Conjugation between 3D and 2D aromaticity: does it really exist? The case of carborane-fused heterocycles

Although several synthesized icosahedral carborane fused 2D π-ring systems are known, and even considerable conjugation has been noted between them in some cases, the phenomenon itself is not fully understood. Based on the results of our computational study, it can be concluded that the 2D aromatic character of the fused (exo) five-membered ring is low, even in cases where significant conjugation was proposed in previous studies. Moreover, the carborane moiety constricts the bonding properties of the exo ring, thus prohibiting or promoting different Lewis resonance structures. These results will shed further light on the design and electronic modulation of new carborane-based materials.


Introduction
Icosahedral closo-dicarbadodecaboranes (C 2 B 10 H 12 ) are the most studied carboranes, since their possible application covers a wide range. 1 These 3D cluster compounds show similarities to the organic aromatic molecules, 2 as they are highly stable and can take part in electrophilic substitution reactions. 3 The 26 skeletal electrons ll 13 orbitals via multicenter (mainly 3c2e) bonding, thus resulting in a fully delocalized system, oen referred to as 3D aromaticity. 4 In the last few years, the similarities and differences of 3D aromatic systems to their p-aromatic analogues have been highlighted in several pioneering studies. 5 Moreover, the existence of planar carborane systems with combined sand p-aromatic ring currents was predicted 6 and they were synthesized, 7 further strengthening the close relationship between the two types of aromaticity. If the statement of Teixidor and Solà is true, and pand 3D aromaticity are two sides of the same coin, 5b then the question arises whether noticeable conjugation can be achieved between them. Although signicant interaction was found in some arylated closo-CB 11 H 12 À anions, 8 it could possibly be augmented by fusing the two compounds into 3D-2D fused systems. Benzocarborane I (Scheme 1) was the rst example of this group; 9a however, these compounds (I and II) have localized double bonds, 9 thus no aromatic character in the exo ring could be detected.
On the other hand, Lavallo demonstrated the aromatic character of the fused ring in the negatively charged HCB 11 -Cl 11 À based system (III). 10 Furthermore, a recent study on heterocycles fused with ortho-carborane revealed a noticeable change in the aromatic character of the exo ring connected via its p-donor atoms, which was proven by NMR spectroscopy and computational studies (IV). 11 It was suggested that the negative hyperconjugation is responsible for this phenomenon; however, no further explanation was given on the increased aromaticity of the fused ring. Moreover, the interaction of the fusion between carboranes and chalcogencontaining compounds (V) was also interpreted as 3D-2D conjugation. 12 Very recently, the computational study of Teixidor and Solà has conrmed the earlier experiences regarding the non-aromatic character and the lack of conjugation in the benzocarborane derivatives; 13 however, the previously reported conjugating ability of ve-membered ring systems was not discussed.

