Calculated PZT oxygen isotropic δiso and axial 2δax chemical shifts (B3LYP 21 QM atom cluster values from Tables IV), plotted as a function of r s, the shortest B–O bond length of the targeted O atom. For comparison, calculated results for ST, BT, PT, and PZ and from experiment (hollow symbols) are also shown (see Ref. 8). The dashed straight lines are linear fits to calculated values for ST, BT, PT, and PZ from Ref. 8.
GIPAW calculated PMN oxygen isotropic δiso and axial 2δax chemical shifts, plotted as a function of r s. The PMN chemical shifts are from Table V, and the symbols indicate the B-O-B′ configuration, using the convention in that table. For comparison, results for cubic and tetragonal KNbO3 are also shown. The dashed lines are the same as that in Fig. 1. As plotted, the r s values have been increased by 0.12 Å (see text). The unshifted values are shown in the inset.
Pseudopotential construction parameters, see text for description.
Comparison of chemical shielding results, using embedded clusters and GIPAW-PBC from QE and Ref. 19. The principle values of the oxygen chemical shielding tensor are presented for the TiO2 molecule and rutile, cubic ST, cubic BT, and tetragonal PT. All values are from GGA calculations. Embedded cluster results are labeled as C-n, where n is the number of QM atoms in the cluster. The GIPAW-PBC and C-65 calculations were done with relativistic PBE, while the C-21 calculations were done with non-relativistic PW91.
The derived theoretical oxygen reference value, , is used to determine theoretical isotropic chemical shifts from the corresponding calculated isotropic chemical shielding values. Experimental chemical shifts are shown for comparison. The values of are shown in the third row from the bottom of this table. The rms error and maximum deviation of the calculated shifts, compared to experiment, are also shown. Calculated cluster results (21 and 65 QM atoms) with B3LYP and PW91 exchange-correlation are shown together with GIPAW-PBC with PBE exchange-correlation. (PZ experimental chemical shift site assignments were corrected in Ref. 8 and are used here.)
Calculated oxygen isotropic, axial, and anisotropic components (ppm) of the chemical shift tensor for three PZT 50/50 structural models from Ref. 7. The notation B–O–B indicates O atoms with two equidistant nn B atoms, and B-O–B indicates an O atom with one short and one long nn B bond. For cluster-GGA results, numbers in parenthesis show the difference with GIPAW. For cluster-B3LYP results, numbers in square brackets show the difference with cluster-GGA values. For cases where δaniso = 0 by symmetry, this is indicated by an ellipsis.
GIPAW calculated oxygen isotropic, axial, and anisotropic components (ppm) of the chemical shift tensor for PMN. A 60-atom supercell with relaxed internal coordinates was used (see Ref. 39). The B–O–B′ bond notation is the same as in Table IV; bond lengths are categorized as equidistant if they differ by less than 0.05 Å.
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