Tuning the Optical Gap of Nanometer-Size Diamond Cages by Sulfurization: A Time-Dependent Density Functional Study

The optical gap of nanometer sized diamond cages, i.e., diamondoids, lies in the ultraviolet spectral region. Here we show by hybrid functional based time-dependent density-functional calculations that, by varying the number of $\mathrm{C}\mathrm{S}$ double bonds at the surface of diamondoids, the absorption onset can be tuned toward the infrared spectral region. Our finding has an important implication for in vivo biological applications where toxic and unstable dye molecules may be substituted by the luminescent sulfurized diamondoids.

Figure 1

The structures and the lowest energy excitations are shown for sulfurized (a) adamantane and (b) pentamantane[1(2,3)4] as a function of the number of $\mathrm{S}$ double bonds at the surface. Cyan balls depict C atoms. Hydrogen atoms are not shown for clarity. The $\mathrm{S}$ substitutions are indicated by numbers on the upper $x$ axis of the plots for adamantane and by letters for pentamantane[1(2,3)4], where the dictionary for the letter-number correspondence is the following: $a=1$; $b=1$, 12; $c=1$, 9, 10; $d=1$, 3, 10, 12; $e=1$, 4, 5, 7, 10, 11; $f=1$, 4, 5, 7–11; $g=1–3$, 6–12; $h=1–12$. These numbers on the structures next to the graphs represent C atoms to which S atoms bond. $\mathrm{C}\mathrm{S}$ double bonds are involved in the excitations. See text for more details.

Figure 2

(a) Total and projected density of states (PDOS) of adamantanethione are shown where H and L denote the HOMO and LUMO energies, respectively. The projected $s$ and $p$ orbitals of sulfur atoms are depicted by red dotted and green continuous lines, respectively. (b) Schematic diagram about the order of single particle states. On the left the localization of the molecular orbitals is labeled while the symmetry of these orbitals is shown on the right. The HOMO state is $n(b_2)$ while the LUMO is ${\pi }^{*}(b_1)$. Arrows are representing the calculated lowest excitations between these states. The corresponding excitation energies are also given. (c) Adamantanethione structure: small white, larger cyan, and largest yellow balls depict H, C, and S atoms, respectively. The isovalue of the calculated wave functions are shown where red (dark gray) and yellow (light gray) colors represent the positive and negative values with the corresponding label of the molecular orbitals.

Figure 3

Isovalue representation of the (a) HOMO and (b) LUMO states of 12 $\mathrm{C}\mathrm{S}$ double bonds in pentamantane[1(2,3)4] where red (dark gray) and yellow (light gray) colors represent positive and negative values of the corresponding molecular orbitals. Small white, larger cyan, and largest yellow balls depict H, C, and S atoms, respectively.