Metal-ligand covalency enables room temperature molecular qubit candidates

Systems-chart approach to the design of spin relaxation times in molecular qubits

Molecular qubits are a promising platform for future quantum information science technologies; however, to find success in novel devices requires that the molecules exhibit long spin relaxation times. Understanding and optimizing these relaxation times has been shown to be challenging and much experimental work has been done to understand how various chemical features of the molecular qubit influence relaxation times. Here we have curated a data set of relaxation times of metal complex molecular qubits and formulated systems design charts to provide a hierarchical organization of how chemical variables affect relaxation times via known physical processes. We demonstrate the utility of the systems charts by combining examples from the literature with calculated descriptors for molecules in the dataset. This approach helps reduce the complexity associated with de novo molecular design by providing a map of interdependencies and identifying features to prioritize during synthesis.

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.

Detrimental Increase of Spin-Phonon Coupling in Molecular Qubits on Substrates

Molecular qubits are a promising platform for quantum information systems. Although single molecule and ensemble studies have assessed the performance of S = 1/2 molecules, it is understood that to function in devices, regular arrays of addressable qubits supported by a substrate are needed. The substrate imposes mechanical and electronic boundary conditions on the molecule; however, the impact of these effects on spin-lattice relaxation times is not well understood. Here we perform electronic structure calculations to assess the effects of a graphene (Cgr) substrate on the molecular qubit copper phthalocyanine (CuPc). We use a progressive Hessian approach to efficiently calculate and separate the substrate contributions. We also use a simple thermal model to predict the impact of these changes on the spin-phonon coupling from 0 to 200 K. Further analysis of the individual vibrational modes with and without Cgr shows that an overall increase in SPC between the vibrations modes of CuPc with the surface reduces the spin-lattice relaxation time T1. We explain these changes by examining how the substrate lifts symmetries of CuPc in the absorbed configuration. Our work shows that a surface can have a large unintentional impact on SPC and that ways to reduce this coupling need to be found to fully exploit arrays of molecular qubits in device architectures.

Spin-Lattice Relaxation and Spin-Phonon Coupling of ns1 Metal Ions at the Surface

To use transition metal ions for spin-based applications, it is essential to understand fundamental contributions to electron spin relaxation in different ligand environments. For example, to serve as building blocks for a device, transition metal ion-based molecular qubits must be organized on surfaces and preserve long electron spin relaxation times, up to room temperature. Here we propose monovalent group 12 ions (Zn+ and Cd+) as potential electronic metal qubits with an ns1 ground state. The relaxation properties of Zn+ and Cd+, stabilized at the interface of porous aluminosilicates, are investigated and benchmarked against vanadium (3d1) and copper (3d9) ions. The spin-phonon coupling has been evaluated through DFT modeling and found to be negligible for the ns1 states, explaining the long coherence time, up to 2 μs, at room temperature. These so far unexplored metal qubits may represent viable candidates for room temperature quantum operations and sensing.

Ligand Effects on the Spin Relaxation Dynamics and Coherent Manipulation of Organometallic La(II) Potential Qudits

We present pulsed electron paramagnetic resonance (EPR) studies on three La(II) complexes, [K(2.2.2-cryptand)][La(Cp')3] (1), [K(2.2.2-cryptand)][La(Cp″)3] (2), and [K(2.2.2-cryptand)][La(Cptt)3] (3), which feature cyclopentadienyl derivatives as ligands [Cp' = C5H4SiMe3; Cp″ = C5H3(SiMe3)2; Cptt = C5H3(CMe3)2] and display a C3 symmetry. Long spin-lattice relaxation (T1) and phase memory (Tm) times are observed for all three compounds, but with significant variation in T1 among 1-3, with 3 being the slowest relaxing due to higher s-character of the SOMO. The dephasing times can be extended by more than an order of magnitude via dynamical decoupling experiments using a Carr-Purcell-Meiboom-Gill (CPMG) sequence, reaching 161 μs (5 K) for 3. Coherent spin manipulation is performed by the observation of Rabi quantum oscillations up to 80 K in this nuclear spin-rich environment (1H, 13C, and 29Si). The high nuclear spin of 139La (I = 7/2), and the ability to coherently manipulate all eight hyperfine transitions, makes these molecules promising candidates for application as qudits (multilevel quantum systems featuring d quantum states; d >2) for performing quantum operations within a single molecule. Application of HYSCORE techniques allows us to quantify the electron spin density at ligand nuclei and interrogate the role of functional groups to the electron spin relaxation properties.

