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.

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

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

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

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

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.

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.

Comprehensive Studies of Magnetic Transitions and Spin-Phonon Couplings in the Tetrahedral Cobalt Complex Co(AsPh3)2I2

A combination of inelastic neutron scattering (INS), far-IR magneto-spectroscopy (FIRMS), and Raman magneto-spectroscopy (RaMS) has been used to comprehensively probe magnetic excitations in Co(AsPh₃)₂I₂ (1), a reported single-molecule magnet (SMM). With applied field, the magnetic zero-field splitting (ZFS) peak (2D') shifts to higher energies in each spectroscopy. INS placed the ZFS peak at 54 cm^-1, as revealed by both variable-temperature (VT) and variable-magnetic-field data, giving results that agree well with those from both far-IR and Raman studies. Both FIRMS and RaMS also reveal the presence of multiple spin-phonon couplings as avoided crossings with neighboring phonons. Here, phonons refer to both intramolecular and lattice vibrations. The results constitute a rare case in which the spin-phonon couplings are observed with both Raman-active (g modes) and far-IR-active phonons (u modes; space group P2₁/c, no. 14, Z = 4 for 1). These couplings are fit using a simple avoided crossing model with coupling constants of ca. 1-2 cm^-1. The combined spectroscopies accurately determine the magnetic excited level and the interaction of the magnetic excitation with phonon modes. Density functional theory (DFT) phonon calculations compare well with INS, allowing for the assignment of the modes and their symmetries. Electronic calculations elucidate the nature of ZFS in the complex. Features of different techniques to determine ZFS and other spin-Hamiltonian parameters in transition-metal complexes are summarized.

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.

Toward exact predictions of spin-phonon relaxation times: An ab initio implementation of open quantum systems theory

Spin-phonon coupling is the main driver of spin relaxation and decoherence in solid-state semiconductors at finite temperature. Controlling this interaction is a central problem for many disciplines, ranging from magnetic resonance to quantum technologies. Spin relaxation theories have been developed for almost a century but often use a phenomenological description of phonons and their coupling to spin, resulting in a nonpredictive tool and hindering our detailed understanding of spin dynamics. Here, we combine time-local master equations up to the fourth order with advanced electronic structure methods and perform predictions of spin-phonon relaxation time for a series of solid-state coordination compounds based on both transition metals and lanthanide Kramers ions. The agreement between experiments and simulations demonstrates that an accurate, universal, and fully ab initio implementation of spin relaxation theory is possible, thus paving the way to a systematic study of spin-phonon relaxation in solid-state materials.

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.

Generating Pure Spin Current in Heterojunction Organic Solar Cells

We propose a mechanism for generating pure spin current in heterojunction organic solar cells, with the donor and acceptor both being degenerate ground-state polymers; thus, solitons can be formed. This mechanism contains the following steps: (i) the donor is photoexcited to create the electron-hole (e-h) pairs; (ii) the excited electrons are transferred to the acceptor; (iii) the net charges in the donor and acceptor are evolved into the localized charged solitons; (iv) the intermolecule bias is applied to drive the transferred electrons back to donor, and concomitantly, charged solitons are converted to neutral solitons. Here, the on-site Coulomb interaction plays an important role in ensuring the neutral solitons' spins in the donor and acceptor are oppositely polarized. Because spins are separated between the donor and acceptor without any charge separations, pure spin current can be formed. Our mechanism opens a new avenue for exploring potential organic spintronic devices.

Tunable Cr4+ Molecular Color Centers

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

The Impact of Ligand Field Symmetry on Molecular Qubit Coherence

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

Temperature Dependence of Spin-Phonon Coupling in [VO(acac)2]: A Computational and Spectroscopic Study

Molecular electronic spins are good candidates as qubits since they are characterized by a large tunability of their electronic and magnetic properties through a rational chemical design. Coordination compounds of light transition metals are promising systems for spin-based quantum information technologies, thanks to their long spin coherence times up to room temperature. Our work aims at presenting an in-depth study on how the spin-phonon coupling in vanadyl-acetylacetonate, [VO(acac)₂], can change as a function of temperature using terahertz time-domain spectroscopy and density functional theory (DFT) calculations. Powder THz spectra were recorded between 10 and 300 K. The temperature dependence of vibrational frequencies was then accounted for in the periodic DFT calculations using unit-cell parameters measured at two different temperatures and the optimized ones, as usually reported in the literature. In this way, it was possible to calculate the observed THz anharmonic frequency shift with high accuracy. The overall differences in the spin-phonon coupling magnitudes as a function of temperature were also highlighted showing that the computed trends have to be ascribed to the anisotropic variation of cell parameters.

