First-principles calculations of \(^{17}\)O NMR chemical shielding in Pb(Zr\(_{1/2}\)Ti\(_{1/2}\))O\(_3\) and Pb(Mg\(_{1/3}\)Nb\(_{2/3}\))O\(_3\): linear dependence on transition-metal/oxygen bond lengths

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.