Angular-resolved Rabi oscillations of orthorhombic spins in a Co(II) molecular qubit

Magnetic molecules are promising candidates for quantum information processing (QIP) due to their tunable electron structures and quantum properties. A high spin Co(II) complex, CoH2dota, is studied for its potential to be used as a quantum bit (qubit) utilizing continuous wave (CW) and pulsed electron paramagnetic resonance (EPR) spectroscopy at low temperature. On the X-band microwave energy scale, the system can be treated as an effective spin 1/2 with a strongly anisotropic g-tensor resulting from the significant spin-orbital coupling. An experimental and theoretical study is conducted to investigate the anisotropic Rabi oscillations of the two magnetically equivalent spin centres with different orientations in a single crystal sample, which aims to verify the relationship between the Rabi frequency and the orientation of the g-tensor. The findings of this study show that an effective quantum manipulation method is developed for orthorhombic spin systems.

A novel non-adiabatic spin relaxation mechanism in molecular qubits

The interaction of electronic spin and molecular vibrations mediated by spin-orbit coupling governs spin relaxation in molecular qubits. We derive an extended molecular spin Hamiltonian that includes both adiabatic and non-adiabatic spin-dependent interactions, and we implement the computation of its matrix elements using state-of-the-art density functional theory. The new molecular spin Hamiltonian contains a novel spin-vibrational orbit interaction with a non-adiabatic origin, together with the traditional molecular Zeeman and zero-field splitting interactions with an adiabatic origin. The spin-vibrational orbit interaction represents a non-Abelian Berry curvature on the ground-state electronic manifold and corresponds to an effective magnetic field in the electronic spin dynamics. We further develop a spin relaxation rate model that estimates the spin relaxation time via the two-phonon Raman process. An application of the extended molecular spin Hamiltonian together with the spin relaxation rate model to Cu(II) porphyrin, a prototypical S = 1/2 molecular qubit, demonstrates that the spin relaxation time at elevated temperatures is dominated by the non-adiabatic spin-vibrational orbit interaction. The computed spin relaxation rate and its magnetic field orientation dependence are in excellent agreement with experimental measurements.

Determining the key vibrations for spin relaxation in ruffled Cu(ii) porphyrins via resonance Raman spectroscopy

Pinpointing vibrational mode contributions to electron spin relaxation (T1) constitutes a key goal for developing molecular quantum bits (qubits) with long room-temperature coherence times. However, there remains no consensus to date as to the energy and symmetry of the relevant modes that drive relaxation. Here, we analyze a series of three geometrically-tunable S = ½ Cu(ii) porphyrins with varying degrees of ruffling distortion in the ground state. Theoretical calculations predict that increased distortion should activate low-energy ruffling modes (∼50 cm-1) for spin-phonon coupling, thereby causing faster spin relaxation in distorted porphyrins. However, experimental T1 times do not follow the degree of ruffling, with the highly distorted copper tetraisopropylporphyrin (CuTiPP) even displaying room-temperature coherence. Local mode fitting indicates that the true vibrations dominating T1 lie in the energy regime of bond stretches (∼200-300 cm-1), which are comparatively insensitive to the degree of ruffling. We employ resonance Raman (rR) spectroscopy to determine vibrational modes possessing both the correct energy and symmetry to drive spin-phonon coupling. The rR spectra uncover a set of mixed symmetric stretch vibrations from 200-250 cm-1 that explain the trends in temperature-dependent T1. These results indicate that molecular spin-phonon coupling models systematically overestimate the contribution of ultra-low-energy distortion modes to T1, pointing out a key deficiency of existing theory. Furthermore, this work highlights the untapped power of rR spectroscopy as a tool for building spin dynamics structure-property relationships in molecular quantum information science.

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.

