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We preform large-scale \emph{ab initio} density functional theorycalculations to study the lattice strain and the vibrational properties ofcolloidal semiconductor core-shell nanoclusters with up to one thousand atoms(radii up to 15.6~\AA). For all the group IV, III-V and II-VI semiconductorsstudied, we find that the atom positions of the shell atoms, seem unaffected bythe core material. In particular, for group IV core-shell clusters the shellmaterial remains unstrained, while the core adapts to the large latticemismatch (compressive or tensile strain). For InAs-InP and CdSe-CdS, both thecores and the shells are compressively strained corresponding to pressures upto 20 GPa. We show that this compression, which contributes a large blue-shiftof the vibrational frequencies, is counterbalanced, to some degree, by theundercoordination effect of the near-surface shell, which contributes ared-shift to the vibrational modes. These findings lead to a differentinterpretation of the frequency shifts of recent Raman experiments, while theyconfirm the speculated interface nature of the low-frequency shoulder of thehigh frequency Raman peak.

Heavy strain conditions in colloidal core-shell quantum dots and their consequences on the vibrational properties from \emph{Ab initio} calculations