Generation of isomers for icosahedral clusters A12−xBx (x = 0–12) from a symmetry-based algorithm

All isomers of (quasi-)icosahedral, binary A12−xBx clusters were constructed based on a simple symmetry-based algorithm. This algorithm can also be applied to other starting geometries, but it is advantageous to restrict to high starting symmetries and high degeneracies of atom sites. Also, the (relative) degeneracies of the isomers are calculated. Chiral isomers are identified, showing that chirality in binary, (quasi-)icosahedral clusters may play an important role in A8B4, A7B5, A6B6, A5B7, and A4B8. Chirality is of importance in nonlinear optics and asymmetric catalysis. The results provided may stimulate further research in these areas using binary metal clusters.

Graphical abstractThe geometrical isomers of (quasi)-icosahedral clusters A12−xBx were constructed using group theoretical arguments. The degeneracies and chirality of the isomers were analyzed, showing that chirality becomes important at doping with four or more foreign atoms.Figure optionsDownload full-size imageDownload as PowerPoint slide