Yukawa Tsuno equation

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. 

It is observed that solvolyses of the tertiary benzylic / nitrobenzoates A, B and C are correlated by Yukawa-Tsuno equation with reduced resonance components as indicated by a lower coefficient of the resonance parameter r. Offer an explanation. 

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... 

Upward curvature has been observed in the pa plots for stilbene, styrene and a-methylstilbene bromination in methanol (Ruasse and Dubois, 1972 Ruasse et al, 1978 Ruasse and Argile, 1983). In no case can these curvatures be interpreted coherently by Yukawa-Tsuno equations in terms of variable contributions of polar and resonance effects. Application of the multipathway scheme (Ruasse, 1990) leads to the results summarized in Table 4. 

It has been shown that Yukawa-Tsuno equation for 4-substituted benzene derivatives is approximately equivalent to the CR equation1819. This has led to the development of a modified Yukawa-Tsuno (MYT) equation which has the form ... 

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. 

Further insight into the nature of the transition state for carbocation hydration comes from application of the two parameter Yukawa-Tsuno equation (Eq. 21). ... 

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