Computational study

2 Computational Studies. Of the three significant theory reports, two dealt with chemical reactivity while the second focused on eleetronie structure. The electronic and molecular structures of select bis-r -arene lanthanides and actinides were investigated at the scalar-relativistic level with an all-eleetron DFT method using the zero-order regular approximation Hamiltonian and with 

Organometallic Chemistry, Volume 30 The Royal Society of Chemistry, 2002 

Fomine and Tlenkopatchev et al. reported on computational studies on the use of 1,2-difluoroethylene as a chain-transfer agent in the ROMP of norborn-2-ene initiated by RuCl2(PCy3)2(IMesH2)(CHPh) [155]. These calculations revealed a remarkable stability of the resulting ruthenium fluoromethylidene species 

RuCl2(=CF2)(IMesH2), thus explaining the comparable low activity of fluorine substitutes alkenes in metathesis reactions. 

The self-assembly of hypervalent iodine compounds to form macrocyclic trimers was studied using MO calculations. The principal driving force for the self-assembly of iodonium units is the formation of secondary bonding interactions between iodonium units as well as a rearrangement of primary and secondary bonding around iodine to place the least electronegative substituent in the equatorial position for every iodine in the 

The structure and reactivity of several specific classes of hypervalent iodine compounds have been investigated theoretically. Varvoglis, Tsipis and coauthors have studied the geometry and electronic stmcture of some hypervalent iodine compounds PhIX2 by means of extended Hlickel and CNDO/2 quantum chemical approaches [200], The bonding was analyzed in terms of both the model of delocalized MOs on the basis of interactions between fragment MOs derived from EHMO-SCCC calculations and that of localized MOs derived by the CNDO/2 method. The ability of these compounds to afford c -addition products with alkenes via a synchronous molecular addition mechanism was found to be theoretically feasible [200]. 

Widdowson, Rzepa and coworkers reported ab initio and MNDO-d SCF-MO computational studies of the extrusion reactions of diaryliodonium fluorides [202-204]. The results of these studies, in particular, predicted that the intermediates and transition states in these reactions might involve dimeric, trimeric and tetrameric structures. The regioselectivity of nucleophilic substitution in these reactions was investigated theoretically and supported by some experimental observations. 

Goddard and Su have investigated theoretically the mechanism of alcohol oxidation with 2-iodoxybenzoic acid (IBX) on the basis of density functional quantum mechanics calculations [134], It has been found that the rearrangement of hypervalent bonds, so-called hypervalent twisting, is the rate-determining step in this reaction. Based on this mechanism, the authors explain why IBX oxidizes large alcohols faster than small ones and propose a modification to the reagent that is predicted to make it more active [134]. 

Bakalbassis, Spyroudis and Tsiotra reported a DFT study on the intramolecular thermal phenyl migration in iodonium ylides [205]. The results of this study support a single-step mechanism involving a flve-membered ring transition state. The frontier-orbital-controlled migration also confirms the different thermal behavior experimentally observed for two different ylides [205]. 

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In this section, the results of a computational study 48 will be used to illustrate the effects of the solvent—and the significant complexity of these effects—in quantum charge transfer processes. The particular example... 

Levine R D and Wu S F 1971 Resonances in reactive collisions computational study of the H + Hj collision Chem. Rhys. Lett. 11 557... 

Helms and McCammon 1997] Helms, V., McCammon, J.A. Kinase Conformations A computational study of the effect of ligand binding. Prot. Sci. 6 (1997) 2336-2343... 

Figure 4.49 reprinted with permission from Pranata J and W L Jorgensen. Computational Studies on FK506 Conformational Search and Molecular Dynamics Simulations in Water. The Journal of the American Chemical Society 113 9483-9493. 1991 American Chemical Society. 

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. 

Polymers can be crystalline, but may not be easy to crystallize. Computational studies can be used to predict whether a polymer is likely to crystallize readily. One reason polymers fail to crystallize is that there may be many conformers with similar energies and thus little thermodynamic driving force toward an ordered conformation. Calculations of possible conformations of a short oligomer can be used to determine the difference in energy between the most stable conformer and other low-energy conformers. 

GrossHng and G. E. Ericksen, Computer Studies of the Composition of Chilean Nitrates Ores, U.S. Geological Survey, Washington, D.C., Dec. 1970. 

S. H. Oh, Thermal Response of a Monolith Catalyst Converter During Sustained Misfiring A Computational Study, SAE 881591, Society of Automotive Engineers, Warrendale, Pa., 1988. 

Further support for this approach is provided by modern computer studies of molecular dynamics, which show that much smaller translations than the average inter-nuclear distance play an important role in liquid state atom movement. These observations have conhrmed Swalin s approach to liquid state diffusion as being very similar to the calculation of the Brownian motion of suspended particles in a liquid. The classical analysis for this phenomenon was based on the assumption that the resistance to movement of suspended particles in a liquid could be calculated by using the viscosity as the frictional force in the Stokes equation... 

Biological membranes provide the essential barrier between cells and the organelles of which cells are composed. Cellular membranes are complicated extensive biomolecular sheetlike structures, mostly fonned by lipid molecules held together by cooperative nonco-valent interactions. A membrane is not a static structure, but rather a complex dynamical two-dimensional liquid crystalline fluid mosaic of oriented proteins and lipids. A number of experimental approaches can be used to investigate and characterize biological membranes. However, the complexity of membranes is such that experimental data remain very difficult to interpret at the microscopic level. In recent years, computational studies of membranes based on detailed atomic models, as summarized in Chapter 21, have greatly increased the ability to interpret experimental data, yielding a much-improved picture of the structure and dynamics of lipid bilayers and the relationship of those properties to membrane function [21]. 

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 potential energy function presented in Eqs. (2) and (3) represents the minimal mathematical model that can be used for computational studies of biological systems. Currently,... 

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. 

RA Friesner, JR Gunn. Computational studies of protein folding. Annu Rev Biophys Biomol Struct 25 315-342, 1996. 

BW Beck, Q Xie, T Ichiye. Computational study of S—H S hydrogen bonds m [4Ee-4S]-type ferredoxm x-ray and NMR structures Characterization and implications for redox potentials. Protein Sci, submitted. 

Computational studies of nucleic acids offer the possibility to enliance and extend the infonnation available from experimental work. Computational approaches can facilitate the experimental detennination of DNA and RNA structures. Dynamic information. 

A significant advantage of computational studies on nucleic acids is that reasonable guesses of the starting geometries can be made. When studying duplexes, these are typi-... 

Seckler, M.M., Brinsma, O.S.L. and van Rosmalen, G.M. 1995. Influence of hydrodynamics on precipitation a computational study. Chemical Engineering Communications, 135, 113-131. 

O. G. Mouritsen. Computer Studies of Phase Transitions and Critical Phenomena. Berlin Springer, 1984. 

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. ... 

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