Free classical version

The separation problem was solved by esterifying racemic 10 with succinic anhydride. The (R)-ester 145 now has a free carboxylic acid group and can be separated simply by extraction with weak base (NaHC03) without any chromatography. The ester is easily hydrolysed to (5)-(+)-10 which was obtained in 32% overall yield (maximum 50%) and 98.9% ee. They do not say whether they prefer this resolution to the classical version with dibenzoyl tartaric acid but both are good. 

In comparison with the classical version of the Free Wilson analysis, the Fujita Ban variant offers a number of important advantages ... 

Since TD-DFT is applied to scattering problems in its QFD version, two important consequences of the nonlocal nature of the quantum potential are worth stressing in this regard. First, relevant quantum effects can be observed in regions where the classical interaction potential V becomes negligible, and more important, where p(r, t) 0. This happens because quantum particles respond to the shape of K, but not to its intensity, p(r, t). Notice that Q is scale-invariant under the multiplication of p(r, t) by a real constant. Second, quantum-mechanically the concept of asymptotic or free motion only holds locally. Following the classical definition for this motional regime,... 

The model of Marchetti et al. is based on the compressible lattice theory which Sanchez and Lacombe developed to apply to polymer-solvent systems which have variable levels of free volume [138-141], This theory is a ternary version of classic Flory-Huggins theory, with the third component in the polymer-solvent system being vacant lattice sites or holes . The key parameters in this theory which affect the polymer-solvent phase diagram are ... 

For synthetic purposes cyclized radicals are preferentially trapped by chlorine [16], bromine [60], or iodine atom donors [54] to provide y9-functionalized tetrahy-drofurans, for instance halides 35-37 (Scheme 9), which serve as building blocks for subsequent ionic or free-radical reactions. This radical version of the classical halogen cyclization (Bartlett reaction [61]) is particularly useful if functionalized tetrahydrofurans can be obtained from terminal alkyl- or aryl-substituted alkenols. If these compounds are reacted for example with iodine or with A -bromosuccin-imide, tetrahydropyrans are formed from ionic cyclofunctionalizations [62], If, however, the corresponding alkenols are converted into a thiohydroxamic acid... 

The above discussion makes clear that colloidal particles and polyelectrolytes cannot be separated by size during free solution electrophoresis. As a result, many electrophoretic size separations for chemistry and biology are performed in gels. The precision afforded by microfabrication has led to miniaturized version of these classic protocols, as well as a number of novel separation techniques that differ distinctly from the separation principles prevailing in gels [5]. In order to best understand the current research in microfluidic separations of colloids and poly electrolytes, in particular the important apphcations to protein and DNA separations, it is important to first understand the physics of gel electrophoresis. 

Several variations exist for the classic Sommelet-Hauser rearrangement. The most important concern the use of base-free conditions for the [2,3]-sigmatropic rearrangement based on the fluoride anion induced desilylation of substituted benzyldialkyl-[(trimethylsilyl)methyl] ammonium halides" and the asymmetric versions of Sommelet-Hauser rearrangement that appeared recently in the literature. None of the above has ever been used in a modification of the Gassman indole synthesis. 

In a series of publications, Voth and coworkers [21,24,25,26,27] explored various aspects of electron-transfer reactions. Their calculations are based on a version of the Anderson-Newns Hamiltonian presented in Sect. 1.2.4.2, which allows the direct computation of adiabatic free energy surfaces. For a Fe +/Fe " couple at a fixed distance to a Pt(lll) surface, they compared a classical and a quantized water model [24]. The quantization... 

The semi-classical Marcus equation derives from quantum-mechanical treatments of the Marcus model, which consider in wave-mechanical terms the overlap of electronic wave-functions in the donor-acceptor system, and the effects of this overlap on electronic and nuclear motions (see Section 9.1.2.8 above). Such treatments are essential for a satisfactory theory of D-A systems in which the interaction between the reactant and product free-energy profiles is relatively weak, such as non-adiabatic reactions. A full quantum-mechanical treatment, unfortunately, is cumbrous and (since the wave-functions are not accurately known) difficult to relate to experimental measurements but one can usefully test equations based on simplified versions. In a well-known treatment of this type, leading to the semi-classical Marcus equation introduced in Section 9.1.2.8, the vibrational motions of the atomic nuclei in the reactant molecule (as well as the motions of the transferring electron) are treated wave-mechanically, while the solvent vibrations (usually of low frequency) are treated classically. The resulting equation, already quoted (Equation (9.25)), is identical in form with the classical equation (9.16) (Section 9.1.2.5), except that the factor... 

Tragedies of the Commons may also sometimes be versions of a Prisoner s Dilemma . The classic Prisoner s Dilemma [2] goes like this Two people are arrested for mnrder and are held in separate cells, unable to communicate with each other. Each knows if they both stay silent (or cooperate ), they will only receive short sentences. However, if one should offer to provide evidence against the other (or defect ), he will walk free and the other wiU be hanged. The best way forward for their mutual benefit is to cooperate - but they cannot commnnicate with each other. Does each trust the other sufficiently for both to remain silent ... 

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