A Practical Criterion for Screening Stable Boron Nanostructures

Abstract

Due to the electron deficiency, boron clusters evolve strikingly with the increasing size as confirmed by experimentalists and theorists. However, it is still a challenge to propose a model potential to describe the stabilities of boron. On the basis of the 2c-2e and 3c-2e bond models, we have found the constraints for stable boron clusters, which can be used for determining the vacancy concentration and screening the candidates. Among numerous tubular structures and quasi-planar structures, we have verified that the stable clusters with lower formation energies bounded by the constraints, indicating the competition of tubular and planar structures. Notably, we have found a tubular cluster of B₇₆ which is more stable than the B₈₀ cage. We show that the vacancies, as well as the edge, are necessary for the 2c-2e bonds, which will stabilize the boron nanostructures. Therefore, the quasi-planar and tubular boron nanostructures could be as stable as the cages, which have no edge atoms. Our finding has shed light on understanding the complicated electron distributions of boron clusters and enhancing the efficiency of searching stable B nanostructures