Non-classical

Dennison coupling produces a pattern in the spectrum that is very distinctly different from the pattern of a pure nonnal modes Hamiltonian , without coupling, such as (Al.2,7 ). Then, when we look at the classical Hamiltonian corresponding to the Darling-Deimison quantum fitting Hamiltonian, we will subject it to the mathematical tool of bifiircation analysis [M]- From this, we will infer a dramatic birth in bifiircations of new natural motions of the molecule, i.e. local modes. This will be directly coimected with the distinctive quantum spectral pattern of the polyads. Some aspects of the pattern can be accounted for by the classical bifiircation analysis while others give evidence of intrinsically non-classical effects in the quantum dynamics. 

Flowever, we have also seen that some of the properties of quantum spectra are mtrinsically non-classical, apart from the discreteness of qiiantnm states and energy levels implied by the very existence of quanta. An example is the splitting of the local mode doublets, which was ascribed to dynamical tiumelling, i.e. processes which classically are forbidden. We can ask if non-classical effects are ubiquitous in spectra and, if so, are there manifestations accessible to observation other than those we have encountered so far If there are such manifestations, it seems likely that they will constitute subtle peculiarities m spectral patterns, whose discennnent and interpretation will be an important challenge. 

The question of non-classical manifestations is particularly important in view of the chaos that we have seen is present in the classical dynamics of a multimode system, such as a polyatomic molecule, with more than one resonance coupling. Chaotic classical dynamics is expected to introduce its own peculiarities into quantum spectra [29, 77]. In Fl20, we noted that chaotic regions of phase space are readily seen in the classical dynamics corresponding to the spectroscopic Flamiltonian. Flow important are the effects of chaos in the observed spectrum, and in the wavefiinctions of tire molecule In FI2O, there were some states whose wavefiinctions appeared very disordered, in the region of the... 

It should be emphasized that the existence of energy transfer modes hypotliesized earlier with the polyad breakdown is completely consistent with the energy transfer being due to non-classical, dynamical tiumelling processes. This is evident from the observation above that the disorder in the FI2O spechnm is attributable to non-classical effects which nonetheless are accompaniments of cte.s/c CT/bifiircations. 

There are 2 temis in the sum since each site has two configurations with spin eitlier up or down. Since the number of sites N is fmite, the PF is analytic and the critical exponents are classical, unless the themiodynamic limit N oo) is considered. This allows for the possibility of non-classical exponents and ensures that the results for different ensembles are equivalent. The characteristic themiodynamic equation for the variables N, H and T is... 

Winstein, one of the most brilliant chemists of his time, concluded that it is attractive to account for these results by way of the bridged (non-classical) formulation for the norbornyl cation involving accelerated rate of formation from the exo precursor [by anchimeric assistance His formulation of the norbornyl cation as a cr-bridged species stimulated other workers in the solvolysis field to interpret results in a variety of systems in similar terms of rr-delocalized, bridged carbonium... 

Selenolo[2,3-b]pyridine-2-carboxylic acid, 3-hydroxy-synthesis, 4, 1034 Selenolopyridines, 4, 1034—1036 H NMR, 4, 1035, 1036 Selenolo[2,3-c]pyridines synthesis, 4, 1035 Selenolo[3,2-b]pyridines deuteriodeprotonation, 4, 1035 synthesis, 4, 1034 Selenolo[3,2-c]pyridines synthesis, 4, 1035 Selenolo[2,3-b]pyrroles ionization potentials, 4, 1046 Selenolo[3,2-b]pyrroles ionization potentials, 4, 1046 Selenolo[3,4-c]pyrroles non-classical... 

Bohlmann and Arndt (S3) have separated the possible stereoisomers of hexahydrojulolidine (78-80) and subjected them to mercuric acetate oxidation. The rates, which were followed by the precipitation of mercurous acetate, showed that isomer 78 reacted about five times faster than isomer 79, while isomer 80 reacted very slowly. The difference in rates between 78 and 79, both of which have tertiary a-hydrogens trans to the nitrogen electron pair, was explained by pointing out that greater relief of non-classical strain occurs in the oxidation of 78 as compared to 79. Isomer 80 has no tertiary a-hydrogens trans to the nitrogen electron pair except when it is in an unfavorable boat conformation. 

Carbon is known with all coordination numbers from 0 to 8 though compounds in which it is 3- or 4-coordinate are the most numerous. Some typical examples are summarized in the Panel (p. 291). Particular mention should also be made of hypercoordinate non-classical carbo-nium ions such as 5-coordinate CHj", square pyramidal CsHs (cf. the isoelectronic cluster B3H9, p. 154), pentagonal pyramidal C6Me6 " (cf. iso-electronic Bf,Hio, p. 154) and the bicyclic cation 2-norbomyl, C7H] 1... 

Fullerene derivatives such as CgoH, (p. 283), C60H2 (p. 287), and C61H2 (p. 287), and hyperco-ordinated non-classical carbonium ions (p. 290) have already been briefly mentioned. 

Non-classical structures are predicted to be unstable relative to classical structures (for example ethyl cation). 

ChEs exist throughout the entire animal kingdom and appear in locations, where no ACh is released, suggesting that these possess additional non-hydrolytic functional properties, designated non-classical . These may depend on protein-protein interactions,... 

Silman I, Sussman JL (2005) Acetylcholinesterase classical and non-classical functions and pharmacology. Curr Opin Pharmacol 5(3) 293-302... 

Classical complexes are identified [1112] as those species in which the central metal ion possesses a well-defined oxidation number and a set of ligands with a discrete electron population. Non-classical complexes , in contrast, involve highly covalent and/or multiple metal-ligand bonding resulting in indistinct oxidation numbers for both participants. 

A different non-classical approach to the resolution of sulphoxides was reported by Mikolajczyk and Drabowicz269-281. It is based on the fact that sulphinyl compounds very easily form inclusion complexes with /1-cyclodextrin. Since /1-cyclodextrin as the host molecule is chiral, its inclusion complexes with racemic guest substances used in an excess are mixtures of diastereoisomers that should be formed in unequal amounts. In this way a series of alkyl phenyl, alkyl p-tolyl and alkyl benzyl sulphoxides has been resolved. However, the optical purities of the partially resolved sulphoxides do not exceed 22% after... 

Dinjus E., Fornika R., Scholz M. Organic Chemistry in Snpercritical Flnids in Chem. Extreme Non-Classical Cond. 1997 219, Eds. Van Eldick R. and Hubbard C., Pb. Wiley, N.Y. 

The stable 2-norbornyl cation has recently been shown to be a non-classical, unusually stabilized species. Olah et al. (1970) proved spectroscopically that this ion is a comer-protonated nortricyclene with a pentavalent carbon atom. The value for the carbonylation-decarbonyla-tion equilibrium constant K (= of the 2-norbomyl ion illustrates... 

In contrast to the results of the reaction of tertiary and secondary alkyl cations with carbon monoxide (Figs. 1-5), which were obtained under thermodynamically controlled conditions, the results of the carbonylation with the vinyl cations were obtained under kinetically controlled conditions. This presents a difficulty in explaining the occurrence of the 1,2-CH3 shift in the reaction 16->-17, because it involves a strong increase in energy. The exclusive formation of the Z-stereoisomer 18 on carbonylation of the 1,2-dimethylvinyl cation 16 is remarkable, but does not allow an unambiguous conclusion about the detailed structure— linear 19 or bent 20—of the vinyl cation. A non-classical structure 21 can be disregarded, however, because the attack... 

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