Electron—nuclei interaction

The electron-nucleus interaction, or Fermi contact term, arises from ... 

The sole presence of an electron spin causes nuclear relaxation. The correlation time for the electron nucleus interaction is presented as well as equations valid for dipolar and contact interaction. To do so, electron relaxation mechanisms need to be quickly reviewed. All the subtleties of nuclear relaxation enhancements are presented pictorially and quantitatively. 

Relaxation measurements provide a wealth of information both on the extent of the interaction between the resonating nuclei and the unpaired electrons, and on the time dependence of the parameters associated with the interaction. Whereas the dipolar coupling depends on the electron-nucleus distance, and therefore contains structural information, the contact contribution is related to the unpaired spin density on the various resonating nuclei and therefore to the topology (through chemical bonds) and the overall electronic structure of the molecule. The time-dependent phenomena associated with electron-nucleus interactions are related to the molecular system, and to the lifetimes of different chemical situations, for the resonating nucleus. Obtaining either structural or dynamic information, however, is only possible if an in-depth analysis of a series of experimental results provides sufficient data to characterize the system within the theoretical framework discussed in this chapter. 

Two-dimensional (2D) spectroscopy is used to obtain some kind of correlation between two nuclear spins 7 and J, for instance through scalar or dipolar connectivities, or to improve resolution in crowded regions of spectra. The parameters to obtain 2D spectra are nowadays well optimized for paramagnetic molecules, and useful information is obtained as long as the conditions dictated by the correlation time for the electron-nucleus interaction are not too severe. Sometimes care has to be taken to avoid that the fast return to thermal equilibrium of nuclei wipes out the effects of the intemuclear interactions that are sought through 2D spectroscopy. 

For these NMR experiments, the general theory of NMR must be understood and, on top of this, the theory of the electron-nucleus interaction and its consequences for the NMR parameters. Therefore, the field of NMR of paramagnetic molecules has its own niche in the entire scientific panorama. 

The Bom-Oppenheimer principle (Bom-Oppenheimer approximation) [1] says that the electrons in a molecule move so much faster than the nuclei that the two kinds of motion are independent the electrons see the nuclei as being stationary, and so each electron doesn t have to adjust its motion to maintain a minimized electron-nucleus interaction energy. Thus we can calculate the purely electronic energy of a molecule, then the intemuclear repulsion energy, and add the separate energies to get the total molecular energy. 

Helium is not the only three body system under study, but it is likely the most complicated one. The electron-electron interaction is comparable with the electron-nucleus interaction and cannot be considered as a perturbation. The situation is different with helium-like (and lithium-like) ions, where the electron-electron interaction is as small as 1 jZ with respect to the interaction of an electron and the nucleus. 

Relativistic and QED terms of order a4 a.u. and a5 a.u. are also important in the comparison with experiment. Until recently, a complete theory for these terms did not exist, except for the spin-dependent parts of 0(a4) and O(o5) a.u. discussed below in Sect. 7.1. For the spin-independent part, the dominant term comes from the one-loop QED shift due to the electron-nucleus interaction of... 

One- [6] and two-loop [7,8,9] radiative corrections to electron-nucleus interaction give rise to the following energy shifts, respectively ... 

Similar to ISS, except the main focus is on depth-profiling and composition. The momentum transfer in back-scattering collisions between nuclei is used to identify the nuclear masses in the sample, and the smaller, gradual momentum-loss of the incident nucleus through electron-nucleus interactions provides depth-profile information. 

The formalism developed so far is adequate whenever the motion of the atomic nuclei can be neglected. Then the electron-nucleus interaction only enters as a static contribution to the potential r(r, t) in Eq. (41). This is a good approximation for atoms in strong laser fields above the infrared frequency regime. When the nuclei are allowed to move, the nuclear motion couples dynamically to the electronic motion and the situation becomes more complicated. 

Clearly, a complete numerical solution of the coupled KS equations (67,68) for electrons and nuclei will be rather involved. Usually only the valence electrons need to be treated dynamically. The core electrons can be taken into account approximately by replacing the electron-nucleus interaction (65) by suitable pseudopotentials and by replacing the nuclear Coulomb potential in Eq. (64) by the appropriate ionic Coulomb potential [38]. This procedure reduces the number of electronic KS equations and hence the numerical effort considerably. 

If the symmetry of the site is lower than cubic the full tensor form of the electron-nucleus interaction needs to be used, so that in addition to an isotropic term there is an anisotropic contribution. If in the PAS of the Knight shift tensor the components of the tensor are Kx, Ky and Kz, then in the laboratory frame with its orientation in the frame defined by Bo described by the Euler angles 0 and [Pg.49]

Second, the Hamiltonian operator for a relativistic many-body system does not have the simple, well-known form of that for the non-relativistic formulation, i.e. a sum of a sum of one-electron operators, describing the electronic kinetic energy and the electron-nucleus interactions, and a sum of two-electron terms associated with the Coulomb repulsion between the electrons. The relativistic many-electron Hamiltonian cannot be written in closed form it may be derived perturbatively from quantum electrodynamics.46... 

Recent years have seen a growing interest in the simultaneous description of electronic and nuclear motion. The nonadiabatic coupling between the electronic and nuclear motion manifest itself in numerous and rather diverse phenomena. An independent particle model can be formulated in which the averaged interactions between the electrons, between the electrons and the nuclei and between the nuclei are described quantum mechanically. Multicomponent MBPT can then be used to formulate the corresponding correlation problem accounting for electron-electron interactions, electron-nucleus interactions and nucleus-nucleus interactions in either algebraic or diagrammatic terms. 

Here, p is the electron moment, y the magnetogyric ratio of the species of nucleus being observed ( H,13C, or possibly 19 F) cos is the angular precessional frequency of the electron in the field employed, and rc the characteristic average time of the modulation of the electron-nucleus interaction r is the distance from the metal to the observed nucleus i. When the ion is tightly bound to the protein, rc becomes the rotational correlation time of the protein, usually of the order of 10"8 s. 

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