Conservation of spin

The electrons do not undergo spin inversion at the instant of excitation. Inversion is forbidden by quantum-mechanical selection rules, which require that there be conservation of spin during the excitation process. Although a subsequent spin-state change may occur, it is a separate step from excitation. 

The transfer of energy must proceed with net conservation of spin. In the usual case, the acceptor molecule is a ground-state singlet, and its reaction with the triplet state of the sensitizer will produce the triplet state of the acceptor. The mechanism for triplet photosensitization is outlined below ... 

There does not seem to be any selection rule such as conservation of spin or orbital angular momentum which this reaction does not satisfy. It is also not clear that overall spin conservation, for example, is necessary in efficient reactions (5, 16, 17, 20). Further, recent results (21) seem to show a greatly enhanced (20 times) reaction rate when the N2 is in an excited vibrational state (vibrational temperature 4000 °K. or about 0.3 e.v.). This suggests the presence of an activation energy or barrier. A barrier of 0.3 e.v. is consistent with the low energy variation of the measured cross-section in Figure 1. 

The spin rule is satisfied, but the orbital angular momentum rule is not. The reaction is apparently fast at low ion energies (4) hence, if there is an important selection rule in the combination of reactants, it is seemingly the spin rule. Conservation of spin in combining reactants is probably more likely than conservation of orbital angular momentum, since the latter will be more strongly coupled to collision angular momentum. 

A/=+l. (One way of thinking about this is that the photon has zero spin and one unit of angular momentum. Conservation of spin and angular momentum then produces these rules.) For a sodium atom, for example, the 35 electron can absorb one photon and go to the 3jo level. (There is no restriction on changes of the principal quantum number.) The 3s electron will not, however, go to the 3d or 4s level. Figure 8.1 illustrates allowed and forbidden transitions. 

This bizarre prediction, known as the Einstein-Podolsky-Rosen paradox, has been verified many times in the laboratory. The most famous version involves two electrons manipulated into a mixed state with combined spin of 0, The electrons are separated in space before the spin of one (and only one) electron is measured, say, in a Stern-Gerlach machine. If that electron is found to be spin up, then by conservation of spin angular momentum, the other electron must be spin down, and vice versa. This holds true even if the ratio of the distance between the measurements to the time between the measurements is greater than the speed of light. See the discussion in Townsend [To, Sections 5,4 and 5,5] and the references therein. 

These rules also predict the nature of photoproducts expected in a metal-sensitized reactions. From the restrictions imposed by conservation of spin, we expect different products for singlet-sensitized and triplet-sensitized reactions. The Wigner spin rule is utilized to predict the outcome of photophysical processes such as, allowed electronic states of triplet-triplet annihilation processes, quenching by paramagnetic ions, electronic energy transfer by exchange mechanism and also in a variety of photochemical primary processes leading to reactant-product correlation. 

The primary step in the ultraviolet photolysis of ozone almost certainly gives rise to an electronically excited, 1D, oxygen atom (see, for example, references 62 and 63) and if there is conservation of spin, then the product oxygen molecule should also be a singlet ... 

Due to the conservation of spin, a new radical species is formed. If the atom that is transferred is a hydrogen, then the process is called hydrogen abstraction and is die most common atom transfer reaction however, other atoms can be transferred to free radicals as well. The driving force for atom transfer (abstraction) reactions is usually the formation of a stronger bond and/or a more stable free radical. 

Another common feature of free-radical reactions is that they tend to be chain processes. Since any chemical reaction must exhibit conservation of spin, the reaction of a free radical widi a closed-shell (fully electron paired) molecule must result in the production of a new free-radical species which can participate in subsequent free-radical reactions. The series of free-radical reactions leading to product is often a cyclic process in which the initial free radical is produced once again in die last step of the cycle so that the reaction sequence starts over again. The process is termed a chain reaction because each step of the process is linked directly to die preceding step. 

Despite closely reasoned counter-arguments (DeMore and Benson, 1964), the commonly held view, due to Skell, is that singlet carbenes add to olefins in a stereospecific cia-manner, whereas attack by triplet carbenes leads to non-stereospecific addition (Skell and Woodworth, 1956). The rationale of this view is that a singlet carbene should react with the olefin to form a cyclopropane in a one-step, concerted process because in this way it could occur with conservation of spin (equation 23) the addition would thus be stereospecifically cis. On the other hand, a concerted addition of a triplet carbene would violate the rule of spin conservation in consequence, a multistep reaction, in which spin inversion of an intermediate 1,3-diradical constitutes a discrete process... 

In the absence of external perturbation, photodecomposition of azides must occur with overall conservation of spin. Within this restriction there are four possibilities for the fragmentation ... 

The chemical reaction is the most chemical event. The first application of symmetry considerations to chemical reactions can be attributed to Wigner and Witmer [2], The Wigner-Witmer rules are concerned with the conservation of spin and orbital angular momentum in the reaction of diatomic molecules. Although symmetry is not explicitly mentioned, it is present implicitly in the principle of conservation of orbital angular momentum. It was Emmy Noether (1882-1935), a German mathematician, who established that there was a one-to-one correspondence between symmetry and the different conservation laws [3, 4],... 

FIGURE 8.1 The formation and subsequent recombination of S and T RPs from closed shell, neutral molecules with conservation of spin state. Examples of the three most common methods of RP formation are illustrated. 

A spin-dependent recombination rate is another consequence of the electron-hole correlation. The conservation of spin selection rule is preserved in amorphous materials. The final state of the recombination process has zero spin and both radiative and phonon-assisted non-radiative transitions occur without change in spin, so that recombination can only proceed from an initial state of zero spin. A weakly interacting electron-hole pair forms four possible spin states, one singlet and one triplet. Of the four states, only the singlet and one... 

Note that Roman capitals (S, P, D) are used for the states of atoms and Greek capitals (X, II, A) for those of molecules, and that the ground state of 02 is a triplet 02(3X). The reaction 03 + hv — 0(1D) + 02(1A) has an energy threshold at 310 nm, and the other possible reaction 03 + hv — OOD) + Oz(3X) is formally forbidden by conservation of spin. Increasing evidence has, however, accumulated to show that the rate of production of OOD) and therefore hydroxyl radicals at wavelengths >310 nm is significant, and that, therefore, in contrast to previous assumptions, the latter reaction makes an important contribution (Ravishankara et al. 1998). 

The quantum levels of nuclei are characterized by several quantum numbers, an important one being the nuclear spin. The spin value for the Cs ground state level is 7/2, while that of " Ba is 11/2. The electron emitted is an elementary particle of spin 1/2. In nuclear reactions the nuclear angular momentum must be conserved (4.8), which means that in radioactive decay processes the difference in total spin between reactant and products must be an integral value (4.10). Inspection of our example shows that this conservation of spin rule is violated if the reaction is complete as we have written it. The sum of the spin of the " Ba and of the electron is 11/2 + 1/2 or 6, while that of the Cs is 7/2. Therefore, the change in spin (AT) in the process would seem to be 5/2 spin units. Inasmuch as this is... 

Precursors of these rules are the Wigner - Wittmer rules [23], concerning the symmetry of chemical reactions. The Wigner- Wittmer rules deal with the conservation of spin and orbital angular momentum in the course of the reaction of diatomic molecules. 

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