Transmission factors

These and other studies of the relative substituent effects of X and CH X in nitration were considered in terms of the transmission factor a of the methylene group. To avoid complications from conjugative interactions, attention was focussed mainly on substitution at the meta-position, and ct was defined in terms of partial rate factors by the equation ... 

Acoustic transmission factor T Average linear gas velocity IX... 

LEIS the energies of the ions are too low for PIPS detectors and would lead to a sig-nal-to-noise ratio less than unity. A stack of microchannel plates is, therefore, used to detect the ions in LEIS. The detection efficiency of the microchannel plates is included in the experimental transmission factor Tin Eq. (3.34). 

Next we turn to the magnitudes of the p constants. Evidently if p = 0, there is no substituent effect on reactivity. Moreover because p = -I-1.000 by definition for the aqueous ionization of benzoic acids, we have a scale calibration of sorts. Wiberg gives examples of p as a measure of the extent of charge development in the transition state. McLennan" has pointed out that p values must first be adjusted for the transmission factor before they can be taken as measures of charge devel-... 

Table 2-15 [15] tabulates the transmission factors of the various equations. Most of these are established as correction factors to the correlation of various test data. 

Gas transmission factor, or sometimes termed efficiency factor, see Table 2-15, f = Fanning friction factor... 

E = transmission factor, usually taken as 1.10 X 11.2 d0167 (omit for pipe sizes smaller than 24 in.) d = pipe I.D., in. 

American Gas Association method, 121 Complex pipe systems, 122 Low pressure air, steam, 131 Panhandle formula, 120, 121 Panhandle-A formula, 121 Parallel system, 122 Series system, 122 Transmission factors, 120 Weymouth formula, 120 Flowsheet symbols, 17... 

Here, as before, the transmission factor F expresses the fraction of the trajectories which continue to the product state after arriving at X (see Fig. 

FIGURE 2.2. A schematic description of the evaluation of the transmission factor F. The figure describes three trajectories that reach the transition state region (in reality we will need many more trajectories for meaningful statistics). Two of our trajectories continue to the product region XP, while one trajectory crosses the line where X = X (the dashed line) but then bounces back to the reactants region XR. Thus, the transmission factor for this case is 2/3. 

Reaction coordinates Reactive trajectories transition states, 43 transmission factor, 42 solution reactions, 46,90 Reaction coordinates, 41-44, 88,91 for enzymatic reactions, 215 reactive trajectories, see Reactive trajectories... 

Transition state theory, 46,208 Transmission factor, 42,44-46,45 Triosephosphate isomerase, 210 Trypsin, 170. See also Trypsin enzyme family active site of, 181 activity of, steric effects on, 210 potential surfaces for, 180 Ser 195-His 57 proton transfer in, 146, 147 specificity of, 171 transition state of, 226 Trypsin enzyme family, catalysis of amide hydrolysis, 170-171. See also Chymotrypsin Elastase Thrombin Trypsin Plasmin Tryptophan, structure of, 110... 

Various statistical treatments of reaction kinetics provide a physical picture for the underlying molecular basis for Arrhenius temperature dependence. One of the most common approaches is Eyring transition state theory, which postulates a thermal equilibrium between reactants and the transition state. Applying statistical mechanical methods to this equilibrium and to the inherent rate of activated molecules transiting the barrier leads to the Eyring equation (Eq. 10.3), where k is the Boltzmann constant, h is the Planck s constant, and AG is the relative free energy of the transition state [note Eq. (10.3) ignores a transmission factor, which is normally 1, in the preexponential term]. 

A quantitative determination of such matrix elements (to be elaborated below) is of crucial importance because it not only allows an absolute evaluation of the desired rate constants but also helps to reveal the qualitative aspects of the mechanism. In particular, questions regarding the magnitude of electronic transmission factors and the relative importance of ligands and metal ions in facilitating electron exchange between transition metal complexes can be assessed from a knowledge of... 

Figure 4. Calculated HAB values as a function of Fe -Fe separation, based on the structural model given in Figure 1 and the diabatic wavefunctions I/a and f/B. Curves 1 and 2 are based on separate models in which the inner-shell ligands are represented, respectively, by a point charge crystal field model [Fe(H20)62 -Fe(HsO)63 ] and by explicit quantum mechanical inclusion of their valence electrons [Fe(HgO)s2 -Fe(H20)s3+] (as defined by the dashed rectangle in Figure 1). The corresponding values of Kei, the electronic transmission factor, are displayed for various Fe-Fe separations of interest.

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