Synthetic Approach To Determine the Effect of Nuclear Spin Distance on Electronic Spin Decoherence

Stable organic radical qubits and their applications in quantum information science

The past century has witnessed the flourishing of organic radical chemistry. Stable organic radicals are highly valuable for quantum technologies thanks to their inherent room temperature quantum coherence, atomic-level designability, and fine tunability. In this comprehensive review, we highlight the potential of stable organic radicals as high-temperature qubits and explore their applications in quantum information science, which remain largely underexplored. Firstly, we summarize known spin dynamic properties of stable organic radicals and examine factors that influence their electron spin relaxation and decoherence times. This examination reveals their design principles and optimal operating conditions. We further discuss their integration in solid-state materials and surface structures, and present their state-of-the-art applications in quantum computing, quantum memory, and quantum sensing. Finally, we analyze the primary challenges associated with stable organic radical qubits and provide tentative insights to future research directions.

CaY@C2n: Exploring Molecular Qubits with Ca-Y Metal-Metal Bonds

Metal-metal bonding is crucial in chemistry for advancing our understanding of the fundamental aspects of chemical bonds. Metal-metal bonds based on alkaline-earth (Ae) elements, especially the heavier Ae elements (Ca, Sr, and Ba), are rarely reported due to their high electropositivity. Herein, we report two heteronuclear di-EMFs CaY@Cs(6)-C82 and CaY@C2v(5)-C80, which contain unprecedented single-electron Ca-Y metal-metal bonds. These compounds were characterized by single-crystal X-ray crystallography, electron paramagnetic resonance (EPR) spectroscopy, and DFT calculations. The crystallographic study of CaY@Cs(6)-C82 shows that Ca and Y are successfully encapsulated into the carbon cage with a Ca-Y distance of 3.691 Å. The CW-EPR study of both CaY@Cs(6)-C82 and CaY@C2v(5)-C80 exhibits a doublet, suggesting the presence of an unpaired electron located between Ca and Y. The combined experimental and theoretical results confirm the presence of a Ca-Y single-electron metal-metal bond with substantial covalent interaction, attributed to significant overlap between the 4s4p orbitals of Ca and the 5s5p4d orbitals of Y. Furthermore, pulse EPR spectroscopy was used to investigate the quantum coherence of the electron spin within this bond. The unpaired electron, characterized by its s orbital nature, is effectively protected by the carbon cage, resulting in efficient suppression of both spin-lattice relaxation and decoherence. CaY@Cs(6)-C82 behaves as an electron spin qubit, displaying a maximum decoherence time of 7.74 μs at 40 K. This study reveals an unprecedented Ae-rare-earth metal-metal bond stabilized by the fullerene cages and elucidates the molecular qubit properties stemming from their unique bonding character, highlighting their potential in quantum information processing applications.

(η8-Cyclooctatetraene)(η5-fluorenyl)titanium: a processable molecular spin qubit with optimized control of the molecule-substrate interface

Depositing single paramagnetic molecules on surfaces for sensing and quantum computing applications requires subtle topological control. To overcome issues that are often encountered with sandwich metal complexes, we exploit here the low symmetry architecture and suitable vaporability of mixed-sandwich [FluTi(cot)], Flu = fluorenyl, cot = cyclooctatetraene, to drive submonolayer coverage and select an adsorption configuration that preserves the spin of molecules deposited on Au(111). Electron paramagnetic resonance spectroscopy and ab initio quantum computation evidence a d z 2 ground state that protects the spin from phonon-induced relaxation. Additionally, computed and measured spin coherence times exceed 10 μs despite the molecules being rich in hydrogen. A thorough submonolayer investigation by scanning tunneling microscopy, X-ray photoelectron and absorption spectrocopies and X-ray magnetic circular dichroism measurements supported by DFT calculations reveals that the most stable configuration, with the fluorenyl in contact with the metal surface, prevents titanium(iii) oxidation and spin delocalization to the surface. This is a necessary condition for single molecular spin qubit addressing on surfaces.

Relativistic Douglas-Kroll-Hess calculations of hyperfine interactions within first-principles multireference methods

A relativistic magnetic hyperfine interaction Hamiltonian based on the Douglas-Kroll-Hess (DKH) theory up to the second order is implemented within the ab initio multireference methods, including spin-orbit coupling in the Molcas/OpenMolcas package. This implementation is applied to calculate relativistic hyperfine coupling (HFC) parameters for atomic systems and diatomic radicals with valence s or d orbitals by systematically varying active space size in the restricted active space self-consistent field formalism with restricted active space state interaction for spin-orbit coupling. The DKH relativistic treatment of the hyperfine interaction reduces the Fermi contact contribution to the HFC due to the presence of kinetic factors that regularize the singularity of the Dirac delta function in the nonrelativistic Fermi contact operator. This effect is more prominent for heavier nuclei. As the active space size increases, the relativistic correction of the Fermi contact contribution converges well to the experimental data for light and moderately heavy nuclei. The relativistic correction, however, does not significantly affect the spin-dipole contribution to the hyperfine interaction. In addition to the atomic and molecular systems, the implementation is applied to calculate the relativistic HFC parameters for large trivalent and divalent Tb-based single-molecule magnets (SMMs), such as Tb(III)Pc2 and Tb(II)(CpiPr5)2 without ligand truncation using well-converged basis sets. In particular, for the divalent SMM, which has an unpaired valence 6s/5d hybrid orbital, the relativistic treatment of HFC is crucial for a proper description of the Fermi contact contribution. Even with the relativistic hyperfine Hamiltonian, the divalent SMM is shown to exhibit strong tunability of HFC via an external electric field (i.e., strong hyperfine Stark effect).

