Chromium(iii)-based potential molecular quantum bits with long coherence times

Electronic Structure and Excited-State Dynamics of the NIR-II Emissive Molybdenum(III) Analogue to the Molecular Ruby

Photoactive chromium(III) complexes saw a conceptual breakthrough with the discovery of the prototypical molecular ruby mer-[Cr(ddpd)2]3+ (ddpd = N,N'-dimethyl-N,N'-dipyridin-2-ylpyridine-2,6-diamine), which shows intense long-lived near-infrared (NIR) phosphorescence from metal-centered spin-flip states. In contrast to the numerous studies on chromium(III) photophysics, only 10 luminescent molybdenum(III) complexes have been reported so far. Here, we present the synthesis and characterization of mer-MoX3(ddpd) (1, X = Cl; 2, X = Br) and cisfac-[Mo(ddpd)2]3+ (cisfac-[3]3+), an isomeric heavy homologue of the prototypical molecular ruby. For cisfac-[3]3+, we found strong zero-field splitting using magnetic susceptibility measurements and electron paramagnetic resonance spectroscopy. Electronic spectra covering the spin-forbidden transitions show that the spin-flip states in mer-1, mer-2, and cisfac-[3]3+ are much lower in energy than those in comparable chromium(III) compounds. While all three complexes show weak spin-flip phosphorescence in NIR-II, the emission of cisfac-[3]3+ peaking at 1550 nm is particularly low in energy. Femtosecond transient absorption spectroscopy reveals a short excited-state lifetime of 1.4 ns, 6 orders of magnitude shorter than that of mer-[Cr(ddpd)2]3+. Using density functional theory and ab initio multireference calculations, we break down the reasons for this disparity and derive principles for the design of future stable photoactive molybdenum(III) complexes.

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.

Towards Luminescent Vanadium(II) Complexes with Slow Magnetic Relaxation and Quantum Coherence

Molecular entities with doublet or triplet ground states find increasing interest as potential molecular quantum bits (qubits). Complexes with higher multiplicity might even function as qudits and serve to encode further quantum bits. Vanadium(II) ions in octahedral ligand fields with quartet ground states and small zero-field splittings qualify as qubits with optical read out thanks to potentially luminescent spin-flip states. We identified two V²⁺ complexes [V(ddpd)₂ ]²⁺ with the strong field ligand N,N'-dimethyl-N,N'-dipyridine-2-yl-pyridine-2,6-diamine (ddpd) in two isomeric forms (cis-fac and mer) as suitable candidates. The energy gaps between the two lowest Kramers doublets amount to 0.2 and 0.5 cm^-1 allowing pulsed EPR experiments at conventional Q-band frequencies (35 GHz). Both isomers possess spin-lattice relaxation times T₁ of around 300 μs and a phase memory time T_M of around 1 μs at 5 K. Furthermore, the mer isomer displays slow magnetic relaxation in an applied field of 400 mT. While the vanadium(III) complexes [V(ddpd)₂ ]³⁺ are emissive in the near-IR-II region, the [V(ddpd)₂ ]²⁺ complexes are non-luminescent due to metal-to-ligand charge transfer admixture to the spin-flip states.

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.

Shedding Light on the Oxidizing Properties of Spin-Flip Excited States in a CrIII Polypyridine Complex and Their Use in Photoredox Catalysis

The photoredox activity of well-known Ru^II complexes stems from metal-to-ligand charge transfer (MLCT) excited states, in which a ligand-based electron can initiate chemical reductions and a metal-centered hole can trigger oxidations. Cr^III polypyridines show similar photoredox properties, although they have fundamentally different electronic structures. Their photoactive excited state is of spin-flip nature, differing from the electronic ground state merely by a change of one electron spin, but with otherwise identical d-orbital occupancy. We find that the driving-force dependence for photoinduced electron transfer from 10 different donors to a spin-flip excited state of a Cr^III complex is very similar to that for a Ru^II polypyridine, and thereby validate the concept of estimating the redox potential of d³ spin-flip excited states in analogous manner as for the MLCT states of d⁶ compounds. Building on this insight, we use our Cr^III complex for photocatalytic reactions not previously explored with this compound class, including the aerobic bromination of methoxyaryls, oxygenation of 1,1,2,2-tetraphenylethylene, aerobic hydroxylation of arylboronic acids, and the vinylation of N-phenyl pyrrolidine. This work contributes to understanding the fundamental photochemical properties of first-row transition-metal complexes in comparison to well-explored precious-metal-based photocatalysts.

