Tolman parameters

That the degree of consistency observed for the various routes to the determination of the surface tension is not the result of a cancellation of errors is demonstrated by the agreement displayed by the surfaces of tension in Figure 4. Also shown is the limiting form whose slope is one and whose intercept defines the Tolman parameter (24)... 

Radially dependent surface tensions computed from the YBG theory are compared with representations in the Tolman parameter, which for this state is 1.668or, using the Irving-Kirkvood localization function. The reduced temperature is 0.76. 

Ve see in Figure 7 that Tolman s representation of the radially dependent surface tension also leads to a vanishing thermodynamic barrier, at high but metastable supersaturations, when a value of 6 computed from solutions of the YBG equation on the planar interface is used. This value of the Tolman parameter is consistent with values obtained from simulation studies of the planar Lennard-Jones surface (28,29). It is apparent that the physical picture of nucleation is highly dependent upon the assumed radial dependence of the surface tension. 

In a first step, the free parameters of the condensation model ia Sand were determined by comparing calculated and measured pressure profiles. As an example, results for an expansion of the equimolar mixture are shown in Fig.7. In the left part, the condensation coefficient was varied with constant values of the parameters and 8- In the right diagram, the Tolman parameter 8 of the surface tension is varied, while and are kept constant. As a result of a gre at number of such comparisons it followed that the agreement between measured and calculated pressure profiles was the best, on the whole, if the following set of parameters... 

LNi(CO)3 species are not available for all cla ses of ligands, and to extend the Tolman parameters to other clas.ses the v (CO) values of LNi(CO)3 have been predicted computationally. ... 

L. Perrin, E. Clot, O. Eisenstein, J. Loch and R. H. Crabtree. Computed ligand electronic parameters from quantum chemistry and their relation to Tolman parameters. Lever parameters, and Hammett constants. Inorg. Chem. 40, 2001, 5806-5811. 

The nucleophilic carbcnes are phosphine-mimics but they are much more. They reside at the upper end of the Tolman electronic and steric parameter scales. Much remains to be explored with these ligands. With a rudimentary understanding of ligand stereoelectronic properties, we feel confident much exciting chemistry remains to be explored. 

For monodentate ligands, e.g., triphenylphosphane, Tolman s cone-angle 0 and the electronic parameter x have a significant influence on the activity and the selectivity of the resulting catalyst system [24,25]. As regards bidentate ligands, which provide two coordination centers for the transition metal, the so-called bite angle fi determines the selectivity of the formed aldehydes. 

Many attempts have been undertaken to define a reliable steric parameter complementary to the electronic parameter. Most often Tolman s parameter 0 (theta) is used. Tolman proposed to measure the steric bulk of a phosphine ligand from CPK models in the following way. From the metal centre, located at a distance of 2.28 A from the phosphorus atom in the appropriate direction, a cone is constructed which embraces all the atoms of the substituents on the phosphorus atom (see Figure 1.6). 

The transition metal catalysed addition of HCN to alkenes is potentially a very useful reaction in organic synthesis and it certainly would have been more widely applied in the laboratory if its attraction were not largely offset by the toxicity of HCN. Industrially the difficulties can be minimised to an acceptable level and we are not aware of major accidents. DuPont has commercialised the addition of HCN to butadiene for the production of adiponitrile [ADN, NC(CH2)4CN], a precursor to 1,6-hexanediamine, one of the components of 6,6-nylon and polyurethanes (after reaction with diisocyanates). The details of the hydrocyanation process have not been released, but a substantial amount of related basic chemistry has been published. The development of the ligand parameters % and 0 by Tolman formed part of the basic studies carried out in the Du Pont labs related to the ADN process [1],... 

Unfortunately, for all these reasons the conclusions cannot be applied quantitatively for description of the pH effects in the RCH-RP process. There are gross differences between the parameters of the measurements in [97] and those of the industrial process (temperature, partial pressure of H2, absence or presence of CO), furthermore the industrial catalyst is preformed from rhodium acetate rather than chloride. Although there is no big difference in the steric bulk of TPPTS and TPPMS [98], at least not on the basis of their respective Tolman cone angles, noticable differences in the thermodynamic stability of their complexes may still arise from the slight alterations in steric and electronic parameters of these two ligands being unequally sulfonated. Nevertheless, the laws of thermodynamics should be obeyed and equilibria like (4.2) should contribute to the pH-effects in the industrial process, too. 

The preparation of carbonyl-lr—NHC complexes (Scheme 3.1) and the study of their average CO-stretching frequencies [7], have provided some of the earliest experimental information on the electron-donor power of NHCs, quantified in terms of Tolman s electronic parameter [8]. The same method was later used to assess the electronic effects in a family of sterically demanding and rigid N-heterocyclic carbenes derived from bis-oxazolines [9]. The high electron-donor power of NHCs should favor oxidative addition involving the C—H bonds of their N-substituents, particularly because these substituents project towards the metal rather than away, as in phosphines. Indeed, NHCs have produced a number of unusual cyclometallation processes, some of which have led to electron-deficient... 

The surface tension is very insensitive to changes in supersaturation. While the planar surface tension is, of course, temperature-dependent, the ratio of the small system surface tension to the planar limit is nearly independent of temperature. This simplicity in the functional dependence of the radially dependent surface tension has been anticipated by a number of workers in terms of the parameter defined by Equation 18. Tolman obtained the following differential equation... 

Strohmeier showed that the IR carbonyl frequencies of metal complexes could be used as a measure of the electronic properties of the ligands [8]. Tolman introduced a systematic approach to describe electronic and steric ligand effects [9]. The electronic parameter / is based on the difference in the IR frequencies of Ni(CO)3L and the reference compound Ni(CO)3(P Bu3), similar to the method introduced by Strohmeier. For phosphorus ligands the cone angle 6 is defined as the apex angle of a cylindrical cone, centered at 2.28 A from the center of the P atom, which touches the outermost atoms of the model. 

Table 2.4-2. Correlation of Tolman s steric parameter with other steric parameters, using the isosteric principle 74, 7S) ...

The El Lever parameter was also shown [71] to correlate linearly with other parameters that measure the net electron-donor character of a ligand (L), namely the Tolman s electronic parameter TEP) [81] for phosphines and a computed electronic parameter CEP) [71] based (as TEP) on the infrared A v CO) frequency in complexes [NiL(CO)3], which is determined by the electronic effect of L. 

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