A new hole density as a stability measure for boron fullerenes

Abstract

We investigate the stability of boron fullerene sets B76, B78 and B82. We evaluate the ground state energies, nucleus-independent chemical shift (NICS), the binding energies per atom and the band gap values by means of first-principles methods. We construct our fullerene design by capping of pentagons and hexagons of B60 cage in such a way that the total number of atoms is preserved. In doing so, a new hole density definition is proposed such that each member of a fullerene group has a different hole density which depends on the capping process. Our analysis reveal that each boron fullerene set has its lowest-energy configuration around the same normalized hole density and the most stable cages are found in the fullerene groups which have relatively large difference between the maximum and the minimum hole densities. The result is a new stability measure relating the cage geometry characterized by the hole density to the relative energy.The geometric structure of boron allotropes in respect to their ground state energy is a subject of great interest. Studies focused on searching the lowest energy configurations has yielded a variety of stable boron structures due to electron deficient nature of boron. Such structures involve molecular wheels [1,2], boron sheets composed of triangular and hexagonal motifs [3][4][5][6][7][8][9][10][11][12] [17,18]. Boron based forms are known for their complex chemistry. Unlike carbon, both pure boron and many boron rich compounds contain B 12 cage structures in their crystalline state. Furthermore, boron crystals show peculiarities such as uncommon 2c-1e and 3c-2e bonding [19] and unique aromaticity [20,21]. Most crystal samples exhibit defects, vacancies and interstitials, due to the flexible bond structure [22]. Among such structures, the newest form, orthorhombic γ-B 28 , is found to be the second hardest elemental material after diamond with a value of 58 GPa [23,24] and has strong covalent interatomic interactions even higher than the intraicosahedral bonds [25].A key concept in stability analysis of boron sheets is the hole density. This is defined as the ratio of the number of hexagonal holes to the number of atoms in the triangular sheet. The so called α-sheet was found to be the most stable boron sheet with η=1/9 [10]. In a recent work, it is shown that hexagonal holes of α-sheet are the scavengers of extra electrons from the filled hexagons [26]: a unique aspect of α-sheet, in conjunction with the hole density, is that the ratio η=1/9 exactly corresponds to the ratio of the extra π electron to the number of σ electrons in a filled hexagon. Boron layers composed of hexagonal hole doped triangular lattices manifest polymorphism [27] i.e. multiple 2D boron layers have comparable stabilities even some of them have lower energy than the α sheet [28,29]. Boron sheets g(1/8), g(2/15), α 1 and α 2 are the examples of such ground state structures. Such correlation between the

B28: the smallest all-boron cage from an ab initio global search

“…Our previous benchmark calculations showed that both PBE and PBE0 are able to distinguish the structural isomers of B 20 and give the correct energy order of the eight isomers compared to CCSD(T)/6-311G* results 34 . Vibrational analysis of these cluster isomers in their equilibrium configurations has also been carried out at the PBE0/6-311+G(d) level of theory to ensure that there are no imaginary frequencies corresponding to the saddle points on the PES.…”

DFT study on endohedral and exohedral B38fullerenes: M@B38(M = Sc, Y, Ti) and M&B38(M = Nb, Fe, Co, Ni)

“…As the nearest neighbor of carbon in the periodic table, all boron fullerene analogues have been pursued in the past few years since the pioneering theoretical prediction of the B 80 cage in 2007. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] However, evidence for boron fullerenes is scarce. Recent studies have revealed that core-shell structures are more energetically favorable in the size range with n Z 68.…”

Ribbon Aromaticity of Double-Chain B2n C2H2 Clusters (n = 2–9): A First Principle Study

“…Therefore, these double-chain ribbons with different lengths have the similar aromaticity. Obviously, the average NICS(1) values (from -8.9 to -11.4 ppm) of these doublechain B 2n C 2 H 2 are more than those of the medium-sized boron cages (from -22.1 to -55.3 ppm) [34][35][36][37] so that their aromaticity is generally less than those of boron cages interwoven by the double-chains.…”

“…In particular, the B 40 -/0 and B 39 -fullerenes are composed of interwoven boron double-chain ribbons. Furthermore, many similar medium-sized boron cages have been proposed from the first principle methods [34][35][36][37][38]. On the other hand, the free-standing and metalsupported two-dimensional boron sheets are predicted to be mainly composed of interwoven double-chain ribbons [39][40][41][42][43][44][45].…”