Synthesis, structural characterization, antioxidant, cytotoxic activities and docking studies of schiff base Cu(II) complexes

By combining hydrazide with 2-Acetylpyridine, a hydrazone ligand (HL) was successfully created. Several copper (II) salts have been used to create three copper (II) hydrazone complexes (acetate, sulphate, and chloride). The hydrazide ligand and its copper (II) complexes (1-3) were studied via variety of analytical techniques, including elemental analysis, electronic, infrared, UV-vis Spectrum, XRD study, thermal analysis, also molar conductivity amounts. The spectrum results indicate that in all complexes, the ligand exhibits monobasic tridentate behavior. Octahedral geometries were present in all metal complexes. The Coats-Redfern equations were used to compute and describe the dynamics properties of several steps of TGA (Ea, A, ΔH*, ΔS*, and ΔG*). Calculations using the density functional theory (DFT) were done at the molecular studio software toward examine ligands agent's and its complexes' best structures. The MCF-7 in addition to HepG-2 cell lines was resistant to tumor-inducing effects of the copper (II) chelates. The in vitro antioxidant capacities of all complexes have been estimated via DPPH free radical scavenger assays. Furthermore, zones of inhibition length accustomed to test antimicrobial effect of particular complexes in vitro towards Staphylococcus aureus (Gram positive bacteria) E. coli (Gram negative bacteria). Both absorption spectra and viscosity measurements in calf thymus DNA binding have been used to study the complexes. In order to explore docking research of copper (II) chelates, the crystallographic construction of the SARS-active CoV-2's site protein (PDB ID:6XBH) was used (COVID-19) and breast cancer distorted (PDB ID: 3hb5).

A Review of the Current State of Magnetic Force Microscopy to Unravel the Magnetic Properties of Nanomaterials Applied in Biological Systems and Future Directions for Quantum Technologies

Magnetism plays a pivotal role in many biological systems. However, the intensity of the magnetic forces exerted between magnetic bodies is usually low, which demands the development of ultra-sensitivity tools for proper sensing. In this framework, magnetic force microscopy (MFM) offers excellent lateral resolution and the possibility of conducting single-molecule studies like other single-probe microscopy (SPM) techniques. This comprehensive review attempts to describe the paramount importance of magnetic forces for biological applications by highlighting MFM's main advantages but also intrinsic limitations. While the working principles are described in depth, the article also focuses on novel micro- and nanofabrication procedures for MFM tips, which enhance the magnetic response signal of tested biomaterials compared to commercial nanoprobes. This work also depicts some relevant examples where MFM can quantitatively assess the magnetic performance of nanomaterials involved in biological systems, including magnetotactic bacteria, cryptochrome flavoproteins, and magnetic nanoparticles that can interact with animal tissues. Additionally, the most promising perspectives in this field are highlighted to make the reader aware of upcoming challenges when aiming toward quantum technologies.

Characterizing Excited States of a Copper-Based Molecular Qubit Candidate with Correlated Electronic Structure Methods

Molecular spins have a variety of potential advantages as qubits for quantum computation, such as tunability and well-understood design pathways through organometallic synthesis. Organometallic and heavy-metal-based molecular spin qubits can also exhibit rich electronic structures due to ligand field interactions and electron correlation. These features make consistent and reliable modeling of these species a considerable challenge for contemporary electronic structure techniques. Here, we elucidate the electronic structure of a Cu(II) complex analogous to a recently proposed room-temperature molecular spin qubit. Using active space methods to describe the electron correlation, we show the nuanced interaction between the metal d orbitals and ligand σ and π orbitals makes these systems challenging to model, both in terms of the delocalized spin density and the excited state ordering. We show that predicting the correct spin delocalization requires special consideration of the Cu d orbitals and that the excited state spectrum for the Cu(III) complex also requires the explicit inclusion of the π orbitals in the active space. These interactions are rather common in molecular spin qubit motifs and may play an important role in spin-decoherence processes. Our results may lend insight into future studies of the orbital interactions and electron delocalization of similar complexes.

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.

