The Swain-Lupton Equation

The F and R parameters may be determined using the Roberts and Moreland a values which are assumed to measure the field effect (F) and are related by Equation (23) from which a and b are calculated from a basis set of and Op values (originally 14 substituents). 

Values of F for other substituents (not possessing ct values) are calculated using Equation (23) from known Hammett ct and Cp parameters. 

Fand R come close to a universal set of parameters measuring polarity of a given substituent. 

An estimation of r, R, f and F parameters may be derived from Equation (25) by a non-linear least squares procedure to fit all the parameters r,/, Rj and Fj. 

The parameters F and K depend on the substituent y f, r, and h depend on the identity of the series, i. The procedure utilises an iterative calculation to converge to a best fit between predicted and observed values of logA, the term A, is added to avoid A,h for the unsubstituted compound having infinite weight. The parameters are transformed so that F = R = 0 for the hydrogen substituent, F = R = i for -NO2 and r = 0 for the o (KJK. ) values (cr ) of Zra/z.s-4-substituted cyclohexanecarboxylic acids in water and K = 0 for the -NMcj substituent. 

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Fit the data in Table 6 for the solvolysis of wcZtz-substituted phenyldimethylmethyl chlorides according to the Swain-Lupton equation using values of F and R tabulated by Leo and Hansch (Appendix 3, Table 1). 

The data fit the Swain-Lupton equation for the solvolysis of the />6zra-substituted phenyl dimethylmethyl chlorides (Figure 10) ... 

It should be recognized that all of the approaches to linear free-energy relationships have been developed on an empirical basis. The reaction constants, substituent constants, and other parameters involved are specified by the definitions of the correlation equation. The data are then treated by the equation, and the variable parameters arise from the best fit to the correlation equation. In the case of the Hammett equation, each reaction series gives rise to its characteristic p value. For the Swain-Lupton equation, the meta series and the para series would each give rise to / and r. 

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 ... 

According to the Swain-Lupton approach (SL), the a electronic constant is defined as a linear combination of the two basic electronic contributions [Swain and Lupton Jr., 1968 Swain et al., 1983 Swain, 1984 Reynolds and Topsom, 1984] based on the equation ... 

Swain-Lupton equation A dual-parameter approach to the correlation analysis of substituent effects, which involves a field constant (F) and a resonance constant (R). The original treatment was modified later. The procedure has been considerably applied, but also much criticized. 

The Yukawa-Tsuno and Young-Jencks equations have the advantage that they utilise both meta and para substituents in the same equation unlike the Dewar-Grisdale and Swain-Lupton equations (Sections... 

The Swain-Lupton, Taft and Dewar-Grisdale equations all require that the substituent in the reaction under investigation remains at the same position relative to the reaction centre. Thus meta and para series have to be treated separately unlike the Yukawa-Tsuno method where both meta and para substituents may be taken together. The Swain-Lupton treatment may be illustrated by the reaction of chloride ion with substituted benzenediazonium chlorides (Figure 7, Equation 26). ... 

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

The Swain-Lupton treatment was a reaction against the proliferation of scales of polar substituent constants. The authors maintained that the polar effect of any given substituent could be adequately expressed in terms of just two basic characteristics a field constant and a fixed resonance constant Swain and Lupton maintained that the correlation analysis of chemical reactivity data and spectroscopic data of aromatic systems could be carried out satisfactorily in terms of and 9. cf the four cri -type parameters introduced for the DSP equation), meta and para series being dealt with separately, as in the case of the DSP equation. The assumptions involved in establishing the and 9 . scales provoked much criticism. Nevertheless, the treatment achieved fair success when applied to chemical reactivity data and some spectroscopic data, particularly The most... 

The fact that two cr-constants are needed to explain the substituent elfects led to the proposal that each a value is a dilferent linear combination of two separate factors field and resonance elfects, for example, the Swain-Lupton Tand R (see Table 3.1), as shown in equation (3.4). 

The successful decomposition of a values into field and resonance components could eliminate the need for several sets of o values. The Swain-Lupton system must treat meta- and para-substituted compounds as separate reaction series, with differing values for r and / for a meta versus para placement of the substituent. The reason is that resonance interactions are usually stronger in the para series. There must also be an additional parameter for each reaction, since the relative sensitivity to resonance and field effects differs from reaction to reaction. Swain and Lupton have observed satisfactory correlation for over forty reaction series using and This treatment also provides an indication of the relative importance of resonance and field interactions. The mathematical manipulations are, of course, more complex than in the simple Hammett equation. The Swain-Lupton correlations are carried out by a computer program that provides a best-fit correlation in terms of /, r, and The computation also yields percent resonance by comparing the magnitude of/ andr. 

Theoretical Studies and Physical Properties.—Quantum chemical calculations on the reactivity of thienothiophens have been carried out. " The e.s.r. spectra of the radical anions of carbonyl, nitro, and cyano derivatives of the two [b]-fused thiophens have been studied. The proton chemical shifts of 2-substituted thieno[2,3-b]thiophens have been correlated with the two-parameter equation of Swain and Lupton. " ... 

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... 

Several approaches have been made to calculate 13C chemical shifts of coumarins by MO methods. Good correlations were found between the 13C chemical shift values of coumarin (also protonated) and the n charge densities calculated by the CNDO/2 method [962], and of coumarins with it charge densities calculated by the Hiickel MO method (which, however, fails for methoxylated coumarins) [965]. Chemical shifts of mono- and dimethoxycoumarins have been correlated with parameters determined by refined INDO MO calculations, in which n bond orders, atom-atom polarizabilities, excitation energies and electron-nucleus distances were taken into consideration [966], In 3-substituted 4-hydroxy and 4-hydroxy-7-methoxycoumarins chemical shifts were found to be related to Swain and Lupton s parameters iF and M [388], according to equation 5.4 (SE = Substitution Effect) ... 

Swain and Lupton (25) defined their localized parameter, F, by again using the 4-substituted bicyclo[2.2.2]octane-l-carboxylic acids as the model system. The pKa values measured by Holtz and Stock (26) in 50% aqueous ethanol at 25° constituted the major part of the data which were then used to define F by means of the equation... 

As we have seen, a values may involve some resonance contribution, so the use of cr and cr terms does not totally distinguish between field and resonance effects. Swain and Lupton proposed using discrete field (f) and resonance R) substituent constants (equation 6.94). Instead of a single reaction constant p, two terms measured the influence of field effects (/) and resonance (r) on the reaction. ... 

Undoubtedly, the possible addition of other potential independent parameters to equation 3e would increase the correlation coefficient and decrease the standard error of the estimate. Specifically, the following variables were also investigated but were found to result only in negligible contributions to the quality of the regressions modified Swain and Lupton s field (F) and resonance (R) parameters (Hansch and Leo 1979), (log P), (AMR), the number of conjugated double bonds, ionization potential (in methanol), and several indicator variables for structural fragments, such as N, NH2, CO, and so forth. However, for several of these parameters only incomplete data sets are available and no significant increase of the correlations over that of equation 3d with up to five independent variables was observed. 

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