Electron Spin Resonance Spectra of Methyl-Substituted Naphthalene Anion Radicals

An analysis of the ring‐ and methyl‐proton hyperfine splitting constants in ten methyl‐substituted naphthalene anion radicals has been carried out. In addition to the seven radicals in this series studied by earlier investigators, we have obtained experimental data on the 1‐ and 2‐methylnaphthalene anions and on the 1,4,5,8‐tetramethylnaphthalene anion. The new results provide 15 additional ring‐proton splittings and three additional methyl‐proton splittings; earlier work provided 19 and seven splittings, respectively. Hückel molecular orbital calculations were carried out for all the radicals using both an inductive and an inductive‐hyperconjugative model for the effects of methyl‐group substitution. Both models gave comparable results, as did calculations employing the McLachlan method of including configuration interaction in an approximate way. The changes in proton splittings caused by methyl‐group substitution were found to obey an additivity relationship, i.e., methyl‐group substitution at positions $i$ and $j$ produces a change in the splitting at position $k$ equal to the sum of the effects observed at $k$ in radicals which are substituted only at $i$ or only at $j$ . By using the additivity relations, it was found that the MO calculations lead to the wrong assignment of some of the splittings to positions in the 1‐methylnaphthalene anion. Reasonably good agreement was obtained between the calculations and the ring‐proton splittings using a value of the inductive parameter ${\delta }_C\text{\hspace{0.17em}=\hspace{0.17em}−\hspace{0.17em}0.13}$ (in units of the carbon–carbon resonance integral $\beta$ ), but there were a number of significant discrepancies. Similarly, good agreement was obtained for the methyl‐proton splittings at the $\alpha$ positions, but for reasons which are not understood, the inductive parameter required to fit these data was ${\delta }_C\text{\hspace{0.17em}=\hspace{0.17em}−\hspace{0.17em}0.31}$ instead of ${\delta }_C\text{\hspace{0.17em}=\hspace{0.17em}−\hspace{0.17em}0.13}$ . The β‐methyl‐proton splittings, however, could not be adequately accounted for by any of the calculations. It was found that deceptively good agreement is obtained between calculated and experimental results if correlations are made in the usual way between actual splittings and spin densities rather than between the changes in these quantities arising from substitution. Several types of relations have been derived among the hyperfine splittings that do not depend on the detailed values of the calculated spin‐density distribution. One of these relates the sum of the methyl‐proton splittings in a substituted radical to the difference between the total extent of the spectrum from the unsubstituted naphthalene anion and the sum of the ring‐proton splittings from the substituted anion. An excellent correlation was obtained from which it was found that the sigma–pi parameter $Q_{\mathrm{Me}}^H$ in the relation $a_{\mathrm{Me}}^H{\mathrm{\hspace{0.17em}=\hspace{0.17em}Q}}_{\mathrm{Me}}^H\rho$ between methyl splittings $a_{\mathrm{Me}}^H$ and ring‐carbon‐atom spin densities $\rho$ is related to the parameter $Q_{\mathrm{CH}}^H$ in the analogous relation for ring‐proton splittings by ${\mathrm{(Q}}_{\mathrm{Me}}^H{\mathrm{\hspace{0.17em}/\hspace{0.17em}Q}}_{\mathrm{CH}}^H\text{)\hspace{0.17em}=\hspace{0.17em}−0.80\hspace{0.17em}±\hspace{0.17em}0.02}$ , or $Q_{\mathrm{Me}}^H\text{≅22}\mathrm{G}$ . On the other hand, a detailed comparison of substitution‐induced changes in methyl‐proton splittings with the changes in ring‐proton splittings, which again does not depend in any way on the calculated spin densities, gives inconsistent results. The discrepancies indicate that the sigma–pi relations for either or both the ring‐proton and methyl‐group‐proton splittings are not sufficiently accurate for detailed predictions of the splittings at each position in a radical, although in an over‐all average sense the sigma–pi relations appear to be valid. The analysis does not indicate which of the two relations is more in error. Difficulties thus arise in both the calculations of spin densities arising from methyl‐group substitution and in the sigma–pi parameters relating splittings to spin densities.