How accurately defined are the overtone coefficients in the Gd(III)-Gd(III) RIDME?

Relaxation-induced dipolar modulation enhancement (RIDME) is a pulse EPR technique that is particularly suitable to determine distances between paramagnetic centers with a broad EPR spectrum, e.g. metal-ion-based ones. As far as high-spin systems (S > 1/2) are concerned, the RIDME experiment provides not only the basic dipolar frequency but also its overtones, which complicates the determination of interspin distances. An r.m.s.d.-based approach for the calibration of the overtone coefficients is proposed and illustrated for a series of molecular rulers doubly labelled with Gd(III)-PyMTA tags. The constructed 2D total-penalty diagrams clearly show that there is no unique set but rather a certain pool of overtone coefficients, which can be used to extract distance distributions between high-spin paramagnetic centers as determined from the RIDME experiment.