The theory of the pseudocontact contribution to NMR shifts of d1 and d2 transition metal ion systems in sites of octahedral symmetry

A partial differential equation for pseudocontact shift

“…If chemical shielding is considered instead of the chemical shift, the minus sign on the right hand side disappears. Simplicity of Equations ( 16) and ( 17) stands in sharp contrast with the unfathomable spherical harmonic expansions [10] generated by ab initio treatments using the ligand field theory.…”

“…(A) Point model versus Equation ( 16) for the PCS in the complex of europium(III) with 1,4,7,10-tetrakis(2-pyridylmethyl)-1,4,7,10-tetraazacyclododecane [24] using the magnetic susceptibility tensor obtained from a DFT calculation. (B) Point model versus the PCS part of Equation (10) using hyperfine tensors and the magnetic susceptibility tensor from a DFT calculation. (C) Volumetric stereo plot of the PCS field computed using Equation ( 16) with the electron probability density and the susceptibility tensor obtained from a DFT calculation.…”

“…A significant advantage of these equations over other physically equivalent formulations is that the excitation structure of the quantum chemistry part of the problem is hidden from the user -both the hyperfine tensor and the susceptibility tensor are effective quantities that already incorporate all of the formidable complexities of the electronic structure theory. 7 The derivations given above are classical, but the only assumption in eqn (10) is that v { 1 (meaning also that magnetic hyperpolarizability terms in the electronic structure theory are negligible) and that the electron relaxes sufficiently rapidly for eqn (3) to always remain valid.…”

“…It should be noted that eqn (16) and (17) only apply to pseudocontact and dipolar shift respectively. For contact shifts a convenient description is provided by eqn (10), where the isotropic part of the hyperfine tensor is proportional to the local spin density.…”

“…1 is, at least for this complex, that the accuracy of the point PCS model is very high, presumably due to the localized nature of the f orbitals under the relatively low Fig. 1 An example of the forward problem solution and a demonstration of the mutual consistency of eqn ( 8), (10) and (17). The red points refer to the symmetry-unique atoms in the ligand, including carbons and protons, but excluding nitrogens that have significant contact shifts.…”