Spin-allowed transitions intensities

In the next chapter we look at the intensities of d-d electronic transitions. We shall see that transitions between terms of the same spin-multiplicity are much more intense than those involving a change of spin. It is for this reason that our focus in the present chapter has been on the former. We have seen that for d d , d and configurations in octahedral or tetrahedral environments, there is only one so-called spin-allowed transition. For

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Consider now spin-allowed transitions. The parity and angular momentum selection rules forbid pure d d transitions. Once again the rule is absolute. It is our description of the wavefunctions that is at fault. Suppose we enquire about a d-d transition in a tetrahedral complex. It might be supposed that the parity rule is inoperative here, since the tetrahedron has no centre of inversion to which the d orbitals and the light operator can be symmetry classified. But, this is not at all true for two reasons, one being empirical (which is more of an observation than a reason) and one theoretical. The empirical reason is that if the parity rule were irrelevant, the intensities of d-d bands in tetrahedral molecules could be fully allowed and as strong as those we observe in dyes, for example. In fact, the d-d bands in tetrahedral species are perhaps two or three orders of magnitude weaker than many fully allowed transitions. 

CsNiCl3-type). Table 6 summarizes results on electronic spectra. The three spin-allowed transitions are usually observed and extensive vibrational contribution has been observed in single crystal spectra.120,121 Intense spin-forbidden transitions may also be observed122 due to exchange interactions in the solid phase. The diiodide123,124 and the complex halides121 show trigonal distortion. 

The decay time of this emission is very long, viz. some 5 ms [57,58]. There are two reasons for this. First the transition involved is spin forbidden [48, 51] secondly, the spin-allowed transition from which the spin-forbidden transition steals its intensity is unusually weak [58, 59],... 

There are experimental disadvantages that detract from the advantages just listed. The extinction coefficients may be so low that lines are obscured even by remote tails from spin-allowed transitions. The transition energies may span a wide range, requiring UV-visible, near-IR, and mid-IR instrumentation. Electronic lines may also be accompanied by many vibrational satellites whose intensities are high enough to make the distinction between electronic and vibronic lines very difficult. 

Taking into account all of the factors influencing intensities of crystal field spectra discussed so far, the following generalizations may be made. Transitions of 3d electrons within cations in octahedral coordination are expected to result in relatively weak absorption bands. Intensification occurs if the cation is not centrally located in its coordination site. In tetrahedral coordination, the intensities of crystal field transitions should be at least one-hundred times larger than those in octahedrally coordinated cations. Spin-forbidden transitions are usually about one-hundred times weaker than spin-allowed transitions in centrosymmetric, octahedrally coordinated cations, but become... 

The hue or vividness of colour may be correlated with the intensities of the absorption bands. Thus, Al-Fe epidotes, with relatively low molar extinction coefficients typical of spin-forbidden transitions within Fe3+ ions ( 3.7.2), exhibit pastel shades. The Al-Mn-Fe epidotes, however, display vivid colours correlating with high e values and originating from spin-allowed transitions within Mn3+ ions located in the very distorted acentric octahedral M3 site (fig. 

For Fe11 quite strong ligand fields are required to cause spin pairing, but a number of low-spin complexes such as [Fe(CN)6]4-, [Fe(CNR)6]2+, and [Fe(phen)3]2+ are known. These essentially diamagnetic complexes are often intensely colored due to charge transfer transitions which frequently obscure the two predicted spin allowed transitions 1A1 g — Tlg and lAig — T2g. 

In absorption spectra, the probability of a transition is expressed by its oscillator strength, /. While / is close to unity for allowed transitions, it is of the order of 10 -10 and 10 -10 respectively for spin-allowed transitions within the 3d and 4f configurations. Efficient conversion of a UV radiation to light (as needed in fluorescent lamps) requires strong absorption properties at the wavelength of incident photons. Figure 1 shows a comparison of the luminescence intensity for 4f- 5d (A/ = 1) and 4f- 4f (A/ = 0) excitations in the case of a terbium compound. 

The bands at 9380 and llOOOcm-i in the spectrum of a [NiPcc(BF)](BF4) single crystal are polarized perpendicular to the C3 pseudoaxis, which corresponds to the M2 —transitions. The resolution of these bands indicates that the spin-forbidden transition is of greater energy than the spin-allowed one. The spin-allowed transition is responsible for an increase in the intensity of the spin-forbidden transition. The nonpolarized shoulder at ca 20 500 cm-i was assigned to the forbidden M2 —and/or M2 transitions. The bands of the transitions to the Mi", M2", and E" states occur below 4000 cm-i and therefore were not localized [93]. 

In each multiplet structure, the data are separated according to the spin degeneracy spin quartet state on the right hand and spin doublet state on the left. The electron configuration of the Cr + ion is usually expressed as tP under atomic notation, and the quartet and doublet state correspond to the high spin state and low spin state, respectively. Since the ground. state Mz is a quartet state, the transitions to the quartet states are the spin-allowed transitions which have large intensities and broad bands in the absorption spectra, on the other hand, the transitions to the doublet states are the spin-restricted transitions which have more than one order smaller intensities and narrow line peaks which are not obvious in the experimental spectra in Fig. 3. 

E20.17 If [Co(NH3)6], a d complex, were high spin, the only spin-allowed transition possible would be Eg - l2g (refer to the d Tanabe-Sugano diagram). On the other hand, if it were low spin, several spin-allowed transitions are possible, including Tig - A g, Tjg Aig, Eg - A g, etc. The presence of two moderate-intensity bands in the visible/near-UV spectrum of [Co(NHj)6] suggests that it is low spin. The first two transitions listed above correspond to these two bands. The very weak band in the red corresponds to a spin-forbidden transition such as... 

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