Theoretical Support

Both increasing the bite angle and increasing the steric bulk of the diphosphine ligand stabilize the 14-electron q -acyl complex. Increasing the steric bulk of the ligand strongly disfavors the formation of ethene complex and consequently increases the barrier for ethene insertion, as expected. 

For all methanolysis pathways considered in this study, increasing the bite angle of the diphosphine ligand increases the rate of methanolysis. This is attributed to the involvement of electron-rich intermediates and/or transition states in all three methanolysis pathways. 

The steric bulk of the diphosphine ligand hardly affects the barriers for methanolysis via the stepwise and concerted reductive elimination pathways. Based on these observations, it was postulated that the high activity and chemoselectivity in the methoxycarbonylation of ethene observed for t-butyl substituted wide bite angle diphosphine ligands are determined by a combination of electronic and steric effects induced by the diphosphine ligand. The high electron density at the metal center 

Rhodium-Catalyzed Methanol Carbonylation the Ligand-Modified Monsanto Process 

The process presents a 100% atom economy with all the atoms in the reactants going into the product (see Equation 1.1), and compared to previous methods benefits of a reduced waste and easier (and cheaper) product separation. 

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These calculations lend theoretical support to the view arrived at earlier on phenomenological grounds, that adsorption in pores of molecular dimensions is sufficiently different from that in coarser pores to justify their assignment to a separate category as micropores. The calculations further indicate that the upper limit of size at which a pore begins to function as a micropore depends on the diameter a of the adsorbate molecule for slit-like pores this limit will lie at a width around I-So, but for pores which approximate to the cylindrical model it lies at a pore diameter around 2 5(t. The exact value of the limit will of course depend on the actual shape of the pore, and may well be raised by cooperative effects. 

Scheme 41 Experimental and theoretical supports for the electrostatic interaction...

The acid dissociation of neutral molecules is such a highly endothermic reaction that the acid dissociation of nitromethane can hardly take place. The results of the calculations presented here provide a theoretical support for nitromethane as an ideal model of aprotic solvent in the acid-base theory of organic molecules. 

Product analysis by NMR indicated an isotope effect at 118°C of = 2.14, corrected for numbers of H versus D. On lowering the temperature to -12°C, however, it was found that the isotope effect increased to 3.25. Referring to earlier experimental results on the C-H shift in methylchlorocarbene, " the authors cited the normal temperature dependence of the isotope effect as evidence against tunneling in 64. In retrospect, however, as noted above, theoretical support for an atypical inverse temperature dependence in methylchlorocarbene has been refuted. Hence, the involvement of tunneling in 62/64 at ambient temperatures is still an open question. 

What STM established first in 1991 for both Cu(110) K and Cu(110)-Cs systems was the localised nature of the reconstruction process and the atom resolved details of the complexity of the structural changes observed with increasing coverage.15 In 1993, Doyen et al.20 provided theoretical support for the experimental observations with both the Cu(110) and Au(110) surfaces. 

Although, as proposed by Lewis, the octet rule is a purely empirical rule, the advent of orbital models appeared to add some theoretical support to the octet rule. For period 2 elements a maximum of only four orbitals, the 2s and the three 2p orbitals, are available for describing the bonds in terms of localized bonding and nonbonding orbitals, because other orbitals such as 3s, 3p, and 3d have energies that are too high. As a consequence, the octet rule came to be regarded more as a physical law than as a purely empirical rule. So it was... 

We shall review some molecular models, at different levels of approximation, which help theoretically support the previous results. ... 

J. Ji, S. Narayan-Sarathy, R.H. Neilson, J.D. Oxley, D.A. Babb, N.G. Rondon, and W.S. Jr. Smith, [p-( (Trifluorovinyl)oxy)phenyl]lithium formation, synthetic utility, and theoretical support for a versatile new reagent in fluoropolymer chemistry, Organometallics, 17 783-785 (1998). 

Along with the historical events that were mentioned above, one should recall three instances when aromatic systems were detected experimentally but failed to be recognized as such in the absence of theoretical support. The first one involves a carbocy-clic aromatic system, while the other two deal with heteroaromatics. 

