Electron-nuclear Dipolar Interaction Research Articles

Hyperfine interactions in the gas phase electron resonance spectrum of33S16O

We have observed four fine structure transitions in the gas phase electron resonance spectrum of 33S16O, and have measured the 33S magnetic hyperfine splitting. Analysis of the spectrum leads to values of the parameters describing the Fermi contact interaction and the electron-nuclear dipolar interaction. These are discussed in terms of the electronic structure of the radical.

Theory of Saturation and Double-Resonance Effects in ESR Spectra

A theory of saturation in the electron spin resonance spectra of dilute solutions of free radicals has been developed in terms of the general Boltzmann equation for the density matrix given by Bloch and Redfield. It is shown, in contrast to the earlier theories, that, in general, a composite line arising from a set of degenerate nuclear spin states must be described by a generalized (matrix) saturated Lorentzian rather than a single line of over-all saturated Lorentzian shape. The general properties of this solution are discussed in detail for the case when electron—nuclear dipolar interactions are the only important nuclear-spin-dependent relaxation mechanism. A particularly simple situation exists when similar nuclei are completely equivalent. Then each composite line consists of a superposition of saturated Lorentzians, and the linewidths and saturation parameters of each component depend only on the values of the total spin and of the z component of spin of the associated configuration of the completely equivalent nuclei. Thus it would be possible to saturate some components to a greater extent than others. These simple components may become coupled together in a complex fashion when the time-dependent fluctuations of the dipolar interactions for equivalent nuclei are no longer identical, which is often the case for aromatic-ring protons. Further coupling may be expected from the effects of nuclear-quadrupole interactions and from intermolecular-exchange phenomena and are only qualitatively discussed. In the absence of saturation the present theory reduces to the linewidth theory of Freed and Fraenkel. Detailed expressions are obtained for steady-state electron—nuclear double-resonance (ENDOR) effects on radicals containing completely equivalent sets of nuclei. The saturating fields can lead to coherence and induced-transition effects. It is shown how the latter, under appropriate conditions, can result in enhancement of saturated ESR spectra. It appears necessary for enhancements that lattice-induced nuclear spin transitions should be comparable in magnitude to the lattice-induced electron spin transitions, or else cross transitions involving both nuclear and electron spins must be important in the relaxation process. Coherence effects involving both electron and nuclear spin transitions should be unimportant when the main contribution to the ESR linewidths results from secular processes and is nuclear spin independent. This is also the condition for NMR linewidths to be significantly narrower than ESR linewidths. Complications still arise from the coherence and linewidth coupling effects of the different nuclear transitions being excited. A brief discussion of enhancement by a transient ``heating'' effect is also given.

Anisotropic Rotational Diffusion and Electron Spin Resonance Linewidths

The recent general theory of ESR linewidths for dilute solutions of free radicals developed by Freed and Fraenkel is extended to cover the possibility that the rotational motions of the free radicals are anisotropic. The analysis is greatly simplified by expressing the solution of the rotational-diffusion equation as an expansion in Wigner rotation matrices. Only the spectral-density functions in the linewidth expressions given by Freed and Fraenkel are changed by the inclusion of anisotropic rotational diffusion. These spectral-density functions are found to depend upon five different relaxation times which are expressible in terms of the three principal values of the diffusion tensor ${ \germ{ R \germ} $}. It is shown how an analysis of the ESR linewidth effects, which vary from one hyperfine component to another, may be used in conjunction with calculations of the anisotropic electron—nuclear dipolar interactions to estimate the principal values of ${ \germ{ R \germ} $}. The experimental linewidth study on the para-dinitrobenzene anion radical is reanalyzed, and it is shown that an anisotropic rotational-diffusion mechanism cannot by itself explain the anomalous absence of any significant quadratic linewidth dependence on the total Z component of spin of the ring protons. While an order of magnitude estimate of ${ \germ{ R \germ} $} was made, further information permitting a quantitative understanding of the anomalous result (presumably due to fluctuations in isotropic hyperfine interactions) would be necessary to obtain a meaningful estimate of the principal values of ${ \germ{ R \germ} $} for this radical. The physical significance of ${ \germ{ R \germ} $} in the approximation of a Brownian particle as well as in terms of intermolecular potentials is discussed.

Theory of Linewidths in Electron Spin Resonance Spectra

A general theory of the linewidths in the electron spin resonance spectra of dilute solutions of free radicals has been developed in terms of the relaxation-matrix theory of Bloch, Redfield, and Ayant. In contrast to previous theories, it is shown that a composite line arising from a set of degenerate nuclear-spin states should, in general, consist of a sum of superimposed lines of Lorentzian shape with different widths rather than a single line with an over-all Lorentzian shape. A single Lorentzian line is still obtained, however, as a limiting case when the variation of the widths of the different components of a composite line is small compared to the average width. Although the non-Lorentzian shape of a composite line is often difficult to observe experimentally, a number of other observable properties are predicted by the present development that are outside the scope of the previous theories. For example, linewidth effects resulting from differences in the widths of the separate components of a composite line are predicted that explain the alternation in the linewidths from one hyperfine line to another recently observed in the ESR spectra in certain free radicals. The detailed form of the relaxation matrix is presented for intramolecular anisotropic and isotropic electron—nuclear dipolar interactions, quadrupole interactions, and g-tensor relaxations. Modulations of the spin density and hyperfine splittings are included, as are internal motions, and a number of cross terms between the different relaxation mechanisms arise. In general the relaxation matrix of a composite line contains significant off-diagonal elements, and the determination of the linewidths requires the evaluation of the eigenvalues of the matrix. Problems involving rapid chemical exchange, or modulation by jumps to a small number of sites, can be treated by the relaxation-matrix theory and, under special restrictions, by either the modified Bloch equations or the Anderson theory of motional narrowing. When applicable, these latter procedures can be used over the entire range of exchange rates, while the relaxation-matrix theory is limited to fast rates only.

Theory of ESR Linewidths of Free Radicals

A theory of ESR linewidths for substances in which the magnetic anisotropy is small and for which the orbital magnetism has been essentially quenched is developed. Nuclear quadrupole moments, zero field splittings, anisotropic Zeeman terms, and intramolecular electron-nuclear dipolar interactions, as well as motional and exchange effects are considered in the strong field case. The theory is developed in a manner that is particularly adaptable to the study of liquids but it is also applied to crystals since the resulting equations, though only applicable for small anisotropies, are particularly simple. The theory provides an extension of previous theories on ESR spectra in liquids. Several applications of the theory are discussed with particular emphasis on V4+ chelates. The theory of exchange in liquids, a phenomenon which is complicated by the noncommutivity of the motional and exchange Hamiltonians is considered in special detail. It is shown that this theory can be used to explain Hausser's results—the existence of an optimum viscosity for the observation of hyperfine structure.