Two-Electron Mixed Valency in a Heterotrimetallic Nickel-Vanadium-Nickel Complex

Mixed-valence complexes represent an enticing class of coordination compounds to interrogate electron transfer confined within a molecular framework. The diamagnetic heterotrimetallic anion, [V(SNS)₂{Ni(dppe)}₂]^-, was prepared by reducing (dppe)NiCl₂ in the presence of the chelating metalloligand [V(SNS)₂]^- [dppe = bis(diphenylphosphino)ethane; (SNS)^3- = bis(2-thiolato-4-methylphenyl)amide]. Vanadium-nickel bonds span the heterotrimetallic core in the structure of [V(SNS)₂{Ni(dppe)}₂]^-, with V-Ni bond lengths of 2.78 and 2.79 Å. One-electron oxidation of monoanionic [V(SNS)₂{Ni(dppe)}₂]^- yielded neutral, paramagnetic V(SNS)₂{Ni(dppe)}₂. The solid-state structure of V(SNS)₂{Ni(dppe)}₂ revealed that the two nickel ions occupy unique coordination environments: one nickel is in a square-planar S₂P₂ coordination environment (τ₄ = 0.19), with a long Ni···V distance of 3.45 Å; the other nickel is in a tetrahedral S₂P₂ coordination environment (τ₄ = 0.84) with a short Ni-V distance of 2.60 Å, consistent with a formal metal-metal bond. Continuous-wave X-band electron paramagnetic resonance spectroscopy, electrochemical investigations, and density functional theory computations indicated that the unpaired electron in the neutral V(SNS)₂{Ni(dppe)}₂ cluster is localized on the bridging [V(SNS)₂] metalloligand, and as a result, V(SNS)₂{Ni(dppe)}₂ is best described as a two-electron mixed-valence complex. These results demonstrate the important role that metal-metal interactions and flexible coordination geometries play in enabling multiple, reversible electron transfer processes in small cluster complexes.

Room-Temperature Quantitative Quantum Sensing of Lithium Ions with a Radical-Embedded Metal-Organic Framework

Recent advancements in quantum sensing have sparked transformative detection technologies with high sensitivity, precision, and spatial resolution. Owing to their atomic-level tunability, molecular qubits and ensembles thereof are promising candidates for sensing chemical analytes. Here, we show quantum sensing of lithium ions in solution at room temperature with an ensemble of organic radicals integrated in a microporous metal-organic framework (MOF). The organic radicals exhibit electron spin coherence and microwave addressability at room temperature, thus behaving as qubits. The high surface area of the MOF promotes accessibility of the guest analytes to the organic qubits, enabling unambiguous identification of lithium ions and quantitative measurement of their concentration through relaxometric and hyperfine spectroscopic methods based on electron paramagnetic resonance (EPR) spectroscopy. The sensing principle presented in this work is applicable to other metal ions with nonzero nuclear spin.

Understanding the effect of structural changes on slow magnetic relaxation in mononuclear octahedral copper(II) complexes

Current advances in molecular magnetism are aimed at the construction of molecular nanomagnets and spin qubits for their utilization as high-density data storage materials and quantum computers. Mononuclear coordination compounds with low spin values of S = ½ are excellent candidates for this endeavour, but knowledge of their construction via rational design is limited. This particularly applies to the single copper(II) spin center, having been only recently demonstrated to exhibit slow relaxation of magnetisation in the appropriate octahedral environment. We have thus prepared a unique organic scaffold that would allow one to gain in-depth insight into how purposeful structural differences affect the slow magnetic relaxation in monometallic, transition metal complexes. As a proof-of-principle, we demonstrate how one can construct two, structurally very similar complexes with isolated Cu(II) ions in an octahedral ligand environment, the magnetic properties of which differ significantly. The differences in structural symmetry effects and in magnetic relaxation are corroborated with a series of experimental techniques and theoretical approaches, showing how symmetry distortions and crystal packing affect the relaxation behaviour in these isolated Cu(II) systems. Our unique organic platform can be efficiently utilized for the construction of various transition-metal ion systems in the future, effectively providing a model system for investigation of magnetic relaxation via targeted structural distortions.

Chemical control of spin-lattice relaxation to discover a room temperature molecular qubit

The second quantum revolution harnesses exquisite quantum control for a slate of diverse applications including sensing, communication, and computation. Of the many candidates for building quantum systems, molecules offer both tunability and specificity, but the principles to enable high temperature operation are not well established. Spin-lattice relaxation, represented by the time constant T ₁, is the primary factor dictating the high temperature performance of quantum bits (qubits), and serves as the upper limit on qubit coherence times (T ₂). For molecular qubits at elevated temperatures (>100 K), molecular vibrations facilitate rapid spin-lattice relaxation which limits T ₂ to well below operational minimums for certain quantum technologies. Here we identify the effects of controlling orbital angular momentum through metal coordination geometry and ligand rigidity via π-conjugation on T ₁ relaxation in three four-coordinate Cu²⁺ S = ½ qubit candidates: bis(N,N'-dimethyl-4-amino-3-penten-2-imine) copper(ii) (Me₂Nac)₂ (1), bis(acetylacetone)ethylenediamine copper(ii) Cu(acacen) (2), and tetramethyltetraazaannulene copper(ii) Cu(tmtaa) (3). We obtain significant T ₁ improvement upon changing from tetrahedral to square planar geometries through changes in orbital angular momentum. T ₁ is further improved with greater π-conjugation in the ligand framework. Our electronic structure calculations reveal that the reduced motion of low energy vibrations in the primary coordination sphere slows relaxation and increases T ₁. These principles enable us to report a new molecular qubit candidate with room temperature T ₂ = 0.43 μs, and establishes guidelines for designing novel qubit candidates operating above 100 K.

