The electric-field gradients (EFG’s) of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$, ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.5}$, and ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_6$ are calculated on a first-principles basis using the full-potential linear augmented-plane-wave (LAPW) method in which exchange and correlation effects are treated by the local-density approximation (LDA). Good agreement with experimental EFG’s and their anisotropies is found for the Cu(1) position in all three compounds. For ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ the same is true for all oxygen positions, while at Cu(2) the direction of the EFG is predicted correctly, but a transfer of 0.07 electrons from ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ to ${\mathit{d}}_{\mathit{z}}^2$ symmetry would be needed to bring the theoretical EFG into agreement with the experimental value. The EFG calculations on ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_6$ and ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.5}$ [assuming an ordered structure in which Cu(1) is threefold coordinated by oxygens] confirm the experimental assignment and strengthen the confidence in our results. The origin of the EFG is discussed and the relation to the anisotropy of the electronic charge distribution is illustrated in connection with symmetry-decomposed partial charges and difference-electron-density maps. It is shown that the LDA calculations yield reliable charge distributions to which the EFG is so sensitive.

• Received 28 February 1990

DOI:https://doi.org/10.1103/PhysRevB.42.2051