In diradicals

The Franck-Condon question is also an issue in diradical studies. It is particularly relevant in nonrigid systems, such as trimethylenemethane (TMM) and tetramethyleneethylene (TME), °° in which neutral and/or anion states can be planar or nonplanar. Thus, transitions can occur from planar anions to nonplanar neutral states, or from nonplanar anions to planar neutrals. In these cases, the energy differences between the planar and nonplanar states have generally been estimated by using quality electronic structure calculations. 

Full -polarization in diradicals can give rise to zwitterionic products. First examples were studied in detail by Carpenter and coworker who investigated solvent effects on rates and product distribution in Myers-Saito cyclizations.64 Polar solvents and substitution patterns that stabilize either positive or negative charges (or both) favor the zwitterionic products. For example, the presence of a dimethylamino group leads to stabilization of cations and isolation of pyrrolo-quinolines, rather than pyrido-indoles from eneyne-carbodiimides, as reported by Wang and coworkers (Scheme 14).65... 

As far as the size of the exchange integral J between the two open-shell centres is concerned, it can become as high as a few tenths of an eV in diradicals (see Section 3). The /-values between radicals are usually smaller than 0.01 eV. Therefore, we cannot readily expect spin-ordering temperatures higher than a few to 20 K for intermolecular spin alignment. 

As explained in the Introduction, this scheme breaks down both for ground and excited states when orbitals from occupied and virtual subspaces become near-degenerate, e.g. at the dissociation limit or in diradicals (see Figure 2). To overcome this problem, the SF model employs a high-spin triplet reference state which is accurately described by a SR wavefunction. The target states, closed and open shell singlets and triplets, are described as spin-flipping excitations ... 

Lastly, the SF approach implemented within the time-dependent. (TD) density functional theory (DFT) extends DFT to multi-reference situations with no cost increase relative to the non-SF TD-DFT. Similarly to DFT and TD-DFT, the SF-DFT model (27) is formally exact and therefore will yield exact answers with the exact density functional. With the available inexact ftmctionals, the SF-DFT represents an improvement over its non-SF counterparts. It has been shown to yield accurate equilibrium properties and singlet-triplet energy gaps in diradicals (27). 

J. A. Berson, in Diradicals, W. T. Borden, Ed., Wiley-Interscience, New York, 1982, Chapter 4 and references reviewed therein. 

As pointed out by Gaspar and Hammond (1964), the logic of this widely-held and much applied interpretation, despite its plausibility, does not bear close scrutiny. Thus, singlet addition does not have to be concerted merely because it covld be without breaking the spin conservation rule. Moreover, there is little independent evidence concerning the relative rates of spin inversion and rotation about single bonds in diradicals. 

There is no clear evidence which carbon of the double bond forms the first covalent bond in diradical formation. In fact, there is evidence from rearrangement products that each does 148>. 

The formation of propyne and allene by pyrolysis of cyclopropene arises from opposite [1,2]H shifts in diradicals 191 or 192 The substantially larger activation energy (by some 24.5 kJ mol" ) for formation of allene reflects differences in the transition state structures for the two processes. Thus, the propyne-forming reaction requires the migrating hydrogen atom to span a single bond (see 194), whilst in the allene-forming process a double bond is involved and a more strained situation ensues (see 195). The formation of but-2-yne from 3-methylcyclopropene is similarly rationalized but the... 

The concept of coupling units may be traced to McConnell s perturbation theory for A st in diradicals, in which two weakly exchange-coupled radical moieties are separated by the bridging group.56 In particular, 1,3-phenylene was predicted to be... 

The EPR spectra in the Ams — 1 region for diradical anions 252 1 272 1 and diradical dianions 332 2 -352 2 in 2-MeTFlF/TFlF matrix showed typically four-line dipolar pattern assigned to S — 1 states with the values of D hc that were similar (but not identical) to those for the corresponding diradicals 11, 13, and 14.88 In conjunction with the EPR studies of selected diradical anions, this provided evidence for localization of spin density in diradical anions 252 1 272 1 and diradical dianions 332 2 -352 2 at the two adjacent triarylmethyl sites (Fig. 22).88 Also, the IT versus T plot of the EPR Ams — 2 signal drops off with decreasing temperature in the 10-80 K range. 

The E parameter is usually referred to as the symmetry parameter and its value is zero for molecules with high symmetry (C3 or higher) due to the cancellation of the x2 and y2 terms in Eq. (4) (the z axis is defined along the rotational axis). It is convenient to take the z axis for localized diradicals along the line that connects the two radical centers to obtain the spectroscopic zfs parameters directly from Eq. (4), which obey the relation D 3 E 0. In this case, the E parameter becomes very small due to its inverse dependence on the fifth power of the interspin distance ( oc r-5). The D term, or the distance parameter, depends on the inverse cube of r (D ocr 3 since z r) and in the limit Eq. (5) holds [25]. This equation has been applied extensively for estimating the interspin distances in diradicals. 

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