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FULL PAPER Hückel's Rule of Aromaticity Categorizes FULL PAPER Hückel’s Rule of Aromaticity Categorizes Aromatic closo Boron Hydride Clusters Jordi Poater,[a,b] Miquel Solà,*[c] Clara Viñas,[d] and Francesc Teixidor*[d] Abstract: A direct connection is established between tridimensional P, N, or other incorporating transition or lanthanide metal aromatic closo boron hydride clusters and planar aromatic fragments. Consequently, the icosahedron or bicapped square antiprism are very relevant geometrical features in BHs and, by [n]annulenes for medium and large size boron clusters. In particular, extension, to other areas in which clusters are significant, e.g. our results prove the existence of a link between the two-dimensional Zintl phases. Hückel rule followed by aromatic [n]-annulenes and Wade-Mingos’ 2- In the last few years, we have given evidence that the concept rule of three-dimensional aromaticity applied to the aromatic [BnHn] of aromaticity, in terms of planar or tridimensional aromaticity, was closo boron hydride clusters. Our results show that closo boron not too distant, and that most probably -aromaticity and 3D hydride clusters can be categorized into different series according to aromaticity were based on the same grounds.[4] This is why we the n value of the Hückel (4n+2) rule. The distinct categories studied named them as the two sides of the same coin.[4b] To reach such in this work correspond to values of n = 1, 2, and 3. Each category conclusion we compared the conventional (4n+2) planar organic increases in geometrical difficulty but, more importantly, it is possible cyclic compounds with closo BHs. The aromaticity properties of to associate each category with the number of pentagonal layers in planar organic cyclic compounds had been demonstrated by their stability, hydrogenation experimental studies, substitution but not the structure perpendicular to the main axis. Category 1 has one addition reactivity, 1H-NMR downfield shift of peripheral protons pentagonal layer, category 2 has two, and category 3 has three. vs. protons in alkene compounds, and by structural criteria fundamentally based on the equalization of bond lengths, energy criteria based on the aromatic stabilization energies, and magnetic and electronic criteria strongly based on a theoretical Introduction standpoint.[5] The main methods utilized as magnetic criteria[5d] were aromatic ring current shielding (ARCS),[6] nucleus- The most popular closo boron hydrides (BHs) are those that independent chemical shifts (NICS),[7] and mapping ring have a structure derived from the icosahedron. This particular currents.[8] As electronic indices,[5c] we can mention the fluctuation structure provides a great chemical and physico-chemical aromaticity index (FLU)[9] and the multicenter electron sharing stability.[1] The most remarkable example within this class is indices (MCI).[10] 2-,[2] [B12H12] and the most extensively studied are the closo- Thus, aromatic organic compounds are the paradigm of what - carboranes, result of replacing one or two BH fragments by one chemists expect in one aromatic molecule, despite the difficulties or two CH groups. In this way, anionic and neutral carboranes are in finding an appropriate definition of what the term implies. - obtained, e.g. [CB11H12] , or ortho-, meta-, and para-C2B10H12. At Therefore (4n+2) planar organic cyclic compounds have the a large distance, in terms of number of scientific publications, necessary experimental and theoretical support to be the there is the bicapped square antiprism, of which the most genuine archetypes of what “aromaticity” may indicate. On the other hand, example is [B H ]2-.[3] As for the case of icosahedra, [B H ]2- 10 10 10 10 closo BHs that geometrically have the shape of deltahedra have - transforms upon the replacement of one or two BH by one or two been demonstrated, mostly by the NICS magnetic criteria,[1a, 11] to - CH groups into [CB9H10] or C2B8H10, including their different be aromatic. This fact is also sustained by reactivity, mainly isomers. In addition, besides the carbon heteroboranes, do exist substitution vs. addition, stability criteria, and equalization of bond a plethora of other heteroboranes, with heteroatoms such as S, [1a, 12] 2- lengths. Closo BHs respond to the formula [BnHn] , n = 5 to 12 and are electronically interpreted by Wade’s[13] counting rule 2n+2 or by Mingos’ rule that is 4n+2.[14] Both rules are equivalent. Wade’s rule refers to the skeletal electron pairs, whereas Mingos’ [a] Dr. J. Poater Departament de Química Orgànica rule also incorporates the exo electron pairs corresponding to the Universitat de Barcelona B-H bonds, thus referring to the total number of valence electrons [15] [13- Martí i Franquès 1-11, 08028 Barcelona, Catalonia (Spain) (TNVEs). The meaning of n in Hückel’s or Wade-Mingos rule 14] [b] Dr. J. Poater is totally different: in Hückel’s, n has no relation with the Institució Catalana de Recerca i Estudis Avançats (ICREA) structure, whereas in Wade-Mingos rules indicates the number of Pg. Lluís Companys 23, 08010 Barcelona, Catalonia (Spain) vertices in the deltahedron.