Tunable Cr4+ Molecular Color Centers

Cryogenic field-cycling instrument for optical NMR hyperpolarization studies

Optical dynamic nuclear polarization (DNP) offers an attractive approach to enhancing the sensitivity of nuclear magnetic resonance (NMR) spectroscopy. Efficient, optically-generated electron polarization can be leveraged to operate across a broad range of temperatures and magnetic fields, making it particularly appealing for applications requiring high DNP efficiency or spatial resolution. While a large class of systems hold promise for optical DNP, many candidates display both variable electron polarizability and electron and nuclear T1 relaxation times as functions of magnetic field and temperature. This necessitates tools capable of studying DNP under diverse experimental conditions. To address this, we introduce a cryogenic field cycling instrument that facilitates optical DNP studies across a wide range of magnetic fields (10 mT-9.4 T) and temperatures (∼10 K-300 K) for wide-bore magnets. Continuous cryogen replenishment enables sustained, long-term operation. Additionally, the system supports the ability to manipulate and probe rapidly hyperpolarized (∼60 s) nuclear spins via pulse sequences involving millions of RF pulses. We describe innovations in the device design and demonstrate its operation on a model system of 13C nuclear spins in diamond polarized through optically pumped nitrogen vacancy (NV) centers. We anticipate the use of the instrument for a broad range of optical DNP systems and studies.

Molecular Design for Optically Induced Magnetization: Targeting Excited State Orbital Degeneracy in Tungsten(V) Complexes

The rise of quantum information science has spurred chemists to prepare new molecules that serve as useful building blocks in quantum technologies of the future. Implementation of molecular spin-based qubits requires new methods to induce high spin polarization of samples. Herein, we report design criteria to develop axially symmetric spin-1/2 molecules amenable to optically induced magnetization (OIM), a technique using circularly polarized (CP) excitation to deliver spin polarization. We apply these criteria to develop a series of tungsten(V) chalcogenide complexes that are demonstrated to have large spin-sensitive responses to CP light using magnetic circular dichroism (MCD) that could allow up to ∼20% spin polarization through OIM. Pulsed electron paramagnetic resonance (EPR) spectra reveal these systems have improved relaxation times over molecules like K2IrCl6, a species recently investigated by OIM, and field-swept electron spin-echo (FS-ESE) experiments show they have a remarkable lack of anisotropy in their phase-memory Tm times. The design criteria are general and point toward future ways to improve OIM-initializable qubits.

An Accurate, Affordable Density Functional Tight-Binding Model for Excited State Hydrocarbon Polymer Molecular Dynamics

We have developed a density functional tight-binding model for hydrocarbon excited state dynamics by referencing to high-level electronic structure theory and incorporating a many-body repulsive energy. We then validate our model against n-octane geometry optimizations, bond dissociation scans, and vibrational frequencies. Our model is approximately 103 times more efficient than hybrid time-dependent density functional theory calculations with comparable accuracy. Our efforts enable longer timescale excited state simulations of photochemistry and scattering of incident radiation.

Molecular Engineering of Emissive Molecular Qubits Based on Spin-Correlated Radical Pairs

Spin chemistry of photogenerated spin-correlated radical pairs (SCRPs) offers a practical approach to control chemical reactions and molecular emissions by using weak magnetic fields. This capability to harness magnetic field effects (MFEs) paves the way for developing SCRPs-based molecular qubits. Here, we introduce a new series of donor-chiral bridge-acceptor (D-χ-A) molecules that demonstrate significant MFEs on fluorescence intensity and lifetime in solution at room temperature─critical for quantum sensing. By precisely tuning the donor site through torsional locking, distance extension, and planarization, we achieved remarkable control over key quantum properties, including field-response range and line width. In the most responsive systems, emission lifetimes increased by over 200%, and the total emission intensity was modulated by up to 30%. This level of tunability shows the power of synthetic spin chemistry. The rational design principle of optically addressable SCRP-based molecular systems, presented in this work, represents a major leap toward functional synthetic molecular qubits, advancing the field of molecular quantum technologies.