Fig. 2.4 A possible pathway for rhodium-catalyzed hydroboration by RhCI(PPh3)3, based on the mechanism of hydrogenation and the contributions of Evans and others [17], This takes into account the theoretical support for an associative pathway [13] and the observed irreversibility of the H-transfer step with styrenes.

Having selected an appropriate data set, we must select a type of distribution and fit the distribution to the data, or else use an empirical or other nonparametric distribution. There appears to be some mechanistic basis for the log-normal distribution, for environmental concentrations (Ott 1990, 1995). However, in a given situation there may not be very strong theoretical support for a specific type of distribution, log-normal or otherwise. Alternative distributions may need to be considered based on the quality of fit of the distribution to data. Therefore, it is desirable to have quantitative indices that can be used to compare or rank distributions based on agreement with data. The fit of the log-normal distribution (or whatever distributions we may choose) should be evaluated in particular situations, using graphical as well as statistical procedures. 

These experimental results received theoretical support from band calculation results, Brooks found that for UN and PuN the Stoner criterion was just satisfied and that these nitrides were itinerant magnetic systems. 

The most essential progress from the point of view of application of this theory in catalysis and chemisorption has actually been achieved by the very first papers (48-50), where the so-called coherent potential approximation (CPA) was developed and applied. By means of this, photoemission data were explained in a quite satisfying way and the catalytic research got full theoretical support for some of the ideas introduced in catalysis earlier on only semiempirical grounds (5) namely, individual components are distinguishable for molecules from the gas phase and the alloy atoms preserve very much of their metallic individuality also in alloys—something that was impossible according to the RBT and the early electronic theory of catalysis. 

The Process Is Theoretically Supported Considering the Process A. A Potential and Field-Free A Potential General Relativistic Considerations Indefiniteness Is Associated with the A Potential... 

Casassa and Tagami (50) have given a theory for the partition of macromolecules, linear and branched, between a solution and cavities (such as the pores of a GPC gel). They have calculated elution volumes from their results, which agree closely with those derived from the hydrodynamic volume assumption this gives theoretical support to the use of hydrodynamic volume as a correlating parameter for branched polymers. This parameter has been used in studies of branching in polyethylene (Section 10). 

It appears that the formal theories are not sufficiently sensitive to structure to be of much help in dealing with linear viscoelastic response Williams analysis is the most complete theory available, and yet even here a dimensional analysis is required to find a form for the pair correlation function. Moreover, molecular weight dependence in the resulting viscosity expression [Eq. (6.11)] is much too weak to represent behavior even at moderate concentrations. Williams suggests that the combination of variables in Eq. (6.11) may furnish theoretical support correlations of the form tj0 = f c rjj) at moderate concentrations (cf. Section 5). However the weakness of the predicted dependence compared to experiment and the somewhat arbitrary nature of the dimensional analysis makes the suggestion rather questionable. 

Some useful correlations which can be used for a first approximation of the kLa s or c s in laboratory-scale ozone reactors can be found in Dudley (1995) for bubble columns, and Libra (1993) for STRs. Various correlations found in the literature, empirical as well as those based on theoretical or dimensional analysis, have been compared to results from their own experiments. Dudley concluded that correlations based on theoretical support performed better than those developed by curve-fitting. 

FeNO angle of 150.3°. It has been suggested (32) that the bonding of the nitrosyls remote from platinum arises from the interaction of the nitrosyl n orbitals with the orbitals concentrated in the Fe-Fe bond, whose disposition in turn is determined by the puckering of the Fe2S2 ring however, no theoretical support for this idea is yet available. 

A theoretical and an experimental study of die acid-catalysed isomerization of 1-acylaziridines to die oxazolines has been callied out.43 Such isomerization may conceivably proceed by various padis, but the 5ki mechanism, as in (44) and (45), has often been assumed to operate. The re-examination in tiiis paper finds experimental and theoretical support for tiiis in certain cases. 

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