Results and discussion
Due to the discrepancy between the previous results, the phenomenon itself is still a matter of debate; the effect of the ring size and the positions of different heteroatoms is not precisely clear. 9-13 Why does the size of the ring have such a great inuence on the interaction between the systems? Can the effect be explained with the negative hyperconjugation in all cases? Fully understanding the determining effects of this interaction would be highly desirable for both fundamental and practical aspects and would allow us to design and modulate new materials for a given application.
While being not directly measurable, several sub-criteria can contribute to the overall denition of aromaticity. 14 Among the various theoretical approaches (computational details in the ESI ‡), calculations on the nucleus independent chemical shi (NICS) are the most widely applied descriptors of aromaticity. Although Xie studied several systems fused via the C c -C c (carbon-carbon bond of the cluster) bond of the ortho-carborane (IV, Scheme 1), 11 we extended the set of possibly applicable heterocycles with different aromatic characters to perform a widespread comparison (Fig. 1). In this work, we use NICS(1) and NICS(0) values in order to contrast our results with a previous study. 11 However, it should be mentioned that according to Schleyer, NICS(1) zz has been found to provide the most accurate results 15 and showed a similar trend for our investigated systems (see Table S1 in the ESI ‡).
While focusing on ve-membered rings, NICS(1) indices ( Fig. 1, tabulated data and NICS(0) values can be found in Table  S1 ‡) exhibit higher aromatic character in the C 2v symmetric 1 0 -3 0 structures (by 3-4 ppm) than their respective isomers with C s symmetry (1-3). As no electronegative heteroatom is connected directly to the cluster in 1 0 -3 0 , the negative hyperconjugation effect 11 cannot solely explain the increased aromaticity. However, in 4 and 4 0 , the anti-aromatic character is increased in the symmetric system, as the borole moiety is highly antiaromatic in itself (see NICS(1) data in Table S1 in the ESI ‡). In the case of the fused systems with six-membered rings, the difference between the NICS(1) values of the two isomers (5, 5 0 ) becomes negligible and very similar to the value of benzocarborane (I). Furthermore, these indices generally show lower aromaticity compared to their ve-membered counterparts, which cannot be explained simply by the well-known effect of the ring size, 14a since the results of these calculations for the parent heterocycles are similar to each other (Table S1 ‡).
Some unanswered questions still remained; therefore, following the advice of Solà, 16 we expanded the description of aromaticity to include a set of indicators that are based on different properties to either challenge or support the results. First, the thermodynamic stability of these systems via energybased measures was investigated (Scheme 2). The isomerization stabilization energy (DE 1 ) applied by Xie 11 suggested lower aromatic character compared to the parent heterocycles (DE 2 ). On the other hand, it should be noted that DE 1 can also describe the conjugation between a sole double bond and the lone pair of the heteroatom; hence they should be compared to their partially saturated counterparts (DE 3 ). As the values demonstrate, DE 1 and DE 3 are very similar to each other, which suggests a low degree of aromatic conjugation induced by the carborane moiety.
These results can be related to the reported 1 H NMR data, 11 as chemical shis measured in the fused systems are more reminiscent of their corresponding a,b-unsaturated derivatives 17 than the aromatic compounds (Table S2 in the ESI ‡), showing that the delocalization within the exo ring has a denitive inuence on the magnetic shielding compared to the effect of the carborane system. Furthermore, other isodesmic reactions (DE 4 and DE 5 ) also supported the low degree of aromatic conjugation as they were highly positive in all investigated cases; moreover, similarly to the NICS(1) values, they are strongly affected by the position of the heteroatoms. Highest isodesmic reaction energies could be found for symmetric systems, which also possess the strongest aromatic character according to the NICS(1) values. It is known that the more aromatic isoindole isomer (6 0 , Scheme 3) is less stable than indole (6) (by 7.5 kcal mol À1 ); 18 however, even higher destabilization (by 21.6-39.9 kcal mol À1 , see Table S6 in the ESI ‡) occurs in the case of their carborane-fused counterparts.
To explain this destabilizing effect and to get more insight into the aromatic character of these compounds, the calculated bond lengths were compared to those of their purely organic oligo-aromatic counterparts (Scheme 3 shows the corresponding pyrrole derivatives; data for other compounds can be seen in the ESI in Fig. S1 ‡). In all investigated cases, the bond between the cluster and the neighboring exo ring atom can be described as a single bond, based on the bond length and also veried by the low ellipticity of electron density values in the bond critical points (see Fig. S2 in the ESI ‡). For 1, a resonance structure similar to 6 can be envisaged; however, in the case of 1 0 , the primary Lewis structure of 6 018 ( Table S3 in the ESI ‡) cannot be applied, as the bond lengths of the C c -C (cluster-ring C-C) bonds are expanded (1.459Å) andin agreement with the high valency of the cluster carbon atomscan only be considered as single bonds. This restriction prohibits the leading resonance structures containing the corresponding double bonds, thus inducing originally less weighted resonance structures to become more dominant. In fact, the bonding situation of the C-N-C unit possesses a stronger 3c4e bond character, which is also supported by the shorter C-N bonds and higher C-N Wiberg indices for 1 0 compared to isoindole (1.31 and 1.22, respectively); therefore, delocalization occurs within the C-N-C system. According to the visualization of 1, 1 0 , and I in a GIMIC plot (Fig. S3 of the ESI ‡), this phenomenon increases the density of the magnetic current in the center of the exo ring in 1 0 , thus affecting the calculated NICS(1) values in these systems.
In view of these ndings, the validity of the NICS values in the context of these systems is debatable, since all the other descriptors suggest non-aromatic character; thus signicant 3D-2D conjugation for fused ve-membered ring systems 1-3 and 1 0 -3 0 cannot be observed. Similar conclusions could be obtained upon the investigation of the Kohn-Sham molecular orbitals ( Fig. 2 and S4 in the ESI ‡). Despite the existence of orbitals spreading over the fused rings and carborane moiety, the outer atoms of the exo system have more signicant contribution to the p-orbitals, and an extensive variance does not occur among sixand ve-membered ring systems. On top of this, we have performed calculations based on the global EDDB (electron density of delocalized bonds) function, 19 which enables the representation of electrons delocalized over the whole system. The calculated data of I, 1, and 1 0 (Fig. 2) show two separable delocalized systems in all cases; therefore, this method further supports our concept that the conjugation between 2D and 3D moieties is minor in all investigated systems.
As a last possible explanation, an obvious difference could be the ring size, which determines the distance of ghost atoms used for the NICS calculations from the carborane cluster. Our train of thought led us to the attempt of calculating the magnetic shielding of ghost atoms along and 1Å away from the perpendicular bisector line of the C c -C c bond drawn from the center of the o-carborane. Surprisingly, our results reveal that the magnetic eld of the carborane has a noticeable impact in a huge radius around the cluster (Table S4 and Fig. S5 in the Scheme 3 Selected bond lengths (inÅ) for the pyrrole derivatives (B3LYP/6-311+G**). The elongated C c -C bond lengths in 1 0 demon-strates¼ the low contribution of the 1 0 b resonance structure. ESI ‡) and is solely able to make a distinction between the NICS values of the veand six-membered exo rings. Therefore, these calculations signicantly overestimate the 2D aromatic character of the fused rings, especially for ve-membered rings, and it can be established that the conjugation between the 3D and the exo system is minor and similar to the notoriously 2D nonaromatic benzocarborane. Our observation broadens the number of studies where the application of NICS failed. 20 For example, in the hydrogen-bonded (HF) 3 hexagon, a negative NICS value was obtained, but it resulted from local paratropic currents at each HF molecule and not a global diatropic ring current as was shown by Sundholm. 20a Similar to our work, a study by Frenking and co-workers conrmed the non-aromatic character of N 6 H 6 2+ and C 2 N 4 H 6 systems based on electronic indices, although their reported NICS indices showed negative values. 20b On top of this, Bultinck and co-workers demonstrated that there is no one-to-one relationship between a NICS value and the magnetically induced current density. 20c In summary, these examples showed that NICS should be utilized carefully (despite being a very powerful tool), as these values only represent the integrated data of the induced ring currents without showing their accurate pattern, which can also be important while determining aromaticity. 16,21 Apart from the investigation of the aromatic character of the fused ring, another interesting observation of this study is that the carborane lacks the ability to form double bonds with the outer member atoms of the exo rings, thus promoting generally less dominant resonance structures. To test the limitations of this phenomenon, we chose several unique structures (Fig. 3) in which the weights of the original principal resonance structures are altered; therefore, their geometry and aromatic properties can be ambiguous. Moreover, certain compounds were also considered in which the formation of all common Lewis structures is disabled; thus the system is forced to solve its electronic problems in inconvenient ways. First, the benzenefused exo ring was extended to oligo-aromatic compounds (7,8). It should be mentioned that the singlet-triplet gap decreases, and the HOMO orbitals are less polarized towards the outer ring, which suggests the increased weight of the biradicaloid character. By squeezing the exo ring between two clusters (9), the system is trying to prevent conjugation at any cost, pushing their electrons to the unfused C atoms, resulting in a more stable triplet state (by 11.6 kcal mol À1 ) compared to the closed-shell singlet system.
In the case of the symmetric phosphole and silolide anion derivatives (10 and 11), the carborane unit is able to planarize the phosphorus 22 and silicon centers, 23 in agreement with the 3c4e bond delocalization. Therefore, the effect is strong enough to compensate for the energy of the planarization, although it should be noted that the singlet-triplet gap is drastically decreased in these systems (28.7 and 4.0 kcal mol À1 for the silicon and phosphorus analogues, respectively). On the other hand, fusing the cluster with a cyclopentadiene unit (12) causes the 3c4e bond to become no longer available. Astonishingly, the system still obeys the regulatory effect by destabilizing the closed shell singlet system; therefore, the triplet state becomes more stable (by 11.4 kcal mol À1 ).

