Atomic and Electronic Structures of Zr Atomic Chains

The atomic, binding and electronic structures of very thin Zr chains are studied by the first-principles density functional method. The present calculations reveal that zirconium can form planar chains in zigzag, dimer and ladder structures. The zigzag geometry has two minima. The most stable geometry is the zigzag one with a unitcell rather close to equilateral triangles with four nearest neighbours. The other stable zigzag structure has awide bond angle and allows for two nearest neighbours. An intermediary structure has the ladder geometry andis formed by two strands. The dimer structure is also found to be more stable than the truly linear chain. Allthese planar geometries are more favourable energetically than the linear chain. We also show that by going fromZr bulk to a Zr chain, the characters of bonding do not change significantly.