Coherent manipulation of Zr(III) aryloxide qudits

Chemists have long sought molecules that can hold quantum information long enough to be useful, but the most successful systems so far have often relied on rare or expensive metals. Now a research team reports the rare isolation of a family of stable zirconium(III) aryloxide complexes built around zirconium, an earth-abundant metal, whose unpaired electron spins can be coherently controlled with microwave pulses. Writing in Nature Chemistry, the researchers show that these trigonal planar molecules deliver spin-lattice relaxation times of up to 87 milliseconds and dephasing times reaching 123 microseconds under pulsed electron paramagnetic resonance (EPR), figures that place them among the leading molecular spin systems reported to date.

The three compounds, Zr(OC6H2-2,6-tBu2-4-R)3 where R is hydrogen, tert-butyl or methoxy, were prepared by reducing the corresponding zirconium(IV) chloride precursors with potassium graphite (KC8) in refluxing toluene. The reactions produced yellow solids in yields of 80 to 95 percent, and single crystals suitable for X-ray diffraction were grown for the hydrogen- and tert-butyl-substituted members from concentrated diethyl ether solutions at minus 35 degrees Celsius. The crystal structures revealed a strikingly flat arrangement: the three oxygen donors form a nearly ideal plane around the metal, with O-Zr-O bond angles ranging from 118.53 to 122.50 degrees and the zirconium sitting essentially within that plane, offset by only hundredths of an angstrom. The Zr-O distances of 1.914 to 1.945 angstroms are similar to those in the starting zirconium(IV) precursors, a trend the authors attribute to the simultaneous drop in coordination number that accompanies reduction.

Zirconium(III) complexes with fully characterized crystal structures remain scarce, and only one homoleptic example, the triscyclopentadienide (C5H5)3Zr, had been previously reported. The new aryloxides appear to owe their thermal stability partly to an increase in intramolecular dispersion-force contacts between the methyl groups of the 2,6-di-tert-butyl substituents, which the crystallographic data show rises from five or six in the precursors to ten in the reduced products. That packing of weak attractive interactions, the team suggests, may help hold the molecules together at ambient conditions, an important practical consideration for any candidate quantum material.

The quantum-relevant magic, however, lies in the electronic structure. Density functional theory calculations performed with the PBE0-D4 functional and a triple-zeta basis set showed that the trigonal planar d1 geometry stabilizes a singly occupied molecular orbital that is a hybrid of the zirconium 4dz2 orbital and the 5s orbital, oriented perpendicular to the O3 plane and pointing along the molecule’s threefold rotation axis. Mulliken population analysis put the s character of this orbital at 25 to 27 percent across the series. This matters because a high s contribution at the metal has been shown to minimize spin-orbit coupling in metal-based qubits, and suppressed spin-orbit coupling in turn lengthens the spin-lattice relaxation time T1, the fundamental clock that limits how long a hyperfine clock qubit can retain phase memory.

Continuous-wave X-band EPR spectroscopy confirmed the picture experimentally. In fluid toluene solution at room temperature, all three complexes gave isotropic signals dominated by the even-mass, spinless zirconium isotopes that together account for 88.8 percent of natural abundance, accompanied by six low-intensity hyperfine lines from the 91Zr isotope, which carries a nuclear spin of 5/2 and makes up 11.2 percent of natural zirconium. The measured isotropic hyperfine coupling constants were enormous for this class of compound: 803 megahertz for the hydrogen derivative, 807 for the tert-butyl and 809 for the methoxy. By comparison, (C5H5)3Zr shows a coupling of only 115 megahertz. Deriving the s character of the singly occupied orbital from these values gave 29 percent for all three complexes, closely matching the computational prediction and approaching the 33 percent estimated for a leading lutetium(II) qubit, [Lu(OC6H2-2,6-Ad2-4-tBu)3]−.

At 77 kelvin, where molecular tumbling freezes and the full anisotropy of the interactions becomes visible, the spectra turned axial, and best-fit simulations with the EasySpin software yielded hyperfine constants of roughly 820 to 826 megahertz along both principal axes, together with quadrupole coupling constants of 1.23 to 1.51 megahertz. Those quadrupole terms are about four times larger than that of vanadium-51 in oxovanadium tetraphenylporphyrin, a compound previously proposed as a prototype nuclear qudit with an electronic ancilla. Energy-level diagrams revealed a rich structure: each electron spin state splits into six sublevels through hyperfine coupling, and at zero field the 91Zr nuclei and the unpaired electron combine into multiplets of total angular momentum F equal to 2 and 3, split into five and seven sublevels respectively. Avoided crossings between these multiplets under an applied field create hyperfine clock transitions, predicted at about 2.5 gigahertz for the tert-butyl compound, which are in principle immune to the magnetic-field fluctuations that normally drive decoherence.

