The Yukawa-Tsuno Equation

Where resonance occurs between substituent and a reaction centre suffering negative charge build-up, Equation (13) may be employed.  

Young and Jencks proposed a modified form of the Yukawa-Tsuno Equation (14) which has the advantage over Equation (12) in that P (g - g) directly measures the proportion of free energy change caused by electron donation via a resonance route.  

A similar argument applies to the case where electron withdrawal involves a resonance pathway.  

The r value of the Yukawa-Tsuno equation compares the energy of the resonance route with that in the standard (where r is defined as unitv). 

In the case of the alkaline hydrolysis of aryl carbamates the p is 2.64 0,44 which is, within experimental error, the same as the p for the dissociation of substituted phenols (2.23) this is consistent with complete expression of the resonance interaction between developing oxyanion and the substituent. 

The addition of extra terms will naturally improve a correlation and the a and correlations essentially do this for reactions with a resonance component. The simple approach neglects the possibility that the resonance and inductive transmissions may differ in model and reaction in question. Yukawa and Tsuno [48] proposed a correlation where p and p (Eqn. 60) are essentially measures of transmission of substituent effects by induction and resonance. 

The form of equation used by Yukawa and Tsuno expressed the p value as a linear function of the inductive one (Eqn. 61). Humffray and Ryan [38] extended Eqn. 61 to the electron-releasing substituents where (a ) replaces (a ) in Eqns. 60 and 61. 

When r is zero the correlation is a simple Hammett function and if r is unity the correlation is with or a. Fig. 16 illustrates the application of Eqn. 61 to the alkaline hydrolysis of triethylphenoxysilanes where the simple Hammett a values 

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One approach is to correct for the added resonance interaction. This is done in a modification of the Hammett equation known as the Yukawa-Tsuno equation. ... 

Another example of enhanced sensitivity to substituent effects in the gas phase can be seen in a comparison of the gas-phase basicity for a series of substituted acetophenones and methyl benzoates. It was foimd that scnsitivtiy of the free energy to substituent changes was about four times that in solution, as measured by the comparison of A( for each substituent. The gas-phase data for both series were correlated by the Yukawa-Tsuno equation. For both series, the p value was about 12. However, the parameter r" ", which reflects the contribution of extra resonance effects, was greater in the acetophenone series than in the methyl benzoate series. This can be attributed to the substantial resonance stabilization provided by the methoxy group in the esters, which diminishes the extent of conjugation with the substituents. 

In the Yukawa-Tsuno equation (1959)58 (equation 4), the sliding scale is provided by multiple regression on a and (cr+ — electron demanding than the ionization of benzoic acid. 

Yukawa, Tsuno and their colleagues121 have made studies more specifically related to determining substituent constants, which have included both methylsulfinyl and methylsulfonyl groups. Hydroxyl chemical shifts were determined for a large number of m-and p-substituted phenols in DMF and in DMSO. The results were treated by the LArSR relationship121 (usually called the Yukawa-Tsuno equation, see Section II.B) ... 

There have been a number of attempts, by the introduction of a further parameter into the Hammett equation, to quantify this graded response—via through-conjugation—on the part of a p-substituent. Among the best known of these is the Yukawa-Tsuno equation, [7], which, in the form shown here, is... 

Relative activation enthalpies (Aif) in Table 2 were converted to o% kx k ) at 298 K, and were plotted against Hammett a constants. Here, we used enthalpies, because the size of the entropy and hence the free energy depend much on low frequencies, which are less reliable than higher frequencies, especially for compounds with weak interactions such as TS (8). The use of free energy (AG ) gave similar correlations with more scattered points. As for the Hammett o constant, we used dual-parameter o constants in the form of the Yukawa-Tsuno equation (LArSR equation) (9) as defined in eq 3. Here, the apparent a constant (aapp) has a variable resonance contribution parameter (r), which varies depending on the nature of the reaction examined for t-cumyl... 

The electronic effect of the substituents on nitro-aromatics is rationalized by the Yukawa-Tsuno equation. 

Multiparameter treatments such as the Yukawa-Tsuno equation and the dual substituent-parameter equation have long been important and further treatments have been devised in recent years. A final section is devoted to some of these, with an indication of the place of NO2, NH2 and some other groups in these treatments. 

In the Yukawa-Tsuno equation (1959)85 (equation 3), the sliding scale is provided by multiple regression on a and (cr+ — a) or (a — a), depending on whether the reaction is more or is less electron-demanding than the ionization of benzoic acid. (There is a corresponding equation for equilibria.) The quantity r gives the contribution of the enhanced 7 effect in a given reaction. (The equation was modified in 196686 to use cr° instead of a values, see below, but the essential principles are unaltered.)... 

