Evaluation of the finite-temperature thermodynamic properties of the electrode materials generally helps to accurately describe the performance of Li-ion battery.To know the characteristics of the layered LiMn1/3Co1/3Ni1/3O2 comprehensively,therefore,the vibrational and related thermodynamic quantities of LiMn1/3Co1/3Ni1/3O2 are investigated by using density functional perturbation theory(DFPT).As there are twelve atoms in the cell of LiMn1/3Co1/3Ni1/3O2,three acoustic modes and thirty-three optical modes are presented in the dispersion curves.From Fig.1,it is found that the phonon dispersioncurves of LiMn1/3Co1/3Ni1/3O2 with GGA+U method are basically similar to that with LDA+U method.The calculated phonon dispersions without soft modes,indicating that the compound is dynamically stable.In sight of phonon density-of-states,we discover that the high frequency section and medium frequency section are contributed by oxides atoms motion and lithium atoms,while low frequency section motion is contributed by transition metal atoms.Furthermore,temperature variations of thermodynamical functions such as helmholtz free energy,entropy and lattice specific heat at constant volume are also calculated and discussed in Fig.2.The vibrational entropy S and constant-volume specific heat Cv at a given temperature T of LiMn1/3Co1/3Ni1/3O2 from GGA+U is slightly higher than LDA+U,While the phonon contributions to Helmholtz free energy F,the GGA+U result is a little lower than LDA+U.