Unusual Slow Magnetic Relaxation in a Mononuclear Copper(II) Complex

A hexacoordinate Cu(II) complex with the {CuO4O’N} donor set shows an intermolecular π-πstacking owing to which a 1D-chain structure is formed. The DC magnetic data at low temperature is consistent...

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.

Spin-Phonon Coupling and Slow-Magnetic Relaxation in Pristine Ferrocenium

We report the spin dynamic properties of non-substituted ferrocenium complexes. Ferrocenium shows a field-induced single-molecule magnet behaviour in DMF solution while cobaltocene lacks slow spin relaxation neither in powder nor in solution. Multireference quantum mechanical calculations give a non-Aufbau orbital occupation for ferrocenium with small first excitation energy that agrees with the relatively large measured magnetic anisotropy for a transition metal S=1/2 system. The analysis of the spin relaxation shows an important participation of quantum tunnelling, Raman, direct and local-mode mechanisms which depend on temperature and the external field conditions. The calculation of spin-phonon coupling constants for the vibrational modes shows that the first vibrational mode, despite having a low spin-phonon constant, is the most efficient process for the spin relaxation at low temperatures. In such conditions, vibrational modes with higher spin-phonon coupling constants are not populated. Additionally, the vibrational energy of this first mode is in excellent agreement with the experimental fitted value obtained from the local-mode mechanism.

The Impact of Ligand Field Symmetry on Molecular Qubit Coherence

Developing quantum bits (qubits) exhibiting room temperature electron spin coherence is a key goal of molecular quantum information science. At high temperatures, coherence is often limited by electron spin relaxation, measured by T₁. Here we develop a simple and powerful model for predicting relative T₁ relaxation times in transition metal complexes from dynamic ligand field principles. By considering the excited state origins of ground state spin-phonon coupling, we derive group theory selection rules governing which vibrational symmetries can induce decoherence. Thermal weighting of the coupling terms produces surprisingly good predictions of experimental T₁ trends as a function of temperature and explains previously confounding features in spin-lattice relaxation data. We use this model to evaluate experimental relaxation rates across S = 1/2 transition metal qubit candidates with diverse structures, gaining new insights into the interplay between spin-phonon coupling and molecular symmetry. This methodology elucidates the specific vibrational modes giving rise to decoherence, providing insight into the origin of room temperature coherence in transition metal complexes. We discuss the outlook of symmetry-based modeling and design strategies for understanding molecular coherence.

Binding Sites, Vibrations and Spin-Lattice Relaxation Times in Europium(II)-Based Metallofullerene Spin Qubits

To design molecular spin qubits with enhanced quantum coherence, a control of the coupling between the local vibrations and the spin states is crucial, which could be realized in principle by engineering molecular structures via coordination chemistry. To this end, understanding the underlying structural factors that govern the spin relaxation is a central topic. Here, we report the investigation of the spin dynamics in a series of chemically designed europium(II)-based endohedral metallofullerenes (EMFs). By introducing a unique structural difference, i. e. metal-cage binding site, while keeping other molecular parameters constant between different complexes, these manifest the key role of the three low-energy metal-displacing vibrations in mediating the spin-lattice relaxation times (T1 ). The temperature dependence of T1 can thus be normalized by the frequencies of these low energy vibrations to show an unprecedentedly universal behavior for EMFs in frozen CS2 solution. Our theoretical analysis indicates that this structural difference determines not only the vibrational rigidity but also spin-vibration coupling in these EMF-based qubit candidates.

