Hund coupling cases

When the molecule is not in a S state there is an interaction between the rotation of the molecule and S and/or L, and the details of coupling the angular momenta are involved. Most nonsinglet molecules with electronic orbital angular momentum A = 0 obey Hund s case (b) coupling. In Case (b), the electronic orbital angular momentum combines with the nuclear orbital angular... 

Figure 7.16 (a) Hund s case (a) and (b) Hund s case (c) coupling of orbital and electron spin... 

Application of the symmetry correlation scheme to reaction (12) is summarized in Table 4 where N is the Himd s coupling case (b) rotational quantum number for O2 and - 5 is the difference of the Hund s coupling case (a) quantum numbers of total angular momentum and electron spin (5 = 1/2) angular momentum, respectively. To consider the high-symmetry isotopomer system first, the results in Table 4 indicate that only odd / collisions - 5 = odd) with 2 can lead... 

I 2.1 Rotational Energy Levels of Diatomic Molecules, K I 2.2 Vibrational Energy Levels of Diatomic Molecules, 10 I 2.3 Electronic Stales of Diatomic Molecules, 11 I 2.4 Coupling of Rotation and Electronic Motion in Diatomic Molecules Hund s Coupling Cases, 12 1-3 Quantum States of Polyatomic Molecules, 14... 

Recent work on these systems includes Cl2, Br2, and several of the interhalogen molecules. The results can be summarized in terms of the potential curves in Figs. 3 and 4. The excited electronic states of the halogens are described in Hund s case c coupling, so that spin is not a good quantum number, and reasonably strong... 

These considerations are strictly applicable, however, only if the sym-metry plane is well defined, which for OH( n) as an example of Hund s coupling case (b) is valid only for large rotational quantum numbers j. In a more refined treatment (Andresen and Rothe 1985 Bigio and Grant 1987b) one expands the true A-doublet states in terms of the idealized wavefunctions depicted in Figure 11.3 and obtains for the electronic densities... 

In the more general case S 0 and the molecular angular momenta can be coupled in various ways. It is of primary importance to ascertain to what extent the interaction of the spin momentum S with the orbital momentum L is comparable to the rotation of the molecule, as well as to the interaction of each of the momenta L and S with the internuclear axis. An attempt to establish a hierarchy of interactions yields a number of possible, certainly idealized, coupling cases between angular momenta, first considered by Hund and known as Hund s coupling cases. Here we will discuss the three basic (out of five) cases of coupling of momenta in a linear molecule. 

Let the diatomic (or linear) molecule satisfy the conditions for the Hund s case (a) coupling scheme (see Section 1.2, Fig. 1.3(a)), where the electronic orbital and spin angular momenta are coupled with the internuclear axis. The magnetic moment which is directed along the internuclear axis and corresponds to the projection Cl of the total angular momentum J upon the internuclear axis, has the value... 

Fig. 4.24. Vector scheme for the interaction of momenta of a diatomic molecule in a magnetic field in Hund s case (a) coupling scheme. The frequency u)q of nutation of fl and (j,q around J considerably exceeds the frequency u>j of the precession of J around B.

The case of intermediate coupling of momenta (between Hund s cases (a) and (6)), as well as that of breaking weak field approximation axe discussed in [294]. The molecular (/-factors for Hund s case (c) coupling are discussed in [92, 364]. 

Typically, Hund s case (b)161 applies to molecules with A = 0, to which spin-orbit effects do not contribute in first order. For states with a nonzero A value and a rotational parameter Bv of the same order-of-magnitdue as the spin-orbit parameter Av, rotational coupling cannot be neglected. In this case, it... 

The strong coupling limit, Hund s case (c)161, cannot be dealt with in first order. Rather, it requires the inclusion of higher-order (at least second-order) spin-orbit coupling in the calculations. 

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