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Modeling Compact Boron Clusters with the Next Generation of Environment-Dependent Semi-Empirical Hamiltonian

A highly efficient semi-empirical Hamiltonian has been developed and applied to model the compact boron clusters with the intermediate size. The Hamiltonian, in addition to the inclusion of the environment-dependent interactions and electron-electron correlations with the on-site charge calculated self-consistently, has contained the environment-dependent excitation orbital energy to take into account the atomic aggregation effect on the atomic orbitals. The Hamiltonian for boron has successfully characterized the electron deficiency of boron and captured the complex chemical bonding in various boron allotropes including the planer and quasi-planer, the convex, the ring, the icosahedra, the fullerene-like clusters, the two-dimensional monolayer sheets, and the alpha boron bulk, demonstrating its transferability, robustness, reliability, and has the predict power. The Hamiltonian has been applied to explore the existence of the compact structure of boron clusters with the intermediate size. Over 230 compact clusters including the random, the rhombohedra, and the spherical icosahedra structures are obtained with the size up to 768 atoms. It has been found that, energetically, clusters containing most compacted icosahedra B12 balls (i.e., the body-like rhombohedra clusters and trimmed spherical cut icosahedra clusters) are the most stable for large size (Natom >200) of boron clusters, while the spherical cut icosahedra, random structures, and cage-like boron clusters are competitive for the small or intermediate size (24 < Natom <200) of boron clusters.