Designed polynuclear lanthanide complexes for quantum information processing

The design of dissymmetric organic ligands featuring combinations of 1,3-diketone and 2,6-diacetylpyridine coordination pockets has been exploited to produce dinuclear and trinuclear lanthanide-based coordination compounds. These molecules exhibit two or more non-equivalent Ln ions, most remarkably enabling the access to well-defined heterolanthanide compositions. The site-selective disposition of each metal ion within the molecular entities allows the study of each centre individually as a spin-based quantum bit, affording unparalleled versatility for quantum gate design. The inherent weak interaction between the Ln ions permits the performance of multi-qubit quantum logical operations realized through their derived magnetic states, or implementing quantum-error correction protocols. The different studies performed to date on these systems are revised, showing their vast potential within spin-based quantum information processing.

Computational Discovery of Transition-metal Complexes: From High-throughput Screening to Machine Learning

Transition-metal complexes are attractive targets for the design of catalysts and functional materials. The behavior of the metal-organic bond, while very tunable for achieving target properties, is challenging to predict and necessitates searching a wide and complex space to identify needles in haystacks for target applications. This review will focus on the techniques that make high-throughput search of transition-metal chemical space feasible for the discovery of complexes with desirable properties. The review will cover the development, promise, and limitations of "traditional" computational chemistry (i.e., force field, semiempirical, and density functional theory methods) as it pertains to data generation for inorganic molecular discovery. The review will also discuss the opportunities and limitations in leveraging experimental data sources. We will focus on how advances in statistical modeling, artificial intelligence, multiobjective optimization, and automation accelerate discovery of lead compounds and design rules. The overall objective of this review is to showcase how bringing together advances from diverse areas of computational chemistry and computer science have enabled the rapid uncovering of structure-property relationships in transition-metal chemistry. We aim to highlight how unique considerations in motifs of metal-organic bonding (e.g., variable spin and oxidation state, and bonding strength/nature) set them and their discovery apart from more commonly considered organic molecules. We will also highlight how uncertainty and relative data scarcity in transition-metal chemistry motivate specific developments in machine learning representations, model training, and in computational chemistry. Finally, we will conclude with an outlook of areas of opportunity for the accelerated discovery of transition-metal complexes.

Electronic structure of mononuclear Cu-based molecule from density-functional theory with self-interaction correction

We investigate the electronic structure of a planar mononuclear Cu-based molecule [Cu(C₆H₄S₂)₂]^z in two oxidation states (z = -2, -1) using density-functional theory (DFT) with Fermi-Löwdin orbital (FLO) self-interaction correction (SIC). The dianionic Cu-based molecule was proposed to be a promising qubit candidate. Self-interaction error within approximate DFT functionals renders severe delocalization of electron and spin densities arising from 3d orbitals. The FLO-SIC method relies on optimization of Fermi-Löwdin orbital descriptors (FODs) with which localized occupied orbitals are constructed to create SIC potentials. Starting with many initial sets of FODs, we employ a frozen-density loop algorithm within the FLO-SIC method to study the Cu-based molecule. We find that the electronic structure of the molecule remains unchanged despite somewhat different final FOD configurations. In the dianionic state (spin S = 1/2), FLO-SIC spin density originates from the Cu d and S p orbitals with an approximate ratio of 2:1, in quantitative agreement with multireference calculations, while in the case of SIC-free DFT, the orbital ratio is reversed. Overall, FLO-SIC lowers the energies of the occupied orbitals and, in particular, the 3d orbitals unhybridized with the ligands significantly, which substantially increases the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) compared to SIC-free DFT results. The FLO-SIC HOMO-LUMO gap of the dianionic state is larger than that of the monoanionic state, which is consistent with experiment. Our results suggest a positive outlook of the FLO-SIC method in the description of magnetic exchange coupling within 3d-element-based systems.

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.

A reaction-coordinate perspective of magnetic relaxation

Understanding and utilizing the dynamic quantum properties of metal ions is the frontier of many next generation technologies. One property in particular, magnetic relaxation, is a complicated physical phenomenon that is scarcely treated in undergraduate coursework. Consequently, principles of magnetic relaxation are nearly impenetrable to starting synthetic chemists, who ultimately design the molecules that fuel new discoveries. In this Tutorial Review, we describe a new paradigm for thinking of magnetic relaxation in metal complexes in terms of a simple reaction-coordinate diagram to facilitate access to the field. We cover the main mechanisms of both spin-lattice (T1) and spin-spin (T2) relaxation times within this conceptual framework and how molecular and environmental design affects these times. Ultimately, we show that many of the scientific methods used by inorganic chemists to study and manipulate reactivity are also useful for understanding and controlling magnetic relaxation. We also describe the cutting edge of magnetic relaxation within this paradigm.

