Chemical shielding theory

R 350 J.C. Facelli, Calculations of Chemical Shieldings. Theory and Applications , Concepts Magn.Reson., A, 2004,20A,42... 

By applying polarization functions, ab initio shielding calculations for some polyenals and their Schiff bases reproduce the experimental values well even on the carbonyl and the imine carbons using the LORG theory without including correlation effects. In addition, there is a trend that the calculation with polarization functions yields smaller anisotropies of chemical shieldings than those without polarization functions. 

Figure 1. HF-GIAO 19F absolute chemical shieldings for C6H5F (in ppm) using (/) a 6-31G basis on all atoms and (//) a locally-dense basis (6-31G on C and H, and 6-311++G(2d,2p) on F) and geometries optimized at the HF, CASSCF(6,6), MP2, MP4(SDQ) and QCISD levels of theory (all within the 6-31G basis).

It could appear interesting to apply Chestnut s approximate infinite-order perturbation-theory prescription for isotropic NMR chemical shieldings (25) in order to extrapolate our HF//MP2 and MP2//MP2 results to higher orders of perturbation theory. However, due to the feet that reference MP3-GIAO and MP4-GIAO results are not available, even for C6H5F, we did not feel that the use of ratios, derived from MPn-GIAO calculations on smaller moleules, would be sufficiently well justified. 

These effects of changes in geometry on the shielding tensor in PH3 provide the framework for discussion of trends observed in the simple phosphate systems described below. In theory, the difference in the variation for the isotropic and individual principal components of the chemical shielding tensor can be used... 

The QM theory of chemical shielding was originally developed many years ago [22,23], but only later have ab initio methods and density functional theories (DFT) been reliably used for the prediction of NMR properties of isolated molecular systems, and finally of solvated systems. The latter step has been achieved by extending the gas-phase theoretical methods to continuum solvation models (see Ref. [11] for a sufficiently updated list of papers). 

For hydrogen, the Ramsey theory is relatively easy to apply, but, as we see in Section 4.5, external perturbations from neighboring functional groups and solvent molecules are of comparable magnitude to the basic electronic terms, so that the theory is quantitatively of little practical value. For other nuclei, this theory could predict chemical shielding rather accurately if we had true wave functions and knowledge of the energies of all excited states. In practice, approximations must be made, but acceptable results can be obtained provided some fundamental aspects are kept in mind. 

Kleinpeter and Koch have recently introduced spatial magnetic properties as a measure of homoaromaticity. These are calculated as through-space NMR shieldings (TSNMRS) and visualized as iso-chemical shielding surfaces (ICSF). The structures, the intramolecular flexibility, and the and C NMR chemical shifts are calculated on the MP2/6-311 + G level of theory. TSNMRS of benzene and the cyclopropenylium cation as prototype aromatic molecules published earlier are used as references for homoaromaticity in a number of homoaromatic carbocations. The existence and the degree of homoaromaticity are deduced from the TSNMRSs by comparing the experimental and computed H and NMR NMR chemical shifts. 

The application of temperature-dependent line shapes and the measurements of second moments in more complex organic solids like polymers followed soon after. Even nowadays, this simple method still has its place in the characterization of materials like solid polymer electrolytes where the line widths and Ti relaxation of the charge carriers provide information about their mobility that can be correlated with the electrical conductivity of the material. More detailed information can be obtained from cases in which the interaction is well defined, i.e., when an anisotropic single-spin interaction dominates the spectrum. Typical cases are the chemical shielding anisotropy (CSA) and quadrupolar interaction for which the theory is well developed. 

An additional source of chemical shielding anisotropies is that of ab initio theoretical calculations.20 25 There has been considerable progress in this area of molecular quantum mechanics, particularly with the use of gauge-invariant atomic orbitals within the framework of self-consistent-field (SCF) perturbation theory.26 In many cases the theoretical quantities have been extremely accurate and have served not only as a corroboration of experimental quantities but also as a reliable source of new data for molecules of second-row atoms (i.e., Li through F). 

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