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** Benzene derivatives, Yukawa-Tsuno equation **

Note that the sums of the squares of the coefficients in a given MO must equal 1 (e.g., 0.3717 + 0.6015 + 0.3717 + 0.6015 = 1.0 for Pi) because each of the AOs represents a probability distribution of finding the electron at a given point in space. The total probability of finding an electron in all space for an MO must be unity, exactly as for its constituent AOs. We now can see that the LCAO approximation is only one of many possibilities to describe the electron density (= probability) for MOs. We do not have to express the electron density as a linear combination of the electron densities of AOs centered at the atoms. We could also [Pg.378]

As mentioned above, HMO theory is not used much any more except to illustrate the principles involved in MO theory. However, a variation of HMO theory, extended Huckel theory (EHT), was introduced by Roald Hof nann in 1963 [10]. EHT is a one-electron theory just Hke HMO theory. It is, however, three-dimensional. The AOs used now correspond to a minimal basis set (the minimum number of AOs necessary to accommodate the electrons of the neutral atom and retain spherical symmetry) for the valence shell of the element. This means, for instance, for carbon a 2s-, and three 2p-orbitals (2p, 2p, 2p ). Because EHT deals with three-dimensional structures, we need better approximations for the Huckel matrix than [Pg.379]

In the Yukawa-Tsuno equation (1959)58 (equation 4), the sliding scale is provided by multiple regression on a and (cr+ —

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. [Pg.481]

Equilibrium 42A 42B (R = R = H R = XC6H4) according to the Yukawa-Tsuno Equation" [Pg.280]

R = XC5H4) and the electronic characteristics of the substituent X via the Yukawa-Tsuno equation [Pg.281]

The electronic effect of the substituents on nitro-aromatics is rationalized by the Yukawa-Tsuno equation. [Pg.451]

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. [Pg.342]

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. [Pg.210]

Yukawa, Tsuno and their colleagues 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 relationship (usually called the Yukawa-Tsuno equation, see Section II.B) [Pg.514]

Further insight into the nature of the transition state for carbocation hydration comes from application of the two parameter Yukawa-Tsuno equation (Eq. 21). [Pg.23]

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 [Pg.372]

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. [Pg.229]

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** Benzene derivatives, Yukawa-Tsuno equation **

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