Swain equation

We might mention here without further amplification that this equation reduces to several well known empirical relationships under various limiting conditions (e. g. the Swain equation (9), the Bronsted equation (70)), and has the same form as equation (1) of Edwards (4). 

The Swain Equation (34) provides very accurate predictive power for a limited range of solvents and processes based on a statistical analysis of a five-parameter equation. The origins of the Swain parameters are not explicit, although the acity (A) and basity (B) coefficients are related to electrophilic and nucleophilic processes respectively. Many fundamental processes have been implicated in solvent effects and the equation of Koppel and Palm (Equation 37) incorporates the major factors thought to be involved. 

Although the Swain equation made a very important contribution, it led to some confusion because it was originally applied to all types of reactions including alkylation, acylation, and sulfonylation. The nucleophilic order is highly dependent on the nature of the substrate, and the equation was modified in the Swain-Edwards four-parameter equation (7). 

That is, the reactivity is related to the redox potential of N-, and equation 3 reduces to the Swain equation (5) ... 

For a given extent of reaction, Eq. (3-33) is an equation with the two unknowns r and d. The procedure, in essence, is to measure F at two times and to solve the two simultaneous equations. In practice the problem is more difficult than this because an analytical solution cannot be obtained moreover d is itself dependent upon time. Swain " constructed tables of d (and of log d) as a function of r for three different extents of reaction. Curves of log d vs. log r are plotted. The curve... 

In 1955 Swain, et al. proposed a four-parameter equation, Eq. (8-74), to describe the solvent dependence of solvolytic reactions. 

Swain et al. ° analyzed solvent effects on 1080 pieces of rate and equilibrium data, showing that more than 98% of the effects could be correlated by the four-parameter equation... 

The LFER correlation according to the Swain-Scott equation for nucleophilic attack on /3-propiolactone. Data are from Ref. 13. 

Spin trap, 102 Statistical kinetics, 76 Steady-state approximation, 77-82 Stiff differential equations, 114 Stoichiometric equations, 12 Stopped-flow method, 253-255 Substrate titration, 140 Success fraction approach, 79 Swain-Scott equation, 230-231... 

The following overall nucleophilicity order for Sn2 mechanisms (in protic solvents) was given by Edwards and Pearson RS > ArS >1 >CN > OH > Nj > Br > ArO > Cl > pyridine > AcO > H2O. A quantitative relationship (the Swain-Scott equation) has been worked out similar to the linear free energy equations considered in Chapter 9 ... 

Table IV lists comparative SD and / values for fittings of all of the reactions of Table II and III with each of the gr scales derived in this paper. The comparison includes figures for fittings with F and R values of Swain and Lupton (S L) and fitting with the Hammett equation. We believe the results given in Table IV provide a clear confirmation of the uniqueness and limited generality of the o/2(ba) scale. Very consistently, the fit achieved by the or (BA) scale is shown in Table IV to be superior by significant factors to that achieved by any of the other scales or by the simple op treatment. This fact is clearly reflected in the overall / values and the similarly weighted root-mean-square / values, F = y/lfnif lN, sum taken over all reactions. The value of F is. 067 for the basis sets of Table II (compare with overall / of. 058). The comparable F values are. 140 for Or, . 088 for S L, and. 155 for 0(p) with the data differences as explained in Table IV. For all sets of Table IV, the corresponding figures are. 073 for o (ba). -143 for a%, . 097 for S L, and. 209 for 0(py...

There are several systematic nuclear magnetic resonance studies of the interaction between the substituents and the protons and ring atoms of five-membered heterocycles. In some 2-substituted furans, thiophenes, selenophenes, and tellurophenes there is a linear correlation between the electronegativity of the chalcogen and several of the NMR parameters.28 As there also is a good correlation between the shifts of the corresponding protons and carbons in the four heterocycles, the shifts of unknown selenophene and tellurophene derivatives can be predicted when those of thiophene are known. This is of special interest for the tellurophene derivatives, since they are difficult to synthesize. In the selenophene series, where a representative set of substituents can be introduced in the 2- as well as in the 3-position, the correlation between the H and 13C shifts and the reactivity parameters according to Swain and Lupton s two-parameter equation... 

Diparametric equation A relationship in which the effect of structure on a property is represented by two parameters, one of which is generally composite. Examples discussed in this work include the LD, CR and MYT equations. Other examples are the Taft, Ehrenson and Brownlee DSP (dual substituent parameter), Yukawa-Tsuno YT and the Swain, Unger, Rosenquist and Swain SURS equations. The DSP equation is a special case of the LDR equation with the intercept set equal to zero. It is inconvenient to use and has no advantages. The SURS equation uses composite parameters which are of poorer quality than... 

The secondary deuterium KIEs obtained by converting the secondary tritium KIEs found for the E2 reactions of several different 2-arylethyl substrates into secondary deuterium KIEs with the Swain-Schaad equation (Swain et al., 1958) are in Table 36. As discussed above, one would expect the secondary deuterium isotope effect to reflect the extent to which rehybridization of the /3-carbon from sp3 of the reactant to sp2 in the product has taken place in the transition state. According to this reasoning, the secondary tritium EIE should be a good estimate of the maximum secondary tritium KIE. Because these reactions were not reversible, the EIE could not be measured. However, one can estimate the EIE (the maximum expected secondary KIE) using Hartshorn and Shiner s (1972) fractionation factors. The predicted EIE (Kh/Kd) values were 1.117 at 40°C and 1.113 at 50°C. Seven of the reactions... 

In reactions 10.16 and 10.17 we label the corresponding rate constants ko and kT, respectively. The relationship between kn/ko and kp/kr is approximately described by the Swain-Schaad equation... 

For harmonic oscillators recall that the ZPE s, (ZPE = (l/2)hc(//p,)1/2), and ZPE differences scale proportionally to (1/p-h) and (1/ jid), respectively. The q s are oscillator reduced masses and / is the isotope independent force constant. Thus, writing equations analogous to Equation 10.19 for tritium substitution, and taking the ratio, we obtain kH/kT = (kH/kD)x where x, the Swain-Schaad exponent in the harmonic approximation is expressed... 

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