Identification of an X-Band Clock Transition in Cp'3Pr- Enabled by a 4f25d1 Configuration

Molecular qubits offer an attractive basis for quantum information processing, but challenges remain with regard to sustained coherence. Qubits based on clock transitions offer a method to improve the coherence times. We propose a general strategy for identifying molecules with high-frequency clock transitions in systems where a d electron is coupled to a crystal-field singlet state of an f configuration, resulting in an MJ = ±1/2 ground state with strong hyperfine coupling. Using this approach, a 9.834 GHz clock transition was identified in a molecular Pr complex, [K(crypt)][Cp'3PrII], leading to 3-fold enhancements in T2 relative to other transitions in the spectrum. This result indicates the promise of the design principles outlined here for the further development of f-element systems for quantum information applications.

Magnetic Relaxations of Chromium Nitride Porphyrinato Complexes Driven by the Anisotropic g-Factor

Molecule-based magnetic materials are useful candidates as the spin qubit due to their long coherence time and high designability. The anisotropy of the g-values of the metal complexes can be utilized to access the individual spin of the metal complexes, making it possible to achieve the scalable molecular spin qubit. For this goal, it is important to evaluate the effect of g-value anisotropy on the magnetic relaxation behaviour. This study reports the slow magnetic relaxation behaviour of chromium nitride (CrN2+ ) porphyrinato complex (1), which is structurally and magnetically similar with the vanadyl (VO2+ ) porphyrinato complex (2) which is known as the excellent spin qubit. Detailed analyses for vibrational and dynamical magnetism of 1 and 2 revealed that g-value anisotropy accelerates magnetic relaxations greater than the internal magnetic field from nuclear spin does. These results provide a design criterion for construction of multiple spin qubit based on g-tensor engineering.

Quantum spin coherence and electron spin distribution channels in vanadyl-containing lantern complexes

We herein investigate the heterobimetallic lantern complexes [PtVO(SOCR)4] as charge neutral electronic qubits based on vanadyl complexes (S = 1/2) with nuclear spin-free donor atoms. The derivatives with R = Me (1) and Ph (2) give highly resolved X-band EPR spectra in frozen CH2Cl2/toluene solution, which evidence the usual hyperfine coupling with the 51V nucleus (I = 7/2) and an additional superhyperfine interaction with the I = 1/2 nucleus of the 195Pt isotope (natural abundance ca. 34%). DFT calculations ascribe the spin density delocalization on the Pt2+ ion to a combination of π and δ pathways, with the former representing the predominant channel. Spin relaxation measurements in frozen CD2Cl2/toluene-d8 solution between 90 and 10 K yield Tm values (1-6 μs in 1 and 2-11 μs in 2) which compare favorably with those of known vanadyl-based qubits in similar matrices. Coherent spin manipulations indeed prove possible at 70 K, as shown by the observation of Rabi oscillations in nutation experiments. The results indicate that the heavy Group 10 metal ion is not detrimental to the coherence properties of the vanadyl moiety and that Pt-VO lanterns can be used as robust spin-coherent building blocks in materials science and quantum technologies.

Enhancing Coherence Times of Chromophore-Radical Molecular Qubits and Qudits by Rational Design

An important criterion for quantum operations is long qubit coherence times. To elucidate the influence of molecular structure on the coherence times of molecular spin qubits and qudits, a series of molecules featuring perylenediimide (PDI) chromophores covalently linked to stable nitroxide radicals were synthesized and investigated by pulse electron paramagnetic resonance spectroscopy. Photoexcitation of PDI in these systems creates an excited quartet state (Q) followed by a spin-polarized doublet ground state (D0), which hold promise as spin qudits and qubits, respectively. By tailoring the molecular structure of these spin qudit/qubit candidates by selective deuteration and eliminating intramolecular motion, coherence times of Tm = 9.1 ± 0.3 and 4.2 ± 0.3 μs at 85 K for D0 and Q, respectively, are achieved. These coherence times represent a nearly 3-fold enhancement compared to those of the initial molecular design. This approach offers a rational structural design protocol for effectively extending coherence times in molecular spin qudits/qubits.

Spin Qubit in a 2D GdIII NaI -Based Oxamato Supramolecular Coordination Framework

Qubits are the basic unit of quantum information and computation. To realize quantum computing and information processing, the decoherence times of qubits must be long enough. Among the studies of molecule-based electron spin qubits, most of the work focused on the ions with the spin S=1/2, where only single-bit gates can be constructed. However, quantum operations require the qubits to interact with each other, so people gradually carry out relevant research in ions or systems with S>1/2 and multilevel states. In this work, a two-dimensional (2D) oxygen-coordinated GdIII NaI -based oxamato supramolecular coordination framework, Na[Gd(4-HOpa)4 (H2 O)] ⋅ 2H2 O (1, 4-HOpa=N-4-hydroxyphenyloxamate), was selected as a possible carrier of qubit. The field-induced slow magnetic relaxation shows this system has phonon bottleneck (PB) effect at low temperatures with a very weak magnetic anisotropy. The pulse electron paramagnetic resonance studies show the spin-lattice and spin-spin relaxation times are T1 =1.66 ms at 4 K and Tm =4.25 μs at 8 K for its diamagnetically diluted sample (1Gd0.12 %). It suggested that the relatively long decoherence time is mainly ascribed to its near isotropic and the PB effect from resonance phonon trapped for pure sample, while the dilution further improves its qubit performance.

Redox-Controlled Self-Assembly of Vanadium-Seamed Hexameric Pyrogallol[4]Arene Nanocapsules

Here we report the controlled self-assembly of vanadium-seamed metal-organic nanocapsules with specific metal oxidation state distributions. Three supramolecular assemblies composed of the same numbers of components including 24 metal centers and six pyrogallol[4]arene ligands were constructed: a VIII24L6 capsule, a mixed-valence VIII18VIV6L6 capsule, and a VIV24L6 capsule. Crystallographic studies of the new capsules reveal their remarkable structural complexity and geometries, while marked differences in metal oxidation state distribution greatly affect the photoelectric conversion properties of these assemblies. This work therefore represents a significant step forward in the construction of intricate metal-organic architectures with tailored structure and functionality.

