Hund’s coupling

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... 

Fig. 6. Ground state of the Cg0 molecule. The ground state is nonmagnetic because the Jahn-Teller effect overcomes Hund s coupling. There is a large contribution to the energy gap not only of S but also of U.

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. 

With the introduction of electronic angular momentum, we have to consider how the spin might be coupled to the rotational motion of the molecule. This question becomes even more important when electronic orbital angular momentum is involved. The various coupling schemes give rise to what are known as Hund s coupling cases they are discussed in detail in chapter 6, and many practical examples will be encountered elsewhere in this book. If only electron spin is involved, the important question is whether it is quantised in a space-fixed axis system, or molecule-fixed. In this section we confine ourselves to space quantisation, which corresponds to Hund s case (b). 

Coupling of electronic and rotational motion Hund s coupling cases... 

We have already seen in chapter 5 the importance of angular momenta in diatomic molecules. We now consider the various ways in which these angular momenta can be coupled in diatomic molecules, giving rise to Hund s coupling cases [57], As we will see many times elsewhere in this book, Hund s coupling cases are idealised situations which help us to understand the pattern of rotational levels and the resulting spectra. They are also central to the theory underlying the quantitative analysis of spectra and the consequent definition and determination of molecular parameters. 

As Lefebvre-Brion and Field [61] point out, the only coupling cases for which the electronic and nuclear motions can be separated are cases (a) and (c) consequently only in these cases can potential curves be defined unambiguously and accurately. However, as we have already pointed out, Hund s coupling cases are idealised descriptions and for most molecules the actual coupling corresponds to an intermediate situation. Moreover, the best description of the vector coupling often changes as the molecular rotation increases. In this section we consider the nature of the intermediate coupling schemes in more detail some of these will appear elsewhere in this book in connection with the observed spectra of specific molecules. 

In many instances in this book we shall discuss the transition from one Hund s coupling case to another, in connection with the spectra of specific molecules. We now summarise a particularly common example, the transition from case (a) to case (b). This is probably the most frequently encountered example it is discussed in considerable detail in chapter 9 so we will confine ourselves to a brief outline here. Figure 6.18, which reappears in chapter 9 in our description of the NO molecule, shows the correlation between case (a) levels on the left-hand side, and case (b) on the right-hand side. 

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... 

E.E.Nikitin and R.N.Zare, Correlation diagrams for Hund s coupling cases in diatomic molecules with high rotational angular momentum. Mol. Phys. 82, 85... 

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