The pulsed EPR measurements on frozen toluene solutions delivered the most striking numbers. Spin-lattice relaxation times T1 rose as the samples were cooled, becoming strongly temperature dependent down to 3 kelvin and reaching 58.5 milliseconds for the hydrogen compound, 87.4 milliseconds for the methoxy derivative and 77.7 milliseconds for the tert-butyl analogue. For comparison, the trigonal planar lanthanum(II) cyclopentadienyl qudits previously studied showed T1 values of only 9 to 50 milliseconds, with their smaller SOMO s character of 7.7 to 10 percent, and could only be measured up to 80 kelvin, whereas the zirconium complexes remained measurable to 120 kelvin. Intriguingly, the lutetium(II) qubit with its 33 percent s character manages only about 1.5 milliseconds, showing that s character alone does not dictate relaxation and that the aryloxide framework confers additional advantages.

Phase memory times, measured with a two-pulse Hahn echo sequence, were long and nearly temperature-independent below 20 kelvin, at 5.6 microseconds for the hydrogen compound, 5.9 for the methoxy and 4.9 for the tert-butyl. Applying the Carr-Purcell-Meiboom-Gill dynamical decoupling pulse sequence, which suppresses slow fluctuations, extended these dephasing times dramatically to 102 microseconds for 2-H, 110 microseconds for 2-OMe and 123 microseconds for 2-tBu at 3 kelvin for the spinless isotopes, falling to 60 to 76 microseconds at 10 kelvin. These figures are especially remarkable given that the measurements were made in hydrogenated toluene with no effort to optimize spin concentration or remove nuclear spins from the environment. The authors attribute the robust coherence partly to the diffuse, metal-centered character of the singly occupied orbital, which is 86 percent metal in character and has limited contact with ligand nuclei, and partly to steric confinement of the bulky tert-butyl groups that limits ligand motion. Further gains, they note, could come from ligand deuteration, dilution or nuclear spin-free solvents.

Crucially, the spins could actually be driven. Nutation experiments at both X and Q band showed clean Rabi oscillations for the electron spin transitions of the spinless isotopes and, selectively, for each of the six hyperfine-resolved transitions of 91Zr, including at 80 kelvin. The oscillation frequencies scaled linearly with microwave field strength, confirming genuine coherent control. The spin-flip time, which corresponds to a single NOT operation on a qubit, was 21 to 28 nanoseconds at low microwave power, thousands of times shorter than the measured dephasing times. The resulting qubit figure of merit, defined as twice the Rabi frequency times the phase memory time, came to 4,053, 4,987 and 5,100 for the hydrogen, methoxy and tert-butyl compounds respectively, values that rank highly among molecular spin qubits.

The study positions zirconium(III) aryloxides as competitive molecular qudits, quantum units that encode more than two levels, and notably demonstrates that the para-substituent on the aryl rings plays only a secondary role in tuning the orbital s character, in contrast to substituted cyclopentadienyl lanthanide systems where substituents mattered greatly. Instead, the three-fold pseudo-D3 symmetry imposed by the aryloxide ligands appears to be the dominant driver of the favorable orbital composition. Because natural-abundance 91Zr samples already display well-resolved, individually addressable hyperfine transitions, the authors argue that isotope-enriched 91Zr versions of these complexes, with a total of twelve available spin states, could serve as promising qudits, and they identify future work on enriched material as the necessary next step toward assessing that full capability.

Subject of Research: Coherent spin manipulation and quantum coherence in earth-abundant zirconium(III) aryloxide molecular qudits

Article Title: Coherent manipulation of Zr(III) aryloxide qudits

Article References: Mahaney, M. E., Zhu, Y., Renard, S., Brown, A. M., Brookfield, A., Goodwin, C. A. P., Robinson, J. R., Tuna, F., & Huh, D. N. (2026). Coherent manipulation of Zr(III) aryloxide qudits. Nature Chemistry. https://doi.org/10.1038/s41557-026-02269-5

Image Credits: AI Generated

DOI: 10.1038/s41557-026-02269-5

Keywords: zirconium, qudits, molecular qubits, EPR spectroscopy, spin coherence, quantum information, aryloxide ligands, hyperfine coupling, spin-lattice relaxation, earth-abundant metals, quantum chemistry, Coherent