Conclusions
In conclusion, it was demonstrated that the magnetic eld induced by the carborane has a noticeable impact in a huge radius around the cluster. Moreover, this phenomenon solely offers an explanation for the difference between the NICS values of the veand six-membered exo rings, thus showing the inadequacy of this descriptor to estimate the aromaticity of these systems. Our study concluded that the 2D aromatic properties of the investigated carborane fused ve-membered rings are very similar to benzocarborane and can denitely be considered as a 2D non-aromatic compound; therefore, their aromatic character was signicantly overestimated in earlier studies. The bonding situation of the exo ring strongly depends on the position of the heteroatom, and the symmetric carborane fused systems showed shorter bonds and higher Wiberg indices around the heteroatom compared to their oligo-aromatic counterparts, promoting the 3c4e bonding structure in the C-X-C moieties while forcing C c -C to become a single bond. This effect turned out to be strong enough to planarize phosphorus and silicon in C-P-C and C-Si-C analogue systems. The appearance of this phenomenon is also a sign of hindered conjugation; nevertheless, various isodesmic reactions were applied which showed no aromatic stabilization in the investigated systems. As decisive proof, fusing the system with a cyclopentadiene unit or squeezing the benzene ring between Fig. 3 Singlet-triplet gap of selected fused compounds and the HOMO of the closed shell systems (B3LYP/6-311+G**, in kcal mol À1 ). The escalating localization of the HOMO clearly demonstrates the increased biradicaloid character. More data can be found in the ESI in Table S5 and Fig. S6, S7. ‡ two carborane systems encouraged the formation of biradicaloid systems. These results will shed further light on the electronic structure of these compounds and should inspire the community to rene the theoretical approach and the practical applications of carborane-fused systems.

Data availability
The data sets supporting this article have been uploaded as part of the ESI. ‡

Conflicts of interest
There are no conicts to declare.