Dual substituent-parameter equation

A more ambitious goal is to separate completely resonance effects from polar effects. This involves using separate substituent constants to account for resonance and polar effects. The modified equation, called a dual-substituent-parameter equation, takes... 

Dodecahydrododecaborate dianion 380 Dual substituent parameter (equations) 50,... 

Linear free energy relationships, see Bronsted equation, Dual substituent parameter (equations), Hammett equation(s), Quantitative structure-activity relationships, Ritchie nucleophilicity equation... 

Multiple regression on ar and parameters employs the dual substituent-parameter equation, which may be written as in equation 964. 

However, in more recent years it has become usual to employ ar or crR-type constants, either together in the dual substituent-parameter equation or individually in special linear regression equations which hold for particular infrared magnitudes. In this connection a long series of papers by Katritzky, Topsom and their colleagues on Infrared intensities as a quantitative measure of intramolecular interactions is of particular importance. We will sample this series of papers, insofar as they help to elucidate the electronic effects of sulfinyl and sulfonyl groups. 

A Generalized Treatment of Substituent Effects in Benzene Series. A Statistical Analysis by the Dual Substituent Parameter Equation. By S. Eh REN SON, Department of Chemistry, Brookhaven National Laboratory, Upton, Long Island, New York R. T. C. BROWNLEE, Department of Chemistry, La Trobe University, Bundorra, Victoria, Australia R. W. Taet, Department of Chemistry, University of California, Irvine, California. I... 

A Generalized Treatment of Substituent Effects in the Benzene Series. A Statistical Analysis by the Dual Substituent Parameter Equation (1)... 

The previous analysis by the dual substituent parameter equation of substituent effects in the naphthalene series provided support for the scale, especially for sets involving nonconjugating positions (2p). The available data yield six basis sets which presumably give a critical analysis and, in particular, provide distinctions between conjugative (three sets) and nonconjugative positions (three sets). The results (using the earlier symbolism (2p)) are given in Table X. 

It is important to note that the fitting according to eq. (1) requires zero intercept behavior i.e., F =. 00 for H (for which Oj = Or =. 00). While we recognize that the data for the unsubstituted (H) member of a set may be as subject to experimental error as any other member, such error is generally relatively small for a set of reliable data. Any constant error from this source will be distributed among all of the substituents in such a manner as to achieve best fit. Any loss in precision of fitting of the set which may result by such a procedure we believe is a small price to pay compared to the violence done by introduction in eq. (I) of a completely variable constant parameter. The latter procedure has been utilized by other authors both in treatments by the simple Hammett equation and by the dual substituent parameter 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. 

Multiple regression on j and og-type parameters employs the dual substituent-parameter equation, which may be written as in equation 891. (The combining of the k and k° terms implies that there is no intercept term allowed, and k° is now the actual value for the parent system, cf below.) For any given reaction series the equation is applied to meta- and para-substituents separately, and so values of pi and pr characteristic both of reaction and of substituent position are obtained. The various op-type scales are linearly related to each other only approximately. In any given application the scale which gives the best correlation must be found92. 

The most fruitful treatment of the electronic effects of ozt/zo-substituents involves the use of the same cr/ and correlation analysis for meta- and para-substituents by means of the dual substituent-parameter equation 91 or the extended Hammett equation 95 (Section II.B). Obviously it is a considerable assumption that these are valid for ort/zo-substituents and the implication is that in the correlation analysis any peculiarities may be adequately expressed through the coefficients of the inductive and resonance terms. Really satisfactory correlation analysis for any given reaction system requires a large amount of data and can only rarely be accomplished. 

THYMIDYLATE SYNTHASE Dual substituent-parameter equation, PHYSICAL ORGANIC CHEMISTRY NOMENCLATURE... 

Lately it has been established (8lJCS(P2)409) that effects (for fi- or y-substituents) on nitrogen reactivity are an intrinsic property of the system and they are independent of reaction type and solvent. Furthermore, a convincing argument is made against the use of the dual substituent parameter equation (equation 4) which has been employed to try to... 

In the oxidation of alkanethiols to disulfides with chloramine-T (CAT), in alkaline solution, the proposed reactive species are hypochlorous acid and TsNCl- anion. A correlation of reaction rate with Taft s dual substituent parameter equation yielded p = -5.28 and 5 = -2.0, indicating the rate-enhancing effect of electron-donating substituents.133 Michaelis-Menten-type kinetics have been observed in the oxidation of atenolol with CAT in alkaline solutions. TsNHCl is assumed to be reactive species. A mechanism has been suggested and the activation parameters for the rate-determining step were calculated.134 The Ru(III)-catalysed oxidation of diphenyl... 

Hammett, L. P. Physical Organic Chemistry. McGraw-Hill New York (1940). Ehrenson, S., Brownlee, R. T. C., and Taft, R. W. Generalized treatment of substituent effects in the benzene series. A statistical analysis by the dual substituent parameter equation (1). Progr. Phys. Org. Chem 10, 1-80 (1973). 

In a short section the electronic effect of the isocyano group is discussed. The possibility of including unipolar substituents in Hammett and similar treatments has long been a matter of controversy and this problem is discussed with special reference to the N2 substituent. The effects of acetylenic groups are examined in some detail and various unsatisfactory aspects are uncovered. 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 CN, and to a lesser extent of the other groups of interest, in these treatments. 

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