Crystalline Arrays of Copper Porphyrin Qubits Based on Ion-Paired Frameworks

Molecular electronic spin qubits have great potential for use in quantum information science applications because their structure can be rationally tuned using synthetic chemistry. Their integration into a new class of materials, ion-paired frameworks, allows for the formation of ordered arrays of these molecular spin qubits. Three ion-paired frameworks with varying densities of paramagnetic Cu(II) porphyrins were isolated as micron-sized crystals suitable for characterization by single-crystal X-ray diffraction. Pulse-electron paramagnetic resonance (EPR) spectroscopy probed the spin coherence of these materials at temperatures up to 140 K. The crystals with the longest Cu-Cu distances had a spin-spin relaxation time (Tm) of 207 ns and a spin-lattice relaxation time (T1) of 1.8 ms at 5 K, which decreased at elevated temperature because of spin-phonon coupling. Crystals with shorter Cu-Cu distances also had lower T1 values because of enhanced cross-relaxation from qubit-qubit dipolar coupling. Frameworks with shorter Cu-Cu distances exhibited lower Tm values because of the increased interactions between qubits within the frameworks. Incorporating molecular electronic spin qubits in ion-paired frameworks enables control of composition, spacing, and interqubit interactions, providing a rational means to extend spin relaxation times.

VdW Mediated Strong Magnetic Exchange Interactions in Chains of Hydrogen-Free Sublimable Molecular Qubits

Sulfur-rich molecular complexes of dithiolene-like ligands are appealing candidates as molecular spin qubits because spin coherence properties are enhanced in hydrogen-free environments. Herein, we employ the hydrogen-free mononegative 1,3,2-dithiazole-4-thione-5-thiolate (dttt^-) ligand as an alternative to common dinegative dithiolate ligands. We report the first synthesis and structural characterization of its Cu²⁺, Ni²⁺, and Pt²⁺ neutral complexes. The XPS analysis of thermal deposition of [Cu(dttt)₂] in UHV conditions indicates that films of intact molecules can be deposited on surfaces by sublimation. Thanks to a combined approach employing DC magnetometry and DFT calculations, we highlighted AF exchange interactions of 108 cm^-1 and 36 cm^-1 attributed to the two different polymorph phases. These couplings are exclusively mediated by S···S VdW interactions, which are facilitated by the absence of counterions and made particularly efficient by the diffuse electron density on S atoms. Furthermore, the spin dynamics of solid-state magnetically diluted samples was investigated. The longest observed T _m is 2.3 μs at 30 K, which significantly diverges from the predicted T _m > 100 μs. These results point to the diluting matrix severely affecting the coherence lifetime of Cu²⁺ species via different factors, such as the contributions of neighboring ¹⁴N nuclei and the formation of radical impurities in a non-completely controllable way. However, the ease of processing [Cu(dttt)₂] via thermal sublimation can allow dispersion in matrices better suited for coherent spin manipulation of isolated molecules and the realization of AF-coupled VdW structures on surfaces.

Observation of slow magnetic relaxation phenomena in spatially isolated π-radical ions

The use of molecular spins as quantum bits is fascinating because it offers a wide range of strategies through chemical modifications. In this regard, it is very interesting to search for organic radical ions that have small spin-orbit coupling values. On the other hand, the feature of the magnetic relaxation of π-organic radical ions is rarely exploited due to the difficulty of spin dilution, and π-stacking interaction. In this study, we focus on N,N',N''-tris(2,6-dimethylphenyl)benzenetriimide (BTI-xy), where three xylene moieties connected to the imide groups cover the π-plane of the BTI core. As a result, BTI-xy radical anions without π-stacking interaction were obtained. This led to the slow magnetization relaxation, which is reported for the first time in organic radicals. Furthermore, the relaxation times in a solution state revealed the importance of spin interaction.

Slow magnetic relaxation of a S = 1/2 copper(II)-substituted Keggin-type silicotungstate

This is the first report on slow magnetic relaxation in an S = 1/2 system based on a first-row transition metal ion with the polyoxometalate skeleton [(n-C₄H₉)₄N]₄H₂[SiW₁₁O₃₉Cu] (1). The X-band electron-spin-resonance spectrum of 1 measured at room temperature indicates that the copper ion experiences significantly reduced intermolecular interactions compared to the potassium salt and that it adopts a five-coordinated square-pyramidal coordination geometry. The AC magnetic-susceptibility measurements revealed that 1 undergoes slow magnetic relaxation in an applied static magnetic field (H_dc). The extracted spin-lattice relaxation time (92 ms at 1.8 K and H_dc = 5000 Oe) for 5% magnetically diluted 1, [(n-C₄H₉)₄N]₄H₂[SiW₁₁O₃₉Cu_0.05Zn_0.95] (dil.1), is comparable to those of other potential S = 1/2 spin qubits. A relaxation-time analysis indicated that Raman spin-lattice relaxation dominates even at low temperatures in an optimized field. The extracted Raman exponent (n = 2.30) is smaller than those of other S = 1/2 complexes that carry organic ligands, which implies that the decrease in relaxation time at higher temperatures is likely to be moderate.

