Illustration of cluster embedding for the O-centered QM cluster (Sec. ???), shown for a  plane of the ideal perovskite structure. The QM A, B, and O atoms are depicted by filled black, blue, and red circles, respectively. In the left panel, the QM atoms are embedded in point charges, “” or “−” signs colored coded according to the QM atom they replace in the crystalline lattice. In the right panel, the boundary O QM atoms have had their nn and nnn cation point charges replaced by “empty” pseudopotentials (Sec. ???), indicated by thick, large circles, with corresponding color coding.
Calculated oxygen isotropic and uniaxial chemical shifts in ST, BT, PT, and PZ as a function of , the shortest B–O bond length of the targeted O atom. 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 (e.g., along the polar -axis in P4mm PT). The straight lines are linear fits.
Calculated paramagnetic and components (see text), as a function of , the shortest B-O bond length of the targeted O atom. The straight lines are linear regressions of the points. Symbols as in Fig. 2.
Calculated oxygen chemical shielding principal values (in ppm) for ST, BT, PT, and PZ. In all cases, denotes the principal axis that is most closely along the B-O bond direction. Unless otherwise indicated, the CSGT gauge method was used, with B3LYP for exchange and correlation. For some cases, GGA results are given in parenthesis. RHF and GIAO gauge method B3LYP results are given for ST. GIAO results for the isolated diamagnetic atom are also shown. See the text for a discussion of the fake ST calculation. For PZ, we adopt the site labeling convention of Ref. 53; the O(i) site notation of Ref. 55 is also given in brackets.
Comparison between calculated and measured single crystal and powder spectra chemical shifts (in ppm) for BT and ST. Calculated isotropic shifts and uniaxial components are derived from Table I, referenced to liquid water, (Ref. 74). Calculated values are from B3LYP (GGA values are in parenthesis), and RHF results are also shown for ST.
Comparison between calculated and experimental isotropic chemical shifts (in ppm) for PT and PZ. Calculated isotropic shifts are derived from Table I, referenced to liquid water, (Ref. 74). Calculated values are from B3LYP (GGA values are in parenthesis). For PZ, we adopt the site labeling convention of Ref. 53; the O(i) site notation of Ref. 55 is also given.
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