Pathway stability dynamics

Dilithiation of Af-methyl-3-phenylpropaneamide (261) and subsequent addition of a slight excess of (—)-sparteine (11) form a mixture of epimeric ion pairs 262/epi-262, which is substituted by electrophiles to give the -substitution products 263 with good ee values (equation 63) . The intermediates are not configurationally stable, but at low temperature one epimer 262 or epi-262 dominates due to the higher thermodynamic stability. Consequently, Beak and coworkers propose on the basis of a detailed mechanistic investigation the pathway of dynamic thermodynamic resolution . 

The basic idea is very simple In many scenarios the construction of an explicit kinetic model of a metabolic pathway is not necessary. For example, as detailed in Section IX, to determine under which conditions a steady state loses its stability, only a local linear approximation of the system at this respective state is needed, that is, we only need to know the eigenvalues of the associated Jacobian matrix. Similar, a large number of other dynamic properties, including control coefficients or time-scale analysis, are accessible solely based on a local linear description of the system. 

Hiickel calculations have been employed extensively in other approaches such as the angular overlap model and the method of moments developed by Burdett and coworkers. Stabilities of crystal structures, pressure- and temperature-induced transitions, dynamical pathways in reactions and other phenomena have been analysed using angular overlap models. Thus, the electronic control of rutile structures and the stability of the defect structure of NbO have been examined (Burdett, 1985 Burdett Mitchell, 1993). In the case of NbO, the structure is stable at involving the formation... 

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