ENDOR

Electron nuclear double resonance (ENDOR) is a magnetic resonance technique for elucidating the molecular and electronic structure of paramagnetic species. The technique was first introduced to resolve interactions in electron paramagnetic resonance (EPR) spectra. It is currently practiced in a variety of modalities, mainly in the areas of biophysics and heterogeneous catalysis.

In the standard continuous wave (cwENDOR) experiment, a sample is placed in a magnetic field and irradiated sequentially with a microwave followed by radio frequency. The changes are then detected by monitoring variations in the polarization of the saturated electron paramagnetic resonance (EPR) transition.

ENDOR is illustrated by a two spin system involving one electron (S=1/2) and one proton (I=1/2) interacting with an applied magnetic field.

The Hamiltonian for the two-spin system mentioned above can be described as

The four terms in this equation describe the electron Zeeman interaction (EZ), the nuclear Zeeman interaction (NZ), the hyperfine interaction (HFS), and the nuclear quadrupole interaction (Q), respectively.

The electron Zeeman interaction describes the interaction between an electron spin and the applied magnetic field. The nuclear Zeeman interaction is the interaction of the magnetic moment of the proton with an applied magnetic field. The hyperfine interaction is the coupling between the electron spin and the proton's nuclear spin. The nuclear quadrupole interaction is present only in nuclei with I>1/2.

ENDOR spectra contain information on the type of nuclei in the vicinity of the unpaired electron (NZ and EZ), on the distances between nuclei and on the spin density distribution (HFS) and on the electric field gradient at the nuclei (Q).

The right figure illustrates the energy diagram of the simplest spin system where a is the isotropic hyperfine coupling constant in hertz (Hz). This diagram indicates the electron Zeeman, nuclear Zeeman and hyperfine splittings. In a steady state ENDOR experiment, an EPR transition (A, D), called the observer, is partly saturated by microwave radiation of amplitude ${\displaystyle \mathrm {B} _{\mathrm {1} }}$ while a driving radio frequency (rf) field of amplitude ${\displaystyle \mathrm {B} _{\mathrm {2} }}$, called the pump, induces nuclear transitions. Transitions happen at frequencies ${\displaystyle \nu _{\mathrm {1} }}$ and ${\displaystyle \nu _{\mathrm {2} }}$ and obey the NMR selection rules ${\displaystyle \Delta M_{I}=\pm 1}$ and ${\displaystyle \Delta M_{S}=0}$. It is these NMR transitions that are detected by ENDOR via the intensity changes to the simultaneously irradiated EPR transition. It is important to realize that both the hyperfine coupling constant (a) and the nuclear Larmor frequencies (${\displaystyle \nu _{\mathrm {n} }}$) are determined when using the ENDOR method.

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