Absorption spectra and frequency-dependent polarizabilities of small silicon clusters: A density functional study

Abstract

The absorption spectra and frequency-dependent polarizabilities of Si n ( n = 3–10) clusters have been calculated using time-dependent density functional theory (TDDFT) with 6-311+G ∗ basis set and frequency-dependent coupled perturbed Hartree–Fock (CPHF) method within DFT/6-311+G ∗ level, respectively. Four hybrid functionals (B3LYP, B3P86, B3PW91 and BHandHLYP) have been used to calculate the dynamic polarizabilities. With the input photon energy ( E inp) ranging from 0.0 to 1.1 eV, several behaviors of the static polarizabilities hold for the dynamic values. The polarizabilities of all considered clusters exhibit the obvious anisotropic behavior and the near-resonance of E inp enhances the anisotropic behavior. The electronic origin of resonant polarizabilities of Si 3 and Si 4 clusters has been investigated using sum-over-states (SOS) method. The electronic transitions of π → σ and σ → n make a significant contribution to the dynamic polarizabilities of Si 3 and Si 4 cluster at E inp = 1.612 and 1.488 eV, respectively.