Hammett Equation and Generalized Pauling's Electronegativity Equation

Abstract

Substituent interaction energy (SIE) was defined as the energy change of the isodesmic reaction X-spacer-Y + H-spacer-H --> X-spacer-H + H-spacer-Y. It was found that this SIE followed a simple equation, SIE(X,Y) = -ksigma(X)sigma(Y), where k was a constant dependent on the system and sigma was a certain scale of electronic substituent constant. It was demonstrated that the equation was applicable to disubstituted bicyclo[2.2.2]octanes, benzenes, ethylenes, butadienes, and hexatrienes. It was also demonstrated that Hammett's equation was a derivative form of the above equation. Furthermore, it was found that when spacer = nil the above equation was mathematically the same as Pauling's electronegativity equation. Thus it was shown that Hammett's equation was a derivative form of the generalized Pauling's electronegativity equation and that a generalized Pauling's electronegativity equation could be utilized for diverse X-spacer-Y systems. In addition, the total electronic substituent effects were successfully separated into field/inductive and resonance effects in the equation SIE(X,Y) = -k(1)F(X)F(Y) - k(2)R(X)R(Y) - k(3)(F(X)R(Y) + R(X)F(Y)). The existence of the cross term (i.e., F(X)R(Y) and R(X)F(Y)) suggested that the field/inductive effect was not orthogonal to the resonance effect because the field/inductive effect from one substituent interacted with the resonance effect from the other. Further studies on multi-substituted systems suggested that the electronic substituent effects should be pairwise and additive. Hence, the SIE in a multi-substituted system could be described using the equation SIE(X1, X2, ..., Xn) = Sigma(n-1)(i=1)Sigma(n)(j=i+1)k(ij)sigma(X)isigma(X)j.

Differential Polarization of Spin and Charge Density in Substituted Phenoxy Radicals

“…[4][5][6][7][8] In so doing, the physical-organic community in particular has been able to develop tremendous physical and mechanistic insights into the cause-and-effect relationship between charge polarization and chemical reactivity. [9][10][11][12][13] A comparable level of understanding of the effect of spin on chemical reactivity suffers in part from the lack of a similarly intuitive counterpart to electronegativity for spin polarization. Experimental techniques for measuring the distribution of unpaired spin density, most notably EPR and ENDOR spectroscopies, have contributed greatly toward describing spin polarization in a wide range of chemical systems.…”

Combined Experimental and Computational Studies on the Nature of Aromatic C−H Activation by Octahedral Ruthenium(II) Complexes: Evidence for σ-Bond Metathesis from Hammett Studies

“…Computational studies that employ Hammett relationships to model substituent effects of reactions have been reported. [49][50][51][52] Herein, we seek to use the F value of a Hammett plot to discriminate between SBM and electrophilic substitution pathways for arene activation. Krogh-Jespersen, Goldman, et al have used similar electronic effects to study oxidative addition of dihydrogen and C-H bonds to Ir(I) metals.…”

Theoretical Study of Remote Substituent Effects on X–H(X=CH2, NH, O) Bond Dissociation Energies of Azulene

“…In another aspect, when neither X nor Y is a radical (Figures 2a and 2c), the correlations are significantly good, as reflected on the correlation coefficients -0.96 and -0.95, respectively, which are even better than those of the para-substituted benzene counterparts reported previoursly. 13 It is worth noting that these two correlations have quite similar slopes (k), -6.37 and -6.72 kJ/mol, which implies that there is little difference between SIE(X,Y) values of 2-Y-C 10 H 8 -XH and 6-Y-C 10 H 8 -XH. When X is changed to a radical, the correlations decline dramatically, especially the one of 2-Y-C 10 H 8 -X•, which is totally nonlinear according to Figure 2d, though the one of 2-Y-C 10 H 8 -X• is relatively better with a correlation coefficient 0.87.…”

“…13 We defined universal substituent interaction energy (SIE) as the energy change of the isodesmic reaction X-spacer-Y＋H-spacer-H→X-spacer-H＋H-spacer-Y (8) And we found SIE fitted a simple equation…”