## 3 Results and Discussion
### Electrical and Optical Properties, Raman Scattering and DFT Calculations
To avoid the optimization of large supercells, model stoichiometries were chosen to be close to the studied systems while maintaining a single unit cell. Optimized cell parameters agreed with the experimental data (less than 2% deviation in cell length) and are presented in Table 4. Deviation between repetitions of the same stoichiometry (\(\sigma\)) was low, indicating that the results were robust. Regarding the electronic structure of the different spinels, the Cr centers concentrated most of the spin density; Mulliken spin populations were always around 3.2-3.3 electrons. A smaller spin polarization featuring the opposite spin was observed for S/Se atoms. Cu ions showed small spin polarization, suggesting a monovalent state for this ion. The different models showed minor changes, as the electronic configuration did not change qualitatively when the elemental composition was modified. The calculated magnetic moment was consistent with the presence of monovalent Cu ions and Cr\({}^{\text{III}}\) (S = 3/2) centers coupled antiferromagnetically with a delocalized electron with relevant spin density at the S/Se atoms. This picture is in line with neutron diffraction measurements of CuCr\({}_{2}\)Se\({}_{4}\) performed by [PERSON] [38]. Band structures for all models were consistent with the observed semiconductor behavior and presented noticeable spin polarization (Figure S4). The density of states clearly reflected the spin configuration of the systems. Figure 4 present the element and spin-resolved DOS for Cu\({}_{8}\)Cr\({}_{8}\)Sn\({}_{8}\)S\({}_{16}\)Se\({}_{16}\). The unpaired electrons associated with the Cr\({}^{\text{III}}\) ion appear as a large contribution in the upper part of the valence band between \(-6\) and \(-7\) eV. Unoccupied beta d-orbitals appear as a broad peak ranging from \(-5.5\) eV to \(-2.5\) eV. The unpaired electron from S/Se is connected with the larger contribution of these ions in the occupied part of the beta density of states. Other models feature similar DOS plots (shown as Figure S5 in SI). \begin{table}
\begin{tabular}{c c c c c} \hline
**Model Stoichiometry** & **Reference Formula** & \(a\) **Exp (Å)** & \(a\) **Calc (Å)** & \(\sigma\) \\ \hline Cu\({}_{8}\)Cr\({}_{8}\)Sn\({}_{5}\)S\({}_{16}\)Se\({}_{16}\) & Cu\({}_{1}\)Cr\({}_{1}\)Sn\({}_{1}\)S\({}_{2}\)Se\({}_{2}\) & 10.398  & 10.521 & 0.0197 \\ Cu\({}_{8}\)Cr\({}_{8}\)Sn\({}_{5}\)S\({}_{19}\)Se\({}_{13}\) & Cu\({}_{1}\)Cr\({}_{1}\)Sn\({}_{1}\)S\({}_{2\text{-}3}\)Se\({}_{1.7}\) & 10.370 & 10.465 & 0.0195 \\ Cu\({}_{8}\)Cr\({}_{11}\)Sn\({}_{5}\)S\({}_{13}\)Se\({}_{19}\) & Cu\({}_{1}\)Cr\({}_{1\text{-}4}\)Sn\({}_{0\text{-}6}\)S\({}_{1\text{-}7}\)Se\({}_{2\text{-}3}\) & 10.322 & 10.413 & 0.0170 \\ Cu\({}_{8}\)Cr\({}_{11}\)Sn\({}_{5}\)S\({}_{19}\)Se\({}_{13}\) & Cu\({}_{1}\)Cr\({}_{1\text{-}4}\)Sn\({}_{0\text{-}6}\)S\({}_{2\text{-}3}\)Se\({}_{1.7}\) & 10.24 & 10.307 & 0.0155 \\ Cu\({}_{8}\)Cr\({}_{13}\)Sn\({}_{5}\)S\({}_{13}\)Se\({}_{19}\) & Cu\({}_{1}\)Cr\({}_{1\text{-}6}\)Sn\({}_{0\text{-}4}\)S\({}_{1\text{-}7}\)Se\({}_{2\text{-}3}\) & 10.25 & 10.277 & 0.0499 \\ Cu\({}_{8}\)Cr\({}_{13}\)Sn\({}_{5}\)S\({}_{19}\)Se\({}_{13}\) & Cu\({}_{1}\)Cr\({}_{1\text{-}6}\)Sn\({}_{0\text{-}4}\)S\({}_{2\text{-}3}\)Se\({}_{1\text{-}7}\) & 10.18 & 10.197 & 0.0100 \\ \hline \end{tabular}
\end{table} 
Table 4: Experimental and calculated cell parameters for different CuCr\({}_{2\text{-}3}\)Sn\({}_{x}\)S\({}_{4\text{-}y}\)Se\({}_{y}\) compounds. The standard deviation was calculated from three optimizations with the same stichometry but different ion arrangements.