A quantum mechanically guided view of Mg44Rh7.

We present a new geometric description of Mg(44)Rh(7), a compound with 408 atoms in its cubic unit cell. Using both experimental site preferences and LDA-DFT-calibrated extended Hückel (eH) calculations as guides, we highlight the structural units within Mg(44)Rh(7) that reflect the electron-richness or electron-poorness of each crystallographic site. The units that best account for these site preferences and electron populations are 34- and 25-atom fragments of the Ti(2)Ni structure, rather than the variety of clusters often used to describe complicated intermetallic and ionic structures. These Ti(2)Ni pieces, located using a systematic search algorithm, fit together in a beautifully intricate network. An examination of this network reveals some surprising geometric features of Mg(44)Rh(7), including a fractal-like arrangement of similar atomic formations on different length scales, geometrically connected to an approximate fivefold symmetry.