A Molecular Approach to Quantum Sensing

Guest-responsive coherence time of radical qubits in a metal-organic framework

Metal-organic frameworks (MOFs) integrated with molecular qubits are promising for quantum sensing. In this study, a new UiO-type MOF with a 5,12-diazatetracene (DAT)-containing ligand is synthesized, and the radicals generated in the MOF exhibit high stability and a relatively long coherence time (T2) responsive to the introduction of various guest molecules.

Correlation between Radical and Quartet State Coherence Times in Photogenerated Triplet-Radical Conjugates

Molecular quartet states, generated by photoexcitation of chromophore-radical conjugates, have been shown to exhibit attractive properties for applications in the field of molecular spintronics. Many of these applications, such as quantum sensing, require a coherent manipulation of the spin system, implying the need to control the quartet state spin coherence properties. By examining the influence of structural and matrix-related factors, we demonstrate a correlation between the coherence decay of the photogenerated quartet state and that of the tethered stable radical, paving the way for a rational design of photogenerated molecular three-spin systems with optimized coherence properties.

Alternant Hydrocarbon Diradicals as Optically Addressable Molecular Qubits

High-spin molecules allow for bottom-up qubit design and are promising platforms for magnetic sensing and quantum information science. Optical addressability of molecular electron spins has also been proposed in first-row transition-metal complexes via optically detected magnetic resonance (ODMR) mechanisms analogous to the diamond-nitrogen-vacancy color center. However, significantly less progress has been made on the front of metal-free molecules, which can deliver lower costs and milder environmental impacts. At present, most luminescent open-shell organic molecules are π-diradicals, but such systems often suffer from poor ground-state open-shell characters necessary to realize a stable ground-state molecular qubit. In this work, we use alternancy symmetry to selectively minimize radical-radical interactions in the ground state, generating π-systems with high diradical characters. We call them m-dimers, referencing the need to covalently link two benzylic radicals at their meta carbon atoms for the desired symmetry. Through a detailed electronic structure analysis, we find that the excited states of alternant hydrocarbon m-diradicals contain important symmetries that can be used to construct ODMR mechanisms leading to ground-state spin polarization. The molecular parameters are set in the context of a tris(2,4,6-trichlorophenyl)methyl (TTM) radical dimer covalently tethered at the meta position, demonstrating the feasibility of alternant m-diradicals as molecular color centers.

Single-Spin Sensing: A Molecule-on-Tip Approach

Magnetometry plays a pivotal role in addressing the requirements of ultradense storage technology and overcoming challenges associated with downscaled spin qubits. A promising approach for atomic-scale single-spin sensing involves utilizing a magnetic molecule as a spin sensor, although such a realization is still in its early stages. To tackle this challenge and underscore the potential of this method, we combined a nickelocene molecule with scanning tunneling microscopy to perform versatile spin-sensitive imaging of magnetic surfaces. We investigated model Co islands on Cu(111) of different thicknesses having variable magnetic properties. Our method demonstrates robustness and reproducibility, providing atomic-scale sensitivity to spin polarization and magnetization orientation, owing to a direct exchange coupling between the nickelocene-terminated tip and the Co surfaces. We showcase the accessibility of magnetic exchange maps using this technique, revealing unique signatures in magnetic corrugation, which are well described by computed spin-density maps. These advancements significantly improve our capacity to probe and visualize magnetism at the atomic level.

Photoinduced Magnetic Exchange-Jump Promotes Ground State Biradical Electron Spin Polarization

