Computational methods substitution

The Ti4+ distribution in TS-1 has also been studied by computational methods (34,62,160-163). The actual location of the Ti atoms in the framework of titanosilicates is difficult to determine experimentally because of the low Ti content (Section II), and information obtained from theoretical methods is, therefore, of considerable interest. In the orthorhombic MFI structure, substitution can take place at 12 crystallographically different tetrahedral (T) sites (T1-T12) (Fig. 1 and Section II.A.l.b). In the monoclinic MFI framework, the mirror symmetry is lost and 24 crystallographically different T sites can be distinguished (Fig. 31) (160). 

Gaul and Seebach showed that lithiated methylthiomethyl-substituted chiral oxazolidi-nones react with aldehydes, ketones, imines and chalcones (Scheme 41). In this case, the oxazolidinone is derived from diphenylvalinol. The products, with two new asymmetric centers, are formed in good yield and excellent diastereoselectivity.A detailed mechanistic study of this and related systems, using computational methods, IR and NMR... 

The exact structure of carbonyl ylides has been the subject of a variety of theoretical investigations over the past few decades since their intermediacy was suggested in 1965 during the cycloaddition reaction of substituted epoxides (1). Houk et al. (2) has undertaken a detailed smdy of the carbonyl ylide structure and reactivity by the application of computational methods (Fig. 4.3). 

The study of carbocations has now passed its centenary since the observation and assignment of the triphenylmethyl cation. Their existence as reactive intermediates in a number of important organic and biological reactions is well established. In some respects, the field is quite mature. Exhaustive studies of solvolysis and electrophilic addition and substitution reactions have been performed, and the role of carbocations, where they are intermediates, is delineated. The stable ion observations have provided important information about their structure, and the rapid rates of their intramolecular rearrangements. Modem computational methods, often in combination with stable ion experiments, provide details of the stmcture of the cations with reasonable precision. The controversial issue of nonclassical ions has more or less been resolved. A significant amount of reactivity data also now exists, in particular reactivity data for carbocations obtained using time-resolved methods under conditions where the cation is normally found as a reactive intermediate. Having said this, there is still an enormous amount of activity in the field. 

These M + 1 equations in M + 1 unknowns p and Xm may be solved by the Newton-Raphson method, in which the unknowns are iteratively adjusted until the right and left sides of the equations agree. The object spectrum number-count set hm and noise em are then computed by substitution of p and the Xm into Eqs. (31) and (32). 

The relative Michael-acceptor abilities of a variety of substituted aromatic and aliphatic nitroalkenes have been elucidated by computational methods. Several global and local reactivity indices were evaluated with the incorporation of the natural charge obtained from natural bond orbital (NBO) analysis. Natural charges at the carbon atom to the NO2 group and the condensed Fukui functions derived by this method were found to be consistent with the reactivity.187... 

AH°t) and the sum of bond-energy terms ( °b) of the species under consideration. Here, Nab stands for the number of equivalent bonds having E°b. The bond-energy terms are obtained from a set of reference compounds. The heat of atomization is evaluated from the difference of the heat of formation of the constituent atoms and the species under consideration (2). The procedure depends on the reliability of the heat of formation of the individual molecules. In cases where experimental values exist it is not necessary to have recourse to computational methods. However, the heats of formation of many molecules which are of interest in the context of captodative substitution are not known experimentally. 

Computational methods are increasingly being brought to bear on the crystallographic aspects of chiral crystals. The possibility that one could predict the crystal structures of a particular diastereomeric salt pair with an error in calculated lattice energy of less than 4 kcal/mole has been demonstrated for the system formed by a chlorine-substituted cyclic phosphoric acid and ephedrine [64]. In another study, it was demonstrated that the stability difference of the diastereomeric salt pairs of... 

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