Phonon properties of copper oxide phases from first principles

We present density functional theory (DFT) calculations on phonon dispersions, phonon density of states, and thermodynamic quantities for the three copper oxide phases ${\mathrm{Cu}}_{2}\mathrm{O},{\mathrm{Cu}}_{4}{\mathrm{O}}_{3}$, and CuO. For monoclinic CuO we consider the correct antiferromagnetic ground state. Sound velocities for the acoustic phonon branches and Debye temperatures are calculated and are found to be in good agreement with experiment. We further show how the method for the treatment of dipole-dipole interactions in dynamical matrices of Gonze and Lee [Phys. Rev. B 55, 10355 (1997)] may be incorporated in the real-space (direct) method for interatomic force constants (FCs). The role of the long-ranged dipole-dipole interactions in the phonon dispersion is discussed. Based on this method, we outline a perturbationlike scheme to compute first-order derivatives of the phonon mode frequencies with respect to the wave vector which can be used to compute velocities of sound.