Photoinduced electron spin polarization (ESP) is reported in the electronic ground states of three Pt(II) complexes comprised of two S = 1/2 nitronyl nitroxide (NN) radicals attached through different length para-phenylethynyl bridges to the 3,6 positions of a catecholate (CAT, donor) and 4,4'-di-tert-butyl-2,2'-bipyridine (bpy, acceptor). Complexes 1-3 have from 17 to 41 bonds separating NN radicals and display cw-EPR spectra consistent with |JNN-NN| ≫ |aN|, |JNN-NN| ≥ |aN|, and |JNN-NN| < |aN|, respectively, where JNN-NN is the magnetic exchange coupling between NN radicals in the electronic ground state, and aN is the isotropic 14N hyperfine coupling constant. Light-induced transient EPR spectra characterized as enhanced ground-state absorption were observed for all three complexes using 532 nm pulsed laser excitation into the ligand-to-ligand charge transfer (LL'CT) band of the (CAT)Pt(bpy) chromophore. The magnitude of the observed ESP increases in the order 1 < 2 < 3 and is inversely correlated with the magnitude of ground-state JNN-NN. In addition to the experimental observation of net absorptive polarization in 1-3, light excitation also produces multiplet polarization in 2. Since the weak dipolar coupling leads to a strong spectral overlap of the absorptive and emissive components, the multiplet polarization is not observed in 1 and 3 and is very weak in 2. The ability to spin-polarize multiple radical spins with a single photon is anticipated to advance new photoinduced multi qubit/qudit ESP protocols for quantum information science applications.

Molecular and Supramolecular Materials: From Light-Harvesting to Quantum Information Science and Technology

The past two decades have witnessed immense advances in quantum information technology (QIT), benefited by advances in physics, chemistry, biology, and materials science and engineering. It is intriguing to consider whether these diverse molecular and supramolecular structures and materials, partially inspired by quantum effects as observed in sophisticated biological systems such as light-harvesting complexes in photosynthesis and the magnetic compass of migratory birds, might play a role in future QIT. If so, how? Herein, we review materials and specify the relationship between structures and quantum properties, and we identify the challenges and limitations that have restricted the intersection of QIT and chemical materials. Examples are broken down into two categories: materials for quantum sensing where nonclassical function is observed on the molecular scale and systems where nonclassical phenomena are present due to intermolecular interactions. We discuss challenges for materials chemistry and make comparisons to related systems found in nature. We conclude that if chemical materials become relevant for QIT, they will enable quite new kinds of properties and functions.

Assessing the importance of multireference correlation in predicting reversed conductance decay

In a classical electronic resistor, conductance decays as the device length increases according to Ohm's Law. While most molecular series display a comparable exponential decay in conductance with increasing molecular length, a class of single-molecule device series exists where conductance instead increases with molecular/device length, a phenomenon called reversed conductance decay. While reversals of conductance decay have been repeatedly theoretically predicted, they have been far more difficult to demonstrate experimentally. Previous studies have suggested that theoretical multi-reference(static) correlation errors may be a major cause of this discrepancy, yet most single-molecule transport methods are unable to treat multireference correlation. Using our unique multireference transport method based on non-equilibrium Green's function and multiconfigurational pair-density functional theory (NEGF-MCPDFT), we examined a previously predicted case of reversed conductance decay in systems of linear chains of phenyl rings with varying lengths and electrode designs. We compare our NEGF-MCPDFT results to those of non-multireference NEGF methods to quantify the exact role of static correlation in conductance decay reversals and clarify their relative importance to geometric and electrode design/coupling considerations.

How Precisely Can Individual Molecules Be Analyzed? A Case Study on Locally Quantifying Forces and Energies Using Scanning Probe Microscopy

Recent advances in scanning probe microscopy methodology have enabled the measurement of tip-sample interactions with picometer accuracy in all three spatial dimensions, thereby providing a detailed site-specific and distance-dependent picture of the related properties. This paper explores the degree of detail and accuracy that can be achieved in locally quantifying probe-molecule interaction forces and energies for adsorbed molecules. Toward this end, cobalt phthalocyanine (CoPc), a promising CO2 reduction catalyst, was studied on Ag(111) as a model system using low-temperature, ultrahigh vacuum noncontact atomic force microscopy. Data were recorded as a function of distance from the surface, from which detailed three-dimensional maps of the molecule's interaction with the tip for normal and lateral forces as well as the tip-molecule interaction potential were constructed. The data were collected with a CO molecule at the tip apex, which enabled a detailed visualization of the atomic structure. Determination of the tip-substrate interaction as a function of distance allowed isolation of the molecule-tip interactions; when analyzing these in terms of a Lennard-Jones-type potential, the atomically resolved equilibrium interaction energies between the CO tethered to the tip and the CoPc molecule could be recovered. Interaction energies peaked at less than 160 meV, indicating a physisorption interaction. As expected, the interaction was weakest at the aromatic hydrogens around the periphery of the molecule and strongest surrounding the metal center. The interaction, however, did not peak directly above the Co atom but rather in pockets surrounding it.

