Energy Landscape of Fullerene Materials: A Comparison of Boron to Boron Nitride and Carbon

Abstract

Using the minima hopping global geometry optimization method on the density functional potential energy surface we show that the energy landscape of boron clusters is glass like. Larger boron clusters have many structures which are lower in energy than the cages. This is in contrast to carbon and boron nitride systems which can be clearly identified as structure seekers. The differences in the potential energy landscape explain why carbon and boron nitride systems are found in nature whereas pure boron fullerenes have not been found. We thus present a methodology which can make predictions on the feasibility of the synthesis of new nano structures. The experimental synthesis of fullerenes is a very difficult task. The carbon fullerene structures were therefore theoretically predicted [1] long before they could be produced in the lab [2]. Many more hollow and enhodedrally doped fullerene structures made out of elements different from carbon have also been proposed since then theoretically [3] in searches of other possible building blocks for nano-sciences. It is however surprising that since the experimental discovery of the carbon fullerenes some 25 years ago no other fullerenes have been synthesized. So the question is whether experimentalists have just not yet found a way to synthesize these theoretically predicted fullerenes, or whether they do not exist at all in nature. We have recently shown [4] that all the theoretically proposed endohedral Si 20 fullerenes are meta-stable and can thus most likely not be found in nature. In this letter we investigate in detail boron clusters. Following the B 80 fullerene structure proposed by Szwacki et al. [5] various other fullerene [6] and stuffed fullerene structures [7] were proposed. Subsequently it was however shown for B 80 that there exist non-fullerene structures [8] which are lower in energy. We will contrast the characteristics of the potential energy landscape (PES) of these boron clusters with those of systems found in nature, namely carbon and boron nitride fullerenes and find that there are important differences.To explore the energy landscape of the boron, carbon and boron nitride clusters we do global geometry optimizations on the density functional potential energy surface with the minima hopping algorithm [9]. This algorithm can render the global minimum configuration as well as many other low energy meta-stable structures. All the density functional calculations are done with the BigDFT electronic structure code [10] which uses a systematic wavelet basis together with pseudopotentials [11] and the standard LDA [11] and PBE [12] exchange correlation functionals.We start out by analyzing the B 16 N 16 cluster which was found to be short lived in experiments [13]. In this system structural rigidity is imposed by a strong preference for sp2 hybridization [14] as well as by the requirement that bonds are only formed between atoms of different type. This leads to a small configurational density of states. As shown in Fig. 1 there exists a fairly large energ...

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