Osmium(IV) Tetraaryl Complexes Formed from Prefunctionalized Ligands

Transition metal(IV) tetraaryl, M(aryl)4, complexes hold great promise as functional building blocks for complex organometallic materials, yet their widespread utility depends on the development of improved synthetic protocols and a deeper understanding of their chemical structure-property relationship(s). Here we show that Os(aryl)4 complexes with preinstalled functional groups (-F, -Cl, -Br, -I, and -SMe) can be prepared from reactions between (Oct4N)2[OsBr6] and Grignard reagents formed by halogen/magnesium insertion or exchange. This approach provides access to compounds that may otherwise prove challenging to prepare through postfunctionalization strategies, such as those comprising halogens in the 2- or 5-positions. We characterize these, as well as previously reported, materials using single-crystal X-ray diffraction, solution voltammetry, and UV-vis spectroscopy. Through a comparison of 13 differently substituted complexes, we identify correlations between their electrochemical and optical gaps, and between the E1/2 of their 0/1+ redox event and an adjusted Hammett parameter that accounts for all aryl ligand substituents. The electronic property trends observed are further rationalized through a series of first-principles calculations based on density functional theory. Together, this work lays a foundation for advancing new preparative methods to further derivatize such species, and a robust experimental data set to help benchmark future experimental and computational compound characterization.

Effect of Chemical Modification in Trigonal Gd(III) Molecular Qubits

Molecular quantum bits (qubits) are often hailed for the tunability of their properties through chemical backbone modifications. This concept has been explored in detail for transition metal-based systems. However, the effect of chemical modifications in the ligand backbone on the spin dynamics of 4f molecular qubits remains relatively unexplored. We present herein a study of the effect of the addition, and topology thereof, of methoxy groups in the ligand backbone of a Gd(III) qubit while maintaining the molecular symmetry. Continuous wave X-band Electron Paramagnetic Resonance measurements on single crystals of two such derivatized Gd-based molecular qubits provide detailed information on their eigenvector composition. Their dynamic properties were examined by pulse electron paramagnetic resonance on single crystals, revealing that both complexes display coherent spin dynamics up to 100 K, where spin-lattice relaxation limits the coherence. Furthermore, we show that tuning of the ligand field-derived anisotropy leads to control of the eigenvector composition, which translates to control of the Rabi nutation frequency and hence of the time for quantum gate implementation. This demonstrates that molecular qubits offer the possibility for synthetic control and tuning of the speed of coherent manipulations.

Enhancing the Optically Detected Magnetic Resonance Signal of Organic Molecular Qubits

In quantum information science and sensing, electron spins are often purified into a specific polarization through an optical-spin interface, a process known as optically detected magnetic resonance (ODMR). Diamond-NV centers and transition metals are both excellent platforms for these so-called color centers, while metal-free molecular analogues are also gaining popularity for their extended polarization lifetimes, milder environmental impacts, and reduced costs. In our earlier attempt at designing such organic high-spin π-diradicals, we proposed to spin-polarize by shelving triplet M S = ±1 populations as singlets. This was recently verified by experiments albeit with low ODMR contrasts of <1% at temperatures above 5 K. In this work, we propose to improve the ODMR signal by moving singlet populations back into the triplet M S = 0 sublevel, designing a true carbon-based molecular analogue to the NV center. Our proposal is based upon transition-orbital and group-theoretical analyses of beyond-nearest-neighbor spin-orbit couplings, which are further confirmed by ab initio calculations of a realistic trityl-based radical dimer. Microkinetic analyses point toward high ODMR contrasts of around 30% under experimentally feasible conditions, a stark improvement from previous works. Finally, in our quest toward ground-state optically addressable molecular spin qubits, we exemplify how our symmetry-based design avoids Zeeman-induced singlet-triplet mixings, setting the scene for realizing electron spin qubit gates.

Room-Temperature Optical Spin Polarization of an Electron Spin Qudit in a Vanadyl-Free Base Porphyrin Dimer

Photoexcited organic chromophores appended to molecular qubits can serve as a source of spin initialization or multilevel qudit generation for quantum information applications. So far, this approach has been primarily investigated in chromophore-stable radical systems. Here, we extend this concept to a meso-meso linked oxovanadium(IV) porphyrin-free-base porphyrin dimer. Femtosecond transient absorption experiments reveal that photoexcitation of the free-base porphyrin leads to picosecond triplet state formation via enhanced intersystem crossing. Time-resolved electron paramagnetic resonance (TREPR) experiments carried out at both 85 K and room temperature reveal the formation of a long-lived spin-polarized quartet state through triplet-doublet spin mixing. Notably, a distinct hyperfine structure arising from the interaction between the electron spin quartet state and the vanadyl nucleus (51V, I = 7/2) is evident, with the quartet state showing long-lived spin polarization even at room temperature. Theoretical simulations of the TREPR spectra confirm the photogenerated quartet state and provide insights into the non-Boltzmann spin populations. Exploiting this phenomenon affords the possibility of using photoinduced triplet states in porphyrins for quantum information as a resource to polarize and magnetically couple molecular electronic or nuclear spin qubits and qudits.