Radical qubits photo-generated in acene-based metal-organic frameworks

A series of metal-organic frameworks (MOFs) assembled with diazatetracene (DAT)-based linkers were synthesized and characterized. Despite different chromophore orientations and spacings, photoinduced persistent radicals were generated in all the MOFs, and their spin-lattice relaxation time (T1) and spin-spin relaxation time (T2) were found to be relatively long even at room temperature. The generality of long T1 and T2 values of photogenerated radicals in the chromophore-assembled MOFs provides a new platform towards quantum sensing applications.

Patterned immobilization of polyoxometalate-loaded mesoporous silica particles via amine-ene Michael additions on alkene functionalized surfaces

Polyoxometalates (POM) are anionic oxoclusters of early transition metals that are of great interest for a variety of applications, including the development of sensors and catalysts. A crucial step in the use of POM in functional materials is the production of composites that can be further processed into complex materials, e.g. by printing on different substrates. In this work, we present an immobilization approach for POMs that involves two key processes: first, the stable encapsulation of POMs in the pores of mesoporous silica nanoparticles (MSPs) and, second, the formation of microstructured arrays with these POM-loaded nanoparticles. Specifically, we have developed a strategy that leads to water-stable, POM-loaded mesoporous silica that can be covalently linked to alkene-bearing surfaces by amine-Michael addition and patterned into microarrays by scanning probe lithography (SPL). The immobilization strategy presented facilitates the printing of hybrid POM-loaded nanomaterials onto different surfaces and provides a versatile method for the fabrication of POM-based composites. Importantly, POM-loaded MSPs are useful in applications such as microfluidic systems and sensors that require frequent washing. Overall, this method is a promising way to produce surface-printed POM arrays that can be used for a wide range of applications.

Spin-Polarized Radicals with Extremely Long Spin-Lattice Relaxation Time at Room Temperature in a Metal-Organic Framework

The generation of spin polarization is key in quantum information science and dynamic nuclear polarization. Polarized electron spins with long spin-lattice relaxation times (T1) at room temperature are important for these applications but have been difficult to achieve. We report the realization of spin-polarized radicals with extremely long T1 at room temperature in a metal-organic framework (MOF) in which azaacene chromophores are densely integrated. Persistent radicals are generated in the MOF by charge separation after photoexcitation. Spin polarization of a triplet generated by photoexcitation is successfully transferred to the persistent radicals. Pulse electron spin resonance measurements reveal that the T1 of the polarized radical in the MOF is as long as 214 μs with a relatively long spin-spin relaxation time T2 of the radicals of up to 0.98 μs at room temperature. The achievement of extremely long spin polarization in MOFs with nanopores accessible to guest molecules will be an important cornerstone for future highly sensitive quantum sensing and efficient dynamic nuclear polarization.

Optically Addressing Exciton Spin and Pseudospin in Nanomaterials for Spintronics Applications

Oriented exciton spins that can be generated and manipulated optically are of interest for a range of applications, including spintronics, quantum information science, and neuromorphic computing architectures. Although materials that host such excitons often lack practical coherence times for use on their own, strategic transduction of the magnetic information across interfaces can combine fast modulation with longer-term storage and readout. Several nanostructure systems have been put forward due to their interesting magneto-optical properties and their possible manipulation using circularly polarized light. These material systems are presented here, namely two-dimensional (2D) systems due to the unique spin-valley coupling properties and quantum dots for their exciton fine structure. 2D magnets are also discussed for their anisotropic spin behavior and extensive 2D magnetic states that are not yet fully understood but could pave the way for emergent techniques of magnetic control. This review also details the experimental and theoretical tools to measure and understand these systems along with a discussion on the progress of optical manipulation of spins and magnetic order transitions.

