  We studied the dynamics of the reconstructed Si (111) surface using a
total-energy-vibrational-spectrum approach based on a non-orthogonal
tight-binding Hamiltonian. We first established the size of the supercell
sufficient to yield a reliable determination of surface parameters by the
structural optimization. The site density of vibrational states (SDOS) for the
semi-infinite system (the optimized slab on top of the bulk) was then
calculated using the method of real space Green's function. A decomposition
scheme for the SDOS that identifies directly coupled vibrations for a given
mode was also proposed. Our study has uncovered and elucidated, for the first
time, all the important surface dynamical features associated with the dimers,
adatoms, stacking faults, and rest atoms.
