  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.
