Singlet pairs

The classical VB wave function, on the other hand, is build from the atomic fragments by coupling the unpaired electrons to form a bond. In the H2 case, the two electrons are coupled into a singlet pair, properly antisymmetrized. The simplest VB description, known as a Heitler-London (HL) function, includes only the two covalent terms in the HF wave function. 

A singlet pair of <-butyl radicals produced by peroxide decomposition disproportionate to yield isobutane and isobutene [equation (41)]. Both products show E/A multiplet effects. 

Note that the quasi-particle energy is independent of color and flavor in this case, since we have assumed a singlet pair in flavor and color. 

In the first of the two notations used in this equation, a singlet pair is associated with each combination of an a and a p spin function enclosed within a matching pair of left and right parentheses. The second notation indicates all singlet pairs explicitly. It is easiest to visualize the spin-coupling patterns (3) by means of the familiar five... 

Accordingly, the most important spin function becomes (1 - 2, 3-4, 5-6), which couples the spins associated with the bonded orbitals in singlet pairs (see Fig. 6). The fact that the largest overlaps in Fig. 7 are ( i/i i/2) = (tirsItKe) and ( 3l 4) completes the picture of the now almost completely formed cA-l,3,5-hexatriene chain. 

The eigenstates of are symmetric spin-free two-electron functions corresponding to singlet pairs, those of F are antisymmetric spin-free two-electron functions corresponding to triplet pairs. Tr(F+) is the probability that two electrons are coupled to a singlet pair, while Tr(F ) is the probability that two electrons are coupled to a triplet pair. 

The phenomenon of pair annihilation depends on the spin state of the e+-e pair. Two y-ray photons are emitted in opposite directions if it is a singlet pair (S = 0), and three y rays are emitted in directions on a common plane if it is triplet (S = 1). The absorption potential appropriate for the singlet and the triplet annihilation in the absence of any other particles is [9,10]... 

The theory underlying this effect depends critically on two selection principles the nuclear spin dependence of intersystem crossing in a radical pair, and the electron spin dependence of the rates of radical pair reactions. Combined, these selection principles cause a sorting of nuclear spin states into different products and result in characteristic nonequilibrium populations in the nuclear spin levels of geminate reaction products (whose formation is allowed for singlet pairs but spin forbidden for triplet pairs) and in complementary nonequilibrium populations in the spin levels of free-radicals ( escape ) products (whose formation is electron spin independent). The transitions between these levels will be in the direction towards restoring the normal Boltzmann population their intensities will depend on the extent of nonequilibrium population. The observed effects are... 

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