Spin-orbit corrections

It is well-known that the hyperfine interaction for a given nucleus A consists of three contributions (a) the isotropic Fermi contact term, (b) the spin-dipolar interaction, and (c) the spin-orbit correction. One finds for the three parts of the magnetic hyperfine coupling (HFC), the following expressions [3, 9] ... 

In this way it was shown that the opt values derived from data for MCl, MFi, and MFg species gave excellent correlations with the occupation number, q, and that the n -<-75 (ys) peak positions could be well reproduced using Eqs. 5 (7) and 5 (2), with spin-orbit corrections. In all cases the correlations were significantly better when the relativistic terms were included than when they were omitted, and in Table 30 we list the xopt and oPt values derived from the 5 d data for MFg, MFg, and MF6 complexes. In the Table we also show the observed and the calculated band positions using the corrected forms of Eqs. 5 (7) and 5 (2). Once again the xopt vs. q plots yield slopes in excellent agreement with the ( —ri) values deduced from these equations. Finally, in Figs. 16... 

For the 5 d series therefore the inclusion of the spin-orbit corrections leads to improved x0pt vs. q plots, satisfactory predictions of the charge-transfer band via Eqs 5 (/) and 5 (2), and a strong correlation between... 

Thus, DFT-IGLO calculations of the 31P chemical shift without spin-orbital corrections yielded a value of S = 274, whereas additional spin-... 

Spin-orbit correction Eso is included for atomic species only. The spin-orbit correction is taken from experiment [49] where available and accurate theoretical calculations [50] in other cases. These corrections are particularly important for halide-containing systems [24], Molecular spin-orbit corrections are not included in G3 theory. 

On the other hand, high-level computational methods are limited, for obvious reasons, to very simple systems.122 Calculations are likely to have limited accuracy due to basis set effects, relativistic contributions, and spin orbit corrections, especially in the case of tin hydrides, but these concerns can be addressed. Given the computational economy of density functional theories and the excellent behavior of the hybrid-DFT B3LYP123 already demonstrated for calculations of radical energies,124 we anticipate good progress in the theoretical approach. We hope that this collection serves as a reference for computational work that we are certain will be forthcoming. 

Includes 5s5p core-valence and spin-orbit corrections These values were cited in Ref (13). 

For atoms, G3 energies are defined to include a spin-orbit correction taken either from experiment or other high-level calculations. In addition, different coefficients are used in step (8). 

Table 10.2 Experimental values and spin- -orbit corrections...

A DFT-based third order perturbation theory approach includes the FC term by FPT. Based on the perturbed nonrelativistic Kohn-Sham orbitals spin polarized by the FC operator, a sum over states treatment (SOS-DFPT) calculates the spin orbit corrections (35-37). This approach, in contrast to that of Nakatsuji et al., includes both electron correlation and local origins in the calculations of spin orbit effects on chemical shifts. In contrast to these approaches that employed the finite perturbation method the SO corrections to NMR properties can be calculated analytically from... 

The MP4/6-31G(d) energy and the four corrections from step 4 are combined in an additive manner along with a spin-orbit correction AE(SO) for atoms only (hydrogen through chlorine) ... 

The atomic spin-orbit correction is taken from experiment96 where available and accurate theoretical calculations in other cases. The values are listed in Table 7. 

Table 7 Atomic Spin-Orbit Corrections (millihartrees) ...

Spin-orbit corrections are from Ref. 96 except where noted. Calculated value, Ref. 30. 

Atomic spin-orbital corrections, sometimes empirical, and a higher-level correction , HLC, to (hopefully) take any remaining inadequacies into account... 

At B3LYP, including ZPE and atomic spin-orbit corrections from Reference 153. 

Plane et al. made further DPT calculations on the OlO + NO system [54], These included bond-additivity corrections for I2 and 10, absorbed into "spin-orbit" corrections for 1 and 10. The bond strengths shown in Table 9.4 are derived from the differences between the computed reaction enthalpies reported by Plane et al. [54], as noted by Golden [55], and are reasonably close to the present values, both falling about 8 kj mol smaller. 

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