Magnetic field orbiting electrons

In the absence of an external magnetic field, orbitally nondegenerate levels with spin multiplicity greater than 2 split due to direct electron spin—spin coupling (in first order) and spin—orbit coupling (in second and higher orders of perturbation theory). This phenomenon is called zero-field splitting (ZFS). The SH that describes this phenomenon can be formulated in... 

When one electron is assigned to an orbital in an atom, the electron can spin in either direction. In a magnetic field, this electron acts as a micromagnet and aligns with the magnetic field. An element with an unpaired electron is usually magnetic. 

On the other hand, magnetic fields that are very strong can be applied. In the presence of a uniform magnetic field, free electrons are deflected into circular or helical orbits, with a characteristic frequency of (O = eHIme, called the cyclotron frequency. In this formula, is given in radians per second if e is written as... 

The chemical shift is due to the orbital effects of the nearby electrons. When an atom or a molecule is placed in a static magnetic field, the electrons produce a small auxiliary field the direction and the magnitude of which depend in a complex way on the electronic structure of the atom or molecule. Because the ability of the electrons to shield the nucleus depends in part on the direction of the magnetic field with respect to the electronic orbits, the chemical shift is a tensor quantity. The shift observed in liquids as well as that in MAS experiments are motional averages of the tensor components. 

The two primary causes of shielding by electrons are diamagnetism and temperature-independent paramagnetism (TIP). Diamagnetism arises from the slight unpairing of electron orbits under the influence of the magnetic field. This always occurs so as to oppose the field and was first analysed by Lamb [7]. A simplified version of his fomuila. 

The coupling of S to the intemuclear axis is caused not by the electrostatic field, which has no effect on it, but by the magnetic field along the axis due to the orbital motion of the electrons. Figure 7.16(a) shows that the component of S along the intemuclear axis is Ffi. The quantum number F is analogous to Mg in an atom and can take the values... 

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