Approximate Calculations and Models

One of the most useful approximations of nuclear shielding is that for the diamagnetic term by Flygare et With the origin at the nucleus N, a can be written as a free atom contribution plus the contribution of the electronic point charges centered at the other nuclei N  

The correction terms allow for the displacement of the point charges from the centers of the other N nuclei and for their spatial extension. They need to be included in the individual components, and can be summed up for a molecule from the tabulated atomic dipole contributions. The corrections nearly cancel in the sum over the components and can be ignored in calculations of the isotropic average j. Thus, 

The success of this approximation, which allows the calculation of (s for molecules without knowledge of the wave functions, continues to be demonstrated as more accurate calculations of o (including electron correlation) become available. 

The atom-in-a-molecule approach is a one-center approximation to the shielding tensor. The calculation is restricted to terms centered on the nucleus in question, which is taken to be the origin. The expression for the shielding tensor components is then unsuitable for accurate prediction of individual shieldings, but is simple enough to be used for discussion of general empirical trends  

Here P, and D, represent the degree of imbalance of valence electrons in the p and d orbitals on atom 4. P, may be written in terms of orbital populations or in terms of qualitative constants such as ionicity of the bond, pi bond order, degree of s character  

---

We have seen (in Section 1.1) Ramsey s formulation for the different terms contributing to the coupling constant. In this section we will consider the computational schemes used in the application of equations (8)-(12) to specific systems, the relative importance of the Fermi contact, spin dipolar, and orbital terms to the isotropic coupling constant, relativistic effects, and approximate calculations and models. Where possible we will note the theoretical basis for the general trends enumerated in the previous sections. 

---