Ab-initio Calculations of the Vibrational Properties of Nanostructures

We study, via ab initio density functional theory (DFT), the vibrational properties of semiconductor colloidal nanostructures. The calculations are performed on the NEC Nehalem clusters at the High Performance Computing Center Stuttgart (HLRS). We find a relatively large blue shift of the longitudinal acoustic, transverse and longitudinal optical modes with decreasing nanocrystal size. This blue shift originates from a bond length reduction at the surface of the clusters. We also find a red shift of the vibrational modes in the case of unpassivated nanostructures. This red shift can be attributed to the presence of unpaired electrons in the sp3 hybrid orbitals and the ensuing reduction in bond length. A subsequent structural relaxation leads to the formation of more favorable sp2 bonds and the vibrational modes shift to the blue. We can also identify the coherent acoustic modes and find good agreement with experiment.