Computational studies addition

Empirical energy functions can fulfill the demands required by computational studies of biochemical and biophysical systems. The mathematical equations in empirical energy functions include relatively simple terms to describe the physical interactions that dictate the structure and dynamic properties of biological molecules. In addition, empirical force fields use atomistic models, in which atoms are the smallest particles in the system rather than the electrons and nuclei used in quantum mechanics. These two simplifications allow for the computational speed required to perform the required number of energy calculations on biomolecules in their environments to be attained, and, more important, via the use of properly optimized parameters in the mathematical models the required chemical accuracy can be achieved. The use of empirical energy functions was initially applied to small organic molecules, where it was referred to as molecular mechanics [4], and more recently to biological systems [2,3]. 

The activation energies were computed to 3.0 (toward 183), 0.3 (toward 182), and 21.8 kcal/mol (toward 184) at the B3-LYP/6-31G level, and thus the mechanism leading to 182 is the preferred one. The transition states of all three reactions belong to concerted but asynchronous reaction paths. The transacetalization of 177 with acylium cations results in the formation of the thermodynamically stabilized 187 (Scheme 121) [97JCS(P2)2105]. 186 is less stable than 187, and 185 is destabilized by 32.5 kcal/mol. Moreover, transacetalization of 177 with sulfinyl cations is not a general reaction. Further computational studies on dioxanes cover electrophilic additions to methylenedioxanes [98JCS(P2)1129] and the influence... 

Palladium(II) complexes provide convenient access into this class of catalysts. Some examples of complexes which have been found to be successful catalysts are shown in Scheme 11. They were able to get reasonable turnover numbers in the Heck reaction of aryl bromides and even aryl chlorides [22,190-195]. Mechanistic studies concentrated on the Heck reaction [195] or separated steps like the oxidative addition and reductive elimination [196-199]. Computational studies by DFT calculations indicated that the mechanism for NHC complexes is most likely the same as that for phosphine ligands [169], but also in this case there is a need for more data before a definitive answer can be given on the mechanism. 

Additional computational studies [16] provided detailed information about the nature of the dative bond, the strength of the acid-base interaction and the... 

Let us consider the general trends of the reactivity of C-C, C-S, and C-Q (Q = Cl, Br, I) bonds towards oxidative addition and reductive elimination (Scheme 7-25). In many cases, either C-C bond-forming reductive elimination from a metal center (a) or the oxidative addition of a C-Q bond to a low-valent metal center is a thermodynamically favorable process (c). On the other hand, the thermodynamics of the C-S bond oxidative addition and reductive elimination (b) lies in between these two cases. In other words, one could more easily control the reaction course by the modulation of metal, ligand, and reactant Further progress for better understanding of S-X bond activation will be achieved by thorough stoichiometric investigations and computational studies. 

A DFT study found a corresponding TS to be the lowest energy.167 This study also points to the importance of the solvent, DMSO, in stabilizing the charge buildup that occurs. A further computational study analyzed the stereoselectivity of the proline-catalyzed aldol addition reactions of cyclohexanone with acetaldehyde, isobu-tyraldehyde, and benzaldehyde on the basis of a similar TS.168 Another study, which explored the role of proline in intramolecular aldol reactions, is discussed in the next section.169... 

Olefination Reactions Involving Phosphonium Ylides. The synthetic potential of phosphonium ylides was developed initially by G. Wittig and his associates at the University of Heidelberg. The reaction of a phosphonium ylide with an aldehyde or ketone introduces a carbon-carbon double bond in place of the carbonyl bond. The mechanism originally proposed involves an addition of the nucleophilic ylide carbon to the carbonyl group to form a dipolar intermediate (a betaine), followed by elimination of a phosphine oxide. The elimination is presumed to occur after formation of a four-membered oxaphosphetane intermediate. An alternative mechanism proposes direct formation of the oxaphosphetane by a cycloaddition reaction.236 There have been several computational studies that find the oxaphosphetane structure to be an intermediate.237 Oxaphosphetane intermediates have been observed by NMR studies at low temperature.238 Betaine intermediates have been observed only under special conditions that retard the cyclization and elimination steps.239... 

Computational studies of both hydroalumination and carboalumination have indicated a four-center TS for the addition.220 The aluminum reagents, however, have more nucleophilic character than do boranes. Whereas the TS for hydroboration is primarily electrophilic and resembles that for attack of CH3+ on a double bond, the... 

A thorough computational study of this process has been carried out using B3LYP/ONIOM calculations.31 The rate-determining step is found to be the formation of the rhodium hydride intermediate. The barrier for this step is smaller for the minor complex than for the major one. Additional details on this study can be found at ... 

In addition, another computational study in the frame of DFT, using the hybrid functional MPW1K,53 had suggested that o-QM may be an intermediate in the reaction of the peroxy radical (HO2") with the benzyl radical at the ortho-position (Scheme 2.16),54 which should be significant in atmospheric processes and low-temperature combustion systems (T < 1500 K). 

Aromatic rings containing, s/j2-hybridized silicon atoms also constitute members of the silene family. Interest in these compounds largely focuses on the possible delocalization of electron density in the rings, the extent to which they display aromatic character, and their relative stabilities. Raabe and Michl6 have reported much data, which will not be repeated here other computational studies are reported in Section III.D. A few interesting additions to our knowledge of these systems have been reported in recent years. 

The Brookhart laboratory has contributed much of the knowledge of the polymerization mechanism for the late transition metal a-diimine catalysts. The review by Ittel provides a concise summary of the mechanistic understanding as of the year 2000 [26]. Some of the early findings will be reviewed here and additional insights reported afterward will be presented. In addition to the experimental work, many theoretical and computational studies worthy of discussion have also been carried out. These efforts have been most important in providing insight into the mechanistic details of the highly reactive nickel system, which is often difficult to study experimentally. 

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