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.

Electronic structure study of divanadium complexes with rigid covalent coordination: potential molecular qubits with slow spin relaxation

The electronic structures of homovalent [V₂(μ-S₂)₂(R₂dtc)₄] (R = Et, ⁱBu) and mixed-valent [V₂(μ-S₂)₂(R₂dtc)₄]⁺ are reported here. The soft-donor, eight-coordinate ligand shell combined with the fully delocalised ground state provides a highly rigid and covalent environment that will nurture long spin relaxation times in vanadyl-based molecular qubits.

Macromolecular crystallography for f-element complex characterization

Single crystal X-ray diffraction is a technique that measures interatomic distances with atomic resolution. Utilizing this technique for metal complexes featuring lanthanide and actinide elements is complicated by the scarcity and radioactivity of many of the metals of the f-block, as sub-milligram samples are difficult to crystallize for small molecule X-ray diffraction experiments. In this chapter, we present a protocol developed in our group that circumvents these challenges by exploiting macromolecular crystallography, wherein a protein with a large and well-characterized binding calyx is used as a scaffold to crystallize small-molecule metal complexes. Highlighting several examples, we identify the structural and chemical information that can be acquired by this method, and delineate the benefits of directing crystal growth with proteins, such as decreasing the amount of metal used to the sub-microgram scale. Moreover, since protein recognition depends on the nature of the metal-chelator bonds, subtle effects in the lanthanide and actinide coordination chemistry, such as metal-ligand covalency, can be qualitatively assessed.

Magnetic anisotropy in YbIII complex candidates for molecular qubits: a theoretical analysis

The magnetic properties of mononuclear YbIII complexes have been explored by using multiconfigurational CASPT2/RASSI calculations. Such complexes, in particular the case of [Yb(trensal)] complex, have been proposed as molecular qubits due to their spin dynamics properties. We have verified the accuracy of the theoretical approach to study such systems by comparing with experimental magnetic data. In order to have a wide overview of the magnetic properties of mononuclear YbIII complexes, we have considered simple charged and neutral models, [Yb(H2O)n]3+ and [Yb(OH)3(H2O)n-3], for many coordination modes. Thus, the results for more than 100 models allow extraction of some conclusions about the best ligand distributions in the coordination sphere to tailor the magnetic properties. Some low coordination, between 3 and 5, complexes that have no experimental magnetic data have been studied computationally to check if they can present high magnetic anisotropy.

Quantum Information and Algorithms for Correlated Quantum Matter

Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.

Trigonal Bipyramidal V3+ Complex as an Optically Addressable Molecular Qubit Candidate

Synthetic chemistry enables a bottom-up approach to quantum information science, where atoms can be deterministically positioned in a quantum bit or qubit. Two key requirements to realize quantum technologies are qubit initialization and read-out. By imbuing molecular spins with optical initialization and readout mechanisms, analogous to solid-state defects, molecules could be integrated into existing quantum infrastructure. To mimic the electronic structure of optically addressable defect sites, we designed the spin-triplet, V3+ complex, (C6F5)3trenVCNtBu (1). We measured the static spin properties as well as the spin coherence time of 1 demonstrating coherent control of this spin qubit with a 240 GHz electron paramagnetic resonance spectrometer powered by a free electron laser. We found that 1 exhibited narrow, near-infrared photoluminescence (PL) from a spin-singlet excited state. Using variable magnetic field PL spectroscopy, we resolved emission into each of the ground-state spin sublevels, a crucial component for spin-selective optical initialization and readout. This work demonstrates that trigonally symmetric, heteroleptic V3+ complexes are candidates for optical spin addressability.

