Improved nonorthogonal tight-binding Hamiltonian for molecular-dynamics simulations of silicon clusters

We present an improvement over the nonorthogonal tight-binding molecular-dynamics scheme recently proposed by Menon and Subbaswamy [Phys. Rev. B 47, 12 754 (1993)]. The proper treatment of the nonorthogonality and its effect on the Hamiltonian matrix elements has been found to obviate the need for a bond-counting term, leaving only two adjustable parameters in the formalism. With the improved parametrization we obtain values of the energies and bonding distances which are in better agreement with the available ab initio results for clusters of size up to N=10. Additionally, we have identified a lowest energy structure for the ${\mathrm{Si}}_9$ cluster, which to our knowledge has not been considered to date. We show that this structure (a distorted tricapped trigonal prism with ${\mathit{C}}_{2\mathit{v}}$ symmetry) is also a minimum at the Hartree-Fock level and in approximate density-functional theory, and should therefore be seriously considered as a candidate for the ground-state structure of the ${\mathrm{Si}}_9$ cluster.