Molecular-dynamics determination of electronic and vibrational spectra, and equilibrium structures of small Si clusters

We have used a new, approximate method for computing total energies and forces in covalent systems and investigated the electronic and vibrational spectra and equilibrium structures of small Si clusters (${\mathrm{Si}}_{\mathit{n}}$ with n=2–7). The method uses an electronic-structure tight-binding formalism based on density-functional theory within the pseudopotential scheme. Slightly excited pseudo-atomic-orbitals are used to find the tight-binding Hamiltonian matrix in real space. Unlike other simplified tight-binding schemes, no parameters or fits to data are introduced. Forces are determined from the total-energy functional, so that molecular-dynamics simulations can be performed. The molecular-dynamics simulations yield the ground-state structure, and the vibrational spectrum. Excellent overall agreement is found with experiment and other first-principles calculations for Si clusters. The technique is immediately transferable to bulk systems and surfaces.