CHAPTER 1
Theoretical and Physical Aspects of Nuclear Shielding
BY CYNTHIA J. JAMESON
BY CYNTHIA J. JAMESON
1 Theoretical Aspects of Nuclear Shielding
A. General Theory — The relativistic analog of Ramsey's theory of nuclear magnetic shielding has been derived by Pyper and Pyykkö but no computed results based on these expressions have been pubUshed until recently. In the latter paper the relativistic corrections are determined by finding the nonrelativisitic limits of various matrix elements of the operators in the relativistic theory. The results show a shielding relativistic effect for the component perpendicular to the bond to X for 1H in H-X, and for C* in H-C [equivalent to] C*-X, and C*H3-X. The 'heavy atom shift' appears to be connected with a spin-orbit induced carbon spin density in mainly halogen (X)π1/2 MOs and a spin-orbit induced pi character in the highest occupied sigma MO.
General relationships between second order quantities and sum rules have been described by considering the electric and magnetic moments induced in a molecule in the presence of a radiation field. In the global approach taken by Lazzeretti and Zanasi all the tensors of the second order properties are obtained from the same set of transition amplitudes and excitation energies calculated by some method (such as random phase approximation (RPA) to the equations of motion methods (EOM). Results are given for shielding in the CH4 molecule:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
to be compared with experiment for the ground vibrational state
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
and for the total shielding σe(13C) = 193.991, to be compared with experiment σe(13C) = 198.7.5
Another version of the paper (reviewed in this chapter, vol. 17 of this series) giving the parity nonconservation contribution to nuclear magnetic shielding has appeared, in which the left- and right-handed enantiomers have additional shielding terms ±σPNC, resulting in a splitting in each Une of a racemic mixture in an achiral solvent. Expected magnitudes of this contribution are very small even in the most favorable cases.
A theory of magnetic properties has been presented which is shown to reduce to other known approximate theories under certain conditions. The perturbed state which depends explicitly on the strength of the external magnetic field is determined variationally as a linear combination of Slater determinants associated with a gauge transformation factor. The gauge factor is taken to be a linear function of the position of the electrons with the coefficients being variational parameters. A global gauge function is used, not a different local gauge factor for each AO (Ditchfield's GIAO) or each MO (Schindler and Kutzelnigg's IGLO or Hansen and Bouman's LORG). Also, the gauge function does not depend solely on the external magnetic field. This method is said to ensure current conservation as well as gauge-invariance. As in other methods, when large basis sets of AOs are used, large systems of linear equations have to be solved. Some results are shown in Table 1 for H2O and CO.
B. Ab Initio Calculations — A large number of ab initio calculations of nuclear shielding tensors for heavy atoms have been reported in this review period, in molecular systems with many more heavy atoms than previously attempted. Coupled Hartree Fock methods used include standard CHF (common gauge origin) method, individual gauge for localized molecular orbitals (IGLO) method, and gauge-including atomic orbitals (GIAO) method. Sum-over-states calculations have also been reported. The very large number of systems studied preclude a report of the values obtained for the components of the shielding tensor. We list only the systems studied (in Tables 2, 3 and 4) and some comparisons of the calculated isotropic average shielding with experiments at the zero-pressure limit (Table 5) or with other calculations in a selected number of molecules (Tables 6 and 7).
In addition IGLO calculations of 13C chemical shift tensors in all the molecules shown in Figure 1 have been reported.
Some of the important general conclusions are as follows:
1. Local origin calculations such as IGLO invariably give superior agreement with experiment compared to standard CHF methods using a common gauge origin. The latter tend to underestimate the paramagnetic terms.
2. Basis sets including at least two sets of polarization functions for the second row atoms are necessary to obtain satisfactory agreement with experiments. Larger basis sets are required for 14,15N, 17O, 19F, than for 13C, for 31P than for 29Si. d functions are mandatory for 31P shielding: without a d function on P, calculations are off by almost 1000 ppm.
3. Lone pair contributions have a dominating role, they seem to determine the orientation of σ(33S) for example, and the lone pair contributions of the pyridine-like N in azines are so strongly anisotropic that their anisotropy governs the direction of the principal components of σ(14,15N).
4. There is some indication in some molecules that correlation effects may be important, i.e., the gap between experiment and calculation remains large even when the basis sets are expanded. Multiple bonds are usually involved. Examples are NNO (center 1BN is too deshielded by about 50 ppm compared to experiment), SO2 (17O is too deshielded by 160-170 ppm), NF3 (19F is too shielded by 55 ppm), NSF (14N is too deshielded by about 700 ppm), H2CNN (end 14N is too deshielded by about 150 ppm), and pyridine-like nitrogens show discrepancies of more than 120 ppm. For 13C in olefinic systems the components perpendicular to the double bond and in the plane of the molecule are 10 to 60 ppm less shielded than experiment whereas the components perpendicular to the double bond and in the plane of the molecule are 10 to 60 ppm less shielded than experiment, whereas the components perpendicular to the double bond and the molecular plane are too shielded by about the same amount leading to a fortuitously good agreement of σ.
5. There is some indication that part of the nonrelativistic heavy atom effects, in replacement of F by Cl for example, is accounted for even without relativistic...