There are extensive data for the acid-catalyzed protiodesilylation of XCgELrSiMes in methanol-aqueous perchloric acid or acetic acid-aqueous sulphuric acid at 50°C225. Correlation analysis of the partial rate factors (relative rate constants) by means of the Yukawa-Tsuno equation (Section n.B) finds p = —5.3 and r+ = 0.65. These values are consistent with a relatively low demand for stabilization of the transition state by electron delocalization, i.e. the transition state is early along the reaction coordinate, p-NO2 is highly deactivating with / = 14 x 10 but 0-NO2 is even more deactivating, with / = 6.8 x 10-5. This contrasts with the deactivation order discussed above for nitration and chlorination (Table 6), and may be explained in terms of the early transition state, well removed from the Wheland intermediate. 

In considering quantitatively the response of these groups to high electron-demand there are certain caveats. In the first place it must be remembered that amino and related groups are liable to be protonated in the kind of media often used for studying electrophilic aromatic substitution. The observed substituent effect will then be that of the positive pole. Secondly, the straightforward application of the tr+ scale to electron-demanding reactions is not necessarily appropriate. It may well be that some form of multiparameter treatment is needed, perhaps the Yukawa-Tsuno equation (Section II.B). 

Equilibrium 42A 42B (R = R = H R = XC6H4) according to the Yukawa-Tsuno Equation"... 

Data from Dzvinchuk and Lozinskii (88ZOR2167). Determined by H-NMR at 25°C (in CHCI3 at 20°C). The values (Xt)o were directly measured, rather than obtained from regression analysis. The standard errors of the slope are in the range 0.01-0.03. n = 8 (X = H, 3-NO2, 4-NO2, 4-Br, 4-Ph, 4-Me, 4-MeCONH, 4-MeO). Molar ratio. This is the coefficient of the Yukawa-Tsuno equation, not the correlation coefficient. The correlation coefficients lie in the range 0.997-0.999. 

The Yukawa-Tsuno equation for 4-substituted benzene derivatives is approximately equivalent to the CR equation . This observation has led to the development of a modified Yukawa-Tsuno (MYT) equation which has the form of equation 6 ... 

The Yukawa-Tsuno equation [Eq. (5)] appears best to correlate the results, but as commented previously the a values used for the five-membered rings, 2- and 3-thienyl and 2-furyl, appear hard to rationalize although other workers have also argued for their authenticity.247... 

Similar conclusions have been reached for the triarylmethane mono-antipyrine dyes (48) where here r in the Yukawa-Tsuno equation is 1.50334 and the isokinetic temperature is 740°K.335... 

The solvolysis rates of 2-(dimethylphenylsilyl)-l-(Y-phenyl)ethyl 3,5-dinitroben-zoates (62) in 60% aqueous ethanol were analysed using using the Yukawa-Tsuno equation.103 The p value of -2.95 with r 1.04 found by changing the a-aryl substituent was much smaller than the p value of -5.45 found for the corresponding non-silylated system. This, the fact that the rate constant for the silylated substrate was > 105-fold faster than the rate of the non-silylated compound, and the small a value of 0.52 found from the log( Y/ H)si = a log( Y/ H)non-si plot was taken as evidence that the reaction of the silyl compound occurred via a tight transition state with significant neighbouring silyl participation (Scheme 25). 

They further suggest the Yukawa-Tsuno equation for substitution should take the form... 

Finally, we should mention a review article,425 some of whose content is already of historical interest and which will be increasingly of such interest as the years go by, since it will effectively summarize the state of the art of an important topic at the time it was written. This is an account by Tsuno and Fujio of the applications of the Yukawa-Tsuno equation (an extended Hammett equation originating in 1959) to car-bocationic systems. The article has about 120 pages and more than 200 references. 

Partial rate factors for trifluoroacetylation at the 5-position of 2-substi-tuted furans in 1,2-dichloroethane at 75°C [Table 6.7, [72JCS(P2)71]] correlate approximately with u+ values, with p = -10. The effects of para substituents on the rate of acetylation and trifluoroacetylation of 2-aryl-5-methylfurans have been studied. In the latter reaction, the relative rates of substitution at the 3-position (to give 6.10) were H, 1.0 Cl, 0.43 Me, 5.3 and OMe, 35.4, which correlated with the Yukawa-Tsuno equation, p = -2.6, r = 0.74. For acetylation, the corresponding relative rates for... 

It should be stressed that there is nothing exceptional about the benzo[f>] compounds in not providing constant literature data for practically every aromatic shows the ct+ values to be variable. For some molecules that are not very polarizable, the variation in ct+ is quite small, leading to the erroneous conclusion of their constancy. The presently described molecules are particularly polarizable and show that satisfactory treatment of reactivity data can generally be achieved only through the use of a multiparameter equation, notably the Yukawa-Tsuno equation (59BCJ971). 

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