Spin multiplicity changes

The interconversion between different spin states is closely related to the intersystem crossing process in excited states of transition-metal complexes. Hence, much of the interest in the rates of spin-state transitions arises from their relevance to a better understanding of intersystem crossing phenomena. The spin-state change can alternatively be described as an intramolecular electron transfer reaction [34], Therefore, rates of spin-state transitions may be employed to assess the effect of spin multiplicity changes on electron transfer rates. These aspects have been covered in some detail elsewhere [30]. 

Both mechanisms have in common a spin-multiplicity change however, the fundamental difference between them is that in the diradical mechanism (Eq. 66), the intersystem-crossing step is reversible, while in the concerted mechanism (Eq. 67) it is irreversible. Thus, the classical mechanistic dilemma of distinguishing between normal spin-conserved diradical and concerted reactions, particularly [2+2]-cycloaddition, is still further complicated by the fact that in the dioxetane retrocyclization distinct spin-multiplicity changes are involved. The theoretical and experimental work on this challenging problem will be briefly discussed. 

For simple outer-sphere self-exchange reactions of transition-metal complexes in both aqueous and polar organic solvents, is dominated by AVj and hence is expected to be negative, regardless of whether electron transfer is fully adiabatic. In cases in which this expectation is not realized, there is usually an identifiable departure from a simple outer-sphere mechanism attributable to inner-sphere pathways, cationic catalysis of anion-anion electron transfer, or structural distortions associated with spin multiplicity changes. Thus, AV can serve as a mechanistic criterion. 

To fill out Table 8-1, change the element symbols in the last line to Li, Be, or B and designate the charge and spin multiplicities as 1 1, 2 1, 3 1 in that order. In line 5, the first number is the single positive charge and the second number is the spin multiplicity, 1 for paired electronic spins and 2 for an unpaired election. A... 

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

[Pg.58]

Regardless of the nature of the space parts, Q vanishes if V spin V spm- If Q vanishes, so does /. Thus we have the so-called spin-selection rule which denies the possibility of an electronic transition between states of different spin-multiplicity and we write AS = 0 for spin-allowed transitions. Expressed in different words, transitions between states of different spin are not allowed because light has no spin properties and cannot, therefore, change the spin. 

Within its orbit, which has some of the characteristics of a molecular orbital because it is shared with electrons on the surrounding atoms, the electron has two possible spin multiplicity states. These have different energies, and because of the spin-multiplicity rule, when an (N-V) center emits a photon, the transition is allowed from one of these and forbidden from the other. Moreover, the electron can be flipped from one state to another by using low-energy radio-frequency irradiation. Irradiation with an appropriate laser wavelength will excite the electron and as it returns to the ground state will emit fluorescent radiation. The intensity of the emitted photon beam will depend upon the spin state, which can be changed at will by radio-frequency input. These color centers are under active exploration for use as components for the realization of quantum computers. 

In this way, the SP-DFT using p,ps as variables set provides global and local reactivity indexes that give us the possibility to study processes that involve changes in the number of electrons, multiplicity (changes in the spin number), or both. Some examples are discussed in Section 10.4. 

Spin selection rule The spin selection rule, AS = 0, specifies that there should be no change in the spin multiplicity. Weak spin-forbidden bands may occur when spin-orbit coupling is possible. Spin-forbidden transitions are more intense in complexes of heavy atoms as these lead to a larger spin-orbit coupling. 

The nature of the emission by these three lanthanide ions is phosphorescence, since the emission of light is accompanied by a change in spin multiplicity. For example, the emission by the Eu3+ cation involves a change in the spin multiplicity from 5 to 7 on going from the excited state to the ground state (5Eu —> 7Eu). 

One expects the impact of the electronic matrix element, eqs 1 and 2, on electron-transfer reactions to be manifested in a variation in the reaction rate constant with (1) donor-acceptor separation (2) changes in spin multiplicity between reactants and products (3) differences in donor and acceptor orbital symmetry etc. However, simple electron-transfer reactions tend to be dominated by Franck-Condon factors over most of the normally accessible temperature range. Even for outer-... 

T g) change in spin multiplicity, Franck-Condon factors... 

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