Complex-as-Ligand Strategy as a Tool for the Design of a Binuclear Nonsymmetrical Chromium(III) Assembly: Near-Infrared Double Emission and Intramolecular Energy Transfer

The chromium(III) polypyridyl complexes are appealing for their long-lived near-infrared (NIR) emission reaching the millisecond range and for the strong circularly polarized luminescence of their isolated enantiomers. However, harnessing those properties in functional polynuclear Cr^III devices remains mainly inaccessible because of the lack of synthetic methods for their design and functionalization. Even the preparation and investigation of most basic nonsymmetrical Cr^III dyads exhibiting directional intramolecular intermetallic energy transfer remain unexplored. Taking advantage of the inertness of heteroleptic chromium(III) polypyridyl building blocks, we herein adapt the "complex-as-ligand" strategy, largely used with precious 4d and 5d metals, for the preparation of a binuclear nonsymmetrical Cr^III complex (3d metal). The resulting [(phen)₂Cr(L)Cr(tpy)]⁶⁺ dyad shows dual long-lived NIR emission and a directional intermetallic energy transfer that is controlled by the specific arrangements of the different coordination spheres. This strategy opens a route for building predetermined polynuclear assemblies with this earth-abundant metal.

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.

Molecular Ruby: Exploring the Excited State Landscape

The discovery of the highly NIR-luminescent Molecular Ruby [Cr(ddpd)2]3+ 13+ (ddpd = N,N’-dimethyl-N,N’-dipyridine-2-ylpyridine-2,6-diamine) has been a milestone in the development of earth-abundant luminophors and has led to important new impulses...

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.

Radiofrequency to Microwave Coherent Manipulation of an Organometallic Electronic Spin Qubit Coupled to a Nuclear Qudit

We report here a comprehensive characterization of a 3d organometallic complex, [V(Cp)2Cl2] (Cp = cyclopentadienyl), which can be considered as a prototypical multilevel nuclear qudit (nuclear spin I = 7/2) hyperfine coupled to an electronic qubit (electronic spin S = 1/2). By combining complementary magnetic resonant techniques, such as pulsed electron paramagnetic resonance (EPR) and broadband nuclear magnetic resonance (NMR), we extensively characterize its Spin Hamiltonian parameters and its electronic and nuclear spin dynamics. Moreover, we demonstrate the possibility to manipulate the qubit-qudit multilevel structure by resonant microwave and radiofrequency pulses, driving coherent Rabi oscillations between targeted electronuclear states. The obtained results demonstrate that this simple complex is a promising candidate for quantum computing applications.

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 Crossover and Long-Lived Excited States in a Reduced Molecular Ruby

The chromium(III) complex [Cr^III(ddpd)₂]³⁺ (molecular ruby; ddpd=N,N′‐dimethyl‐N,N′‐dipyridine‐2‐yl‐pyridine‐2,6‐diamine) is reduced to the genuine chromium(II) complex [Cr^II(ddpd)₂]²⁺ with d⁴ electron configuration. This reduced molecular ruby represents one of the very few chromium(II) complexes showing spin crossover (SCO). The reversible SCO is gradual with T_1/2 around room temperature. The low‐spin and high‐spin chromium(II) isomers exhibit distinct spectroscopic and structural properties (UV/Vis/NIR, IR, EPR spectroscopies, single‐crystal XRD). Excitation of [Cr^II(ddpd)₂]²⁺ with UV light at 20 and 290 K generates electronically excited states with microsecond lifetimes. This initial study on the unique reduced molecular ruby paves the way for thermally and photochemically switchable magnetic systems based on chromium complexes complementing the well‐established iron(II) SCO systems.

Reversible four-color electrochromism triggered by the electrochemical multi-step redox of Cr-based metallo-supramolecular polymers

Four color electrochromism (yellow, magenta, blue, and navy) has been achieved in Cr(iii)-based metallo-supramolecular polymers (polyCr), which were synthesized by 1 : 1 complexation of Cr ions and 1,4-di[[2,2′:6′,2′′-terpyridin]-4′-yl]benzene (L).

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

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