Hund coupling mechanism

The mechanism by which spin-orbit coupling can impact molecular bonding becomes more obvious if the wave function is reformulated in terms of molecular spinors (Hund s case c coupling). One should keep in mind, however, that even for the heaviest elements the angular momentum coupling is generally intermediate between case a and case c, and the following picture is therefore an oversimplification. 

In the case of the mixed-valence manganites with the perovskite stracture, Zener s double-exchange (DE) mechanism has been used to explain the CMR effect (Zener, 1951c). In this model, a strong Hund s coupling is presumed to exist between the itinerant... 

To summarize, much more works, with taking various aspects into account, are needed to obtain a full understanding of the mechanism of superconductivity in sCeo. Even in the E (8> e and Tiu <8> hg model systems, setting aside the fullerides, the JT effect on superconductivity, especially in the presence of the Coulomb effect including the Hund s-rule coupling, is not known well. To some extent we shall address this issue in the model JT systems in Sect. 4 of this article. 

Hund s third rule is a relativistic correction to the first two rules, introducing a splitting of the terms given by the previous rules. The energy operator (Hamiltonian) commutes with the square of the total angular momentum J = L - - S, and therefore, the energy levels depend rather on the total momentum Jp = J J + This means that they depend on the mumal orientation of L and S (this is a relativistic effect due to the spin-orbit coupling in the Hamiltonian). The vectors L and S add in quantum mechanics in a specific way (see... 

Fig. 12.17. Is the proton-proton coupling constant through two bonds (H-C-H), i.e., Juu positive or negative Recall that Jhh >0 (shown in Fig. 12.14a), where the induction mechanism is described. The interaction through two bonds depends on what happens at the central carbon atom are the spins of the two electrons there (one from each bond C-H) parallel or antiparallel Hund s rule suggests they prefer to be parallel This means that the situation with the two proton spins parallel is more energetically favorable, and this means JhH < 0. This rule of thumb may fail when the carbon atom participates in multiple bonds, as in ethylene. For more information, see the section Fwm the Research Fnmt," later in this drapter.

Fig. 13.16 The polarization mechanism for /hh spin-spin coupling. The spin information is transmitted from one bond to the next by a version of the mechanism that accoimts for the lower energy of electrons with parallel spins in different atomic orbitals (Hund s rule of maximum multiplicity). In this case, 7 < 0, corresponding to a lower energy when the nuclear spins are paraUeL...

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