The Swain Equation

Swain advanced Equation (34) analogous to that in the Swain-Lupton treatment of polar effects (Equation 21). 

The terms a and b are reaction parameters and A and B are dependent only on the solvent. A data set of 61 solvents and 77 reactions and processes were fitted to Equation (34) using 1080 data points, yielding a set of 154 reaction parameters ( and / ) and 122 solvent parameters (A and B). The solvent parameter scale was calculated using the following defined boundary conditions = B = 1 for water solvent, A = B = 0 for 

The two-parameter equations possess a family resemblance. The original Swain-Scott equation (Chapter 2) was written as a special case of the general equation Xogk Jk - ns y es where the parameters n and s have already been defined. The term es is a function of the 

The polar displacement reaction involves attack of nucleophile (N) and electrophile (E) on the substrate (S). 

---

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) ... 

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

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...

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... 

There are two ways in which an enzymic reaction can fail to satisfy the Swain-Schaad relationship, one of which is if tunneling occurs. In order to use violations of this rule to diagnose the presence of tunneling, it is necessary to eliminate the other possible reason for a violation, namely, limitation of the rate by more than one step. The derivation of the Swain-Schaad equation in Chart 3 assumes that the step that produces the isotope effect is fully rate-limiting, and if this should be untrue, then the relationship should fail without any significance for tunneling. 

Correlations between substituent-induced chemical shift differences and reactivity parameters have been examined. Good linear correlations have been obtained using the Swain-Lupton two-parameter equation ... 

Griffiths and Gutsche (23) recently studied the interconversion of deuterated mandelaldehyde dimer and 2-hydroxyacetophenone in pyridine to obtain information concerning the glyceraldehyde-dihydroxy-acetone rearrangement. Their results support an enolization mechanism requiring a base and an acid catalyst. They found a deuterium isotope effect of ca. 1.3 for the transformation of the aldehyde to the ketone. When they corrected this for the apparently differing amounts of the aldehyde form in equilibrium with the proteo dimer and the deuterio dimer, they obtained a value of 3.9. By the Swain-Schaad equation (26) ... 

To get a better understanding of what the Swain-Scott equation means, we have rewritten it in Equation 4.22 in the form that makes the linear free-energy relationship more apparent. 

A point of key importance in study of solvolysis is the nucleophilicity of the solvent. Whereas the Y and other scales have been available for measuring ionizing power for some years, there has been no satisfactory scale for nucleophilicity. Swain, Mosely, and Bown attempted to set up an equation for correlation of solvolysis rates that included both nucleophilicity and ionizing power 112 their system did not prove particularly helpful for understanding mechanism.113 The Swain-Scott equation, discussed in Chapter 4 (p. 185), was not evaluated for solvents. 

Second-order rate constants for the reactions of phenacyl bromide with a number of anionic or neutral nucleophiles in 3 2 (v/v) acetone-water have been measured at several temperatures.141 Correlation analysis with the Bronsted equation or Swain-Scott equation is not satisfactory. Better results were obtained with the two-parameter Edwards equation. 

Solvolysis of the R,R and R,S isomers of 2-bromo-9-(l-X-ethyl)fluorenes, X = Cl, Br, I, or OBs, in 25% (v/v) acetonitrile in water has been studied with respect to rates of formation of elimination products and of substitution products (X = OH or NHCOMe).142 The parent 9-(l-X-ethyl)fluorenes and the 2,2/-dibromo-9-(l-X-ethyl)-fluorenes were also studied. Various effects of leaving group and of the presence of nucleophiles on the competition between the reactions were observed and the Bronsted equation was applied to the results for the elimination reactions. A related study of solvolysis of 9-(X-methyl)fluorenes, X = I, Br, or Bs, was also carried out, in which the Swain-Scott equation was applied to nucleophilic selectivities in the S 2 reactions.143... 

---