How accurately defined are the overtone coefficients in 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 > ½) are concerned, the RIDME experiment provides not only the basic dipolar frequency but also its overtones, which complicates the determination of interspin distances. Here, we present and discuss in a step-by-step fashion an r.m.s.d.-based approach for the calibration of the overtone coefficients for a series of molecular rulers doubly labeled with Gd(III)-PyMTA tags. The constructed 2D total-penalty diagrams help revealing that there is no unique set of overtone coefficients but rather a certain pool, which can be used to extract distance distributions between high-spin paramagnetic centers, as determined from the RIDME experiment. This is of particular importance for comparing RIDME overtone calibration and distance distributions obtained in different labs.