$^{17}$O Nuclear Magnetic Resonance Chemical Shielding Calculations of PZT Solid Solutions

First principles B3LYP calculations of $^{17}$O NMR in PbTiO$_3$, Pb(Zr$_\frac{1}{2}$Ti$_\frac{1}{2}$)O$_3$ (PZT), and PbZrO$_3$ will be presented. These systems were modeled with finite size quantum clusters embedded in point charge arrays. The embedding reproduces the Ewald Coulomb potential to better simulate the crystal environment.\footnote{M. K. Klintenberg, S. E. Derenzo, and M. J. Weber. Comput. Phys. Commun.{\bf 131}, 120, (2000).} For polar systems, the calculations were performed in the presence of an external electric field to cancel surface depolarization effects.\footnote{S. Li and K. Rabe. APS March Meeting abstract (2007).} PZT was modeled using three chemically ordered structures: P4mm, P2mm, and R3m. Two groupings of $^{17}$O isotropic chemical shifts $\delta_{iso}$ are seen in all of our PZT calculations with [001] ordering. One is at $\delta_{iso}$ $\approx$ 400ppm and the other is at $\delta_{iso} \approx$ 650ppm. We relate these to variations in the Ti-O and Zr-O bond lengths and use this to interpret recent experimental measurements.\footnote{ A. Baldwin, P.A. Thomas and R. Dupree, J. Phys: Cond. Matt. {\bf 17}, 7159 (2005).}