Soccer-Ball Copper Cages Put a Classic Ruler for Molecular Distances to a Six- and Eight-Spin Test

A molecular cage that looks like a tiny soccer ball has become the proving ground for one of the most widely used tools in structural biology. In a preprint posted in Magnetic Resonance, a team of chemists and spectroscopists from Leiden University, the University of Amsterdam and Bielefeld University set out to measure distances between not two, but six and eight copper ions held in precise geometric arrangements inside self-assembled nanospheres. The work, led by Leonardo Passerini and corresponding author Martina Huber, asks a deceptively simple question: can double electron-electron resonance, a technique built around pairs of spins, still deliver meaningful structural information when a single molecule carries a whole cluster of paramagnetic centers?

The two compounds at the heart of the study are known as Cu6 and Cu8. Both belong to a family of spherical cages assembled from palladium ions and organic ligands, structures that self-organize into nanometer-scale spheres reminiscent of soccer balls. In Cu6, six copper(II) ions occupy positions corresponding to the vertices of an octahedron, while in Cu8 eight copper ions sit at what should be the corners of a cube. The parent cages, Pd12M6L(DMAP)24 and Pd12M8L(Pro)24, are attractive to chemists because they allow different metal ions to be introduced in a defined spatial arrangement, a property with obvious appeal for catalysis, where several metal centers acting in concert can enable reaction pathways unavailable to isolated atoms.

To read out the geometry of these metal clusters, the team turned to pulsed electron paramagnetic resonance, specifically the double electron-electron resonance experiment known as DEER, sometimes called PELDOR. In a DEER measurement, a sequence of microwave pulses interrogates a population of electron spins: observer pulses monitor the echo of one set of spins while a pump pulse flips a second set at a variable time. When the pump pulse flips a spin near an observed spin, the dipolar coupling between the two slightly shifts the echo frequency. Sweeping the pump pulse position across the time trace therefore produces an oscillating signal whose frequency encodes the distance between the spins. The technique is a workhorse for measuring nanometer-scale separations, routinely mapping distances between two nitroxide labels or two metal centers on proteins and synthetic molecules with sub-nanometer precision.

What makes the copper cages a compelling test case is that DEER theory was developed with isolated spin pairs in mind. When a molecule contains six or eight coupled spins, the observed signal becomes a superposition of many pairwise contributions, and additional phenomena appear. Multiple spins can be excited simultaneously, sum and difference frequencies can contaminate the distance distribution, and the modulation depth of the signal, the fraction by which the echo is modulated, no longer scales in the simple way it does for two spins. In principle, that complexity is an opportunity: if the multi-spin signature can be decoded, DEER might report not just distances but the number of spins in a cluster and their arrangement, turning a ruler into a three-dimensional structural probe.

The measurements did reveal clear evidence of multi-spin interaction in both cages. For Cu6, the analysis of the distance distribution allowed the team to establish an octahedral arrangement of the copper ions, consistent with the crystallographic model. For Cu8, two distinct distances were observed, and these were found to be consistent with two structural models that had been proposed for the compound, one of which places the eight copper ions at the vertices of a cube. In an ideal cube, there are two characteristic separations between vertices, the edge length and the face diagonal, so detecting two dominant distances is exactly what such a geometry would predict. The authors also measured a model compound containing just two copper centers, intended to serve as a calibration standard for relating modulation depth to the number of spins contributing to the signal.

However, the path from these observations to firm conclusions proved contentious. The preprint underwent open peer review on the Copernicus platform, and all three referees declined to support publication of the revised manuscript, which remains a discussion-stage preprint rather than an accepted paper. Their reports, published alongside the authors’ response, offer an unusually transparent window into how demanding multi-spin DEER is in practice, and they highlight technical issues that anyone attempting similar measurements will need to confront.

