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Interplay of electronic structure and unusual development in crystal structure of YbAuIn and Yb$_{3}$AuGe$_{2}$In$_{3}$

First-principles calculations within the DFT are employed to investigate the relationship between the electronic structure and the unexpected features of the hexagonal cell parameters of YbAuIn and Yb$_{3}$AuGe$_{2}$In$_{3}$. Calculations indicate that YbAuIn is an intermediate valent system with one Yb 4\textit{f} state pinned to the Fermi level, while Yb$_{3}$AuGe$_{2}$In$_{3}$ is closer to integer valency with all Yb 4\textit{f} states occupied. Structural relaxations performed on LaAuIn and LuAuIn analogs reveal that expansion of the \textit{c}-parameter in Yb$_{3}$AuGe$_{2}$In$_{3}$ is attributable to larger size of the divalent Yb compared with intermediate valent Yb.