Diradical state

No similar meta substituent effect exists for ions since resonance between a singlet and triplet (diradical) state is prohibited. The dipolar ion theory would suggest that suitably disubstituted radicals should be especially stable, particularly in polar solvents, because of structures like III. 

A diradical is an atom or molecule containing two impaired electrons. The properties of diradicals are for the most part like those of monoradicals. They are paramagnetic and show paramagnetic resonance absorption. Although they are very reactive chemically, this is not a reliable criterion for the diradical state. Spectroscopically the diradical will probably be a triplet state if a double bond structure coupling the two electrons is geometrically possible. But when the two electrons are fairly well isolated from each other the state is probably a double doublet, like two independent radicals. 

Any unsaturated molecule has diradical as well as singlet (nonradical) states. Usually one of the non-radical states will have a decisively lower free energy than the most stable of the diradical states, in which case the substance is not paramagnetic. Special circumstances can make the diradical state the ground state then the singlet state is an excited one. Some substances have detectable amounts of both forms in equilibrium. It is unknown whether the radical-like reactions of some compounds are characteristic of their singlet states directly or due to an undetectable amount of a more reactive triplet state in equilibrium. 

But the comparable reaction of organic radicals with olefins does not necessarily mean that the reacting olefins are first excited to a diradical state. In fact, as will be discussed later, there is some reason to believe that diradicals are not involved in the purely thermal polymerization of olefins either. 

One of the possible mechanisms of cis-trans isomerization of olefins is excitation to the triplet or diradical state.98-96 The two paths, one by way of singlet and triplet states and the other solely by way of singlet states, are diagrammed in Fig. 1. The two lines with minima at 0° and... 

Therefore, the SF ansatz (2) is sufficiently flexible to describe changes in ground state wavefunctions along a single bond-breaking coordinate. Moreover, it treats both closed-shell (e.g., N and Z) and open-shell (V and T) diradicals states in a balanced fashion, i.e., without overemphasizing the importance of one of the configurations. 

The observed products correspond to the formation of the most stable intermediate by the addition of the photoexcited triplet (diradical) state of acetophenone to the alkene. 

Moreover, there are two diradical states of symmetry Cs constructed on the basis of 1-electron base states. To help visualizing the analysis we use the planes associated to the CH2 groups. At n/4 the planes defining each CH2 sigma base states at opposite sites have normal vectors making a nil angle. The local 7i-axis serve to identify new 1-e-base states Yj+ and y. The + state has two local NPs the minus (-) state increases the number of nodes by one unit. The... 

Figure 2. To the left, quasi-diabatic potential energy surfaces in the B3LYP/cc-pvtz Dunning s basis set. AA represents a cis state (solid line) BB a trans state (solid line) AB is the excited diradical state spin singlet (dashed line) Triplet is the diradical state S=1 (dotted line). To the right, extrapolated diabatic potential energy surfaces for the same states. The angle used to plot energy entries is a = 2 0. All calculations were done with Gaussian 98 [23].

The access to different -regions is controlled by the vibration spectra. In particular, it is the anti-symmetric vibration mode that may shift the geometry towards the point of maximal mixing. The other way round, freezing this mode will trap the quantum system at the initial state, cis or trans as the case may be. Now, a vibration excitation along this anti-symmetric mode will be prompting the electronic activity of the system. For example, a perpendicular symmetric attack of carbene can only proceed if non-zero amplitude develops at the diradical states. This concept includes the elementary orbital considerations and overcome them. 

C-P-Q is converted to the charge separated diradical state C h-P -Q-. Then an electron is transferred from Q to the lipid-soluble 2,5-diphenylbenzoquinone Qs 133b yielding Qs. In the third step uncharged semiquinone QsH is formed when the latter accepts a proton from the external aqueous solution. The basic function of a proton shuttle is carried out when the semiquinone radical diffuses through the membrane in the fourth step. It is then oxidized to Qs + by the carotenoid radical cation... 

Dipole moment, 236-237 Hartree-Fock, 237 Diradical state, 212... 

The triplet dimer diradical DR2(Ti) finally will relax into thermal equilibrium (kT) with its singlet ground state DR2(So). As we have seen from the ESR spectra (see Fig, 10) the energy separation between the singlet and triplet diradical states is very low and thermally activated transitions occur even at low temperatures. Furthermore the ESR spectra have revealed an admixture of about 10% carbene character with the diradical intermediates. This carbene character may be important in determining the probability x of the side reactions (see Eq. (19)) for the DR -+ AC chain termination reaction. It surely is not, however, the only essential factor, otherwise there should be no difference in the optical and thermal termination reaction steps. Up to now a direct observation of the metastable triplet state Ti(M) has been possible only in two specific crystals where the polymerization reactions are very weak. 

Zi) < E(Zt). The remaining two states arise from homolytic dissociation of the bond and therefore are diradical in character. Both singlet and triplet states arise. If any residual interaction persists (i.e., if the bond broken was a tt bond or the products are held together in a solvent cage), then the triplet diradical state is lower than the singlet diradical state. Otherwise the two have the same energy. Since the electrons end up in different orbitals, the spatial symmetry of the diradical states is determined by the symmetry properties of and The diradical is symmetric (S) if and are both... 

It is still surprising that so many of the reactions in water show the correlation between AG°5 and AG+. No theory of which we are aware anticipates such a correlation. The theory of curve crossings (9-11 S. Shaik, personal communication, 1985) ascribes the activation barriers for these reactions to an avoided crossing of surfaces, one for a diradical state and the other for an ionic state. The two surfaces, however, are related by vertical transitions, and solvation energies, particularly, make these far different from the adiabatic differences such as AG°5 (S. Shaik, personal communication, 1985). Unfortunately, the fundamental data necessary to even begin to apply this theory to the present reactions are not available. 

---