Electronic Spin Qubit Candidates Arrayed within Layered Two-Dimensional Polymers

Molecular electronic spin qubits are promising candidates for quantum information science applications because they can be reliably produced and engineered via chemical design. Embedding electronic spin qubits within two-dimensional polymers (2DPs) offers the possibility to systematically engineer inter-qubit interactions while maintaining long coherence times, both of which are prerequisites to their technological utility. Here, we introduce electronic spin qubits into a diamagnetic 2DP by n-doping naphthalene diimide subunits with varying amounts of CoCp₂ and analyze their spin densities by quantitative electronic paramagnetic resonance spectroscopy. Low spin densities (e.g., 6.0 × 10¹² spins mm^-3) enable lengthy spin-lattice (T₁) and spin-spin relaxation (T₂) times across a range of temperatures, ranging from T₁ values of 164 ms at 10 K to 30.2 μs at 296 K and T₂ values of 2.36 μs at 10 K to 0.49 μs at 296 K for the lowest spin density sample examined. Higher spin densities and temperatures were both found to diminish T₁ times, which we attribute to detrimental cross-relaxation from spin-spin dipolar interactions and spin-phonon coupling, respectively. Higher spin densities decreased T₂ times and modulated the T₂ temperature dependence. We attribute these differences to the competition between hyperfine and dipolar interactions for electron spin decoherence, with the dominant interaction transitioning from the former to the latter as spin density and temperature increase. Overall, this investigation demonstrates that dispersing electronic spin qubits within layered 2DPs enables chemical control of their inter-qubit interactions and spin decoherence times.

Computational Insights into Electronic Excitations, Spin-Orbit Coupling Effects, and Spin Decoherence in Cr(IV)-Based Molecular Qubits

The great success of point defects and dopants in semiconductors for quantum information processing has invigorated a search for molecules with analogous properties. Flexibility and tunability of desired properties in a large chemical space have great advantages over solid-state systems. The properties analogous to point defects were demonstrated in the Cr(IV)-based molecular family, Cr(IV)(aryl)₄, where the electronic spin states were optically initialized, read out, and controlled. Despite this kick-start, there is still a large room for enhancing properties crucial for molecular qubits. Here, we provide computational insights into key properties of the Cr(IV)-based molecules aimed at assisting the chemical design of efficient molecular qubits. Using the multireference ab initio methods, we investigate the electronic states of Cr(IV)(aryl)₄ molecules with slightly different ligands, showing that the zero-phonon line energies agree with the experiment and that the excited spin-triplet and spin-singlet states are highly sensitive to small chemical perturbations. By adding spin-orbit interaction, we find that the sign of the uniaxial zero-field splitting (ZFS) parameter is negative for all considered molecules and discuss optically induced spin initialization via non-radiative intersystem crossing. We quantify (super)hyperfine coupling to the ⁵³Cr nuclear spin and to the ¹³C and ¹H nuclear spins, and we discuss electron spin decoherence. We show that the splitting or broadening of the electronic spin sub-levels due to superhyperfine interaction with ¹H nuclear spins decreases by an order of magnitude when the molecules have a substantial transverse ZFS parameter.

Three individually addressable spin qubits in a single molecule

An asymmetric bis-phenol-β-diketone (H₄L) has been designed as a ligand programmed to promote the assembly of a molecular arrangement composed of three magnetically exchanged [NiCu] pairs, each exhibiting an S = 1/2 spin. The latter are shown by EPR and magnetometry to be good qubit realizations and non-equivalent within the molecule in the solid state, as required for conditional quantum gates.

Using Molecular Design to Enhance the Coherence Time of Quintet Multiexcitons Generated by Singlet Fission in Single Crystals

Multiexciton quintet states, ⁵(TT), photogenerated in organic semiconductors using singlet fission (SF), consist of four quantum entangled spins, promising to enable new applications in quantum information science. However, the factors that determine the spin coherence of these states remain underexplored. Here, we engineer the packing of tetracene molecules within single crystals of 5,12-bis(tricyclohexylsilylethynyl)tetracene (TCHS-tetracene) to demonstrate a ⁵(TT) state that exhibits promising spin qubit properties, including a coherence time, T₂, = 3 μs at 10 K, a population lifetime, T_pop, = 130 μs at 5 K, and stability even at room temperature. The single-crystal platform also enables global alignment of the spins and, consequently, individual addressability of the spin-sublevel transitions. Decoherence mechanisms, including exciton diffusion, electronic dipolar coupling, and nuclear hyperfine interactions, are elucidated, providing design principles for increasing T₂ and the operational temperature of ⁵(TT). By dynamically decoupling ⁵(TT) from the surrounding spin bath, T₂ = 10 μs is achieved. These results demonstrate the viability of harnessing singlet fission to initiate multiple electron spins in a well-defined quantum state for next-generation molecular-based quantum technologies.

Solid polymorphism and dynamic magnetic properties of a dodecylated vanadyl–porphyrinato complex: spin–lattice relaxations modulated by phase stabilisation

Phase stabilisation elongates spin–lattice relaxation times.

Tunable Cr4+ Molecular Color Centers

The inherent atomistic precision of synthetic chemistry enables bottom-up structural control over quantum bits, or qubits, for quantum technologies. Tuning paramagnetic molecular qubits that feature optical-spin initialization and readout is a crucial step toward designing bespoke qubits for applications in quantum sensing, networking, and computing. Here, we demonstrate that the electronic structure that enables optical-spin initialization and readout for S = 1, Cr(aryl)₄, where aryl = 2,4-dimethylphenyl (1), o-tolyl (2), and 2,3-dimethylphenyl (3), is readily translated into Cr(alkyl)₄ compounds, where alkyl = 2,2,2-triphenylethyl (4), (trimethylsilyl)methyl (5), and cyclohexyl (6). The small ground state zero field splitting values (<5 GHz) for 1-6 allowed for coherent spin manipulation at X-band microwave frequency, enabling temperature-, concentration-, and orientation-dependent investigations of the spin dynamics. Electronic absorption and emission spectroscopy confirmed the desired electronic structures for 4-6, which exhibit photoluminescence from 897 to 923 nm, while theoretical calculations elucidated the varied bonding interactions of the aryl and alkyl Cr⁴⁺ compounds. The combined experimental and theoretical comparison of Cr(aryl)₄ and Cr(alkyl)₄ systems illustrates the impact of the ligand field on both the ground state spin structure and excited state manifold, laying the groundwork for the design of structurally precise optically addressable molecular qubits.

