# The UV Plasmonic Behavior of Rhodium Tetrahedrons--A Numerical Analysis
## 3 Results and Discussion
### Rh Tetrahedra: Effect of a Concavity  
Recent studies have reported the possibility of synthesizing Rh TDs with concave faces with defect-rich surfaces [12; 13]. These defects have been shown to enhance the photocatalytic energy conversion [13]. Therefore, in this section we will evaluate how the near-field enhancement and the charge density are distributed over the TD's surface when concavities are introduced at their flat faces. In this way, we can look for the concavity parameters that maximize the surface \(|\mathbf{E}|^{2}\) and \(\sigma\) inside the cavity to enhance its catalytic properties, while keeping high values of these magnitudes at the outer  
Figure 5: (**a**) Normalized spectral values of surface charge distribution (\(\sigma\)) averaged over edges and corners and (**b**) the flat faces of the TDs with rounded edges and corners as function of the curvature radii \(R_{c}\). (**c**) Surface charge distribution (\(\sigma\)) over Rh TDs with rounded edges and corners with a curvature radii \(R_{c}\) when illuminated at the resonant wavelength. The red/blue regions represent positive/negative charge densities. edges and corners to maintain their inherent reactivity. In order to do this, we have varied the size of the concavity \(t\) and its depth \(d\) (see Figure 1b). First, we will address the effect of the size of the concavity \(t\) while keeping its depth constant (\(d=3\)nm) in a \(L=20\) nm TD. Figure 6 shows the (a) \(C_{abs}\) and (b) \(\langle|\mathbf{E}|^{2}\rangle\) spectra as the value of \(t\) decreases starting from the perfect TD. It can be seen that as we increase the size of the concavity (lower values of \(t\)), both the \(C_{abs}\) and \(\langle|\mathbf{E}|^{2}\rangle\) peaks red-shift and narrow. The peak value of \(C_{abs}\) remains almost constant while those of \(\langle|\mathbf{E}|^{2}\rangle\) slightly decreases (\(\approx\)10%). The narrowing of the LSPR peak can be understood attending to the oscillation amplitude of the electrons in the TD. When the TD has flat faces, the electrons can oscillate with an amplitude going from the side length (oscillation between bottom corners of the TD) to progressively smaller amplitudes as the oscillations go up along the flat face, leading to broad LSPR peaks. When a concavity is introduced, some of the previously allowed oscillations are blocked by the presence of the concavity, narrowing the LSPR peak. In fact, for the biggest concavity, only the oscillation along the bottom edge of the TD is allowed (the widest amplitude), consistent with a LSPR peak at lower photon energy. Figure 6c shows the near-field distribution over the TD's surface when illuminated at resonance. It can be seen how the most intense hot spots are produced at the external edges and bottom corners of the TDs. When increasing the size of the concavity, the hot spots, initially evenly distributed along the external edges (oscillation of the electrons all across the flat surface of the TD), become concentrated in the bottom corners. This is consistent with the fact that, for the largest concavity, the electron oscillation is constraint along the bottom edge of the TD. In order to potentially increase the reactivity of the concavity, it is important to maximize the surface charge density on its surface. Therefore, in order to address this issue, we have calculated the averaged value of \(\sigma\) outside and inside the concavity to see how its value is affected when the size of the concavity increases. Figure 7 shows the average of the absolute value of the surface charge density (a) outside \(\langle|\sigma|\rangle_{out}\) and (b) inside \(\langle|\sigma|\rangle_{in}\) the concavity. The general trend is that as the concavity size increases, the value of \(\langle|\sigma|\rangle_{out}\) increases while \(\langle|\sigma|\rangle_{in}\) decreases.