The boron conundrum: Bonding in the bowl B 30 and B 36 , fullerene B 40 and triple ring B 42 clusters Hung Tan Pham a , L.V. Duong a , Nguyen Minh Tam a,b , M.P. Pham-Ho a , Minh Tho Nguyen b,⇑ a Institute for Computational Science and Technology (ICST), Quang Trung Software City, Ho Chi Minh City, Viet Nam b Department of Chemistry, University of Leuven, B-3001 Leuven, Belgium article info Article history: Received 14 April 2014 In final form 23 May 2014 Available online 7 June 2014 abstract Geometries and bonding of B 30 ,B 36 ,B 40 and B 42 clusters were studied using quantum chemical compu- tations. The bowl B 30 and B 36 and planar B 42 clusters exhibit disk aromaticity. Diatropic ring current is strong in B 30 and weaker in B 42 . A fullerene-like B 40 (D 2d ) having two hexagons and four heptagons was found as the lowest-lying isomer. Such a fullerene whose MOs closely mimic those of the buckyball B 80 , represents novel structural feature of boron clusters. The most stable B 42 (C 2h ) isomer is a triple ring tube with consistent r + p diatropic magnetic responses making it a tubular aromatic species. Ó 2014 Elsevier B.V. All rights reserved. 1. Introduction Boron compounds continue to provide us with full of surprise about their structural features. Regarding boron clusters, a pleth- ora of two-dimensional (planar, quasi-planar) and three-dimen- sional (tubular, cage, spherical, fullerene...) shapes apparently suggests several distinct growth patterns. Extensive effort has been devoted to the search for new forms of boron allotropes and nanocages [1,2], and most boron clusters appear to exhibit polymorphism and multi-center bonding [3,4]. In relation to C 60 , particular attention has been paid on the boron buckyball B 80 [5], and larger fullerene derivatives such as B 100 and B 112 [6] have been predicted by computations. Some smaller all-boron fullerenes have also been identified by computations including B 14 [7],B 32 ,B 38 ,B 44 , B 50 and B 56 [8,9],B 40 ,B 48 ,... (B 32+8k , with 0 6 k 6 7) [10]. In many cases, the fullerene-like form reported is however not the most sta- ble isomer of the size considered. In addition, the buckyball B 80 has so far not been detected by experiment yet [11]. Boron has been proved to be a rare element whose atomic B n clusters retain either planar or quasi-planar (QP) geometries even when the cluster size n goes up beyond >20, depending on the charge state. The cations B n + prefer to adopt 3D structures at smal- ler sizes (at n  18) [12,13], whereas the anions B n  and dianions B n 2 species tend to have planar or QP structures with n being up to >30. There is an effective charge effect in which addition of extra electrons consistently favors QP boron cluster anions, and removal of electrons leads to 3D cations [14]. Let us briefly summarize the main geometrical features of the bare clusters B n , with n being an even number, in their neutral state: (i) most of the sizes up to B 18 have planar or QP geometries [15–18], except for the surprising B 14 fullerene [7]; (ii) the most stable B 20 isomer is a tubular double ring (DR) in which the two 10-membered rings are connected together in an antiprism bonding motif [19]; (iii) Similar to B 20 , each of the neutrals B 22 , B 24 ,B 26 and B 28 also exists in a DR ground state [20,14]. These observations resulted in a popular belief that intermediate-sized B n with n P 30 still prefer tubular geometries; (iv) we recently found that B 30 has a bowl structure [21] which is composed of a pentagon base and successively built up by two strings of 10 and 15 boron atoms yielding a fivefold symmetry (C 5v ). This 5@10@15 strings bowl turns out to be 5 kcal/mol more stable than the tubular 310 triple ring (TR). The slightly higher thermo- dynamical stability of the bowl B 30 has been shown to arise from its disk aromatic character [22,23]. In spite of its non-planarity, the 20 P-type electrons of bowl B 30 are distributed in a way similar to those of the planar disk aromatic B 20 2 dianion [25,26]. Although the bowl B 30 is not established yet as the lowest-lying isomer, it constitutes an appropriate building-block whose recombination eventually leads to B 80 and larger buckyballs [24], (v) previous computations [19,24] also predicted that B 32 has a DR shape com- posed of two 16-membered ring. There is no previous report on the B 34 isomers yet, but it seems that the latter seemingly has the low- est-lying DR structure, and (vi) more recently, B 36 has been found by computations to have a bowl structure which is based on a hex- agonal background and successively caped on it by two strings of 12 and 16 B atoms. The 6@12@18 strings thereby lead to a sixfold symmetry (C 6v ) bowl form which is calculated to be the lowest- lying structure being 20 and 32 kcal/mol more stable than the http://dx.doi.org/10.1016/j.cplett.2014.05.069 0009-2614/Ó 2014 Elsevier B.V. All rights reserved. ⇑ Corresponding author. Fax: +32 16 32 79 92. E-mail address: minh.nguyen@chem.kuleuven.be (M.T. Nguyen). Chemical Physics Letters 608 (2014) 295–302 Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett