Optical absorption of diamond nanocrystals from ab initio density-functional calculations

Absorption spectrum of small nanodiamonds, i.e., diamondoids has been recently measured exhibiting features that are not understood. Previous calculations, even beyond standard density-functional theory (DFT), failed to obtain the experimental optical gaps $\left(E_{\text{g}}\right)$ of diamondoids. We show that all-electron time-dependent DFT (TD-DFT) calculations including hybrid functional in the TD-DFT kernel are able to provide quantitatively accurate results. Our calculations demonstrate that Rydberg transitions are characteristic even for relatively large nanodiamonds resulting in low $E_{\text{g}}$. The nonmonotonic size dependence of $E_{\text{g}}$ is explained by symmetry considerations.

Figure 1

(Color online) Ball and stick geometries of the studied diamondoids: their name and point group symmetry.

Figure 2

(Color online) (a) Calculated and experimental absorption spectrum for selected diamondoids. Green (dashed) line shows the experimental spectrum while black (continuous) line is the calculated spectrum. Arrows: see text. Inset: radial distribution function of LUMO; vertical line: radius of DNP (b) States associated with Rydberg-like excitations in [1(2,3)4]pentamantane are illustrated and indicated with numbers in the spectrum. Red (dark gray) and yellow (light gray) lobes show the selected positive and negative isovalues of the corresponding PBE0 unoccupied states. Large (small) spheres indicate C(H) atoms.

Figure 3

(Color online) Density of states close to HOMO and LUMO for DNPs with same number of atoms but different point group symmetries as indicated. Note the broken axis in midgap.