Allowed and forbidden lines

E.2.9 An ESEEM signal occurs in the presence of an anisotropic hyperfine interaction that is of a magnitude comparable to the nuclear Zeeman energy. The schematic ESR spectrum in the left part of the figure below contains allowed and forbidden lines due to a mixing of nuclear states. For an / = Vi nucleus the ESEEM amplitude is proportional to A = sin a/Z cos of/2 = 7o /, where a is the angle between the effective fields acting on the nucleus for ms = /2 and lo and li are the amplitudes of the outer and inner ESR lines. 

Fig. 4.17. The spectrum for I = Yi is composed of an inner and an outer doublet as in Fig. 4.18. The inner doublet of the spectrum in Fig. 4.18 is in this case the weakest and these lines are sometimes referred to as forbidden . In other cases like for the F hfc of the MnFe complex in Fig. 4.16 the allowed and forbidden lines can have comparable intensities, making the distinction immaterial.

In this system, by superimposing probable conformers of 2-amino-carboxylic acids - as in Fig. 5 - one can indicate positions allowed and forbidden for sweet compounds (Fig.9). Even if there is only information regarding one forbidden position on the +z side and the dotted line is therefore hypothetical, it is still clearly recognizable that the forbidden positions as a whole are not arranged symmetrically to the x-axis. 

At first glance, it may appear that radiation could be absorbed and emitted by atoms between any pair of the states shown in Figure 24-20, but in fact only certain transitions are allowed, while others are forbidden. The transitions that aie allowed and forbidden to produce lines in the atomic spectra of the elements are determined by the laws of quantum mechanics in what are called selection rules. These rules are beyond the scope of our discussion. ... 

Energy level schemes are very instructive representations for describing the line splitting of simple spin systems such as AX or AMX spin systems and for visualizing the quantum mechanical allowed and forbidden transitions. The relative population of each state can be calculated and the signal enhancement by polarization transfer using a double-quantum, forbidden transition calculated. 

Figure 14 Variation of similarity index g(cp) (standard of the McWeeny type) with the systematic change of reaction coordinate q> for the allowed and forbidden 2+2 ethene dimerization. The Ml line corresponds to forbidden and the dashed line to allowed reaction mechanisms.

Considering the resolution of the nuclear frequency spectrum, this two-pulse echo experiment is not optimal. The nuclear frequencies are here measured as differences of frequencies of the ESR transitions, so that the line widths correspond to those of ESR transitions. The nuclear transitions have longer transverse relaxation times Tin and thus smaller line widths. In fact, if the second mw pulse is changed from a n pulse to a Ji/2 pulse, coherence is transferred to nuclear transitions instead of forbidden electron transitions. This coherence then evolves for a variable time T and thus acquires phase v r or vpT. Nuclear coherence cannot be detected directly, but can be transferred back to allowed and forbidden electron coherence by another nil pulse. The sequence (jt/2)-x-(Jt/2)-r-(jt/2)-x generates a stimulated echo, whose envelope as a function of T is modulated with the two nuclear frequencies v and vp. The combination frequencies v+ and v are not observed. The modulation depth is also 8 211. The lack of combination lines simplifies the spectrum and the narrower lines lead to better resolution. There is also, however, a disadvantage of this three-pnlse ESEEM experiment. Depending on interpulse delay x the experiment features blind spots. Thus it needs to be repeated at several x values. 

Experimentally, free-ion spectra (both neutral and ionic species) are usually observed in emission, and the energy level structure is deduced from coincidences of energy differences of pairs of spectral lines, subject to verification by isotope shift, hyperfine structure and magnetic gf-factor tests. In condensed phases, spectra are more commonly measured in absorption. Relative intensities associated with parity-allowed and forbidden transitions are reflected in the nature of two processes transitions in which the initial and final states belong to electronic configurations of different parity (parity-allowed transitions, e.g. 5f - 5f 6d) and those in which both states belong to the same configuration (parity-forbidden transitions, e.g. 5f 5f ). The latter are weak and sharp. The... 

The spatial localization of H atoms in H2 and HD crystals found from analysis of the hyperfine structure of the EPR spectrum, is caused by the interaction of the uncoupled electron with the matrix protons [Miyazaki 1991 Miyazaki et al. 1991]. The mean distance between an H atom and protons of the nearest molecules was inferred from the ratio of line intensities for the allowed (without change in the nuclear spin projections. Am = 0) and forbidden (Am = 1) transitions. It equals 3.6-4.0 A and 2.3 A for the H2 and HD crystals respectively. It follows from comparison of these distances with the parameters of the hep lattice of H2 that the H atoms in the H2 crystal replace the molecules in the lattice nodes, while in the HD crystal they occupy the octahedral positions. 

The allowed transitions occur between levels Ex and E3, and between levels Ei and E4 as indicated by the dashed lines. These transitions are governed by selection rules which require that the electron spin changes by one unit while the nuclear spin remains unchanged. Under certain rather restricted conditions these selection rules no longer apply and forbidden transitions occur. 

Induced spectra may appear at frequencies corresponding to molecular transitions that may be allowed or forbidden in the isolated molecules. Induced spectra associated with allowed transitions can sometimes be studied but this is not always easy in the presence of strong, allowed lines. Induced spectra of forbidden transitions (A = 0 in Eq. 1.2), on the other hand, are quite common and are generally easy to recognize. 

So far, this discussion of selection rules has considered only the electronic component of the transition. For molecular species, vibrational and rotational structure is possible in the spectrum, although for complex molecules, especially in condensed phases where collisional line broadening is important, the rotational lines, and sometimes the vibrational bands, may be too close to be resolved. Where the structure exists, however, certain transitions may be allowed or forbidden by vibrational or rotational selection rules. Such rules once again use the Born-Oppenheimer approximation, and assume that the wavefunctions for the individual modes may be separated. Quite apart from the symmetry-related selection rules, there is one further very important factor that determines the intensity of individual vibrational bands in electronic transitions, and that is the geometries of the two electronic states concerned. Relative intensities of different vibrational components of an electronic transition are of importance in connection with both absorption and emission processes. The populations of the vibrational levels obviously affect the relative intensities. In addition, electronic transitions between given vibrational levels in upper and lower states have a specific probability, determined in part... 

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