Toward Magneto-Optical Cryogenic Thermometers with High Sensitivity: A Magnetic Circular Dichroism Based Thermometric Approach

Remote temperature probing at the cryogenic range is of utmost importance for the advancement of future quantum technologies. Despite the notable achievements in luminescent thermometers, accurately measuring temperatures below 10 K remains a challenging endeavor. In this study, we propose a novel magneto-optical thermometric approach based on the magnetic-circular dichroism (MCD) technique, which offers unprecedented capabilities for meticulous temperature variation analysis at cryogenic temperatures. The inherent temperature sensitivity of the MCD C-term, in conjunction with both positive and negative signals, enables highly sensitive magneto-optical temperature probing. Additionally, a groundbreaking relative thermal sensitivity value of 95.3 % K-1 at 2.54 K can be achieved using a mononuclear lanthanide complex, [[Ho(acac)3 (phen)], in the presence of a 0.25 T applied magnetic field and using a combination of multiparametric thermal read-out with multiple regression. These results unequivocally demonstrate the viability and effectiveness of our methodology for cryogenic temperature sensing.

Competitive reversed quartet mechanisms for photogenerated ground state electron spin polarization

Photoinduced electron spin polarization (ESP) of a spin-½ organic radical (nitronyl nitroxide, NN) in a series of Pt(ii) complexes comprised of 4,4'-di-tert-butyl-2,2'-bipyridine (bpy) and 3-tert-butylcatecholate (CAT) ligands, where the CAT ligand is substituted with (CH3)n-meta-phenyl-NN (bridge-NN) groups, is presented and discussed. We show the importance of attenuating the energy gap between localized NN radical and chromophoric excited states to control both the magnitude and sign of the optically-generated ESP, and to provide deeper insight into the details of the ESP mechanism. Understanding electronic structure contributions to optically generated ESP will enhance our ability to control the nature of prepared states for a variety of quantum information science applications, where strong ESP facilitates enhanced sensitivity and readout capabilities at low applied magnetic fields and higher temperatures.

A fresh perspective on metal ammonia molecular complexes and expanded metals: opportunities in catalysis and quantum information

Recent advances in our comprehension of the electronic structure of metal ammonia complexes have opened avenues for novel materials with diffuse electrons. These complexes in their ground state can host peripheral "Rydberg" electrons which populate a hydrogenic-type shell model imitating atoms. Aggregates of such complexes form the so-called expanded or liquid metals. Expanded metals composed of d- and f-block metal ammonia complexes offer properties, such as magnetic moments and larger numbers of diffuse electrons, not present for alkali and alkaline earth (s-block) metals. In addition, tethering metal ammonia complexes via hydrocarbon chains (replacement of ammonia ligands with diamines) yields materials that can be used for redox catalysis and quantum computing, sensing, and optics. This perspective summarizes the recent findings for gas-phase isolated metal ammonia complexes and projects the obtained knowledge to the condensed phase regime. Possible applications for the newly introduced expanded metals and linked solvated electrons precursors are discussed and future directions are proposed.

Reversible spin-optical interface in luminescent organic radicals

Molecules present a versatile platform for quantum information science1,2 and are candidates for sensing and computation applications3,4. Robust spin-optical interfaces are key to harnessing the quantum resources of materials5. To date, carbon-based candidates have been non-luminescent6,7, which prevents optical readout via emission. Here we report organic molecules showing both efficient luminescence and near-unity generation yield of excited states with spin multiplicity S > 1. This was achieved by designing an energy resonance between emissive doublet and triplet levels, here on covalently coupled tris(2,4,6-trichlorophenyl) methyl-carbazole radicals and anthracene. We observed that the doublet photoexcitation delocalized onto the linked acene within a few picoseconds and subsequently evolved to a pure high-spin state (quartet for monoradical, quintet for biradical) of mixed radical-triplet character near 1.8 eV. These high-spin states are coherently addressable with microwaves even at 295 K, with optical readout enabled by reverse intersystem crossing to emissive states. Furthermore, for the biradical, on return to the ground state the previously uncorrelated radical spins either side of the anthracene shows strong spin correlation. Our approach simultaneously supports a high efficiency of initialization, spin manipulations and light-based readout at room temperature. The integration of luminescence and high-spin states creates an organic materials platform for emerging quantum technologies.

