  First-principles density functional theory (DFT) oxygen chemical shift
tensors were calculated for A(B,B$^{\prime}$)O$_3$ perovskite alloys
Pb(Zr$_{1/2}$Ti$_{1/2}$)O$_3$ (PZT) and Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$ (PMN).
Quantum chemistry methods for embedded clusters and the GIPAW method [C.\ J.\
Pickard and F.\ Mauri, {\it Phys. Rev. B} {\bf 63} 245101 (2001)] for periodic
boundary conditions were used. Results from both methods are in good agreement
for PZT and prototypical perovskites. PMN results were obtained using only
GIPAW. Both isotropic $\delta_\mathrm{iso}$ and axial $\delta_\mathrm{ax}$
chemical shifts were found to vary approximately linearly as a function of the
nearest-distance transition-metal/oxygen bond length,$r_\mathrm{s}$. Using
these results, we argue against Ti clustering in PZT, as conjectured from
recent $^{17}$O NMR magic-angle-spinning measurements. Our findings indicate
that $^{17}$O NMR measurements, coupled with first-principles calculations, can
be an important probe of local structure in complex perovskite solid solutions.
