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.

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.

Electronic Structures of Nickel(II)-Bis(indanyloxazoline)-dihalide Catalysts: Understanding Ligand Field Contributions That Promote C(sp2)-C(sp3) Cross-Coupling.

NiII(IB) dihalide [IB = (3aR,3a'R,8aS,8a'S)-2,2'-(cyclopropane-1,1-diyl)bis(3a,8a-dihydro-8H-indeno[1,2-d]-oxazole)] complexes are representative of a growing class of first-row transition-metal catalysts for the enantioselective reductive cross-coupling of C(sp2) and C(sp3) electrophiles. Recent mechanistic studies highlight the complexity of these ground-state cross-couplings but also illuminate new reactivity pathways stemming from one-electron redox and their significant sensitivities to reaction conditions. For the first time, a diverse array of spectroscopic methods coupled to electrochemistry have been applied to NiII-based precatalysts to evaluate specific ligand field effects governing key Ni-based redox potentials. We also experimentally demonstrate DMA solvent coordination to catalytically relevant Ni complexes. Coordination is shown to favorably influence key redox-based reaction steps and prevent other deleterious Ni-based equilibria. Combined with electronic structure calculations, we further provide a direct correlation between reaction intermediate frontier molecular orbital energies and cross-coupling yields. Considerations developed herein demonstrate the use of synergic spectroscopic and electrochemical methods to provide concepts for catalyst ligand design and rationalization of reaction condition optimization.

Photogenerated Ni(I)-Bipyridine Halide Complexes: Structure-Function Relationships for Competitive C(sp2)-Cl Oxidative Addition and Dimerization Reactivity Pathways.

We report the facile photochemical generation of a library of Ni(I)-bpy halide complexes (Ni(I)(Rbpy)X (R = t-Bu, H, MeOOC; X = Cl, Br, I) and benchmark their relative reactivity toward competitive oxidative addition and off-cycle dimerization pathways. Structure-function relationships between the ligand set and reactivity are developed, with particular emphasis on rationalizing previously uncharacterized ligand-controlled reactivity toward high energy and challenging C(sp2)-Cl bonds. Through a dual Hammett and computational analysis, the mechanism of the formal oxidative addition is found to proceed through an SNAr-type pathway, consisting of a nucleophilic two-electron transfer between the Ni(I) 3d(z2) orbital and the Caryl-Cl σ* orbital, which contrasts the mechanism previously observed for activation of weaker C(sp2)-Br/I bonds. The bpy substituent provides a strong influence on reactivity, ultimately determining whether oxidative addition or dimerization even occurs. Here, we elucidate the origin of this substituent influence as arising from perturbations to the effective nuclear charge (Zeff) of the Ni(I) center. Electron donation to the metal decreases Zeff, which leads to a significant destabilization of the entire 3d orbital manifold. Decreasing the 3d(z2) electron binding energies leads to a powerful two-electron donor to activate strong C(sp2)-Cl bonds. These changes also prove to have an analogous effect on dimerization, with decreases in Zeff leading to more rapid dimerization. Ligand-induced modulation of Zeff and the 3d(z2) orbital energy is thus a tunable target by which the reactivity of Ni(I) complexes can be altered, providing a direct route to stimulate reactivity with even stronger C-X bonds and potentially unveiling new ways to accomplish Ni-mediated photocatalytic cycles.

Illuminating Ligand Field Contributions to Molecular Qubit Spin Relaxation via T1 Anisotropy.

Electron spin relaxation in paramagnetic transition metal complexes constitutes a key limitation on the growth of molecular quantum information science. However, there exist very few experimental observables for probing spin relaxation mechanisms, leading to a proliferation of inconsistent theoretical models. Here we demonstrate that spin relaxation anisotropy in pulsed electron paramagnetic resonance is a powerful spectroscopic probe for molecular spin dynamics across a library of highly coherent Cu(II) and V(IV) complexes. Neither the static spin Hamiltonian anisotropy nor contemporary computational models of spin relaxation are able to account for the experimental T1 anisotropy. Through analysis of the spin-orbit coupled wave functions, we derive an analytical theory for the T1 anisotropy that accurately reproduces the average experimental anisotropy of 2.5. Furthermore, compound-by-compound deviations from the average anisotropy provide a promising approach for observing specific ligand field and vibronic excited state coupling effects on spin relaxation. Finally, we present a simple density functional theory workflow for computationally predicting T1 anisotropy. Analysis of spin relaxation anisotropy leads to deeper fundamental understanding of spin-phonon coupling and relaxation mechanisms, promising to complement temperature-dependent relaxation rates as a key metric for understanding molecular spin qubits.

Bootstrap methods for quantifying the uncertainty of binding constants in the hard modeling of spectrophotometric titration data.