Thermally Ultrarobust S = 1/2 Tetrazolinyl Radicals: Synthesis, Electronic Structure, Magnetism, and Nanoneedle Assemblies on Silicon Surface

Open-shell organic molecules, including S = 1/2 radicals, may provide enhanced properties for several emerging technologies; however, relatively few synthesized to date possess robust thermal stability and processability. We report the synthesis of S = 1/2 biphenylene-fused tetrazolinyl radicals 1 and 2. Both radicals possess near-perfect planar structures based on their X-ray structures and density-functional theory (DFT) computations. Radical 1 possesses outstanding thermal stability as indicated by the onset of decomposition at 269 °C, based on thermogravimetric analysis (TGA) data. Both radicals possess very low oxidation potentials <0 V (vs. SCE) and their electrochemical energy gaps, Ecell ≈ 0.9 eV, are rather low. Magnetic properties of polycrystalline 1 are characterized by superconducting quantum interference device (SQUID) magnetometry revealing a one-dimensional S = 1/2 antiferromagnetic Heisenberg chain with exchange coupling constant J'/k ≈ -22.0 K. Radical 1 in toluene glass possesses a long electron spin coherence time, Tm ≈ 7 μs in the 40-80 K temperature range, a property advantageous for potential applications as a molecular spin qubit. Radical 1 is evaporated under ultrahigh vacuum (UHV) forming assemblies of intact radicals on a silicon substrate, as confirmed by high-resolution X-ray photoelectron spectroscopy (XPS). Scanning electron microscope (SEM) images indicate that the radical molecules form nanoneedles on the substrate. The nanoneedles are stable for at least 64 hours under air as monitored by using X-ray photoelectron spectroscopy. Electron paramagnetic resonance (EPR) studies of the thicker assemblies, prepared by UHV evaporation, indicate radical decay according to first-order kinetics with a long half-life of 50 ± 4 days at ambient conditions.

Direct determination of high-order transverse ligand field parameters via µSQUID-EPR in a Et4N[160GdPc2] SMM

The development of quantum technologies requires a thorough understanding of systems possessing quantum effects that can ultimately be manipulated. In the field of molecular magnetism, one of the main challenges is to measure high-order ligand field parameters, which play an essential role in the relaxation properties of SMMs. The development of highly advanced theoretical calculations has allowed the ab-initio determination of such parameters; however, currently, there is a lack of quantitative assessment of how good the ab-initio parameters are. In our quest for technologies that can allow the extraction of such elusive parameters, we develop an experimental technique that combines the EPR spectroscopy and µSQUID magnetometry. We demonstrate the power of the technique by performing EPR-µSQUID measurement of a magnetically diluted single crystal of Et₄N[GdPc₂], by sweeping the magnetic field and applying a range of multifrequency microwave pulses. As a result, we were able to directly determine the high-order ligand field parameters of the system, enabling us to test theoretical predictions made by state-of-the-art ab-initio methods.

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.

Dynamic Electron Polarization Lasting More Than 10 μs by Hybridizing Porphyrin and TEMPO with Flexible Linkers

Dynamic electron polarization (DEP), induced by quenching of photoexcited species by stable radicals, can hyperpolarize electron spins in solution at room temperature. Recently, development of technologies based on electron spin polarization such as dynamic nuclear polarization (DNP) has been progressing, where it is important to design molecules that achieve long-lasting DEP in addition to high DEP. Hybridization by linking dyes and radicals is a promising approach for efficient DEP, but strong interactions between neighboring dyes and radicals often result in the rapid decay of DEP. In this study, we introduce a flexible linker into the hybrid system of porphyrin and TEMPO to achieve both efficient DEP and long-lasting DEP. The structural flexibility of the linker switches the interaction between the radical and the triplet, which promotes the DEP process by bringing the radical and the triplet into close proximity, while avoiding abrupt relaxation due to strong interactions. As a result, the new hybridized system exhibits a larger DEP than the unlinked system, while at the same time achieving a DEP lasting more than 10 μs.

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.

