Splitting of the energy

Of the NMR-active nuclei around tluee-quarters have / > 1 so that the quadnipole interaction can affect their spectra. The quadnipole inter action can be significant relative to the Zeeman splitting. The splitting of the energy levels by the quadnipole interaction alone gives rise to pure nuclear quadnipole resonance (NQR) spectroscopy. This chapter will only deal with the case when the quadnipole interaction can be regarded as simply a perturbation of the Zeeman levels. 

This splitting of the energy levels by the magnetic field leads to the splitting of the lines in the atomic spectrum. The wave number v of the spectral line corresponding to a transition between the state /i mi) and the state nihm2) is... 

Figure S6.2 Crystal field splitting of the energy of five d orbitals when the ion is placed in a site with octahedral symmetry. The magnitude of the splitting, A or 10Dg, depends upon the size of the octahedral site and the charges on the surrounding ions.

In the presence of an external magnetic flux density B the rotational magnetic moment m, equation (1), causes a splitting of the energy levels... 

The theory of the atomic energy levels developed in the previous chapter is incomplete, since we systematically ignored the nuclear spin which leads to an additional splitting of the energy levels. This effect will be the subject of our discussion below. 

Fig. 6.118. The splitting of the energy into two energy states when two atoms approach each other.

Splitting of the energy levels. Both an octahedral complex (two electrons in orbitals) and a tetrahedral complex (four electrons in orbitals) are less favorable in this case. 

In 11-2 we showed how all AOs can be classified according to the irreducible representations of the different molecular point groups. Therefore, if we consult Table 11-2.2, we can determine the splitting of the energy level of a single electron for any particular perturbing environment. 

The above discussion has emphasized that the splitting of the energies of the d-orbitals is dominated by the effects of the formal octahedral or tetrahedral symmetry of the ligand donor atom environment. This dominance is also present for coordination stereochemistries approximating to these symmetries. However, the effects of departure from these cubic symmetries are not negligible, and may be dominant for stereochemistries which do not even approximate to one of the cubic ones, e.g. a square-planar coordination geometry. 

The effect of using relativistic rather than nonrelativistic quantum mechanics to obtain the predicted atomic orbitals is threefold (a) a contraction and stabilization of the s, /2 and p1 /2 shells, (b) the splitting of the energy levels due to the spin-orbit coupling, and (c) an expansion (and destabilization) of the outer d and all f shells. These effects are of approximately equal magnitude and all increase as Z2. In Figure 15.14, we show the magnitude of these effects for uranium. The chemical... 

In a non-relativistic approximation the usual fine structure (splitting) of the energy terms is considered as a perturbation whereas the hyperfine splitting - as an even smaller perturbation, and they both are calculated as matrix elements of the corresponding operators with respect to the zero-order wave functions. 

Ammonia was the first molecule for which the effect of the molecular inversion was studied experimentally and theoretically. Inversion in ammonia was subsequently found to be so important that this molecule played an important role in the history of molecular spectroscopy. Let us recall, for example that microwave spectroscopy started its era with the measurements " of the frequencies of transitions between the energy levels in the ground vibronic state of NH3 split by the inversion effect. Furthermore, the first proposal and realization of a molecular beam maser in 1955 was based on the inversion splittings of the energy levels in NH3. The Nobel Prize which Townes, Basov and Prochorov were awarded in 1964 clearly shows how important this discovery was. Another example of the role which the inversion of ammonia played in the extension of human knowledge is the discovery of NH3 in the interstellar space by Cheung and his co-workers in 1968, by measuring the... 

The infrared and especially microwave spectra of methylamine and its deuterated species have been studied in considerable detail [see paper for further references]. The potential barriers to internal rotation and inversion are both relatively high [Table 6 internal rotation barrier is 684 cm in the ground state of CH3NH2] but the splittings of the energy levels are measurable. 

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