Nuclear electron double resonance in liquids

Abstract

In this contribution we hope to illustrate with preliminary measurements some of the ways in which nuclear-electron double resonance experiments can yield information of value to the chemist. The magnetic coupling between a paramagnetic electron of spin S and a nucleus of spin I may be described (Abragam 1961) by the spin Hamiltonian H s, I = γ e γ n I [3r(S. r)/ r 5 – S/ r 3 + 16 π /3 S| ψ e (0)| 2 ], where γ e , γ n are the electron and nuclear gyromagnetic ratios respectively, r is the vector radius joining I and S and | ψ e (0)| 2 is a measure of the overlap between the electron and nuclear wave functions. The first two terms describe the magnetic dipole-dipole interaction dominant at large interspin distances, and the third covers any short-range scalar or contact interactions. In non-viscous solutions of free radicals the rapid relative motion of the spins causes the Hamiltonian to become time dependent. If the motion is quite random the dipolar terms become entirely time dependent and are significant only in electron-nucleus relaxation phenomena. The scalar term, on the other hand, may not be completely averaged and can thus cause both relaxation phenomena and paramagnetic shifts in the nuclear resonance spectrum of the solvent (Bloembergen 1957). Thus the dynamic parts of both the scalar and the dipolar interactions are effective in producing mutual relaxation of the spins. Just which of the possible two spin processes is the most effective can be found by expanding the time-dependent Hamiltonian from equation (1) into its component spin operators and finding their relative spectral densities (Abragam 1955,1961). The dipole-dipole part of the Hamiltonian then becomes H d.d ( t ) = [ J 1 S z I z + J 2 {S + I_ + S_I + } + J 3 { S z I + + I z S + } ( A ) ( B ) ( C ) + J 3 { S z I_ + I z S_} + J 4 {S + I + } + J 4 {S_I_}] σ 1 /< r 3 SI >, ( D ) ( E ) ( F ) and the scalar part becomes H sc . ( t ) = [ J 5 S z I z + J 6 {S + I_ + S_I + }] σ 2 | ψ e (0)| 2 , where < r 3 SI > is the mean value of the cube of the electron-nuclear distance, σ1 and σ2 are proportionality constants, the J ’s are the spectral densities, S z , I z are the z components of the spin operators and S + I + ; S_I_ are the raising and lowering operators for the electron and nuclear spins respectively. For a white spectrum of relative motions between the spins, terms E and F are not the most important for dipolar coupling. This leads to the established reversal of nuclear polarization in Overhauser experiments between nuclei with positive magnetic moments and electrons (Richards & White 1962 a, b ). Under the same conditions a dominant scalar coupling leads to an enhancement of the nuclear polarization because of its different relaxation operators.