The magnetic properties of paramagnetic species with spin S > 1/2 are parameterized by the familiar g tensor as well as "zero-field splitting" (ZFS) terms that break the degeneracy between spin states even in the absence of a magnetic field. In this work, we determine the mean values and distributions of the ZFS parameters D and E for six Gd(iii) complexes (S = 7/2) and critically discuss the accuracy of such determination. EPR spectra of the Gd(iii) complexes were recorded in glassy frozen solutions at 10 K or below at Q-band (∼34 GHz), W-band (∼94 GHz) and G-band (240 GHz) frequencies, and simulated with two widely used models for the form of the distributions of the ZFS parameters D and E. We find that the form of the distribution of the ZFS parameter D is bimodal, consisting roughly of two Gaussians centered at D and -D with unequal amplitudes. The extracted values of D (σD) for the six complexes are, in MHz: Gd-NO3Pic, 485 ± 20 (155 ± 37); Gd-DOTA/Gd-maleimide-DOTA, -714 ± 43 (328 ± 99); iodo-(Gd-PyMTA)/MOMethynyl-(Gd-PyMTA), 1213 ± 60 (418 ± 141); Gd-TAHA, 1361 ± 69 (457 ± 178); iodo-Gd-PCTA-[12], 1861 ± 135 (467 ± 292); and Gd-PyDTTA, 1830 ± 105 (390 ± 242). The sign of D was adjusted based on the Gaussian component with larger amplitude. We relate the extracted P(D) distributions to the structure of the individual Gd(iii) complexes by fitting them to a model that superposes the contribution to the D tensor from each coordinating atom of the ligand. Using this model, we predict D, σD, and E values for several additional Gd(iii) complexes that were not measured in this work. The results of this paper may be useful as benchmarks for the verification of quantum chemical calculations of ZFS parameters, and point the way to designing Gd(iii) complexes for particular applications and estimating their magnetic properties a priori.
The energy spectrum of a system containing a static quark anti-quark pair is computed for a wide range of source separations using lattice QCD with N f = 2 + 1 dynamical flavours. By employing a variational method with a basis including operators resembling both the gluon string and systems of two separated static mesons, the first three energy levels are determined up to and beyond the distance where it is energetically favourable for the vacuum to screen the static sources through light-or strange-quark pair creation, enabling both these screening phenomena to be observed. The separation dependence of the energy spectrum is reliably parameterised over this saturation region with a simple model which can be used as input for subsequent investigations of quarkonia above threshold and heavy-light and heavy-strange coupled-channel meson scattering.
The four Mn(ii) complexes Mn-DOTA, Mn-TAHA, Mn-PyMTA, and Mn-NO3Py were characterized by electron paramagnetic resonance (EPR), electron-nuclear double resonance (ENDOR), and relaxation measurements, to predict their relative performance in the EPR pulse dipolar spectroscopy (PDS) experiments. High spin density localization on the metal ions was proven by ENDOR on H, D,N, and Mn nuclei. The transverse relaxation of the Mn(ii) complexes appears to be slow enough for PDS-based spin-spin distance determination. Rather advantageous ratios of T/T were measured allowing for good relaxation induced dipolar modulation enhancement (RIDME) performance and, in general, fast shot repetitions in any PDS experiment. Relaxation properties of the Mn(ii) complexes correlate with the strengths of their zero field splitting (ZFS). Further, a comparison of Mn(ii)-DOTA and Gd(iii)-DOTA based spin labels is presented. The RIDME technique to measure nanometer-range Mn(ii)-Mn(ii) distances in biomolecules is discussed as an alternative to the well-known DEER technique that often appears challenging in cases of metal-metal distance measurements. The use of a modified kernel function that includes dipolar harmonic overtones allows model-free computation of the Mn(ii)-Mn(ii) distance distributions. Mn(ii)-Mn(ii) distances are computed from RIDME data of Mn-rulers consisting of two Mn-PyMTA complexes connected by a rodlike spacer of defined length. Level crossing effects seem to have only a weak influence on the distance distributions computed from this set of Mn(ii)-Mn(ii) RIDME data.
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