Russell-Saunders

LS coupling Russell-Saunders coupling. LSD Lysergic acid diethylamide. An hallucinogen. 

A second approximation neglects coupling between the spin of an electron and its orbital momentum but assumes that coupling between orbital momenta is strong and that between spin momenta relatively weak but appreciable. This represents the opposite extreme to the 77-coupling approximation. It is known as the Russell-Saunders coupling approximation and serves as a useful basis for describing most states of most atoms and is the only one we shall consider in detail. 

Figure 7.4 Russell-Saunders coupling of (a) orbital angular momenta li and I2, (b) spin angular momenta Sj and 2 and (c) total orbital and total spin angular momenta, L and S, of sip and a d electron...

However complex the atom, we can use the Russell-Saunders coupling approximation (or jj coupling, if necessary) to derive the states that arise from any configuration. The four general selection mles that apply to transitions between these states are as follows. 

Assume that the Russell-Saunders coupling approximation applies to both configurations. Answer. The ground electron configuration of zirconium (Z = 40) is (see Table 7.1)... 

In the case of atoms, deriving states from configurations, in the Russell-Saunders approximation (Section 7.1.2.3), simply involved juggling with the available quantum numbers. In diatomic molecules we have seen already that some symmetry properties must be included, in addition to the available quantum numbers, in a discussion of selection rules. 

The ground configuration of Ne is ls 2s 2p, giving a sfafe. The excifed configurations give rise fo sfafes fo which fhe Russell-Saunders approximation does nof apply. Nevertheless, any. .. 2p ns or. .. 2p np configuration, wifh n > 2, gives rise fo four or fen sfafes, respectively, as would be fhe case in fhe Russell-Saunders approximation (see... 

Table I. g-values and Ueff of ground states In Russell-Saunders and intermediate coupling for different configurations.

Due to the intermediate coupling the sign of the crystal field matrix element 6 is reversed compared to the pure Russell-Saunders state. Thus for 8-fold cubic coordination a F7 ground state was found. From EPR measurements on Pu3"1" diluted in fluorite host lattices, a magnetic moment at T=0 K can be calculated, ranging from li ff = 1.333 (in Ce02) to y ff = 0.942 (in SrCl2) (24,... 

Hund37 in 1926 and of oxygen and nitric oxide by Van Vleck38 in 1928 were triumphs of the theory of spectra. The magnetic moment of an atom or monatomic ion with Russell-Saunders coupling of the quantum vectors is... 

The bond diagrams provide an obvious simple method of determining the allowed spectral terms for equivalent electrons with Russell-Saunders coupling, which may be convenient for the reason that it separates states of different multiplicity at the start. 

In tier (1) of the diagram (for the electronic structure of iron(III)), only the total energy of the five metal valence electrons in the potential of the nucleus is considered. Electron-electron repulsion in tier (2) yields the free-ion terms (Russel-Saunders terms) that are usually labeled by term ° symbols (The numbers given in brackets at the energy states indicate the spin- and orbital-multiplicities of these states.)... 

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) ... 

In Equation 1.5, A is the spin-orbit coupling within a given Russell-Saunders multiplet, which is related to the spin-orbit coupling constant of the ion, C, by the relation A = f/2.S, the + sign applying for n <7 and the - sign for n > 7 [ 15]. The effect of spin-orbit coupling is to split the terms in multiplets with same L,... 

The general magnetic properties of ionic and molecular actinide compounds have been reviewed recently [15], and only the briefest of overviews is given here. The 5f3 ions U5+ and Np6+ have 2F5/2 ground multiplets in the Russell-Saunders... 

Figure 10.8 Room temperature electronic absorption spectrum recorded on a THF solution of 6. Bands are marked by the nominal Russell-Saunders multiplet to which the excitation occurs. (Adapted from Ref. [34], Copyright (2011) Nature Publishing Group.)...

For diatomic molecules, there is coupling of spin and orbital angular momenta by a coupling scheme that is similar to the Russell-Saunders procedure described for atoms. When the electrons are in a specific molecular orbital, they have the same orbital angular momentum as designated by the m value. As in the case of atoms, the m value depends on the type of orbital. When the internuclear axis is the z-axis, the orbitals that form a bonds (which are symmetric around the internuclear axis) are the s, pz, and dzi orbitals. Those which form 7r bonds are the px, p, dlz, and dyi orbitals. The cip-y2 an(i dxy can overlap in a "sideways" fashion with one stacked above the other, and the bond would be a 8 bond. For these types of molecular orbitals, the corresponding m values are... 

Pj and Po = statistical weights of the respective states and are obtainable from Russell-Saunders coupling,... 

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