Low temperature decoherence dynamics in molecular spin systems using the Lindblad master equation

Understanding the spin dynamics in low-temperature settings is crucial to designing and optimizing molecular spin systems for use in emerging quantum technologies. At low temperatures, irreversible loss occurs due to ensemble dynamics facilitated by electronic-nuclear spin interactions. We develop a combined open quantum systems and electronic structure theory capable of predicting trends in relaxation rates in molecular spin ensembles. We use the Gorini-Kossakowski-Sudarshan-Lindblad master equation and explicitly include electronic structure information in the decoherence channels. We apply this theory to several molecular systems pertinent to contemporary quantum technologies. Our theory provides a framework to describe irreversible relaxation effects in molecular spin systems with applications in quantum information science, quantum sensing, molecular spintronics, and other spin systems dominated by spin-spin relaxation.

Orbital entanglement and the double d-shell effect in binary transition metal molecules

Accurate modeling of transition metal-containing compounds is of great interest due to their wide-ranging and significant applications. These systems present several challenges from an electronic structure perspective, including significant multi-reference characters and many chemically relevant orbitals. A further complication arises from the so-called double d-shell effect, which is known to cause a myriad of issues in the treatment of first-row transition metals with both single- and multi-reference methods. While this effect has been well documented for several decades, a comprehensive understanding of its consequences and underlying causes is still evolving. Here, we characterize the second d-shell effect by analyzing the information entropy of correlated wavefunctions in a periodic series of 3d and 4d transition metal molecular hydrides and oxides. These quantum information techniques provide unique insight into the nuanced electronic structure of these species and are powerful tools for the study of weak and strong correlations in the transition metal d manifold.

Probing Bioinorganic Electron Spin Decoherence Mechanisms with an Fe2S2 Metalloprotein

Recent efforts have sought to develop paramagnetic molecular quantum bits (qubits) as a means to store and manipulate quantum information. Emerging structure-property relationships have shed light on electron spin decoherence mechanisms. While insights within molecular quantum information science have derived from synthetic systems, biomolecular platforms would allow for the study of decoherence phenomena in more complex chemical environments and further leverage molecular biology and protein engineering approaches. Here we have employed the exchange-coupled ST = 1/2 Fe2S2 active site of putidaredoxin, an electron transfer metalloprotein, as a platform for fundamental mechanistic studies of electron spin decoherence toward spin-based biological quantum sensing. At low temperatures, decoherence rates were anisotropic, reflecting a hyperfine-dominated decoherence mechanism, standing in contrast to the anisotropy of molecular systems observed previously. This mechanism provided a pathway for probing spatial effects on decoherence, such as protein vs solvent contributions. Furthermore, we demonstrated spatial sensitivity to single point mutations via site-directed mutagenesis and temporal sensitivity for monitoring solvent isotope exchange. Thus, this study demonstrates a step toward the design and construction of biomolecular quantum sensors.

Luminescent Organic Triplet Diradicals as Optically Addressable Molecular Qubits

Optical-spin interfaces that enable the photoinitialization, coherent microwave manipulation, and optical read-out of ground state spins have been studied extensively in solid-state defects such as diamond nitrogen vacancy (NV) centers and are promising for quantum information science applications. Molecular quantum bits (qubits) offer many advantages over solid-state spin centers through synthetic control of their optical and spin properties and their scalability into well-defined multiqubit arrays. In this work, we report an optical-spin interface in an organic molecular qubit consisting of two luminescent tris(2,4,6-trichlorophenyl)methyl (TTM) radicals connected via the meta-positions of a phenyl linker. The triplet ground state of this system can be photoinitialized in its |T0⟩ state by shelving triplet populations as singlets through spin-selective excited-state intersystem crossing with 80% selectivity from |T+⟩ and |T-⟩. The fluorescence intensity in the triplet manifold is determined by the ground-state polarization, and we show successful optical read-out of the ground-state spin following microwave manipulations by fluorescence-detected magnetic resonance spectroscopy. At 85 K, the lifetime of the polarized ground state is 45 ± 3 μs, and the ground state phase memory time is Tm = 5.9 ± 0.1 μs, which increases to 26.8 ± 1.6 μs at 5 K. These results show that luminescent diradicals with triplet ground states can serve as optically addressable molecular qubits with long spin coherence times, which marks an important step toward the rational design of spin-optical interfaces in organic materials.