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.

A Complete Ab Initio View of Orbach and Raman Spin-Lattice Relaxation in a Dysprosium Coordination Compound

The unique electronic and magnetic properties of lanthanide molecular complexes place them at the forefront of the race toward high-temperature single-molecule magnets and magnetic quantum bits. The design of compounds of this class has so far being almost exclusively driven by static crystal field considerations, with an emphasis on increasing the magnetic anisotropy barrier. Now that this guideline has reached its maximum potential, a deeper understanding of spin-phonon relaxation mechanisms presents itself as key in order to drive synthetic chemistry beyond simple intuition. In this work, we compute relaxation times fully ab initio and unveil the nature of all spin-phonon relaxation mechanisms, namely Orbach and Raman pathways, in a prototypical Dy single-molecule magnet. Computational predictions are in agreement with the experimental determination of spin relaxation time and crystal field anisotropy, and show that Raman relaxation, dominating at low temperature, is triggered by low-energy phonons and little affected by further engineering of crystal field axiality. A comprehensive analysis of spin-phonon coupling mechanism reveals that molecular vibrations beyond the ion’s first coordination shell can also assume a prominent role in spin relaxation through an electrostatic polarization effect. Therefore, this work shows the way forward in the field by delivering a novel and complete set of chemically sound design rules tackling every aspect of spin relaxation at any temperature.

New Materials and Effects in Molecular Nanomagnets

Molecular magnets are a relatively new class of purely organic or metallo-organic materials, showing magnetism even without an external magnetic field. This interdisciplinary field between chemistry and physics has been gaining increased interest since the 1990s. While bulk molecular magnets are usually hard to build because of their molecular structures, low-dimensional molecular magnets are often easier to construct, down to dot-like (zero-dimensional) structures, which are investigated by different scanning probe technologies. On these scales, new effects such as superparamagnetic behavior or coherent switching during magnetization reversal can be recognized. Here, we give an overview of the recent advances in molecular nanomagnets, starting with single-molecule magnets (0D), typically based on Mn12, Fe8, or Mn4, going further to single-chain magnets (1D) and finally higher-dimensional molecular nanomagnets. This review does not aim to give a comprehensive overview of all research fields dealing with molecular nanomagnets, but instead aims at pointing out diverse possible materials and effects in order to stimulate new research in this broad field of nanomagnetism.

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

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

Applying Unconventional Spectroscopies to the Single-Molecule Magnets, Co(PPh3 )2 X2 (X=Cl, Br, I): Unveiling Magnetic Transitions and Spin-Phonon Coupling

Large separation of magnetic levels and slow relaxation in metal complexes are desirable properties of single-molecule magnets (SMMs). Spin-phonon coupling (interactions of magnetic levels with phonons) is ubiquitous, leading to magnetic relaxation and loss of memory in SMMs and quantum coherence in qubits. Direct observation of magnetic transitions and spin-phonon coupling in molecules is challenging. We have found that far-IR magnetic spectra (FIRMS) of Co(PPh₃ )₂ X₂ (Co-X; X=Cl, Br, I) reveal rarely observed spin-phonon coupling as avoided crossings between magnetic and u-symmetry phonon transitions. Inelastic neutron scattering (INS) gives phonon spectra. Calculations using VASP and phonopy programs gave phonon symmetries and movies. Magnetic transitions among zero-field split (ZFS) levels of the S=3/2 electronic ground state were probed by INS, high-frequency and -field EPR (HFEPR), FIRMS, and frequency-domain FT terahertz EPR (FD-FT THz-EPR), giving magnetic excitation spectra and determining ZFS parameters (D, E) and g values. Ligand-field theory (LFT) was used to analyze earlier electronic absorption spectra and give calculated ZFS parameters matching those from the experiments. DFT calculations also gave spin densities in Co-X, showing that the larger Co(II) spin density in a molecule, the larger its ZFS magnitude. The current work reveals dynamics of magnetic and phonon excitations in SMMs. Studies of such couplings in the future would help to understand how spin-phonon coupling may lead to magnetic relaxation and develop guidance to control such coupling.

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

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

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

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

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

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

Spin dynamics in single-molecule magnets and molecular qubits

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

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

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