Resonance singlet state

By including electron correlation in the wave function the UHF method introduces more biradical character into the wave function than RHF. The spin contamination part is also purely biradical in nature, i.e. a UHF treatment in general will overestimate the biradical character. Most singlet states are well described by a closed-shell wave function near the equilibrium geometry, and in those cases it is not possible to generate a UHF solution which has a lower energy than the RHF. There are systems, however, for which this does not hold. An example is the ozone molecule, where two types of resonance structure can be drawn. Figure 4.8. 

N-Aminobenzoxazolin-2-one (4), which was readily prepared by animation of benzoxazolin-2-one with hydroxylamine-O-sulfonic acid, is also a useful nitrene precursor (Scheme 2.2). Oxidation of 4 with lead(iv) acetate in the presence of a conjugated diene resulted in exclusive 1,2-addition of nitrene 5, to yield vinylazir-idine (6) in 71 % yield [6]. The formation of vinylaziridines through 1,2-additions of methoxycarbonylnitrene (2) or amino nitrene 5 contrasts with the claimed 1,4-ad-dition of nitrene itself to butadiene [7]. Since the reaction proceeded stereospecif-ically even at high dilution, the nitrene 5 appears to be generated in a resonance-stabilized singlet state, which is probably the ground state [8]. 

Fig. 1 (Left) Schematic of frequency degenerate 2PA (1) into the first allowed singlet state, (2) above the first allowed singlet state, and (3) a double resonant condition, with a small intermediate state resonance energy difference, A, and a transition into an allowed final 2PA state. (Right) Photograph illustrating the much sharper contrast of two-photon (b) versus one-photon excitation (a) (taken from [2])...

In connection with Chichibabin s hydrocarbon it is appropriate to mention that there is little or no resonance between states of different multiplicity.4 Thus the singlet-triplet transition represented by the covalent and diradical structures of the hydrocarbon is a true equilibrium and not an example of resonance. 

A diradical is likely to be more polarizable and a stronger base than the corresponding singlet state. If so, reaction with an acid should shift the equilibrium enough for the diradical to be detectable in otherwise diamagnetic substances. This seems to be the case for the substances shown below, in which paramagnetic resonance absorption indicates the presence of the diradical conjugate acid to the extent... 

The nitrenium ion +NH2 has been the subject of a detailed, comprehensive calculation. Calculations on (48) with 15 different X substituents reveal a large substituent sensitivity, and also that aqueous solvation preferentially stabilizes the singlet state. This substiment sensitivity agrees with the results of a time-resolved IR study of the diphenylnitrenium ion (49), which shows that resonance contributors such as (50) and (51) are very important to the overall structure. Substituted 4-biphenyl nitrenium ions... 

A number of cases have been reported in the literature where the exchange between pairs of ions in a lattice is piedominant, i.e., ions aie exchange coupled in pairs because of their proximity. An example of this is copper acetate 168), where the copper ions occur in pairs which are relatively close, so that the spins of pairs of copper ions are coupled together to form a singlet state (paired spins) and a triplet state (unpaired spins). Resonance measurements 158) permit determination of the magnitude and sign of J. 

It is easy then to write down the oscillation condition for a dye laser. In its simplest form a dye laser consists of a cuvette of length L [cm], with dye solution of concentration m [cm-3], and of two parallel end windows carrying a reflective layer, each of reflectivity R, which form the laser resonator. With mi molecules/ cm3 excited to the first singlet state, the dye laser will start oscillating at a wavelength A if the overall gain is equal to or greater than one ... 

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