Orbital motion

Initially, we neglect tenns depending on the electron spin and the nuclear spin / in the molecular Hamiltonian //. In this approximation, we can take the total angular momentum to be N(see (equation Al.4.1)) which results from the rotational motion of the nuclei and the orbital motion of the electrons. The components of. m the (X, Y, Z) axis system are given by ... 

Each electron in an atom has two possible kinds of angular momenta, one due to its orbital motion and the other to its spin motion. The magnitude of the orbital angular momentum vector for a single electron is given, as in Equation (1.44), by... 

The strength of coupling between the spin and orbital motions of the electrons, referred to a spin-orbit coupling, depends on the atom concerned. 

The spin of one electron can interact with (a) the spins of the other electrons, (b) its own orbital motion and (c) the orbital motions of the other electrons. This last is called spin-other-orbit interaction and is normally too small to be taken into account. Interactions (a) and (b) are more important and the methods of treating them involve two types of approximation representing two extremes of coupling. 

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... 

At this point the nomenclature used in XPS and AES should be explained. In XPS the spectroscopic notation is used, and in AES the X-ray notation. The two are equivalent, the different usage having arisen for historical reasons, but the differentiation is a convenient one. They are both based on the so-called j-j coupling scheme describing the orbital motion of an electron around an atomic nucleus, in which the... 

The first term on the right-hand side arises from external eleetrie fields. The seeond (B) term arises from external magnetie induetions interaeting with elee-tronie orbital motion. The SL term arises from eleetron spin-orbital motion interaetions. The Z term arises from the Zeeman interaetion between eleetron spin and the external eleetrie field. Hss arises from eleetron spin-eleetron spin interaetions and includes all hyperfine terms arising from nuclear spins. 

Hfi includes a nuclear Zeeman term, a nuclear dipole-dipole term, an electron-nuclear dipole term and a term describing the interaction between the nuclear dipole and the electron orbital motion. 

In other cases, discussed below, the lowest electron-pair-bond structure and the lowest ionic-bond structure do not have the same multiplicity, so that (when the interaction of electron spin and orbital motion is neglected) these two states cannot be combined, and a knowledge of the multiplicity of the normal state of the molecule or complex ion permits a definite statement as to the bond type to be made. 

An anisotropic contribution B from the orbital motion of valence electrons with the quantum number L for the total orbital moment ... 

In addition to the magnetism due to the electron spin, the magnetism of the orbital motion has to be considered. For this purpose the magnetic quantum numbers of the electrons are added to a resultant orbital quantum number L = beginning with the highest magnetic quantum number. For example ... 

Finally, the magnetic moments resulting from the spin and the orbital motion interact. This spin-orbit coupling is taken into account by the total angular momentum quantum number J (Russel-Saunders coupling) ... 

The spin-orbit Hamiltonian (HB0) requires some explanation. The energy of interaction between the magnetic moment M and the magnetic field caused by the orbital motion of an electron can be derived as(134)... 

As a result of orbital motion, an additional magnetic effect is produced, and taking it into account leads to the total magnetic moment for one electron,... 

The first application of quantum theory to a problem in chemistry was to account for the emission spectrum of hydrogen and at the same time explain the stability of the nuclear atom, which seemed to require accelerated electrons in orbital motion. This planetary model is rendered unstable by continuous radiation of energy. The Bohr postulate that electronic angular momentum should be quantized in order to stabilize unique orbits solved both problems in principle. The Bohr condition requires that... 

There are two contributions to the magnetic dipole moment of an electron bound to an atomic nucleus, which, in semiclassical models, are attributed to orbital motion, represented by quantum number l, and spin, represented by quantum number, v. The orbital and spin components are linked, or coupled, on isolated atoms or ions to give an overall magnetic dipole moment for the atom. The total magnetic dipole moment of the atom is given by... 

An interesting correlation exists between the transient signal and the pressure in the ICR cell. [197,201] In a perfect vacuum, the orbiting motion would solely be... 

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