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.

Elucidating ultranarrow 2F7/2 to 2F5/2 absorption in ytterbium(iii) complexes

Achieving ultranarrow absorption linewidths in the condensed phase enables optical state preparation of specific non-thermal states, a prerequisite for quantum-enabled technologies. The 4f orbitals of lanthanide(iii) complexes are often referred to as "atom-like," reflecting their isolated nature, and are promising substrates for the optical preparation of specific quantum states. To better understand the photophysical properties of 4f states and assess their potential for quantum applications, theoretical building blocks are required for rapid screening. In this study, an atomic-level perturbative calculation (i.e., spin-orbit crystal field, SOCF) is applied to various Yb(iii) complexes to investigate their linear absorption and emission through a fitting mechanism of their experimentally determined transition energies and oscillator strengths. In particular, the optical properties of (thiolfan)YbCl(THF) (thiolfan = 1,1'-bis(2,4-di-tert-butyl-6-thiomethylenephenoxy)ferrocene), a recently reported complex with an ultranarrow optical linewidth, are computed and compared to those of other Yb(iii) compounds. Through a transition energy sampling study, major contributors to the optical linewidth are identified. We observe particularly isolated f-f transitions and narrow linewidths, which we attribute to two distinct factors. Firstly, the ultra-high atomic similarity of the orbitals involved in the optical transition, along with the presence of an anisotropic crystal field, collectively contribute to the observed narrow transitions. Secondly, we note highly correlated excited-ground energy fluctuations that serve to greatly suppress inhomogeneous line-broadening. This article illustrates how SOCF can be used as a low-cost method to probe the influence of crystal field environment on the optical properties of Yb(iii) complexes to assist the development of novel lanthanide series quantum materials.

Coherent spin-control of S = 1 vanadium and molybdenum complexes

The burgeoning field of quantum sensing hinges on the creation and control of quantum bits. To date, the most well-studied quantum sensors are optically active, paramagnetic defects residing in crystalline hosts. We previously developed analogous optically addressable molecules featuring a ground-state spin-triplet centered on a Cr4+ ion with an optical-spin interface. In this work, we evaluate isovalent V3+ and Mo4+ congeners, which offer unique advantages, such as an intrinsic nuclear spin for V3+ or larger spin-orbit coupling for Mo4+, as optically addressable spin systems. We assess the ground-state spin structure and dynamics for each complex, illustrating that all of these spin-triplet species can be coherently controlled. However, unlike the Cr4+ derivatives, these pseudo-tetrahedral V3+ and Mo4+ complexes exhibit no measurable emission. Coupling absorption spectroscopy with computational predictions, we investigate why these complexes exhibit no detectable photoluminescence. These cumulative results suggest that design of future V3+ complexes should target pseudo-tetrahedral symmetries using bidentate or tridentate ligand scaffolds, ideally with deuterated or fluorinated ligand environments. We also suggest that spin-triplet Mo4+, and by extension W4+, complexes may not be suitable candidate optically addressable qubit systems due to their low energy spin-singlet states. By understanding the failures and successes of these systems, we outline additional design features for optically addressable V- or Mo-based molecules to expand the library of tailor-made quantum sensors.

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.

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.

Ligand field design enables quantum manipulation of spins in Ni2+ complexes

Creating the next generation of quantum systems requires control and tunability, which are key features of molecules. To design these systems, one must consider the ground-state and excited-state manifolds. One class of systems with promise for quantum sensing applications, which require water solubility, are d8 Ni2+ ions in octahedral symmetry. Yet, most Ni2+ complexes feature large zero-field splitting, precluding manipulation by commercial microwave sources due to the relatively large spin-orbit coupling constant of Ni2+ (630 cm-1). Since low lying excited states also influence axial zero-field splitting, D, a combination of strong field ligands and rigidly held octahedral symmetry can ameliorate these challenges. Towards these ends, we performed a theoretical and computational analysis of the electronic and magnetic structure of a molecular qubit, focusing on the impact of ligand field strength on D. Based on those results, we synthesized 1, [Ni(ttcn)2](BF4)2 (ttcn = 1,4,7-trithiacyclononane), which we computationally predict will have a small D (Dcalc = +1.15 cm-1). High-field high-frequency electron paramagnetic resonance (EPR) data yield spin Hamiltonian parameters: gx = 2.1018(15), gx = 2.1079(15), gx = 2.0964(14), D = +0.555(8) cm-1 and E = +0.072(5) cm-1, which confirm the expected weak zero-field splitting. Dilution of 1 in the diamagnetic Zn analogue, [Ni0.01Zn0.99(ttcn)2](BF4)2 (1') led to a slight increase in D to ∼0.9 cm-1. The design criteria in minimizing D in 1via combined computational and experimental methods demonstrates a path forward for EPR and optical addressability of a general class of S = 1 spins.