Tuning and Enhancing Quantum Coherence Time Scales in Molecules via Light-Matter Hybridization

Protecting quantum coherences in matter from the detrimental effects introduced by its environment is essential to employ molecules and materials in quantum technologies and develop enhanced spectroscopies. Here, we show how dressing molecular chromophores with quantum light in the context of optical cavities can be used to generate quantum superposition states with tunable coherence time scales that are longer than those of the bare molecule, even at room temperature and for molecules immersed in solvent. For this, we develop a theory of decoherence rates for molecular polaritonic states and demonstrate that quantum superpositions that involve such hybrid light-matter states can survive for times that are orders of magnitude longer than those of the bare molecule while remaining optically controllable. Further, by studying these tunable coherence enhancements in the presence of lossy cavities, we demonstrate that they can be enacted using present-day optical cavities. The analysis offers a viable strategy to engineer and increase quantum coherence lifetimes in molecules.

Computational design of magnetic molecules and their environment using quantum chemistry, machine learning and multiscale simulations

Having served as a playground for fundamental studies on the physics of d and f electrons for almost a century, magnetic molecules are now becoming increasingly important for technological applications, such as magnetic resonance, data storage, spintronics and quantum information. All of these applications require the preservation and control of spins in time, an ability hampered by the interaction with the environment, namely with other spins, conduction electrons, molecular vibrations and electromagnetic fields. Thus, the design of a novel magnetic molecule with tailored properties is a formidable task, which does not only concern its electronic structures but also calls for a deep understanding of the interaction among all the degrees of freedom at play. This Review describes how state-of-the-art ab initio computational methods, combined with data-driven approaches to materials modelling, can be integrated into a fully multiscale strategy capable of defining design rules for magnetic molecules.

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.

Multireference Study of Optically Addressable Vanadium-Based Molecular Qubit Candidates

Molecular electron spin qubits with optical manipulation schemes are some of the most promising candidates for modern quantum technologies. Key values that determine a compound's viability for optical-spin initialization and readout include its singlet-triplet gap and zero-field splitting (ZFS) parameters. Generally, these values are very small in magnitude and are thus difficult to reproduce with theoretical methods. Here, we study a previously identified optically addressable molecular qubit, (C₆F₅)₃trenVCN^tBu (tren = tris(2-aminoethyl)amine), using the complete active space self-consistent field (CASSCF) and post-CASSCF methods: complete active space second-order perturbation theory (CASPT2), multiconfiguration pair-density functional theory (MC-PDFT), and hybrid MC-PDFT (HMC-PDFT). Of those methods, we successfully reproduce the singlet-triplet gap and ZFS parameters with reasonable accuracy using 0.5 HMC-PDFT and CASPT2. Four additional V³⁺ complexes with differing ligands were also investigated. We found that the ligands have minimal effect on the spin properties of the molecule and propose them to be optically addressable qubit candidates. These potential qubits are further analyzed in terms of ab initio ligand field theory (AILFT) to understand the influence of the ligands on the singlet-triplet gap and ZFS parameters.

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.

Excited State Magneto-Structural Correlations Related to Photoinduced Electron Spin Polarization

Photoinduced electron spin polarization (ESP) is reported in the ground state of a series of complexes consisting of an organic radical (nitronylnitroxide, NN) covalently attached to a donor-acceptor chromophore either directly or via para-phenylene bridges substituted with 0-4 methyl groups. These molecules represent a class of chromophores that undergo visible light excitation to produce an initial exchange-coupled, three-spin [bpy^•-, CAT^•+ (= semiquinone, SQ) and NN^•], charge-separated doublet ²S₁ (S = chromophore spin singlet configuration) excited state that rapidly decays by magnetic exchange-enhanced internal conversion to a ²T₁ (T = chromophore excited spin triplet configuration) state. The ²T₁ state equilibrates with chromophoric and NN radical-derived excited states, resulting in absorptive ESP of the recovered ground state, which persists for greater than a millisecond and can be measured by low-temperature time-resolved electron paramagnetic resonance spectroscopy. The magnitude of the ground state ESP is found to correlate with the excited state magnetic exchange interaction between the CAT^+• and NN^• radicals, which in turn is controlled by the structure of the bridge fragment.

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.

