Determination of the Static Zero-Field Splitting of Gd3+ Complexes in Solution from the Shifts of the Central Magnetic Fields of Their EPR Spectra

In principle, the Redfield theory of EPR spectra applies only to fast‐rotating complexes with rather small static zero‐field splitting (ZFS) terms. However, at sufficiently high frequencies, typically of 35 GHz and above, it predicts values of the central magnetic fields which are surprisingly accurate well beyond its expected applicability range. This remarkable feature is demonstrated by showing that the Redfield EPR spectrum crosses its baseline at the same point as its “exact” simulated counterpart. It is shown that the shift of the central magnetic field with respect to its limiting value in the absence of ZFS terms is often simply proportional to the square of the magnitude of the static ZFS term divided by the spectrometer frequency. This property is used to determine the magnitude of the static ZFS term independently of its fluctuation dynamics and of the presence of the transient ZFS term. Despite their differences, the approximate EPR spectrum predicted by the Redfield formalism and its “exact” counterpart obtained by Monte Carlo (MC) simulation have equal central field values, mainly proportional to the square of the magnitude of the static zero‐field splitting term (see picture; dota4−=1,4,7,10‐tetraazacyclododecane‐N,N′,N′′,N′′′‐tetraacetate).