Degeneracy, accidental

Most of the many modes of a-Ss have been assigned to their symmetry class. However, some strong infrared absorptions (V4 240 cm V5 470 cm ) and weak Raman lines (Vn 250 cm ) as well as signals originating from accidental degeneracies (e.g., Vi, V5, and Vy at around 475 cm ) were difficult to assign. 

Partial plots extracted from HMBC spectra recorded with the five different low-pass J filters are shown in Figure 7. Clearly, ambiguities may arise, particularly if accidental degeneracy in chemical shifts causes true long-range correlations and residual 1Jch correlations to overlap. 

B) Compare the expected and observed largest-to-smallest intensity ratios. Accidental degeneracies (or am/ line-width dependence) may cause the observed ratio to be bigger than expected. It is rarer (but not unknown) to find a smaller ratio than expected. 

In the solution of this equation, the energy is a function just of the quantum number ii. Thus, states with the same n but different l have the same energy. This is the so-called accidental degeneracy which implies that while the effective potential... 

The ex model has been elaborated in a number of ways. An electrostatic perturbation was added (33) to account for band splittings in the d-d spectra of tetragonal copper(II) ammine complexes where the simple AOM predicted accidental degeneracy the merits of this refinement will be discussed in 2.5.1. Another development has been the introduction of d—s and d—p mixing, which is apparently necessary to account for the d-d spectra of chlorocuprates(II) (34). This requires the additional parameters e, edpa and edpv. 

The Hamiltonians of the previous sections describe realistic vibrational spectra of linear triatomic molecules except when accidental degeneracies (resonances, cf. Section 3.3) occur. A particularly important case is that in which the bending overtone (02°0) is nearly degenerate with the stretching fundamental (10°0) of the same symmetry Fermi, 1929, resonance). This situation occurs when the coefficient in Eq. (4.67) is nearly equal to -A (Figure 4.13). The Majorana... 

Fig. 53 Rotational levels for a prolate symmetric top with A =4.55 and for an oblate symmetric top with B=4.5C. Note the accidental degeneracy of the 7=2, Af 2, and 7=4, K =0 prolate-top levels.

Thus, when allowance is made for these additional interactions, we find that the accidental degeneracies are removed. In the same way, we find that the energies of the and orbitals are... 

This band often appears as a doublet probably resulting from the accidental degeneracy of an overtone of another low-lying vibration mode (Fermi resonance). 7a, 6 8) The C—H stretching vibrations also undergo a high-frequency shift and appear at 3050 cm-1, a position generally characteristic of the methylene stretch in cyclopropyl systems.67)... 

---