Analysis for the Stability of All Sodium Isomers by Graph Theory and Molecular Mechanics

Abstract

All isomers for sodium clusters up to Na9 were investigated by graph theory where a vertex and an edge correspond to atom and bond between adjacent atoms, respectively. All isomers, more than 10 million, for Na10 were listed. Structural features for sodium clusters up to Na9 were elucidated by using graph theory. Furthermore, geometrically forbidden graphs were excluded by using molecular mechanics.