A Heterometallic Porphyrin Dimer as a Potential Quantum Gate: Magneto-Structural Correlations and Spin Coherence Properties

In the development of two-qubit quantum gates, precise control over the intramolecular spin-spin interaction between molecular spin units plays a pivotal role. A weak but measurable exchange coupling is especially important for achieving selective spin addressability that allows controlled manipulation of the computational basis states |00⟩ |01⟩ |10⟩ |11⟩ by microwave pulses. Here, we report the synthesis and Electron Paramagnetic Resonance (EPR) study of a heterometallic meso-meso (m-m) singly-linked VIV O-CuII porphyrin dimer. X-band continuous wave EPR measurements in frozen solutions suggest a ferromagnetic exchange coupling of ca. 8 ⋅ 10-3  cm-1 . This estimation is supported by Density Functional Theory calculations, which also allow disentangling the ferro- and antiferromagnetic contributions to the exchange. Pulsed EPR experiments show that the dimer maintains relaxation times similar to the monometallic CuII porphyrins. The addressability of the two individual spins is made possible by the different g-tensors of VIV and CuII -ions, in contrast to homometallic dimers where tilting of the porphyrin planes plays a key role. Therefore, single-spin addressability in the heterometallic dimer can be maintained even with small tilting angles, as expected when deposited on surface, unlocking the full potential of molecular quantum gates for practical applications.

Stable Dication Diradicals of Triply Fused Metallo Chlorin-Porphyrin Heterodimers: Impact of the Bridge on the Control of Spin Coupling to Reactivity

We report an unexpected rearrangement, controlled by the nature of the bridge, leading to the formation of novel, remarkably stable triply fused dinickel(II)/dicopper(II) chlorin-porphyrin dication diradical heterodimers in excellent yields. Here, a dipyrromethene bridge gets completely fused between two porphyrin macrocycles with two new C-C and one C-N bonds. The two macrocycles exhibit extensive π-conjugation through the bridge, which results in an antiferromagnetic coupling between the two π-cation radicals. In addition, the macrocyclic distortion also favours a rare intramolecular ferromagnetic interaction between the CuII and π-cation radical spins to form a triplet state. The structural and electronic perturbation in the unconjugated dication diradical possibly enables the bridging pyrrolic nitrogen to undergo a nucleophilic attack at the nearby β-carbon of the porphyrin π-cation radical with a computed free energy barrier of >20 kcal mol-1 which was supplied in the form of reflux condition to initiate such a rearrangement process. UV-vis, EPR and ESI-MS spectroscopies were used to monitor the rearrangement process in situ in order to identify the key reactive intermediates leading to such an unusual transformation.

Stable Inner 2H Tautomer of N-Confused-like Porphyrin Embedded with a Carbazole Subunit: Synthesis, Metal Coordination, and Magnetic and Anion Sensing Studies

A new class of N-confused porphyrin 1 embedded with a carbazole subunit was prepared via [3 + 1] acid-catalyzed condensation of appropriate precursors. 1 underwent smooth metal complexation with Pd(II) and Cu(II) salts to provide the corresponding diamagnetic 1-Pd and paramagnetic 1-Cu, respectively. The single-crystal X-ray structure of 1-Pd is evident with a square-planar Pd-center through C-H activation of inverted pyrrole. Superconducting quantum interference device analysis combined with electron paramagnetic resonance (EPR) results provided insights into the paramagnetic nature of 1-Cu. Further, a ratiometric enhancement of near-IR fluorescence at 746 nm was found to be reversible upon adding CN- and F- ions. The solid-state structure of 1-Pd confirms that the anionic species is due to NH deprotonation.

Efficient sampling of molecular orientations for Cu(II)-based DEER on protein labels

Combining rigid Cu(II) labels and pulsed-EPR techniques enables distance constraint measurements that are incisive probes of protein structure and dynamics. However, the labels can lead to a dipolar signal that is biased by the relative orientation of the two spins, which is typically unknown a priori in a bilabeled protein. This effect, dubbed orientational selectivity, becomes a bottleneck in measuring distances. This phenomenon also applies to other pulsed-EPR techniques that probe electron-nucleus interactions. In this work, we dissect orientational selectivity by generating an in silico sample of Cu(II)-labeled proteins to evaluate pulse excitation in the context of double electron-electron resonance (DEER) at Q-band frequencies. This approach enables the observation of the contribution of each protein orientation to the dipolar signal, which provides direct insights into optimizing acquisition schemes to mitigate orientational effects. Furthermore, we incorporate the excitation profile of realistic pulses to identify the excited spins. With this method, we show that rectangular pulses, despite their imperfect inversion capability, can sample similar spin orientations as other sophisticated pulses with the same bandwidth. Additionally, we reveal that the efficiency of exciting spin-pairs in DEER depends on the frequency offset of two pulses used in the experiment and the relative orientation of the two spins. Therefore, we systematically examine the frequency offset of the two pulses used in this double resonance experiment to determine the optimal frequency offset for optimal distance measurements. This procedure leads to a protocol where two measurements are sufficient to acquire orientational-independent DEER at Q-band. Notably, this procedure is feasible with any commercial pulsed-EPR spectrometer. Furthermore, we experimentally validate the computational results using DEER experiments on two different proteins. Finally, we show that increasing the amplitude of the rectangular pulse can increase the efficiency of DEER experiments by almost threefold. Overall, this work provides an attractive new approach for analyzing pulsed-EPR spectroscopy to obtain microscopic nuances that cannot be easily discerned from analytical or numerical calculations.