Understanding Covalent versus Spin-Orbit Coupling Contributions to Temperature-Dependent Electron Spin Relaxation in Cupric and Vanadyl Phthalocyanines

Recent interest in transition-metal complexes as potential quantum bits (qubits) has reinvigorated the investigation of fundamental contributions to electron spin relaxation in various ligand scaffolds. From quantum computers to chemical and biological sensors, interest in leveraging the quantum properties of these molecules has opened a discussion of the requirements to maintain coherence over a large temperature range, including near room temperature. Here we compare temperature-, magnetic field position-, and concentration-dependent electron spin relaxation in copper(II) phthalocyanine (CuPc) and vanadyl phthalocyanine (VOPc) doped into diamagnetic hosts. While VOPc demonstrates coherence up to room temperature, CuPc coherence times become rapidly T₁-limited with increasing temperature, despite featuring a more covalent ground-state wave function than VOPc. As rationalized by a ligand field model, this difference is ascribed to different spin-orbit coupling (SOC) constants for Cu(II) versus V(IV). The manifestation of SOC contributions to spin-phonon coupling and electron spin relaxation in different ligand fields is discussed, allowing for a further understanding of the competing roles of SOC and covalency in electron spin relaxation.

Open questions in transplutonium coordination chemistry

Over the past decade, momentous progress has been made in the characterization of late actinide compounds. Here the authors highlight how advances in spectroscopic and computational tools have developed our understanding of fundamental transplutonium bonding interactions, and discuss whether covalency and heterogeneity changes in 5f-orbital bonding could be harnessed in environmentally and industrially relevant systems.

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.

Spin-phonon coupling and dynamic zero-field splitting contributions to spin conversion processes in iron(II) complexes

Magnetization dynamics of transition metal complexes manifest in properties and phenomena of fundamental and applied interest [e.g., slow magnetic relaxation in single molecule magnets, quantum coherence in quantum bits (qubits), and intersystem crossing (ISC) rates in photophysics]. While spin-phonon coupling is recognized as an important determinant of these dynamics, additional fundamental studies are required to unravel the nature of the coupling and, thus, leverage it in molecular engineering approaches. To this end, we describe here a combined ligand field theory and multireference ab initio model to define spin-phonon coupling terms in S = 2 transition metal complexes and demonstrate how couplings originate from both the static and dynamic properties of ground and excited states. By extending concepts to spin conversion processes, ligand field dynamics manifest in the evolution of the excited state origins of zero-field splitting (ZFS) along specific normal mode potential energy surfaces. Dynamic ZFSs provide a powerful means to independently evaluate contributions from spin-allowed and/or spin-forbidden excited states to spin-phonon coupling terms. Furthermore, ratios between various intramolecular coupling terms for a given mode drive spin conversion processes in transition metal complexes and can be used to analyze the mechanisms of ISC. Variations in geometric structure strongly influence the relative intramolecular linear spin-phonon coupling terms and will define the overall spin state dynamics. While the findings of this study are of general importance for understanding magnetization dynamics, they also link the phenomenon of spin-phonon coupling across fields of single molecule magnetism, quantum materials/qubits, and transition metal photophysics.

A bis-vanadyl coordination complex as a 2-qubit quantum gate

A new bis-hydroxyphenylpyrazolyl ligand, H₄L, allows isolating and structurally characterizing vanadyl and titanyl dinuclear complexes (Bu₄N)₂[(MO)₂(HL)₂] (M = V, Ti). The weak dipolar coupling and relatively short quantum coherence of the divanadyl anions are optimal for a 2-qubit molecular architecture proposed to implement electron-mediated nuclear quantum simulations.

The dynamic ligand field of a molecular qubit: decoherence through spin–phonon coupling

A ligand field model highlights chemical design principles for the development of room temperature coherent materials for quantum information processing.

Mapping Magnetic Properties and Relaxation in Vanadium(IV) Complexes with Lanthanides by Electron Paramagnetic Resonance

Vanadium(IV) complexes are actively studied as potential candidates for molecular spin qubits operating at room temperatures. They have longer electron spin decoherence times than many other transition ions, being the key property for applications in quantum information processing. In most cases reported to date, the molecular complexes were optimized through the design for this purpose. In this work, we investigate the relaxation properties of vanadium(IV) ions incorporated in complexes with lanthanides using electron paramagnetic resonance (EPR). In all cases, the VO₆ moieties with no nuclear spins in the first coordination sphere are addressed. We develop and implement the approaches for facile diagnostics of relaxation characteristics in individual VO₆ moieties of such compounds. Remarkably, the estimated relaxation times are found to be close to those of other vanadium-based qubits obtained previously. In the future, a synergistic combination of qubit-friendly properties of vanadium ions with single-molecule magnetism and luminescence of lanthanides can be pursued to realize new functionalities of such materials.