Photogenerated Spin-Correlated Radical Pairs: From Photosynthetic Energy Transduction to Quantum Information Science

More than a half century ago, the NMR spectra of diamagnetic products resulting from radical pair reactions were observed to have strongly enhanced absorptive and emissive resonances. At the same time, photogenerated radical pairs were discovered to exhibit unusual electron paramagnetic resonance spectra that also had such resonances. These non-Boltzmann, spin-polarized spectra were observed in both chemical systems as well as in photosynthetic reaction center proteins following photodriven charge separation. Subsequent studies of these phenomena led to a variety of chemical electron donor-acceptor model systems that provided a broad understanding of the spin dynamics responsible for these spectra. When the distance between the two radicals is restricted, these observations result from the formation of spin-correlated radical pairs (SCRPs) in which the spin-spin exchange and dipolar interactions between the two unpaired spins play an important role in the spin dynamics. Early on, it was recognized that SCRPs photogenerated by ultrafast electron transfer are entangled spin pairs created in a well-defined spin state. These SCRPs can serve as spin qubit pairs (SQPs), whose spin dynamics can be manipulated to study a wide variety of quantum phenomena intrinsic to the field of quantum information science. This Perspective highlights the role of SCRPs as SQPs, gives examples of possible quantum manipulations using SQPs, and provides some thoughts on future directions.

Deconvolving Contributions to Decoherence in Molecular Electron Spin Qubits: A Dynamic Ligand Field Approach

In the past decade, transition metal complexes have gained momentum as electron spin-based quantum bit (qubit) candidates due to their synthetic tunability and long achievable coherence times. The decoherence of magnetic quantum states imposes a limit on the use of these qubits for quantum information technologies, such as quantum computing, sensing, and communication. With rapid recent development in the field of molecular quantum information science, a variety of chemical design principles for prolonging coherence in molecular transition metal qubits have been proposed. Here the spin-spin, motional, and spin-phonon regimes of decoherence are delineated, outlining design principles for each. It is shown how dynamic ligand field models can provide insights into the intramolecular vibrational contributions in the spin-phonon decoherence regime. This minireview aims to inform the development of molecular quantum technologies tailored for different environments and conditions.

Spectral Addressability in a Modular Two Qubit System

The combination of structural precision and reproducibility of synthetic chemistry is perfectly suited for the creation of chemical qubits, the core units of a quantum information science (QIS) system. By exploiting the atomistic control inherent to synthetic chemistry, we address a fundamental question of how the spin-spin distance between two qubits impacts electronic spin coherence. To achieve this goal, we designed a series of molecules featuring two spectrally distinct qubits, an early transition metal, Ti³⁺, and a late transition metal, Cu²⁺ with increasing separation between the two metals. Crucially, we also synthesized the monometallic congeners to serve as controls. The spectral separation between the two metals enables us to probe each metal individually in the bimetallic species and compare it with the monometallic control samples. Across a range of 1.2-2.5 nm, we find that electron spins have a negligible effect on coherence times, a finding we attribute to the distinct resonance frequencies. Coherence times are governed, instead, by the distance to nuclear spins on the other qubit's ligand framework. This finding offers guidance for the design of spectrally addressable molecular qubits.

Direct measurement of the triple spin flip rate in dynamic nuclear polarization

A previous study of the effect of Gadolinium doping on the dynamic polarization (DNP) of ¹³C using trityls showed that the rate at which the polarization builds up is almost independent of the Gadolinium concentration, while the electron spin-lattice relaxation rate varies over an order of magnitude. In this paper we analyze the polarization build-up in detail and show that in this case DNP is due to the cross-effect (CE) and that the build-up rate can be quantitatively interpreted as the rate of the triple spin flips responsible for the CE. Thus this build-up rate presents a direct measurement of this triple spin flip rate.

A Molecular Approach to Quantum Sensing

The second quantum revolution hinges on the creation of materials that unite atomic structural precision with electronic and structural tunability. A molecular approach to quantum information science (QIS) promises to enable the bottom-up creation of quantum systems. Within the broad reach of QIS, which spans fields ranging from quantum computation to quantum communication, we will focus on quantum sensing. Quantum sensing harnesses quantum control to interrogate the world around us. A broadly applicable class of quantum sensors would feature adaptable environmental compatibility, control over distance from the target analyte, and a tunable energy range of interaction. Molecules enable customizable "designer" quantum sensors with tunable functionality and compatibility across a range of environments. These capabilities offer the potential to bring unmatched sensitivity and spatial resolution to address a wide range of sensing tasks from the characterization of dynamic biological processes to the detection of emergent phenomena in condensed matter. In this Outlook, we outline the concepts and design criteria central to quantum sensors and look toward the next generation of designer quantum sensors based on new classes of molecular sensors.

A Stable Triplet-Ground-State Conjugated Diradical Based on a Diindenopyrazine Skeleton

High-spin conjugated radicals have great potential in magnetic materials and organic spintronics. However, to obtain high-spin conjugated radicals is still quite challenging due to their poor stability. We report the successful synthesis and isolation of a stable triplet conjugated diradical, 10,12-diaryldiindeno[1,2-b:2',1'-e]pyrazine (m-DIP). With the m-xylylene analogue skeleton containing electron-deficient sp² -nitrogen atoms, m-DIP displays significant aromatic character within its pyrazine ring and its spin density mainly delocalizes on the meta-pyrazine unit, making it a triplet ground state conjugated diradical. Our work provides an effective "spin density tuning" strategy for stable high-spin conjugated radicals.

