Study On The Structure And Stability Of (BN)_n Polyhedrons

In this paper, Hartree-Fock (HF) and density functional theory (DFT) calculations were performed on (BN)_n polyhedrons to put insight into the relationship between the geometrical structures and stability.This paper includes the following four parts.1. To gain an insight into the structures and stability of F4F6-(BN)_n polyhedrons with alternation of B and N atoms, a density functional theory (DFT) study was performed on all isomers of F4F6-(BN)_n polyhedrons with n between 10 and 22. The calculation results demonstrate that the lowest energy isomers do not contain B44 bonds (the bonds shared by two squares) and the energies of those isomers containing B44 bonds increase with the number of B44 bonds linearly, indicating that the energetically favored structures of F4F6-(BN)_n polyhedrons satisfy the isolated square rule and square adjacency penalty rule. The structural analysis reveals that the stability is determined by the pyramidalization of B and N atoms at the square-square fusion. The binding energy is fitted to the numbers of edges and a model is proposed for predicting the relative stability of these B-N polyhedral molecules.2. The structures and stability of F4F6-(BN)_n polyhedrons (n= 23-30) with the alternation of B and N atoms were studied with DFT method. The calculation results reveal that the atoms at square-square fusions with large pyramidalization angles are remarkably extruded out of the surfaces of (BN)_n polyhedrons. The energetically favorable isomers do not contain square-square bonds and the energies of those isomers containing square-square bonds increase with the number of square-square bonds linearly, demonstrating that the energetically favorable structures of F4F6-(BN)_n polyhedrons satisfy the isolated square rule and square adjacency penalty rule. The atom pyramidalization determines the stability of the isomers. The binding energy is fitted to the numbers of vertices formed from different faces and a model is proposed to predict the relative stability of these polyhedral molecules.3. The structures and stabilities of B13N13 polyhedrons with alternant B and N atoms formed by squares, hexagons and octagons are studied with DFT method. It is found that the isomers with III octagon(s) also satisfy the square adjacency penalty rule, and their relative energies markedly increase with the number of octagons generally. However, an isomer with one octagon in C₁ symmetry is thermodynamically more stable than other isomers and it has approximate sphericity and fewest B44 bonds. These findings suggest that the isomers with octagon(s) should be considered during the search for the lowest energy isomer of (BN)_n polyhedrons.4. The structures and stabilities of (BN)_n polyhedrons composed of squares, hexagons and octagons with the alternation of B and N atoms are studied with DFT method. The calculated results demonstrate that the lowest energy isomers are the structures without octagon; the second lowest energy isomers of (BN)₁₀, (BN)₁₂ and (BN)₁₄ contain one, one and two octagons, respectively. The isomers with octagon(s) also satisfy the square adjacency penalty rule, and their energies markedly increase with the number of octagons. Usually, the lowest energy isomers with different number of octagons have approximate sphericity, fewest B44 bonds and large HOMO-LUMO gaps. Structural analysis demonstrates that the pyramidalization of B and N atoms determines the stability of (BN)_n polyhedrons.