information Supporting Information is available. Conflict of Interest There is no conflict of interest to report. Acknowledgments This study is supported by the Taishan Scholars Project of Shandong Province (no. ts201712011), the National Natural Science Foundation of China (NSFC) (nos. 21603119 and 21705093), the Natural Science Foundation of Shandong Province (nos. ZR2017BB061 and ZR2016BQ09), the Natural Science Foundation of Jiangsu Province (no. BK20170396), the Project for Scientific Research Innovation Team of Young Scholar in Colleges and Universities of Shandong Province (no. 2019KJC025), the Young Scholars Program of Shandong University (YSPSDU) (no. 2018WLJH48), the Qilu Youth Scholar Funding of Shandong University, and the Fundamental Research Funds of Shandong University (no. 2017TB003). The scientific calculations in this paper have been done on the HPC Cloud Platform of Shandong University.