Out-of-phase PELDOR

Abstract

Pulsed electron–electron double resonance (PELDOR) is a method frequently used to determine the structure of bio-macromolecule on a nanometre scale. Usually PELDOR experiments are carried out in the high-temperature limit, when the Boltzmann population of spins oriented parallel and antiparallel to the external magnetic field are almost equal. Also the well-developed theories describing PELDOR apply to this case. However, the high-temperature conditions are no more fulfilled for experiments done in a high magnetic field (above 6 T) and at low temperatures (below 5 K), when the Zeeman interaction energy of an electron spin becomes comparable with thermal energy . In this work we demonstrate that PELDOR signals measured at these conditions differ from the usual PELDOR signals. Additional to the standard in-phase component the PELDOR signal at low temperature and high magnetic field also contains an out-of-phase component that disappears in the high-temperature limit. This means that we observe not only the modulation of the refocused transverse magnetisation along a single axis in the rotating coordinate system but rather its precession in the x-y plane with a dipolar frequency. Here, we provide a quantitative explanation as well as a detailed analysis of the spin magnetisation dynamics under such conditions based on density matrix formalism. Understanding the PELDOR phenomena in high field and at low temperatures offers a tool to separate intra from intermolecular interactions, which might be extremely helpful and important for applications to biomolecules with a high degree of conformational flexibility.