Raman intensities of Si quantum dots ͑QD's͒ with up to 11489 atoms ͑about 7.6 nm in diameter͒ for different scattering configurations are calculated. First, phonon modes in these QD's, including all vibration frequencies and vibration amplitudes, are calculated directly from the lattice-dynamic matrix by using a microscopic valence force field model combined with the group theory. Then the Raman intensities of these quantum dots are calculated by using a bond-polarizability approximation. The size effects of the Raman intensity in these QD's are discussed in detail based on these calculations. The calculations are compared with the available experimental observations. We are expecting that our calculations can further stimulate more experimental measurements.

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Phonons of single quintuple films of Bi 2 Te 3 and Bi 2 Se 3 and corresponding bulk materials are calculated in detail by MedeA (a trademark of Materials Design) and Vienna ab initio simulation package (VASP). The calculated results with and without spin-orbit couplings are compared, and the important roles that the spin-orbit coupling plays in these materials are discussed. A symmetry breaking caused by the anharmonic potentials around Bi atoms in the single quintuple films is identified and discussed. The observed Raman intensity features in Bi 2 Te 3 and Bi 2 Se 3 quintuple films are explained.

We have erroneously applied Eq. ͑6͒ in our article to the case of the l = 0 spheroidal modes, in spite of the following Errata to earlier publications. 1,2 For the l = 0 cases, the correct equation for the calculation of the eigenmode frequencies should be:The corrected set of ͑S͒ values are now shown in the following Fig.

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