Metal-centered point-dipole approximation

This contribution to the shift is quite difficult to evaluate, because in general the spin density distribution all over the space is not known. The approach to this problem should be stepwise. We first consider that the unpaired electron is localized on the metal nucleus in a paramagnetic metal complex. We refer to this as to the metal-centered point-dipole approximation. Surely this contribution will always be present and often dominant. Then we will discuss the consequences of relaxing this condition. Even in the metal-centered approximation several cases should be discussed. 

Let us now refer to a set of molecules with their jc, y and z axes iso-oriented in an idealized solid state (Fig. 2.5). If the external magnetic field is aligned with the z axis, the dipolar interaction energy between the nuclear magnetic moment and the electron magnetic moments, according to Eq. (1.4), is 

From the dipolar interaction energy, the dipolar shift can be obtained by evaluating from Eq. (2.16) A d,p between two states differing by A A// = 1 and dividing it by the nuclear Zeeman energy hyiBo (Appendix IV)  

This is indeed what is expected in 1H ENDOR spectroscopy in single crystals of isooriented molecules. By integration of Eq. (2.17) overall molecular orientations, the following equation is obtained (Appendix IV)  

This contribution to the shift is isotropic because it is already averaged out over all the orientations. Then it is similar to the contact shift and is called pseudocontact shift 5. In the literature it is also referred to as dipolar shift or isotropic dipolar shift. 

---

As anticipated in Sections 2.2.2 and 3.1, the unpaired electrons should not be considered as point-dipoles centered on the metal ion. They are at the least delocalized over the atomic orbitals of the metal ion itself. The effect of the deviation from the point-dipole approximation under these conditions is estimated to be negligible for nuclei already 3-4 A away [31]. Electron delocalization onto the ligands, however, may heavily affect the overall relaxation phenomena. In this case the experimental Rm may be higher than expected, and the ratios between the Rim values of different nuclei does not follow the sixth power of the ratios between metal to nucleus distances. In the case of hexaaqua metal complexes the point-dipole approximation provides shorter distances than observed in the solid state (Table 3.2) for both H and 170. This implies spin density delocalization on the oxygen atom. Ab initio calculations of R m have been performed for both H and 170 nuclei in a series of hexaaqua complexes (Table 3.2). The calculated metal nucleus distances in the assumption of a purely metal-centered dipolar relaxation mechanism are sizably smaller than the crystallographic values for 170, and the difference dramatically increases from 3d5 to 3d9 metal ions [32]. The differences for protons are quite smaller [32]. 

---