Deltahedra with holes: Structural preferences of supraicosahedral boranes Pattath D. Pancharatna, S. Marutheeswaran, Muthu P. Austeria, Musiri M. Balakrishnarajan ⇑ Chemical Information Sciences Lab, Department of Chemistry, Pondicherry University, Puducherry 605 014, India article info Article history: Received 15 March 2013 Accepted 9 July 2013 Available online 19 July 2013 Keywords: Ab initio calculations Supraicosahedral boranes Fullerenes Wade’s Rule Snub systems Nanostructures abstract A systematic quantum chemical inquiry on supraicosahedral boranes (B n H n 2À , n > 12) reveals that larger polyhedral boranes no longer prefer pure deltahedral structures. In an attempt to avoid vertices that has six polyhedral neighbors (hex-caps), inevitable for larger deltahedra; they resort to faces other than tri- angles (squares and pentagons). These larger faces behave like holes rather than open faces as they obey the Wade’s n + 1 rule for closo boranes. Further, these holes prefer to be isolated, similar to the pentagons in carbon fullerenes. The convex polyhedron, snub dodecahedron (B 60 H 60 2À , I symmetry) derived from these structural preferences, is a promising candidate for experimental characterization. The larger size of borane snub balls allows the hosting of counter ions endohedrally and this increases the rigidity of the cluster. The structural principles deduced in this paper successfully explain the mystery behind the observation of square faces in some of the known supraicosahedral carboranes, and helps in understand- ing the complex MB 66 type borides which are characterized to have a O symmetric snub frameworks. They also provide the fundamental information towards the design of borane based nanostructures. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Supraicosahedral heteroboranes with more than 12 vertices in a single closo cluster are known with transition metals [1] and main- block elements in molecules [2] and solids [3], but pure boranes are yet to be made. Some open frameworks of the associated larger boranes are known; an arachno borane cluster (B 14 H 20 ) associated with closo-B 16 H 16 2À [4], a macropolyhedral B 22 H 22 2À cluster [5] that has a nido-B 12 edge shared with closo-B 12 skeleton are all known experimentally. These indicate that curvature is seldom an issue. The exceptional stability of icosahedral B 12 H 12 2À proved to be the bottleneck for cage expansion strategies. DFT calculations on supraicosahedral boranes of medium and large sizes are re- ported earlier; some are predicted to be energetically more stable than B 12 H 12 2À with comparable or increased aromaticity [6]. Due to the intense experimental efforts to cross the icosahedral barrier [7], some of the lower members (n = 13–15) of the supraicosahe- dral carboranes are reported recently [8–11], but these carboranes show subtle differences in geometry compared to the theoretical predictions on boranes. Despite these impressive achievements, a systematic study of the geometries and their preferred structural motifs for supraicosahedral boranes remains unexplored. The deltahedral motif for larger (n > 12) boranes necessitates that some of its vertices (B–H groups) should have more than five polyhedral neighbors. Geometrically, these polyhedra can only have a maximum of 12 vertices with degree of five (excluding B–H bonds), with the rest of the vertices being forced to have a minimal vertex degree of six (hex-caps). Fragment molecular orbi- tal (FMO) studies [12,13] indicate that the B–H fragment is perfect for capping square face (i.e., B 6 H 6 2À ); pentagonal faces are also suitable if the B–H bonds of the ring bends towards the cap (i.e., B 12 H 12 2À ). But the hexagonal face is large for B–H cap and it rather prefers a capping atom with more diffuse orbitals [14]. In an ideal deltahedron with uniform B–B distances, the B–H hex-caps will fall in the plane of the hexagonal ring it caps, resulting in zero curva- ture. Consequently, the two tangential p orbitals of the B–H frag- ment cease to interact with the frontier FMOs of the hexagonal ring as they arise primarily from the perpendicular p z orbitals. Hence, the shrinking of the hexagon (shortening of the hexagonal B–B distances) and/or elongation of the ring-cap distances are mandatory to optimize the overlap between the ring and the cap. This is exactly observed in all the experimentally known hetero- boranes with a hex-cap [8–11]. As the presence of hex-caps intrin- sically forces bond alternation in the deltahedra, their preferred distribution that minimizes the strain need to be characterized. Qualitative theoretical predictions on larger closo boranes (n > 13) [15] reported earlier were later investigated by higher le- vel calculations [6,16–20]. Interestingly, the conventional belief that ‘boranes prefer deltahedral motif’ itself is compromised in some instances. For example, though closo B 13 H 13 2À is theoretically re- ported [6] to have docosahedral geometry (C 2v ), the synthesized 0277-5387/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.poly.2013.07.017 ⇑ Corresponding author. E-mail address: mmbkr.che@pondiuni.edu.in (M.M. Balakrishnarajan). Polyhedron 63 (2013) 55–59 Contents lists available at SciVerse ScienceDirect Polyhedron journal homepage: www.elsevier.com/locate/poly