Field-Induced Single-Molecule Magnets of Dysprosium Involving Quinone Derivatives

The coordination reaction of the [Dy(hfac)3(H2O)2] units (hfac− = 1,1,1,5,5,5-hexafluoroacetylacetonate) with the two quinone-based derivatives 4,7-di-tert-butyl-2-(3,5-di-tert-butyl-4-oxocyclohexa-2,5-dien-1-ylidene)benzo[d][1,3]dithiole-5,6-dione (L1) and 7,8-dithiabicyclo[4.2.0]octa-1,5-diene-3,4-dione,2,5bis(1,1-dimethylethyl) (L2) led respectively to the complexes [Dy(hfac)3(H2O)(L1)] (1) and [Dy(hfac)3(H2O) (L2)]⋅(C6H14)(CH2Cl2) (2)⋅(C6H14)(CH2Cl2). X-ray structures on single crystal of 1 and 2⋅(C6H14)(CH2Cl2) revealed the coordination of the DyIII on the bischelating oxygenated quinone site and the formation of dimeric species through hydrogen bonds. Ac magnetic measurements highlighted field-induced single-molecule magnet behavior with magnetic relaxation through a Raman process.

Probing Vibrational Symmetry Effects and Nuclear Spin Economy Principles in Molecular Spin Qubits

The selection of molecular spin qubits with a long coherence time, Tm, is a central task for implementing molecule-based quantum technologies. Even if a sufficiently long Tm can be achieved through an efficient synthetic strategy and ad hoc experimental measurement procedures, many factors contributing to the loss of coherence still need to be thoroughly investigated and understood. Vibrational properties and nuclear spins of hydrogens are two of them. The former plays a paramount role, but a detailed theoretical investigation aimed at studying their effects on the spin dynamics of molecular complexes such as the benchmark phthalocyanine (Pc) is still missing, whereas the effect of the latter deserves to be examined in detail for such a class of compounds. In this work, we adopted a combined theoretical and experimental approach to investigate the relaxation properties of classical [Cu(Pc)] and a CuII complex based on the ligand tetrakis(thiadiazole)porphyrazine (H2TTDPz), characterized by a hydrogen-free molecular structure. Systematic calculations of molecular vibrations exemplify the effect of normal modes on the spin-lattice relaxation process, unveiling a different contribution to T1 depending on the symmetry of normal modes. Moreover, we observed that an appreciable Tm enhancement could be achieved by removing hydrogens from the ligand.

Metal-organic frameworks: possible new two-dimensional magnetic and topological materials

Finding new two-dimensional (2D) materials with novel quantum properties is highly desirable for technological innovations. In this work, we studied a series of metal-organic frameworks (MOFs) with different metal cores and discovered various attractive properties, such as room-temperature magnetic ordering, strong perpendicular magnetic anisotropy, huge topological band gap (>200 meV), and excellent spin-filtering performance. As many MOFs have been successfully synthesized in experiments, our results suggest realistic new 2D functional materials for the design of spintronic nanodevices.

Exploring the Organometallic Route to Molecular Spin Qubits: The [CpTi(cot)] Case

The coherence time of the 17-electron, mixed sandwich complex [CpTi(cot)], (η⁸ -cyclooctatetraene)(η⁵ -cyclopentadienyl)titanium, reaches 34 μs at 4.5 K in a frozen deuterated toluene solution. This is a remarkable coherence time for a highly protonated molecule. The intramolecular distances between the Ti and H atoms provide a good compromise between instantaneous and spin diffusion sources of decoherence. Ab initio calculations at the molecular and crystal packing levels reveal that the characteristic low-energy ring rotations of the sandwich framework do not yield a too detrimental spin-lattice relaxation because of their small spin-phonon coupling. The volatility of [CpTi(cot)] and the accessibility of the semi-occupied, non-bonding d z 2 orbital make this neutral compound an ideal candidate for single-qubit addressing on surface and quantum sensing in combination with scanning probe microscopy.

Controllable freezing of the nuclear spin bath in a single-atom spin qubit

The quantum coherence and gate fidelity of electron spin qubits in semiconductors are often limited by nuclear spin fluctuations. Enrichment of spin-zero isotopes in silicon markedly improves the dephasing time [Formula: see text], which, unexpectedly, can extend two orders of magnitude beyond theoretical expectations. Using a single-atom ³¹P qubit in enriched ²⁸Si, we show that the abnormally long [Formula: see text] is due to the freezing of the dynamics of the residual ²⁹Si nuclei, caused by the electron-nuclear hyperfine interaction. Inserting a waiting period when the electron is controllably removed unfreezes the nuclear dynamics and restores the ergodic [Formula: see text] value. Our conclusions are supported by a nearly parameter-free modeling of the ²⁹Si nuclear spin dynamics, which reveals the degree of backaction provided by the electron spin. This study clarifies the limits of ergodic assumptions in nuclear bath dynamics and provides previously unidentified strategies for maximizing coherence and gate fidelity of spin qubits in semiconductors.

Spin dynamics in single-molecule magnets and molecular qubits

Over recent decades, much effort has been made to lengthen spin relaxation/decoherence times of single-molecule magnets and molecular qubits by following different chemical design rules such as maximizing the total spin value, controlling symmetry, enhancing the ligand field or inhibiting key vibrational modes. Simultaneously, electronic structure calculations have been employed to provide an understanding of the processes involved in the spin dynamics of molecular systems and served to refine or introduce new design rules. This review focuses on contemporary theoretical approaches focused on the calculation of spin relaxation/decoherence times, highlighting their main features and scope. Fundamental aspects of experimental techniques for the determination of key Single Molecule Magnet/Spin Qubit properties are also reviewed.