An exchange coupled meso-meso linked vanadyl porphyrin dimer for quantum information processing

We report here the synthesis of a new meso-meso (m-m) singly linked vanadyl-porphyrin dimer that crystallizes in two different pseudo-polymorphs. The single crystal continuous-wave electron paramagnetic resonance investigation evidences a small but crucial isotropic exchange interaction, J, between the two tilted, and thus distinguishable, spin centers of the order of 10^-2 cm^-1. The experimental and DFT studies evidence a correlation between J values and porphyrin plane tilting angle and distortion. Pulsed EPR analysis shows that the two vanadyl dimers maintain the coherence time of the monomer. With the obtained spin Hamiltonian parameters, we identify suitable transitions that could be used as computational basis states. Our results, coupled with the evaporability of porphyrin systems, establish this class of dimers as extremely promising for quantum information processing applications.

Magnetic and Electronic Structural Properties of the S3 State of Nature's Water Oxidizing Complex: A Combined Study in ELDOR-Detected Nuclear Magnetic Resonance Spectral Simulation and Broken-Symmetry Density Functional Theory

ELDOR-detected nuclear magnetic resonance (EDNMR) spectral simulations combined with broken-symmetry density functional theory (BS-DFT) calculations are used to obtain and to assign the ⁵⁵Mn hyperfine coupling constants (hfcs) for modified forms of the water oxidizing complex in the penultimate S₃ state of the water oxidation cycle. The study shows that an open cubane form of the core Mn₄CaO₆ cluster explains the magnetic properties of the dominant S = 3 species in all cases studied experimentally with no need to invoke a closed cubane intermediate possessing a distorted pentacoordinate Mn₄ ion as recently suggested. EDNMR simulations found that both the experimental bandwidth and multinuclear transitions may alter relative EDNMR peak intensities, potentially leading to incorrect assignment of hfcs. The implications of these findings for the water oxidation mechanism are discussed.

Singly and Triply Linked Magnetic Porphyrin Lanthanide Arrays

The introduction of paramagnetic metal centers into a conjugated π-system is a promising approach toward engineering spintronic materials. Here, we report an investigation of two types of spin-bearing dysprosium(III) and gadolinium(III) porphyrin dimers: singly meso-meso-linked dimers with twisted conformations and planar edge-fused β,meso,β-linked tapes. The rare-earth spin centers sit out of the plane of the porphyrin, so that the singly linked dimers are chiral, and their enantiomers can be resolved, whereas the edge-fused tape complexes can be separated into syn and anti stereoisomers. We compare the crystal structures, UV-vis-NIR absorption spectra, electrochemistry, EPR spectroscopy, and magnetic behavior of these complexes. Low-temperature SQUID magnetometry measurements reveal intramolecular antiferromagnetic exchange coupling between the GdIII centers in the edge-fused dimers (syn isomer: J = -51 ± 2 MHz; anti isomer: J = -19 ± 3 MHz), whereas no exchange coupling is detected in the singly linked twisted complex. The phase-memory times, Tm, are in the range of 8-10 μs at 3 K, which is long enough to test quantum computational schemes using microwave pulses. Both the syn and anti Dy2 edge-fused tapes exhibit single-molecule magnetic hysteresis cycles at temperatures below 0.5 K with slow magnetization dynamics.

Long-Range Intramolecular Spin Coupling through a Redox-Active Bridge upon Stepwise Oxidations: Control and Effect of Metal Ions

Dinickel(II) and dicopper(II) porphyrin dimers have been constructed in which two metalloporphyrin units are widely separated by a long unconjugated dipyrrole bridge. Two macrocycles are aligned somewhat orthogonally to each other, while oxidation of the bridge generates a fully π-conjugated butterfly-like structure, which, in turn, upon stepwise oxidations by stronger oxidants result in the formation of the corresponding one- and two-electron-oxidized species exhibiting unusual long-range charge/radical delocalization to produce intense absorptions in the near-infrared (NIR) region and electron paramagnetic resonance (EPR) signals of a triplet state due to interaction between the unpaired spins on the Cu(II) ions. Although the two metal centers have a large physical separation through the bridge (more than 16 Å), they share electrons efficiently between them, behaving as a single unit rather than two independent centers. Detailed UV-vis-NIR, electrospray ionization mass spectrometry, IR, variable-temperature magnetic study, and EPR spectroscopic investigations along with X-ray structure determination of unconjugated, conjugated, and one electron-oxidized complexes have been exploited to demonstrate the long-range electronic communication through the bridge. The experimental observations are also supported by density functional theory (DFT) and time-dependent DFT calculations. The present study highlights the crucial roles played by a redox-active bridge and metal in controlling the long-range electronic communication.

