Electronic structure, bonding and phonon modes in the negative thermal expansion materials ofCd(CN)2 and Zn(CN)2

Abstract

The disordered configuration, band structures, density of states, Mulliken population,elastic constants, zone center optic phonon modes and their Grüneisen parameters ofM(CN)2 (M = Cd, Zn) have been studied for possible cyanide-ordering patterns by the first-principles plane-wavepseudopotential method based on density functional theory. Total energy calculations predict thatMC2N2–MC2N2 is the most favorableconfiguration for Cd(CN)2 whereas all three possible configurations are near equally favorable forZn(CN)2. Effective charges and bond order analyses reveal that theM(CN)2 (M = Cd, Zn) frameworks include much stiffer and weaker M–C/N bonds, which account for the flexing of the M–CN–M linkage duringthe transverse motion of the cyanide-bridge. The transverse translational andthe librational modes give rise to negative Grüneisen parameters and thereforecontribute to the negative thermal expansion. Transverse vibrations of the C andN atoms in the same (transverse translational modes) or opposite (librationalmodes) directions have the same effect of drawing the anchoring metal atomscloser. Among all the optical phonon modes, the lowest-energy transversetranslational optical modes which are neither Raman nor infrared active inCd(CN)2 and Zn(CN)2 give rise to the largest contribution to the negative thermal expansion.