Bull. Mater. Sci., Vol. 22, No. 5, August 1999, pp. 863-867. © Indian Academy of Sciences. The ubiquitous icosahedral B12 in boron chemistry E D JEMMIS* and M M BALAKRISHNARAJAN School of Chemistry, University of Hyderabad, Hyderabad500 046. India Abstract. Though boranes exhibit a wide variety of polyhedral structures, all the three polymorpbs of elemental boron essentially contain icosahedral Bn units as the predominant building block in their unit cell. Theoretical and experimental studies on boranes show that the icosuhedral arrangement leads to most stable boranes and borane anions. This paper attempts to explain the phenomenal stability associated with the icosahedral Bn structure. Using fragment molecular orbital theory, the remarkable stability of BI2Ht2~ among closo boranes are explained. The preferential selection icosahedral B12 unit by elemental boron is explained by improvising a contrived B84 sub-unit of the ~-rhombohedron, the most stable polymorph. This also leads to a novel covalent way of stuffing fnilerenes with icosahedral symmetry. Keywords. Boron; polyhedral closo borane dianions; icosahedral B12; ~-rhombohedral polymorph; orbital compatibility. 1. Introduction Elemental boron exists in three different polymorphic forms (Wells 1979). The thermodynamically most stable The chemistry of boron formed a vast discipline by itself [t-rhombohedral form has 105 boron atoms in its unit cell. and helped to alter the concept of structure and bonding The next stable ~-rhombohedral form has 12 boron atoms. radically (Lipscomb 1963). Starting from the famous The meta stable ~-tetragonal form has fifty boron atoms three-centre two-electron bond, many of the structural in its unit cell. The icosahedral BI2 unit is the primary features exhibited by boron compounds (most signifi- building block in all of these polymorphic forms. The cantly, its hydrides) have extended bonding to multiple most stable polymorph has maximum number of boron centres and aromaticity to three dimensions (Muetterties atoms forming a part of B12 icosahedra. Obviously there is 1975). something unique about the icosahedron for boron. Here It is tempting to compare boron and boranes to their we explore the origin of this preference. neighbours in the periodic table viz. carbon and Let us analyze the role of icosahedron in the com- hydrocarbons. Despite the enormous variety and sophisti- pounds of boron. Amongst the borane anions of figure 1, cation of organic chemistry, most of the carbon structures the icosahedral BI2H~ is known to be more favourable can be explained by sp 3, sp 2 and sp hybridization at than all others. An approximate relative energy ordering carbon. This also extends to the polymorphs of elemental of anions is B12H~ > B6H~- > BTH~- > B10H~ > B9H92-. carbon which forms covalent solids. Diamond, graphite BsH~- > B11H~ > BsH]- (Schleyer 1998). It is natural to and carbyne correspond to sp 3, sp 2 and sp hybridization, search for an equivalent of the connection between respectively. The fullerenes, new polymorphs of carbon hybridization and carbon-polymorphs, for boron through (Kroto et al 1985), can also be explained based on sp 2 the stability of polyhedral borane anions. hybridized carbon array with slight distortion. Is it We have included in figure 1 the bicapped hexagonal possible to generate a similar parallel between the struc- antiprism structure of BI4H~. This structure is conspi- tural motifs of compounds of boron and its polymorphs? cuous by its absence in the chemistry of borane anions Obviously no easily transferable description can be (Jemmis 1982). Another related observation concerns the obtained from the compounds of boron. Boranes alone relative stability of closo carboranes, the neutral analogs present a variety of polyhedral structures represented by of polyhedral borane anions. For example, the trans the dianions BnH2-, n=5-12 and various structural isomer 1,5-closo-C2B3H5 is more favourable than 1,2- fragments derived from them. Representative compounds closo-C2B3H5 (Grimes 1970). Similarly 1,6-closo C2B4H6 are given in figure 1. Despite this wide variety of is more favourable than 1,2-closo-C2B4H6. On the other polyhedra available for boranes, polymorphs of elemental hand, the trans structure 1,7-closo-CeBsH~ is the least boron are based mostly on the icosahedral Bi2 units. An stable isomer; 2,4:closo-C2BsH7 is known to be most explanation for this preference is given in this paper. stable experimentally. An explanation for these relative energies, which naturally leads to the extra stability *Author for correspondence of B12H2~ is developed based on a qualitative electron 863 864 E D Jemmis and M M Balakrishnarajan BsHs2- (D3h) B6H62- (Oh) B~H~- (Dsh) BsH~-(D2a) B9H2~ (D3h) B,oH~8 (D~) BHH~ (C2v) B~2H~ (Ih) BI4H~ (D~) Figure 1. The structure of close-polyhedral