Doublet states, production

Correlated or geminate radical pairs are produced in unimolecular decomposition processes (e.g. peroxide decomposition) or bimolecular reactions of reactive precursors (e.g., carbene abstraction reactions). Radical pairs formed by the random encounter of freely diffusing radicals are referred to as uncorrelated or encounter (P) pairs. Once formed, the radical pairs can either collapse, to give combination or disproportionation products, or diffuse apart into free radicals (doublet states). The free radicals escaping may then either form new radical pairs with other radicals or react with some diamagnetic scavenger... 

Products of this initial reaction generate secondary products including doublet-state oxygen (O2 ), chlorine (CI2), and chlorine trioxide (CI2O3) (Griese et al. 1992 Zika et al. 1984). If chlorine dioxide gas is diluted in air to <15 volume percent, it can be relatively stable in darkness (Vogt et al. 1986). 

We have so far said little about the nature ofthe space function, S. Earlier we implied that it might be an orbital product, but this was not really necessary in our general work analyzing the effects of the antisymmetrizer and the spin eigenfunction. We shall now be specific and assume that S is a product of orbitals. There are many ways that a product of orbitals could be arranged, and, indeed, there are many of these for which the application of the would produce zero. The partition corresponding to the spin eigenfunction had at most two rows, and we have seen that the appropriate ones for the spatial functions have at most two columns. Let us illustrate these considerations with a system of five electrons in a doublet state, and assume that we have five different (linearly independent) orbitals, which we label a, b,c,d, and e. We can draw two tableaux, one with the particle labels and one with the orbital labels. 

The state R in Equation 6.4 strictly keeps the HL wave function of the product P, and is hence a quasi/spectroscopic state that has a finite overlap with R. If one orthogonalizes the pair of states R and R, by, for example, a Graham—Schmidt procedure (see Exercise 6.3), the excited state becomes a pure spectroscopic state in which the A—Y is in a triplet state and is coupled to X to yield a doublet state. In such an event, one could simply use, instead of Equation 6.5, the spectroscopic gap Gs in Equation 6.6 that is simply the singlet—triplet energy gap of the A—Y bond ... 

Doubly excited states of He of doublet symmetry have been observed in studies of electron impact on He [23]. In contrast, data on quartet states are sparse. Selection mles on photoexcitation from the P° ground state limit excited state production to those of S, P and symmetry. Recently, the He photodetachment cross section... 

The correlation of the potential surfaces to the product OH seems obvious. The asymmetric excited state correlates to the asymmetric A-doublet, whereas the symmetric ground state correlates to the symmetric A-doublet. Conservation of electronic symmetry in the fragmentation predicts the formation of OH exclusively in the asymmetric A-doublet state. Conservation of electronic symmetry implies that the motion proceeds along the same potential surface and that transitions to other potential surfaces are negligible. This so called adiabatic behaviour is expected to hold for most molecular processes. It seems immediately clear that the origin for the selective population of A-doublet states is due to adiabatic behavior. 

The OH product state distributions in Fig.l3 are obviously different for different initial rotational states of H2O. This is qualitatively understood by the transfer of motion from parent to product different motion in the parent has to lead to different motion in the products. In addition there is a pronounced quantum structure in these distributions. These and other distributions show, at least in the beginning, an oscillation with AJ=1. This oscillation is essentially caused by the different parity and shows up also for different A-doublet states. 

It turns out that most of the oscillatory structure in the OH product state distributions is due to parity. It is clear that the total parity has to be the conserved. A closer look at the experimental results reveals that the formation probability of OH in different quantum states depends strongly upon the parity of the final state. In the rotational distributions for one A-doublet state, the intensity alternates with AJ=1, i.e., with parity. The alternations are found in both A-doublet states and are opposite to each other, i.e., the rotational distribution decreases in the one A-doublet, if it increases in the other. This is again an oscillation with parity. The oscillations are also opposite in the multiplet states. This implies that most of the complicated structure is due to parity. 

If the OH product state distributions are, for example, averaged over the A-doublet states, the rotational state distributions become smooth Boltzmann-like distributions, reflecting the rotational energy content in the parent molecule. 

The selective population of A-doublet states is exclusively determined by the parent motion and the absorption step. The origin for the selectivity is conservation of the unpaired pir-lobe relative to the direction of initial nuclear rotation. In contrast to the adiabatic picture, it is not simply electronic symmetry that is conserved. The selectivity depends sensitively on the motion of the parent molecule (initial in-or out-of-plane rotations) as well as on the coupling of the electronic motion in the products. Each rotatonal state of the parent molecule leads to another A-doublet distribution. 

---