Investigation of $A_{1g}$ phonons in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$ by means of linearized-augmented-plane-wave atomic-force calculations

We report first-principles frozen-phonon calculations for the determination of the force-free geometry and the dynamical matrix of the five Raman-active $A_{1g}$ modes in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$. To establish the shape of the phonon potentials atomic forces are calculated within the linearized-augmented-plane-wave method. Two different schemes—the local-density approximation (LDA) and a generalized gradient approximation (GGA)—are employed for the treatment of electronic exchange and correlation effects. We find that in the case of LDA the resulting phonon frequencies show a deviation from experimental values of approximately -10%. Invoking GGA the frequency values are significantly improved and also the eigenvectors are in very good agreement with experimental findings.