borane anions, B,H~2, n = 5-12. The un- known Bl4Hi[ is also shown. counting model and the orbital compatibility in B,H~2- satisfies the 4n + 2 rule. B6H~- is second in the overlap. order of stability of boranes with Oh symmetry (figure 1). This can be viewed as a square B4H4 with two caps as in 2. The 4n + 2 Interstitial electron rule the case of BTHJ-. Counting of interstitial electrons can be done in a similar fashion. One interesting feature of B6H~- closo-Boranes can be viewed as a combination of rings is its high symmetry. Due to the presence of three C4 axis, and caps. The overall stability of the system can then be any two trans B-H groups can be considered as caps. This deduced by a (4n + 2) pi-electron rule (Jemmis 1982). symmetrical equivalence accounts for its increased stability. This is actually a generalization of Huckel's 4n + 2 rule This 4n + 2 rule is equivalent to the rules developed by applied in the domain of polycyclic aromatic hydro- Williams and Wade (Williams 1998; Fox and Wade 1998). carbons. As an illustration let us consider the BTHJ- which A similar electron count may be established for more can be schematically constructed from the interaction of a complex polyhedra. For example, the icosahedral Bt2H~ five borocycle and two B-H caps from both sides may be conceptually put together from two pentagonal perpendicular to the plane of the ring (figure 2). We take pyramidal B6H6 units. Pyramidal B6H6 does not have all B-H bonds and the B-B bonds in the BsH5 ring to independent existence because of the lack of 4n + 2 have two centre two electron bonds. Hence all the three electrons. BsHs ring has no electrons to contribute to ring valence electrons in the boron will be exhausted. Now, cap binding. The B-H cap has only two valence electrons. each B-H group in the capping position has three (Additional four electrons can be obtained by adding four electrons left. This will interact with the empty p orbitals hydrogens as indeed found in the pyramidal B6Hio). Two of boron in the borocyclic ring. Hence all boranes with B6H~ pentagonal pyramidal units can be brought together Ubiquitous icosahedral B i2 in boron chemistry 865 to give icosahedral BI2HI2. The - 2 negative charge of the symmetry. This still leaves optimal orbital interactions for molecule makes the six electrons (2 each formally from the octahedron (figure 3d). However, for the pentagonal the two caps and two from the negative charge). It is to be bipyramid, the situation is less than satisfactory. The immediately noticed that there is no unique way to divide overlaps with both the caps are less than ideal. It is as if the icosahedron into two pentagonal pyramids. Any two the ring is too large or the orbitals of the B-H cap is too B-H groups at opposite ends may be taken as capping contracted (figure 3e). It is then not surprising that BTH~2 groups in this analysis. A similar interaction diagram can is not very stable comparatively. The unusual stability of be constructed for pyramidal molecules so that the 4n + 2- B6H~2 over BTH~2 and BsH~ 2 can be seen by the exo- electron rule can be applied for them. For example BsH~ 4 thermicity of the following reaction (Schleyer 1998): (C4~) and B6H~ 4 (Csv) follow this electron count. BTH~2 + BsH~2 ---> 2B6H~2 - 42.6 kcal/mol 3. Orbital compatibility and stability of closo (B 3LYP/6-31 G*). boranes These ideas could explain the absence of a hexagonal bipyramidal BsH 2-. The two B-H caps will have All the pyramidal and bi-pyramidal boron B,Hn com- negligible overlap with the rings. The relative stabilities pounds obey 4n + 2 interstitial electron rule and have of closo-carboranes also stem from similar arguments three dimensional aromaticity. Obviously all compounds (Jemmis 1982; Jemmis et al 1992). with six delocalized electrons cannot have the same It is still not clear why the BI2H/2, which is made up of stability. We find that a convenient geometric parameter two pentagonal pyramids, is unusually stable. Let us look to gauge the stability, can be obtained from the study of at the geometry of the icosahedron. Each B-H bond pyramidal molecules. Let us take hypothetical six-electron makes an angle of 26.6 ° with the B5 ring which contains molecules such as B5H~-4 (C4v) and B6H~4 (Csv). Theo- it (figure 4). The pentagonal pyramidal B6H~ 4 has a retical studies show that the B-H bonds of the B4H4 ring corresponding angle of 17 °. B6Hlo with four bridging in BsH~ 4 is almost in the plane of the B4 ring (Jemmis hydrogens is the neutral analog. The terminal B-H bonds and Pavan Kumar 1984). From a schematic point of view of the B5 ring here are bent towards the B-H cap by an this could be represented as a perfect matching of the angle of 25 °, close to the 26.6 ° dictated by the icosahedral B4H4 orbitals with those of the B-H orbitals (figure 3a).