Quantitative Structure-Based Prediction of Electron Spin Decoherence in Organic Radicals

The decoherence, or dephasing, of electron spins in paramagnetic molecules limits sensitivity and resolution in electron paramagnetic resonance spectroscopy, and it represents a challenge for utilizing paramagnetic molecules as qubit units in quantum information devices. For organic radicals in dilute frozen aqueous solution at cryogenic temperatures, electron spin decoherence is driven by neighboring nuclear spins. Here, we show that this nuclear-spin-driven decoherence can be quantitatively predicted from the molecular structure and solvation geometry of the radicals. We use a fully deterministic quantum model of the electron spin and up to 2000 neighboring protons with a static spin Hamiltonian that includes nucleus-nucleus couplings. We present experiments and simulations of two nitroxide radicals and one trityl radical, which have decoherence time scales of 4-5 μs below 60 K. We show that nuclei within 12 Å of the electron spin contribute to decoherence, with the strongest impact from protons 4-8 Å away.

Decoherence in Molecular Electron Spin Qubits: Insights from Quantum Many-Body Simulations

Quantum states are described by wave functions whose phases cannot be directly measured but which play a vital role in quantum effects such as interference and entanglement. The loss of the relative phase information, termed decoherence, arises from the interactions between a quantum system and its environment. Decoherence is perhaps the biggest obstacle on the path to reliable quantum computing. Here we show that decoherence occurs even in an isolated molecule, although not all phase information is lost, via a theoretical study of a central electron spin qubit interacting with nearby nuclear spins in prototypical magnetic molecules. The residual coherence, which is molecule-dependent, provides a microscopic rationalization for the nuclear spin diffusion barrier proposed to explain experiments. The contribution of nearby molecules to the decoherence has a nontrivial dependence on separation, peaking at intermediate distances. Molecules that are far away affect only the long-time behavior. Because the residual coherence is simple to calculate and correlates well with the coherence time, it can be used as a descriptor for coherence in magnetic molecules. This work will help establish design principles for enhancing coherence in molecular spin qubits and serve to motivate further theoretical work.

Nuclear-spin-pattern control of electron-spin dynamics in a series of V(iv) complexes

Achieving control of phase memory relaxation times (T m) in metal ions is an important goal of molecular spintronics. Herein we provide the first evidence that nuclear-spin patterning in the ligand shell is an important handle to modulate T m in metal ions. We synthesized and studied a series of five V(iv) complexes with brominated catecholate ligands, [V(C6H4-n Br n O2)3]2- (n = 0, 1, 2, and 4), where the 79/81Br and 1H nuclear spins are arranged in different substitutional patterns. High-field, high-frequency (120 GHz) pulsed electron paramagnetic resonance spectroscopic analysis of this series reveals a pattern-dependent variation in T m for the V(iv) ion. Notably, we show that it is possible for two molecules to have starkly different (by 50%) T m values despite the same chemical composition. Nuclear magnetic resonance analyses of the protons on the ligand shell suggest that relative chemical shift (δ), controlled by the patterning of nuclear spins, is an important underlying design principle. Here, having multiple ligand-based protons with nearly identical chemical shift values in the ligand shell will, ultimately, engender a short T m for the bound metal ion.

The Second Quantum Revolution: Role and Challenges of Molecular Chemistry

Implementation of modern Quantum Technologies might benefit from the remarkable quantum properties shown by molecular spin systems. In this Perspective, we highlight the role that molecular chemistry can have in the current second quantum revolution, i.e., the use of quantum physics principles to create new quantum technologies, in this specific case by means of molecular components. Herein, we briefly review the current status of the field by identifying the key advances recently made by the molecular chemistry community, such as for example the design of molecular spin qubits with long spin coherence and the realization of multiqubit architectures for quantum gates implementation. With a critical eye to the current state-of-the-art, we also highlight the main challenges needed for the further advancement of the field toward quantum technologies development.

Three-spin solid effect and the spin diffusion barrier in amorphous solids

Dynamic nuclear polarization (DNP) has evolved as the method of choice to enhance NMR signal intensities and to address a variety of otherwise inaccessible chemical, biological and physical questions. Despite its success, there is no detailed understanding of how the large electron polarization is transferred to the surrounding nuclei or where these nuclei are located relative to the polarizing agent. To address these questions we perform an analysis of the three-spin solid effect, and show that it is exquisitely sensitive to the electron-nuclear distances. We exploit this feature and determine that the size of the spin diffusion barrier surrounding the trityl radical in a glassy glycerol-water matrix is <6 Å, and that the protons involved in the initial transfer step are on the trityl molecule. ¹H ENDOR experiments indicate that polarization is then transferred in a second step to glycerol molecules in intimate contact with the trityl.

Metal-ligand covalency enables room temperature molecular qubit candidates

Metal–ligand covalency enables observation of coherent spin dynamics to room temperature in a series of vanadium(iv) and copper(ii) catechol complexes.

Harnessing synthetic chemistry to design electronic spin-based qubits, the smallest unit of a quantum information system, enables us to probe fundamental questions regarding spin relaxation dynamics. We sought to probe the influence of metal–ligand covalency on spin–lattice relaxation, which comprises the upper limit of coherence time. Specifically, we studied the impact of the first coordination sphere on spin–lattice relaxation through a series of four molecules featuring V–S, V–Se, Cu–S, and Cu–Se bonds, the Ph₄P⁺ salts of the complexes [V(C₆H₄S₂)₃]^2– (1), [Cu(C₆H₄S₂)₂]^2– (2), [V(C₆H₄Se₂)₃]^2– (3), and [Cu(C₆H₄Se₂)₂]^2– (4). The combined results of pulse electron paramagnetic resonance spectroscopy and ac magnetic susceptibility studies demonstrate the influence of greater M–L covalency, and consequently spin-delocalization onto the ligand, on elongating spin–lattice relaxation times. Notably, we observe the longest spin–lattice relaxation times in 2, and spin echos that survive until room temperature in both copper complexes (2 and 4).