Study of Electron-Nuclear Interactions in Doped Calcium Phosphates by Various Pulsed EPR Spectroscopy Techniques

Substituted calcium phosphates (CaPs) are vital materials for the treatment of bone diseases and repairing and replacement of defects in human hard tissues. In this paper, we present some applications of the rarely used pulsed electron paramagnetic resonance (EPR) and hyperfine interaction spectroscopy approaches [namely, electron spin-echo envelope modulation (ESEEM) and electron-electron double-resonance detected nuclear magnetic resonance (EDNMR)] to investigate synthetic CaPs (hydroxyapatite, tricalcium, and octacalcium phosphate) doped with various cations (Li+, Na+, Mn2+, Cu2+, Fe3+, and Ba2+). These resonance techniques provide reliable tools to obtain unique information about the presence and localization of impurity centers and values of hyperfine and quadrupole tensors. We show that revealed in CaPs by EPR techniques, radiation-induced stable nitrogen-containing species and carbonate radicals can serve as sensitive paramagnetic probes to follow CaPs' structural changes caused by cation doping. The most pulsed EPR, ESEEM, and EDNMR spectra can be detected at room temperature, reducing the costs of the measurements and facilitating the usage of pulsed EPR techniques for CaP characterization.

Controlled coherent dynamics of [VO(TPP)], a prototype molecular nuclear qudit with an electronic ancilla

We show that [VO(TPP)] (vanadyl tetraphenylporphyrinate) is a promising system to implement quantum computation algorithms based on encoding information in multi-level (qudit) units. Indeed, it embeds a nuclear spin 7/2 coupled to an electronic spin 1/2 by hyperfine interaction. This qubit-qudit unit can be exploited to implement quantum error correction and quantum simulation algorithms. Through a combined theoretical and broadband nuclear magnetic resonance study, we demonstrate that the elementary operations of such algorithms can be efficiently implemented on the nuclear spin qudit. Manipulation of the nuclear qudit can be achieved by resonant radio-frequency pulses, thanks to the remarkably long coherence times and the effective quadrupolar coupling induced by the strong hyperfine interaction. This approach may open new perspectives for developing new molecular qubit-qudit systems.

Radiation-Induced Stable Radicals in Calcium Phosphates: Results of Multifrequency EPR, EDNMR, ESEEM, and ENDOR Studies

This article presents the results of a study of radiation-induced defects in various synthetic calcium phosphate (CP) powder materials (hydroxyapatite—HA and octacalcium phosphate—OCP) by electron paramagnetic resonance (EPR) spectroscopy at the X, Q, and W-bands (9, 34, 95 GHz for the microwave frequencies, respectively). Currently, CP materials are widely used in orthopedics and dentistry owing to their high biocompatibility and physico-chemical similarity with human hard tissue. It is shown that in addition to the classical EPR techniques, other experimental approaches such as ELDOR-detected NMR (EDNMR), electron spin echo envelope modulation (ESEEM), and electron-nuclear double resonance (ENDOR) can be used to analyze the electron–nuclear interactions of CP powders. We demonstrated that the value and angular dependence of the quadrupole interaction for 14N nuclei of a nitrate radical can be determined by the EDNMR method at room temperature. The ESEEM technique has allowed for a rapid analysis of the nuclear environment and estimation of the structural positions of radiation-induced centers in various crystal matrices. ENDOR spectra can provide information about the distribution of the nitrate radicals in the OCP structure.

Crossover from a Solid Effect to Thermal Mixing 1H Dynamic Nuclear Polarization with Trityl-OX063

Trityl-OX063 is a narrow-line, water-soluble, and biocompatible polarizing agent, widely used for dynamic nuclear polarization (DNP) amplified NMR of ¹³C, but not of the abundant ¹H nuclear spin, for which the ineffective solid effect (SE) is expected to be operational. Surprisingly, we observed a crossover from SE to thermal mixing (TM) DNP of ¹H with increasing Trityl-OX063 concentration at 7 T. We experimentally ascertained diagnostic signatures of TM-DNP that have only been theoretically predicted: (i) an electron paramagnetic resonance (EPR) spectrum that maintains an asymmetrically broadened EPR line from strong e-e couplings and (ii) hyperpolarization, i.e., cooling of select electron-spin populations, manifested in a characteristic pump-probe electron double-resonance spectrum under DNP conditions. Low microwave power requirements, high polarization transfer rates, and efficient DNP at high magnetic fields are the key benefits of TM-DNP.