Record Chemical-Shift Temperature Sensitivity in a Series of Trinuclear Cobalt Complexes

Designing spins that exhibit long-lived coherence and strong temperature sensitivity is central to designing effective molecular thermometers and a fundamental challenge in the chemistry/quantum-information space. Herein, we provide a new pathway to both properties in the same molecule by designing a nuclear spin, which possesses a robust spin coherence, to mimic the strong temperature sensitivity of an electronic spin. This design strategy is demonstrated in the group of trinuclear Co(III) spin-crossover compounds [(CpCo(OP(OR)₂)₃)₂Co](SbCl₆) where Cp = cyclopentadienyl and R = Me (1), Et (2), i-Pr (3), and t-Bu (4). Nuclear magnetic resonance analyses of the ⁵⁹Co nuclear spins reveal ⁵⁹Co chemical-shift temperature sensitivity (Δδ/ΔT) values that span from 101(1) ppm/°C in 1 to 149(1) ppm/°C in 2 and 150(2) ppm/°C in 4, where the latter two are record temperature sensitivities for any nuclear spin. Additionally, complexes 2 and 4 have T₂^* values of 74 and 78 μs in solution at ambient temperatures surpassing those from electron-spin-based complexes, which typically display long coherence times only at extremely low temperatures. Our results suggest that spin-crossover phenomena can enable electron-spin-like temperature sensitivities in nuclear spins while retaining robust coherence times at room temperature.

Isotopomeric Elucidation of the Mechanism of Temperature Sensitivity in 59Co NMR Molecular Thermometers

Understanding the mechanisms governing temperature-dependent magnetic resonance properties is essential for enabling thermometry via magnetic resonance imaging. Herein we harness a new molecular design strategy for thermometry─that of effective mass engineering via deuteration in the first coordination shell─to reveal the mechanistic origin of ⁵⁹Co chemical shift thermometry. Exposure of [Co(en)₃]³⁺ (1; en = ethylenediamine) and [Co(diNOsar)]³⁺ (2; diNOsar = dinitrosarcophagine) to mixtures of H₂O and D₂O produces distributions of [Co(en)₃]³⁺-d_n (n = 0-12) and [Co(diNOsar)]³⁺-d_n (n = 0-6) isotopomers all resolvable by ⁵⁹Co NMR. Variable-temperature ⁵⁹Co NMR analyses reveal a temperature dependence of the ⁵⁹Co chemical shift, Δδ/ΔT, on deuteration of the N-donor atoms. For 1, deuteration amplifies Δδ/ΔT by 0.07 ppm/°C. Increasing degrees of deuteration yield an opposing influence on 2, diminishing Δδ/ΔT by -0.07 ppm/°C. Solution-phase Raman spectroscopy in the low-frequency 200-600 cm^-1 regime reveals a red shift of Raman-active Co-N₆ vibrational modes by deuteration. Analysis of the normal vibrational modes shows that Raman modes produce the largest variation in ⁵⁹Co δ. Finally, partition function analysis of the Raman-active modes shows that increased populations of Raman modes predict greater Δδ/ΔT, representing new experimental insight into the thermometry mechanism.

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.

What the foundations of quantum computer science teach us about chemistry

With the rapid development of quantum technology, one of the leading applications that has been identified is the simulation of chemistry. Interestingly, even before full scale quantum computers are available, quantum computer science has exhibited a remarkable string of results that directly impact what is possible in a chemical simulation with any computer. Some of these results even impact our understanding of chemistry in the real world. In this Perspective, we take the position that direct chemical simulation is best understood as a digital experiment. While on the one hand, this clarifies the power of quantum computers to extend our reach, it also shows us the limitations of taking such an approach too directly. Leveraging results that quantum computers cannot outpace the physical world, we build to the controversial stance that some chemical problems are best viewed as problems for which no algorithm can deliver their solution, in general, known in computer science as undecidable problems. This has implications for the predictive power of thermodynamic models and topics such as the ergodic hypothesis. However, we argue that this Perspective is not defeatist but rather helps shed light on the success of existing chemical models such as transition state theory, molecular orbital theory, and thermodynamics as models that benefit from data. We contextualize recent results, showing that data-augmented models are a more powerful rote simulation. These results help us appreciate the success of traditional chemical theory and anticipate new models learned from experimental data. Not only can quantum computers provide data for such models, but they can also extend the class and power of models that utilize data in fundamental ways. These discussions culminate in speculation on new ways for quantum computing and chemistry to interact and our perspective on the eventual roles of quantum computers in the future of chemistry.