DFT and TDDFT calculation of lead chalcogenide clusters up to (PbX)$_{32}

A series of the lead chalcogenide clusters PbnXn (X=S,Se; n=4,8,16,32) with structures as fragments of the bulk crystalline lattice are calculated at DFT level with B3LYP functional and ECP basis set. Optical absorption spectra are simulated through the TDDFT method. The results are in consistence with experimental data PbS and PbSe for magic size clusters of this size range.