[16] [c] Prof. Dr. Miquel Solà Therefore we had at hand two geometrically and pictorially very Institut de Química Computacional i Catàlisi (IQCC) and distinct type of compounds, both of them aromatic, both satisfying Departament de Química, Universitat de Girona 17071 Girona, Catalonia (Spain) nominal 4n+2 electron counting rules but one having -aromaticity E-mail: [email protected] and the latter 3D-aromaticity. The question that arose was: were [d] Prof. Dr. Clara Viñas, Prof. Dr. Francesc Teixidor they in reality so different? We have recently shown that they are Institut de Ciències dels Materials de Barcelona, CSIC very much related by the number of valence electrons (VE) in a Campus UAB, 08193 Bellaterra (Spain) confined space (CS), and by applying the electronic confined E-mail: [email protected] space analogy (ECSA) method it was possible to bridge fundamental aromatic hydrocarbons (HCs) with closo BH Supporting information for this article is given via a link at the end of [4a] [4a] the document. clusters. The ECSA method was originally intended to be a graphical method by which it was possible, starting from a FULL PAPER bidimensional model compound, to derive a tridimensional to the inorganic target. However, for large clusters, to reach its cluster.[17] The method consists in: 1) state the model organic organic analogue, we needed to go the other way around with the compound; 2) define its confined space (cS) as the number of aim to explore which organic molecules could be compatible with electrons enclosed in the ring of carbon atoms; 3) transmute each the cluster structure. In other words, we needed to produce a retro carbon atom into a boron atom and one electron (eT);[18] 4) ECSA, rECSA. This has been exemplified in Figure 1, in which 2- replace extra electrons by sacrificial atoms (sA); and 5) generate starting from the octahedral [B6H6] , the planar (4n+2) 1- the new BH compound by structural relaxation (sR). Throughout cyclopentadienyl anion [C5H5] is generated. For this case the the whole process, the number of valence electrons in the procedure can be applied easily and the correspondence 3D- corresponding confined space remains unaltered. It must be aromatic BH leading to 2D-aromatic hydrocarbon is easily traced. mentioned that Jemmis et al. made a different proposal to connect The aromaticity of both compounds was previously proven by 2- 1- BHs and HCs that does not keep the total number of valence ourselves with [B6H6] (NICS(0) = -31.0 ppm) and [C5H5] electrons constant.[19] (NICS(0) = -12.7 ppm).[4b] Application of the ECSA method turned out to be very practical for small organic/boron hydride molecules/clusters, and laid the foundations for the application to larger clusters as those analyzed in this work. It did not work only for aromatic organic molecules but also for non-aromatic. In this way, it was shown that - C2H4 was analog of B2H6, that C2H6 was analog of [B2H7] , that C4H10 was analog of B5H11, or that C4H8 was analog of B5H9, among other cases discussed.[4a] And in what concerns aromatics, 2- 2- - 2- it was shown that [C4H4] was analog of [B5H5] , [C5H5] of [B6H6] , 2- + 2- [4b] C6H6 of [B7H7] , or [C7H7] of [B8H8] . Remarkably, ECSA provides the correct structures of the targeted compounds after application of the structural relaxation and considering the most stable geometries in coordination compounds. For instance, in the - 2- analogy of [C5H5] being converted into [B6H6] , just before the sR process the graphical step produces a pentagonal pyramid, however this is not the most stable arrangement for a coordination six surrounding in coordination chemistry; it is the octahedron. 2- Therefore the sR process led to an octahedron for [B6H6] with [20] 2- octahedral aromaticity. Another example is [B8H8] ; again the graphical step just before the sR produces an heptagonal pyramid, but this is not the most stable structure for coordination eight; the 2- 1- most usual ones are cubic, square antiprism, dodecahedron, and Figure 1. rECSA applied to [B6H6] to get hydrocarbon [C5H5] . hexagonal bipyramid. Taking into account that the boranes produce triangular faces (with some exceptions like in 2- 2- tetraborane,[21] B H ) the two first are immediately discarded as Table 1. Calculated NICS values [ppm] for [B10H10] and [B12H12] and their 4 10 equivalent [n]-annulenes. they have square faces; for a different reason the hexagonal bipyramid is also discarded as it would imply two boron atoms with Compound Ring NICS(0) NICS(0)zz an in-cluster connectivity of six, whereas all other boron atoms 2- would have a connectivity of four. This leaves the dodecahedron [B10H10] 4-MR -33.7 -45.1 with four vertexes of in-cluster connectivity four and four vertexes 3-MR -46.1 -53.1 2- of connectivity five as the most plausible structure, as it is the case.
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