Equilibrium hard modeling of spectrophotometric titration data with binding parameters (ΔG° or logK values) involves nonlinear mathematical relationships and correlated experimental uncertainties. Therefore, uncertainty quantification techniques based on standard error computation substantially underestimate the true error for the calculated binding parameters. We show that the bootstrapping technique can provide accurate uncertainty quantification with no a priori knowledge of experimental error levels. Monte Carlo studies on simulated data show that bootstrapping the chemical solutions, whether on the data or residuals, handles absorbance error, transmittance error, and composition error well, producing asymmetric confidence intervals that correctly assess the true uncertainty. Additionally, stock solution error is handled well if it is present with other forms of error. Confidence interval bands for molar absorptivity curves can likewise be calculated. Analogous bootstrapping studies on real datasets confirm that the 95% confidence intervals match the variance observed from experimental replicates, though bootstrapping on the residuals should be used for smaller datasets. Bootstrapping along the titration axis should be used to estimate uncertainty whenever binding parameters are ascertained from titration datasets.

Hard Ferromagnetism Down to the Thinnest Limit of Iron-Intercalated Tantalum Disulfide.

Two-dimensional (2D) magnetic crystals hold promise for miniaturized and ultralow power electronic devices that exploit spin manipulation. In these materials, large, controllable magnetocrystalline anisotropy (MCA) is a prerequisite for the stabilization and manipulation of long-range magnetic order. In known 2D magnetic crystals, relatively weak MCA typically results in soft ferromagnetism. Here, we demonstrate that ferromagnetic order persists down to the thinnest limit of FexTaS2 (Fe-intercalated bilayer 2H-TaS2) with giant coercivities up to 3 T. We prepare Fe-intercalated TaS2 by chemical intercalation of van der Waals-layered 2H-TaS2 crystals and perform variable-temperature transport, transmission electron microscopy, and confocal Raman spectroscopy measurements to shed new light on the coupled effects of dimensionality, degree of intercalation, and intercalant order/disorder on the hard ferromagnetic behavior of FexTaS2. More generally, we show that chemical intercalation gives access to a rich synthetic parameter space for low-dimensional magnets, in which magnetic properties can be tailored by the choice of the host material and intercalant identity/amount, in addition to the manifold distinctive degrees of freedom available in atomically thin, van der Waals crystals.

Elucidating the Mechanism of Excited-State Bond Homolysis in Nickel-Bipyridine Photoredox Catalysts.

Ni 2,2'-bipyridine (bpy) complexes are commonly employed photoredox catalysts of bond-forming reactions in organic chemistry. However, the mechanisms by which they operate are still under investigation. One potential mode of catalysis is via entry into Ni(I)/Ni(III) cycles, which can be made possible by light-induced, excited-state Ni(II)-C bond homolysis. Here, we report experimental and computational analyses of a library of Ni(II)-bpy aryl halide complexes, Ni(Rbpy)(R'Ph)Cl (R = MeO, t-Bu, H, MeOOC; R' = CH3, H, OMe, F, CF3), to illuminate the mechanism of excited-state bond homolysis. At given excitation wavelengths, photochemical homolysis rate constants span 2 orders of magnitude across these structures and correlate linearly with Hammett parameters of both bpy and aryl ligands, reflecting structural control over key metal-to-ligand charge-transfer (MLCT) and ligand-to-metal charge-transfer (LMCT) excited-state potential energy surfaces (PESs). Temperature- and wavelength-dependent investigations reveal moderate excited-state barriers (ΔH‡ ∼ 4 kcal mol-1) and a minimum energy excitation threshold (∼55 kcal mol-1, 525 nm), respectively. Correlations to electronic structure calculations further support a mechanism in which repulsive triplet excited-state PESs featuring a critical aryl-to-Ni LMCT lead to bond rupture. Structural control over excited-state PESs provides a rational approach to utilize photonic energy and leverage excited-state bond homolysis processes in synthetic chemistry.

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.

Strain fields in twisted bilayer graphene.

Van der Waals heteroepitaxy allows deterministic control over lattice mismatch or azimuthal orientation between atomic layers to produce long-wavelength superlattices. The resulting electronic phases depend critically on the superlattice periodicity and localized structural deformations that introduce disorder and strain. In this study we used Bragg interferometry to capture atomic displacement fields in twisted bilayer graphene with twist angles <2°. Nanoscale spatial fluctuations in twist angle and uniaxial heterostrain were statistically evaluated, revealing the prevalence of short-range disorder in moiré heterostructures. By quantitatively mapping strain tensor fields, we uncovered two regimes of structural relaxation and disentangled the electronic contributions of constituent rotation modes. Further, we found that applied heterostrain accumulates anisotropically in saddle-point regions, generating distinctive striped strain phases. Our results establish the reconstruction mechanics underpinning the twist-angle-dependent electronic behaviour of twisted bilayer graphene and provide a framework for directly visualizing structural relaxation, disorder and strain in moiré materials.

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.