Effect of the electronic charge gap on LO bond-stretching phonons in undoped La2CuO4 calculated using LDA+U

Typical density-functional theory calculations that wrongly predict undoped cuprates to be metallic also predict Cu-O half- and full-breathing phonon energies that are significantly softer than observed, presumably because of weak on-site Coulomb repulsion on the Cu 3d orbitals. We used $\mathrm{DFT}+\mathrm{U}$ calculations with antiferromagnetic supercells of ${\mathrm{La}}_{\text{2}}{\mathrm{CuO}}_{\text{4}}$ to establish correlation between the on-site repulsion strength, tuned via adjusting the value of U, and phonon dispersions. We find that breathing and half-breathing phonons reach experimental values when U is tuned to obtain the correct optical gap and magnetic moments. We demonstrate that using distorted supercells within $\mathrm{DFT}+\mathrm{U}$ is a promising framework to model phonons in undoped cuprates and other perovskite oxides with complex, interrelated structural and electronic degrees of freedom.