A central criticism concerned data quality. The referees noted that the phase memory time, Tm, which governs how long the dipolar oscillation can be followed and therefore how precisely distances can be resolved, is short for these copper compounds. Referee 1 pointed out that the measurements were performed at 20 kelvin, whereas the low-temperature maximum of Tm for such systems would be expected between 6 and 15 kelvin, and that because the achievable evolution time depends roughly exponentially on Tm, measuring at too high a temperature can severely degrade the data. The referees also emphasized that DEER experiments are conventionally run in deuterated solvents to extend Tm, and argued that the gain in signal-to-noise ratio from a deuterated solvent such as perdeuterated butyronitrile would have been substantial. With signal-to-noise ratios likely below ten to one, as Referee 2 estimated, quantifying complex distance distributions with multiple populations of different widths becomes hazardous, raising the risk of overinterpreting noise as structure.

The referees also dissected the physics of orientation selection, an effect the authors had struggled to assess. Copper(II) ions have a strongly anisotropic g-tensor, meaning their resonance frequency depends on how the molecule is oriented relative to the magnetic field, and the microwave pulses used in DEER excite only a subset of orientations. Referee 2 argued that in an octahedron, opposite vertices are related by inversion symmetry and therefore share identical g-tensor orientations, so if one copper of a pair is excited, its partner is too, which can inflate the modulation depth in ways that mimic a multi-spin signature. This could rationalize an observed one-to-one ratio of distance peak intensities where a four-to-one ratio was expected. The same referee argued that the two-copper model compound used for calibration, which carries distributed exchange coupling, was not a robust standard, since conformations with strong coupling fall outside the excitation bandwidth and do not contribute to modulation. In that referee’s assessment, the central conclusion about low effective spin numbers rested on a flawed calibration, while the genuinely strong orientation-selection effects went untested and unanalyzed.

Further technical points sharpened the critique. Referee 1 argued that shorter microwave pulses, perhaps 24 or even 20 nanoseconds instead of the 32 nanoseconds used, should have been achievable with the available hardware and would have widened the excitation bandwidth; that density functional theory calculations, feasible on cutouts of the cages because the spin population is localized, could have pinned down the relative orientations of the g-tensors; and that in ideal geometry the principal axes systems of diagonally opposite copper centers must coincide, so the missing cube-diagonal contribution in Cu8 could not be blamed on orientation selection. Referee 3 agreed that the low signal-to-noise ratio, particularly for Cu8, did not permit reliable conclusions from the fits and that a proposed discussion of structural flexibility in that compound was not convincingly supported. The authors submitted a combined point-by-point response in March 2026, but the revision was not accepted, and the discussion is now closed.

Even in its contested state, the study marks out the frontier. It demonstrates that DEER signals from six- and eight-spin copper clusters contain interpretable information, and that an octahedral arrangement can be recognized from the data, while also showing, through the review record, exactly where the method strains: short phase memory times, narrow excitation bandwidths, orientation selection amplified by molecular symmetry, and the absence of validated calibration standards for modulation-depth analysis all conspire to blur the line between genuine multi-spin effects and artifacts of a two-spin formalism pushed past its comfort zone. For the cages themselves, the motivation remains intact, since defined multi-metal arrangements inside self-assembled spheres are promising platforms for cooperative catalysis, and a spectroscopic method that could verify metal geometry in solution, independent of crystallography, would be a valuable quality control. The lesson of this preprint is that getting there will require colder samples, deuterated solvents, faster pulses, computational support from quantum chemistry, and a more careful theoretical treatment of how orientation correlation and exchange coupling reshape the DEER signal when a molecule carries a whole cage of spins rather than a lone pair.

Subject of Research: Pulsed DEER distance measurements between six and eight copper(II) ions in self-assembled spherical coordination cages

Article Title: Pulsed Electron Paramagnetic Resonance on two Cu(II)-Cage Compounds With Six, Respectively Eight Copper Ions

Article References: Passerini, L., Bobylev, E., de Zwart, F. J., Hintz, H., Godt, A., de Bruin, B., Reek, J., & Huber, M. (2025). Pulsed Electron Paramagnetic Resonance on two Cu(II)-Cage Compounds With Six, Respectively Eight Copper Ions. https://doi.org/10.5194/mr-2025-17

Image Credits: AI Generated

DOI: 10.5194/mr-2025-17

Keywords: electron paramagnetic resonance, DEER, copper(II), self-assembled cages, multi-spin systems, distance measurements, orientation selection, modulation depth, coordination chemistry, magnetic resonance, nanospheres, peer review