21
SPINDENSITIES IN ALKYL-SUBSTITUTED BENZENES
Signs of Spin Densities and Vibronic Interactions in 1- and 1,P-Alkyl-SubstitutedBenzene Anions
by E. de Boer1*and J. P. Colpalb Koninklijke/Shell-Laboratorium,Amsterdam (Shell Research N . V . ) The Netherlands (Receiaed September 27, 1966)
Electron-transfer reactions between neutral molecules and their negative ions influence the nuclear magnetic resonance (nmr) spectrum of the neutral species; the proton resonance lines are broadened and shifted from their original positions. The direction of the shift indicates the sign of the spin density at the alkyl protons. Along these lines spin densities have been measured on 1- and 1,4-alkyl-substituted benzenes. This is an interesting series of compounds, because the two lowest states of their anions are almost degenerate. As a consequence, three factors may determine the sign of the spin density in the anions: configuration interaction, vibronic coupling, and thermal equilibrium between the two lowest states. The determination of the sign is found to be helpful in estimating the importance of each. Electron spin resonance (esr) measurements have been used to supplement the nmr evidence as to the temperature dependence of the spin densities. It was found that the proton hyperfine splittings of the monosubstituted benzene anions are temperature dependent. The methyl splitting of the p-xylene system was found to be temperature independent. For toluene and p-xylene, molecular orbital calculations have been carried out, accounting for the inductive and hyperconjugative effects of the methyl group and for configuration interaction with excited states. Analysis of the experimental results, using the calculated spin densities, led to the conclusion that in toluene and p-xylene appreciable vibronic mixing occurs.
I. Introduction Electron- transf er react ions between a diamagnetic molecule and its negative ions modify the nmr spectrum of the molecule in two ways: the proton resonance lines are broadenedza and these lines are shifted from their original positions.*b The direction of the shift indicates the sign of the spin density at the proton. Both effects can be described by the modified Bloch equationsJt4 or by Alexander's spin density matrix method.6 This paper describes the application of this technique to 1- and 1,4-alkyl-substituted benzenes. This class of compounds is of special interest, because the two lowest states of their anions are almost degenerate. Earlier esr spectra of 1- and 1,4-alkyl-substituted benzene anions had shown6,?that the lowest antibonding orbital is antisymmetric with respect to reflection through the plane perpendicular to the molecule and
passing through the carbon atoms to which the substituents are attached. Therefore, one may expect that configuration interaction with excited states will lead to negative spin densities on those atoms which lie in the nodal plane and consequently to negative hyperfine interaction constants. I n a previous publi-
(1) (a) Department of Physical Chemistry, University of Nijmegen, Nijmegen, The Netherlands; (b) Department of Theoretical Chemistry, University of Amsterdam, Amsterdam, The Netherlands. (2) (a) C. R. Bruce, R. E. Norberg, and S. I. Weissman, J . Chem. Phys., 24, 473 (1956); (b) E. de Boer and C. MacLean, Mol. Phys., 9, 191 (1965). (3) H. S. Gutowsky, D. W. McCall, and C. P. Slichter, S. Chem. Phys., 21, 279 (1953). (4) H.M.McConnell, ibid., 25, 709 (1956). (5) S. Alexander, ibid., 37, 974 (1962). (6) T . R. Tuttle and S. I. Weissman, J . Am. Chem. Soc., 80, 5342 (1958). (7) J. R. Bolton and A. Carrington, Mol. Phys., 4, 497 (1961).
Volume 71,Number 1
January 1967
E. DE BOERAND J. P. COLPA
22
cation,8 we reported that the splitting factor for the methyl protons in the negative ion of p-xylene is negative indeed. However, a large discrepancy existed between the theoretically predicted magnitude of the splitting and the experimentally observed value. As Bolton, et ~ l . pointed , ~ out, there are also positive contributions to the splitting factors, arising from a thermal equilibrium and a vibronic interaction between the two nearly degenerate states. Hence the sign of the spin density will depend on the net result of three principal factors, viz., configuration interaction, vibronic coupling, and thermal equilibrium between the two lowest states. To estimate the relative importance of these factors, one has to know first of all the sign of the spin densities at the distant alkyl hydrogens. It was the purpose of the work described in this paper to determine the sign for a series of 1- and 1,4-alkyl-substituted benzene anions by means of nmr in order to gain a better insight into the various factors which determine the net spin density at the alkyl hydrogens. The discussion of the results is supported by esr evidence about the temperature dependence of the spin densities and by the results of molecular orbital calculations of spin densities in the toluene and the p xylene negative ions.
11. Experimental Section For the experimental details, we refer to a recent publication by de Boer and illIacLean.8 All of the esr experiments were carried out in 1,2-dimethoxyethane as solvent and a sodium-potassium alloy as reducing agent. For the nmr experiments, we used completely deuterated tetrahydrofuran (isotopic purity 298%) and cesium as the reducing metal. The esr spectra were measured with a Varian Xband spectrometer, using 100 kc/sec field modulation. The nmr spectra were obtained with a Varian dualpurpose spectrometer, operating at 56.4 Mc/sec. Low temperatures mere achieved with the Varian variable temperature accessories.
and the shift of the lines by
In these formulas, fp and f~ are the fractions of paramagnetic and diamagnetic particles, respectively, T~ is the lifetime of the paramagnetic molecule, T I , is the electron spin lattice relaxation time, and a is the hyperfine interaction constant expressed in radians per second. The other symbols have their usual meaning. The spin densities in the alkyl groups of the 1- and 1,4-alkyl-substituted benzene anions are small. Consequently, the term fDTp2a2/4 1 27,TIe-l
+
so that the contact shift is given by SPH 6, = -afP-
I n the next section, this formula has been applied to determine the sign and the absolute value of the hyperfine interaction constants for the distant protons in the substituents. A shift of a resonance line to high field means negative spin density on the protons in resonance and accordingly a negative hyperfine interaction constant. Analogously, a shift, to low field is caused by a positive spin density on the protons or by a positive hyperfine interaction constant.
IV. Results A . Monoalkyl-Substituted Benzenes. Attempts to
0 9-
08-
0.7-
The two effects, the broadening and the shift of the resonance lines, can be described by the modified Bloch equations324 and by the spin density matrix method of A l e ~ a n d e r . ~I~n' ~ref 8, both methods have been applied; it was found that the broadening of the resonance line due to the electron exchange reaction can be given by
0.5
1
+
The Journal of Physical Chemistry
+
(1)
..:-
*.
.*
. B
.. : . .
..
0 CHS
111. Basic Equations
fPTPU2/4 f ~ ~ ~ ~ 2rpTie-l a ~ / 4
(3)
KT
06-
AT2 tex-' =
