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A highly efficient semi-empirical Hamiltonian has been developed and appliedto model the compact boron clusters with the intermediate size. TheHamiltonian, in addition to the inclusion of the environment-dependentinteractions and electron-electron correlations with the on-site chargecalculated self-consistently, has contained the environment-dependentexcitation orbital energy to take into account the atomic aggregation effect onthe atomic orbitals. The Hamiltonian for boron has successfully characterizedthe electron deficiency of boron and captured the complex chemical bonding invarious boron allotropes including the planer and quasi-planer, the convex, thering, the icosahedra, the fullerene-like clusters, the two-dimensionalmonolayer sheets, and the alpha boron bulk, demonstrating its transferability,robustness, reliability, and has the predict power. The Hamiltonian has beenapplied to explore the existence of the compact structure of boron clusterswith the intermediate size. Over 230 compact clusters including the random, therhombohedra, and the spherical icosahedra structures are obtained with the sizeup to 768 atoms. It has been found that, energetically, clusters containingmost compacted icosahedra B12 balls (i.e., the body-like rhombohedra clustersand trimmed spherical cut icosahedra clusters) are the most stable for largesize (Natom >200) of boron clusters, while the spherical cut icosahedra, randomstructures, and cage-like boron clusters are competitive for the small orintermediate size (24 < Natom <200) of boron clusters.

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