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.

T1 Anisotropy Elucidates Spin Relaxation Mechanisms in an S = 1 Cr(IV) Optically Addressable Molecular Qubit

Paramagnetic molecules offer unique advantages for quantum information science owing to their spatial compactness, synthetic tunability, room-temperature quantum coherence, and potential for optical state initialization and readout. However, current optically addressable molecular qubits are hampered by rapid spin-lattice relaxation (T1) even at sub-liquid nitrogen temperatures. Here, we use temperature- and orientation-dependent pulsed electron paramagnetic resonance (EPR) to elucidate the negative sign of the ground state zero-field splitting (ZFS) and assign T1 anisotropy to specific types of motion in an optically addressable S = 1 Cr(o-tolyl)4 molecular qubit. The anisotropy displays a distinct sin2(2θ) functional form that is not observed in S = 1/2 Cu(acac)2 or other Cu(II)/V(IV) microwave addressable molecular qubits. The Cr(o-tolyl)4 T1 anisotropy is ascribed to couplings between electron spins and rotational motion in low-energy acoustic or pseudoacoustic phonons. Our findings suggest that rotational degrees of freedom should be suppressed to maximize the coherence temperature of optically addressable qubits.

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.

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

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

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.

Quantum Sensing of Electric Fields Using Spin-Correlated Radical Ion Pairs

Quantum sensing affords the possibility of using quantum entanglement to probe electromagnetic fields with exquisite sensitivity. In this work, we show that a photogenerated spin-correlated radical ion pair (SCRP) can be used to sense an electric field change created at one radical ion of the pair using molecular recognition. The SCRP is generated within a covalent donor-chromophore-acceptor system PXX-PMI-NDI, 1, where PXX = peri-xanthenoxanthene, PMI = 1,6-bis(p-t-butylphenoxy)perylene-3,4-dicarboximide, and NDI = naphthalene-1,8:4,5-bis(dicarboximide). The electron-rich PXX donor in 1 acts as a guest molecule that can be encapsulated selectively by a tetracationic cyclophane ExBox⁴⁺ host to give a supramolecular complex 1 ⊂ ExBox⁴⁺. Selective photoexcitation of the PMI chromophore results in ultrafast generation of the PXX^•+-PMI-NDI^•- SCRP. When PXX is encapsulated by ExBox⁴⁺, the cyclophane generates an electric field that repels the positive charge on PXX^•+ within PXX^•+-PMI-NDI^•-, reducing the SCRP distance, i.e., the distance between the centers-of-charge on the donor and acceptor. Pulse-EPR measurements are used to measure the coherent oscillations created primarily by the electron-electron dipolar coupling in the SCRP, which yields the distance between the two charges (spins) of PXX^•+-PMI-NDI^•-. The experimental results show that the distance between PXX^•+ and NDI^•- decreases when ExBox⁴⁺ encapsulates PXX^•+, which demonstrates that the SCRP can function as a quantum sensor to detect electric field changes in the vicinity of the radical ions.

Quantum Gate Operations on a Spectrally Addressable Photogenerated Molecular Electron Spin-Qubit Pair

