Identification of fullerene-like CdSe nanoparticles from optical spectroscopy calculations

Semiconducting nanoparticles are the building blocks of optical nanodevices as their electronic states, and therefore light absorption and emission, can be controlled by modifying their size and shape. CdSe is perhaps the most studied of these nanoparticles, due to the efficiency of its synthesis, the high quality of the resulting samples, and the fact that the optical gap is in the visible range. In this article, we study light absorption of CdSe nanostructures with sizes up to $1.5\mathrm{nm}$ within density functional theory. We study both bulk fragments with wurtzite symmetry and fullerene-like core-cage structures. The comparison with recent experimental optical spectra allows us to confirm the synthesis of these fullerene-like CdSe clusters.

Figure 1

(Color online) Relaxed cages, filled cages, and wurtzite structures of ${\left(\mathrm{Cd}\mathrm{Se}\right)}_n$. Cd atoms are in green and Se atoms are in beige.

Figure 2

(Color online) Distance of Cd atoms (circles) and Se atoms (diamonds) from the center of the cluster after geometry optimization, as a function of their distance before optimization. An atom that lies on the straight line $y=x$ has not changed its position. In panel (a) results of the analysis for ${\left(\mathrm{Cd}\mathrm{Se}\right)}_{33,34}$ core-cage clusters, in panel (b) for the ${\left(\mathrm{Cd}\mathrm{Se}\right)}_{33}$ wurtzite cluster.

Figure 3

(Color online) Calculated total energies per CdSe unit (a) and HOMO-LUMO gaps (b) as a function of the number of CdSe units. The zero of energy is set to the total energy per pair of the ${\left(\mathrm{Cd}\mathrm{Se}\right)}_{34}$ core-cage. The empty (filled) circles refer to cage (core-cage) clusters, while the diamonds refer to wurtzite-based structures.

Figure 4

(Color online) Photoabsorption cross section $\sigma \left(\omega \right)$ of the empty cages. In panel (a) the absorption spectra of ${\left(\mathrm{Cd}\mathrm{Se}\right)}_{48}$ (dotted line) and ${\left(\mathrm{Cd}\mathrm{Se}\right)}_{28}$ (solid line); in panel (b) the absorption spectra of ${\left(\mathrm{Cd}\mathrm{Se}\right)}_{12}$ (dotted line) and ${\left(\mathrm{Cd}\mathrm{Se}\right)}_6$ (solid line).

Figure 5

(Color online) Photoabsorption cross section $\sigma \left(\omega \right)$ of the isomers of ${\left(\mathrm{Cd}\mathrm{Se}\right)}_{13}$. In panel (a) the absorption spectrum of the wurtzite structure; in panel (b) the absorption spectrum of the filled cage.

Figure 6

(Color online) Photoabsorption cross section $\sigma \left(\omega \right)$ of the isomers of ${\left(\mathrm{Cd}\mathrm{Se}\right)}_{33,34}$. The experimental data in arbitrary units (a) are compared with our calculated spectra (b), (c), and (d). The different curves in panels (c) and (d) correspond to distinct relaxed geometries obtained starting from different filled cages.