Computational studies, mechanism

Using MMd. calculate A H and. V leading to ATT and t his reaction has been the subject of computational studies (Kar, Len/ and Vaughan, 1994) and experimental studies by Akimoto et al, (Akimoto, Sprung, and Pitts. 1972) and by Kapej n et al, (Kapeijn, van der Steen, and Mol, 198.V), Quantum mechanical systems, including the quantum harmonic oscillator, will be treated in more detail in later chapters. 

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 temporal behavior of molecules, which are quantum mechanical entities, is best described by the quantum mechanical equation of motion, i.e., the time-dependent Schrdd-inger equation. However, because this equation is extremely difficult to solve for large systems, a simpler classical mechanical description is often used to approximate the motion executed by the molecule s heavy atoms. Thus, in most computational studies of biomolecules, it is the classical mechanics Newtonian equation of motion that is being solved rather than the quantum mechanical equation. 

A recent paper by Singh et al. summarized the mechanism of the pyrazole formation via the Knorr reaction between diketones and monosubstituted hydrazines. The diketone is in equilibrium with its enolate forms 28a and 28b and NMR studies have shown the carbonyl group to react faster than its enolate forms.Computational studies were done to show that the product distribution ratio depended on the rates of dehydration of the 3,5-dihydroxy pyrazolidine intermediates of the two isomeric pathways for an unsymmetrical diketone 28. The affect of the hydrazine substituent R on the dehydration of the dihydroxy intermediates 19 and 22 was studied using semi-empirical calculations. ... 

Further computational studies on adenines and adenosines concern the reaction mechanism of ribonuclease A with cytidyl-3,5 -adenosine [99BP697] and the molecular recognition of modified adenine nucleotides [99JMC5338]. 

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. 

Apart from the question whether the 14-electron species 12-B is a relevant intermediate, computational studies have been conducted in order to shed light on other aspects of the mechanism. Stereochemical issues, for instance, have not yet been investigated by experiment. DFT calculations suggest that attack of the alkene to 12-B occurs trans, because cis attack is associated with a rather high barrier [30b]. 

The detailed mechanism of this enantioselective transformation remains under investigation.178 It is known that the acidic carboxylic group is crucial, and the cyclization is believed to occur via the enamine derived from the catalyst and the exocyclic ketone. A computational study suggested that the proton transfer occurs through a TS very similar to that described for the proline-catalyzed aldol reaction (see page 132).179... 

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... 

These catalysts are activated by hydrogenation of the cyclooctadiene ligand, which releases cyclooctane and opens two coordination sites at iridium. The mechanism has been probed by computational studies.40 It is suggested that the catalytic cycle involves... 

According to a DFT computational study, this mechanism is plausible.256... 

Perhaps the most extensive computational study of the kinetics of NO reactions on Rh and Pd surfaces has been provided by the group of Zgrablich. Their initial simulations of the NO + CO reaction on Rh(lll) corroborated the fact that the formation of N-NO intermediate is necessary for molecular nitrogen production [83], They also concluded that an Eley-Rideal mechanism is necessary to sustain a steady-state catalytic regime. Further simulations based on a lattice-gas model tested the role of the formation of... 

Despite advent of theoretical methods and techniques and faster computers, no single theoretical method seems to be capable of reliable computational studies of reactivities of biocatalysts. Ab initio quantum mechanical (QM) methods may be accurate but are still too expensive to apply to large systems like biocatalysts. Semi-empirical quantum methods are not as accurate but are faster, but may not be fast enough for long time simulation of large molecular systems. Molecular mechanics (MM) force field methods are not usually capable of dealing with bond-breaking and formation... 

In many cases the most interesting results of a computational study are the relative energies of transition states and intermediates because they determine the reaction mechanism. In this section we will try to outline when improved active-site geometries can be expected to have important effects on relative energies. 

Cytosine was the first nucleobase whose radiationless decay was studied with quantum mechanical methods. Nevertheless, its first excited states are not so clearly separated as in uracil and thymine, and this causes complications in the computational studies of the photophysics. So, many computational studies have been reported to elucidate the mechanisms for radiationless decay to the ground state but, not always with the same conclusions. 

Experimentally Merbach et al. (67) found for the DMSO exchange at [Be(DMSO)4]2+ (144) an associative interchange or an associative mechanism by NMR studies. Up to now no adequate computational study investigated the mechanism in detail, but exploratory calculations suggest an associative interchange mechanism (161). 

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