Sub-nanosecond photodriven electron transfer from a molecular donor to an acceptor can be used to generate a radical pair (RP) having two entangled electron spins in a well-defined pure initial singlet quantum state to serve as a spin-qubit pair (SQP). Achieving good spin-qubit addressability is challenging because many organic radical ions have large hyperfine couplings (HFCs) in addition to significant g-anisotropy, which results in significant spectral overlap. Moreover, using radicals with g-factors that deviate significantly from that of the free electron results in difficulty generating microwave pulses with sufficiently large bandwidths to manipulate the two spins either simultaneously or selectively as is necessary to implement the controlled-NOT (CNOT) quantum gate essential for quantum algorithms. Here, we address these issues by using a covalently linked donor-acceptor(1)-acceptor(2) (D-A₁-A₂) molecule with significantly reduced HFCs that uses fully deuterated peri-xanthenoxanthene (PXX) as D, naphthalenemonoimide (NMI) as A₁, and a C₆₀ derivative as A₂. Selective photoexcitation of PXX within PXX-d₉-NMI-C₆₀ results in sub-nanosecond, two-step electron transfer to generate the long-lived PXX^•+-d₉-NMI-C₆₀^•- SQP. Alignment of PXX^•+-d₉-NMI-C₆₀^•- in the nematic liquid crystal 4-cyano-4'-(n-pentyl)biphenyl (5CB) at cryogenic temperatures results in well-resolved, narrow resonances for each electron spin. We demonstrate both single-qubit gate and two-qubit CNOT gate operations using both selective and nonselective Gaussian-shaped microwave pulses and broadband spectral detection of the spin states following the gate operations.

Quantum Mimicry With Inorganic Chemistry

Quantum objects, such as atoms, spins, and subatomic particles, have important properties due to their unique physical properties that could be useful for many different applications, ranging from quantum information processing to magnetic resonance imaging. Molecular species also exhibit quantum properties, and these properties are fundamentally tunable by synthetic design, unlike ions isolated in a quadrupolar trap, for example. In this comment, we collect multiple, distinct, scientific efforts into an emergent field that is devoted to designing molecules that mimic the quantum properties of objects like trapped atoms or defects in solids. Mimicry is endemic in inorganic chemistry and featured heavily in the research interests of groups across the world. We describe a new field of using inorganic chemistry to design molecules that mimic the quantum properties (e.g. the lifetime of spin superpositions, or the resonant frequencies thereof) of other quantum objects, "quantum mimicry." In this comment, we describe the philosophical design strategies and recent exciting results from application of these strategies.

Electronic Spin Qubit Candidates Arrayed within Layered Two-Dimensional Polymers

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

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

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

Multiconfiguration Pair-Density Functional Theory for Chromium(IV) Molecular Qubits

Pseudotetrahedral organometallic complexes containing chromium(IV) and aryl ligands have been experimentally identified as promising molecular qubit candidates. Here we present a computational protocol based on multiconfiguration pair-density functional theory for computing singlet-triplet gaps and zero-field splitting (ZFS) parameters in Cr(IV) aryl complexes. We find that two multireference methods, multistate complete active space second-order perturbation theory (MS-CASPT2) and hybrid multistate pair-density functional theory (HMS-PDFT), perform better than Kohn-Sham density functional theory for singlet-triplet gaps. Despite the very small values of the ZFS parameters, both multireference methods performed qualitatively well. MS-CASPT2 and HMS-PDFT performed particularly well for predicting the trend in the ratio of the rhombic and axial ZFS parameters, |E/D|. We have also investigated the dependence and sensitivity of the calculated ZFS parameters on the active space and the molecular geometry. The methodologies outlined here can guide future prediction of ZFS parameters in molecular qubit candidates.

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.

Spin-flip luminescence

In molecular photochemistry, charge-transfer emission is well understood and widely exploited. In contrast, luminescent metal-centered transitions only came into focus in recent years. This gave rise to strongly phosphorescent Cr^III complexes with a d³ electronic configuration featuring luminescent metal-centered excited states which are characterized by the flip of a single spin. These so-called spin-flip emitters possess unique properties and require different design strategies than traditional charge-transfer phosphors. In this review, we give a brief introduction to ligand field theory as a framework to understand this phenomenon and outline prerequisites for efficient spin-flip emission including ligand field strength, symmetry, intersystem crossing and common deactivation pathways using Cr^III complexes as instructive examples. The recent progress and associated challenges of tuning the energies of emissive excited states and of emerging applications of the unique photophysical properties of spin-flip emitters are discussed. Finally, we summarize the current state-of-the-art and challenges of spin-flip emitters beyond Cr^III with d², d³, d⁴ and d⁸ electronic configuration, where we mainly cover pseudooctahedral molecular complexes of V, Mo, W, Mn, Re and Ni, and highlight possible future research opportunities.

Pushing steric limits in osmium(IV) tetraaryl complexes

Investigations into the reactivity, properties, and applications of osmium(IV) tetraaryl complexes have been hampered by their low yielding syntheses from volatile and toxic OsO4 (typically ≤34%). Here we show that...