A concentrated array of copper porphyrin candidate qubits

Synthetic chemistry offers a pathway to realize atomically precise arrays of qubits, the smallest unit of a quantum information science system. We harnessed framework chemistry to create an array of qubit candidates, featuring one qubit every 13.6 Å, by synthesizing the new copper(ii) variant of the porphyrinic metal-organic framework PCN-224. We subjected the framework to pulse-electron paramagnetic resonance (EPR) measurements, establishing spin coherence at temperatures up to 80 K within a fully spin concentrated framework. Observation of Rabi oscillations further support the viability of the qubits within these arrays. To interrogate the spin dynamics of qubit arrays, we investigated spin-lattice relaxation, T 1, through a combination of pulse-EPR and alternating current (ac) magnetic susceptibility measurements. These data revealed distinct vibrational environments within the frameworks that contribute to spin dynamics. The aggregate results establish a pathway for a synthetic approach to create spatially precise networks of qubits.

Enabling single qubit addressability in a molecular semiconductor comprising gold-supported organic radicals

A bis(dithiolene)gold complex is presented as a model for an organic molecular electron spin qubit attached to a metallic surface that acts as a conduit to electrically address the qubit. A two-membered electron transfer series is developed of the formula [AuIII(adt)2]1-/0, where adt is a redox-active dithiolene ligand that is sequentially oxidized as the series is traversed while the central metal ion remains AuIII and steadfastly square planar. One-electron oxidation of diamagnetic [AuIII(adt)2]1- (1) produces an S = 1/2 charge-neutral complex, [AuIII(adt2 3-˙)] (2) which is spectroscopically and theoretically characterized with a near negligible Au contribution to the ground state. A phase memory time (T M) of 21 μs is recorded in 4 : 1 CS2/CCl4 at 10 K, which is the longest ever reported for a coordination complex possessing a third-row transition metal ion. With increasing temperature, T M dramatically decreases becoming unmeasurable above 80 K as a consequence of the diminishing spin-lattice (T 1) relaxation time fueled by spin-orbit coupling. These relaxation times are 1-2 orders of magnitude shorter for the solid dilution of 2 in isoelectronic [Ni(adt)2] because this material is a molecular semiconductor. Although the conducting properties of this material provide efficient pathways to dissipate the energy through the lattice, it can also be used to electrically address the paramagnetic dopant by tapping into the mild reduction potential to switch magnetism "on" and "off" in the gold complex without compromising the integrity of its structure. These results serve to highlight the need to consider all components of these spintronic assemblies.

Counterion influence on dynamic spin properties in a V(iv) complex

Using transition metal ions for spin-based applications, such as electron paramagnetic resonance imaging (EPRI) or quantum computation, requires a clear understanding of how local chemistry influences spin properties. Herein we report a series of four ionic complexes to provide the first systematic study of one aspect of local chemistry on the V(iv) spin - the counterion. To do so, the four complexes (Et3NH)2[V(C6H4O2)3] (1), (n-Bu3NH)2[V(C6H4O2)3] (2), (n-Hex3NH)2[V(C6H4O2)3] (3), and (n-Oct3NH)2[V(C6H4O2)3] (4) were probed by EPR spectroscopy in solid state and solution. Room temperature, solution X-band (ca. 9.8 GHz) continuous-wave electron paramagnetic resonance (CW-EPR) spectroscopy revealed an increasing linewidth with larger cations, likely a counterion-controlled tumbling in solution via ion pairing. In the solid state, variable-temperature (5-180 K) X-band (ca. 9.4 GHz) pulsed EPR studies of 1-4 in o-terphenyl glass demonstrated no effect on spin-lattice relaxation times (T 1), indicating little role for the counterion on this parameter. However, the phase memory time (T m) of 1 below 100 K is markedly smaller than those of 2-4. This result is counterintuitive, as 2-4 are relatively richer in 1H nuclear spin, hence, expected to have shorter T m. Thus, these data suggest an important role for counterion methyl groups on T m, and moreover provide the first instance of a lengthening T m with increasing nuclear spin quantity on a molecule.

Progress towards creating optically addressable molecular qubits

The emerging field of quantum information science promises to transform a diverse range of scientific fields, ranging from computation to sensing and metrology. The interdisciplinary scientific community laid the groundwork for the next generation of quantum technologies through key advances in understanding the fundamental unit of quantum information science, the qubit. Electronic spin is a promising platform for qubits, demonstrating suitably long coherence times, optical initialization, and single spin addressability. Herein, we discuss recent accomplishments and future progress from our group targeted at imbuing transition metal complexes with the aforementioned properties, creating a pathway to fusing spatial precision with long coherence times. A strong emphasis of this feature article is progressing towards single spin measurements via a chemical approach for imbuing molecular qubits with an optically-induced spin polarization mechanism.

Ligand Radicals as Modular Organic Electron Spin Qubits

The intrinsic redox activity of the dithiolene ligand is presented here as the novel spin host in the design of a prototype molecular electron spin qubit, where the traditional roles of the metal and ligand components in coordination complexes are inverted. A series of paramagnetic bis(dithiolene) complexes with group 10 metals-nickel, palladium, platinum-provides a backdrop to investigate the spin dynamics of the organic ligand radical using pulsed EPR spectroscopy. The temperature dependence of the phase memory time (T_M ) is shown to be dependent on the identity of the diamagnetic metal ion, with the short times recorded for platinum a consequence of a diminishing spin-lattice (T₁ ) relaxation time driven by spin-orbit coupling. The utility of the radical ligand spin center is confirmed when it delivers one of the longest phase memory times ever recorded for a molecular two-qubit prototype.