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

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Abstract
The disordered configuration, band structures, density of states, Mulliken population, elastic constants, zone center optic phonon modes and their Grüneisen parameters of M(CN)2 (M = Cd, Zn) have been studied for possible cyanide-ordering patterns by the first-principles plane-wave pseudopotential method based on density functional theory. Total energy calculations predict that MC2N2–MC2N2 is the most favorable configuration for Cd(CN)2 whereas all three possible configurations are near equally favorable for Zn(CN)2. Effective charges and bond order analyses reveal that the M(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 during the transverse motion of the cyanide-bridge. The transverse translational and the librational modes give rise to negative Grüneisen parameters and therefore contribute to the negative thermal expansion. Transverse vibrations of the C and N atoms in the same (transverse translational modes) or opposite (librational modes) directions have the same effect of drawing the anchoring metal atoms closer. Among all the optical phonon modes, the lowest-energy transverse translational optical modes which are neither Raman nor infrared active in Cd(CN)2 and Zn(CN)2 give rise to the largest contribution to the negative thermal expansion.