Triplet coupling

Reactions occurring on two (or more) electronic states can lead to the same product asymptote. These pathways may occur if more than one electronic state correlates adiabatically to the same asymptote (e.g., single or triplet coupling of two approaching species), or if nonadiabatic transition(s) move population from one state to another. Here, I make the distinction that products of the same structural formula do not represent the same exit channel if they are produced in different electronic states. For example, in the reaction... 

Marian CM, Schneidaer F, Kleinschmidt M, Tatchen J (2002) Electronic excitation and singlet-triplet coupling in uracil tatutomers and uracil-water complexes. Eur Phys J D 20 357... 

Zhang YX, Aslan K, Previte MJR, Malyn SN, Geddes CD (2006) Metal-enhanced phosphorescence Interpretation in terms of triplet-coupled radiating plasmons. J Phys Chem B 110 25108-25114... 

It can be shown [95] that in such a case the T4 contribution cancels the exclusion principle violating (EPV) quadratic terms [59]. This realization led us to the formulation of the so-called ACPQ method (CCSD with an approximate account for quadruples) [95], as well as to CCDQ and CCSDQ [86], the latter also accounting for singles. Up to a numerical factor of 9 for one term involving triplet-coupled pp-hh t2 amplitudes [95], this approach is identical with an earlier introduced CCSD-D(4,5) approach [59] and an independently developed ACCD method of Dykstra et al. [96,97]. This method arises from CCSD by simply discarding the computationally most demanding (i.e., nonfactorizable) terms (see Refs. [59,95-97] for details). 

Figure 3.9b portrays homolytic bond formation by the recombination of radicals and is accompanied by charge transfer from A to B. The radicals must be singlet coupled. The interaction of triplet-coupled electron pairs is repulsive and does not lead to bond formation. The reverse process describes homolytic bond cleavage and results in singlet-coupled free radicals. 

If extended m-phenylene structures have several spin-bearing centers, their triplet coupling (at zero field) depends on spatial spin distribution. Namely, the coupling degree is inversely proportional to R3, where R is the distance between the unpaired electrons. 

Note, that it is not possible to compute the nonvanishing MEs of a triplet-triplet coupling by using Ms = 0 wave functions, because the spin part of... 

We have already seen a molecule with ailylic coupling. We discussed in some detail why cyclo-hexenone has a double triplet for H3. But it also has a less obvious double triplet for H2. The triplet coupling is less obvious because / is small (about 2 Hz) because it is 4/hh —ailylic coupling to the CH2 group at C4. Here is a diagram of the coupling, which you should compare with the earlier one for cyclohexenone. 

The aromaticity of benzene is linked, in spin-coupled theory, to the particular mode of coupling of the electron spins, and so it seems reasonable to suppose that the orbital descriptions of Dih cyclobutadiene and of benzene could be fairly similar, but for these to be associated with very different modes of spin coupling. To a first approximation, this indeed turns out to be the case. With benzene-like orbitals ordered a,b,c,d around the ring, the symmetry requirements of an overall Bu state are such that the electron spins associated with each diagonal (ale and bid) must be strictly triplet coupled. These two triplet subsystems combine to a net singlet. A characteristic feature of antiaromatic situations in spin-coupled theory is the presence of such triplet-coupled pairs of electrons. 

This is not quite the end of this particular story. In the very special case of electron spins which are strictly triplet coupled, the spin-coupled wavefunction is not altered by taking the sums and differences of the corresponding orbitals (a+c), (a-c), (b+d) and (b-d), neglecting normalization. The term antipairs has been coined for such an alternative mode of description. It turns out that this orbital representation already corresponds to the required B1/t symmetry at the square-planar geometry, so that there are now more free parameters in the spin space the relevant spins need no longer be exactly triplet coupled. We find that... 

Spin-coupled calculations at the idealized Dm geometry of cyclooctatetraene reveal a description dominated by triplet coupling of pairs of electrons [12], as anticipated earlier. Expressing the total spin function in the Serber basis [29], we find that the mode made up only of triplet-coupled pairs is responsible for 75% of the total. We find that the n orbitals for this antiaromatic system (see Figure 9) adopt localized forms that resemble closely those shown in Figure 4 for benzene, rather than the antipair representation shown for cyclobutadiene in Figure 6. 

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