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.

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.

First-Principles Investigation of Spin-Phonon Coupling in Vanadium-Based Molecular Spin Quantum Bits.

Paramagnetic molecules can show long spin-coherence times, which make them good candidates as quantum bits (qubits). Reducing the efficiency of the spin-phonon interaction is the primary challenge toward achieving long coherence times over a wide temperature range in soft molecular lattices. The lack of a microscopic understanding about the role of vibrations in spin relaxation strongly undermines the possibility of chemically designing better-performing molecular qubits. Here we report a first-principles characterization of the main mechanism contributing to the spin-phonon coupling for a class of vanadium(IV) molecular qubits. Post-Hartree-Fock and density functional theory methods are used to determine the effect of both intermolecular and intramolecular vibrations on modulation of the Zeeman energy for four molecules showing different coordination geometries and ligands. This comparative study provides the first insight into the role played by coordination geometry and ligand-field strength in determining the spin-lattice relaxation time of molecular qubits, opening an avenue to the rational design of new compounds.

Scaling Up Electronic Spin Qubits into a Three-Dimensional Metal-Organic Framework.

Practical implementation of highly coherent molecular spin qubits for challenging technological applications, such as quantum information processing or quantum sensing, requires precise organization of electronic qubit molecular components into extended frameworks. Realization of spatial control over qubit-qubit distances can be achieved by coordination chemistry approaches through an appropriate choice of the molecular building blocks. However, translating single qubit molecular building units into extended arrays does not guarantee a priori retention of long quantum coherence and spin-lattice relaxation times due to the introduced modifications over qubit-qubit reciprocal distances and molecular crystal lattice phonon structure. In this work, we report the preparation of a three-dimensional (3D) metal-organic framework (MOF) based on vanadyl qubits, [VO(TCPP-Zn2-bpy)] (TCPP = tetracarboxylphenylporphyrinate; bpy = 4,4'-bipyridyl) (1), and the investigation of how such structural modifications influence qubits' performances. This has been done through a multitechnique approach where the structure and properties of a representative molecular building block of formula [VO(TPP)] (TPP = tetraphenylporphyrinate) (2) have been compared with those of the 3D MOF 1. Pulsed electron paramagnetic resonance measurements on magnetically diluted samples in titanyl isostructural analogues revealed that coherence times are retained almost unchanged for 1 with respect to 2 up to room temperature, while the temperature dependence of the spin-lattice relaxation time revealed insights into the role of low-energy vibrations, detected through terahertz spectroscopy, on the spin dynamics.

Structural Effects on the Spin Dynamics of Potential Molecular Qubits.

Control of spin-lattice magnetic relaxation is crucial to observe long quantum coherence in spin systems at reasonable temperatures. Such a control is most often extremely difficult to achieve, because of the coexistence of several relaxation mechanisms, that is direct, Raman, and Orbach. These are not always easy to relate to the energy states of the investigated system, because of the contribution to the relaxation of additional spin-phonon coupling phenomena mediated by intramolecular vibrations. In this work, we have investigated the effect of slight changes on the molecular structure of four vanadium(IV)-based potential spin qubits on their spin dynamics, studied by alternate current (AC) susceptometry. The analysis of the magnetic field dependence of the relaxation time correlates well with the low-energy vibrational modes experimentally detected by time-domain THz spectroscopy. This confirms and extends our preliminary observations on the role played by spin-vibration coupling in determining the fine structure of the spin-lattice relaxation time as a function of the magnetic field, for S = 1/2 potential spin qubits. This study represents a step forward in the use of low-energy vibrational spectroscopy as a prediction tool for the design of molecular spin qubits with long-lived quantum coherence. Indeed, quantum coherence times of ca. 4.0-6.0 µs in the 4-100 K range are observed for the best performing vanadyl derivatives identified through this multitechnique approach.

Spin Dynamics and Low Energy Vibrations: Insights from Vanadyl-Based Potential Molecular Qubits.

Here we report the investigation of the magnetization dynamics of a vanadyl complex with diethyldithiocarbamate (Et2dtc-) ligands, namely [VO(Et2dtc)2] (1), in both solid-state and frozen solution. This showed an anomalous and unprecedentedly observed field dependence of the relaxation time, which was modeled with three contributions to the relaxation mechanism. The temperature dependence of the weight of the two processes dominating at low fields was found to well correlate with the low energy vibrations as determined by THz spectroscopy. This detailed experimental comparative study represents a fundamental step to understand the spin dynamics of potential molecular quantum bits, and enriches the guidelines to design molecule-based systems with enhanced quantum coherence.

Interaction Study of Phospholipid Membranes with an N-Glucosylated ß-Turn Peptide Structure Detecting Autoantibodies Biomarkers of Multiple Sclerosis.

The interaction of lipid environments with the type I' ß-turn peptide structure called CSF114 and its N-glucosylated form CSF114(Glc), previously developed as a synthetic antigenic probe recognizing specific autoantibodies in a subpopulation of multiple sclerosis patients' serum, was investigated by fluorescence spectroscopy and electrochemical experiments using large unilamellar vesicles, mercury supported lipid self-assembled monolayers (SAMs) and tethered bilayer lipid membranes (tBLMs). The synthetic antigenic probe N-glucosylated peptide CSF114(Glc) and its unglucosylated form interact with the polar heads of lipid SAMs of dioleoylphosphatidylcholine at nonzero transmembrane potentials, probably establishing a dual electrostatic interaction of the trimethylammonium  and phosphate groups of the phosphatidylcholine polar head with the Glu5 and His8 residues on the opposite ends of the CSF114(Glc) ß-turn encompassing residues 6-9. His8 protonation at pH 7 eliminates this dual interaction. CSF114(Glc) is adsorbed on top of SAMs of mixtures of dioleoylphosphatidylcholine with sphingomyelin, an important component of myelin, whose proteins are hypothesized to undergo an aberrant N-glucosylation triggering the autoimmune response. Incorporation of the type I' ß-turn peptide structure CSF114 into lipid SAMs by potential scans of electrochemical impedance spectroscopy induces defects causing a slight permeabilization toward cadmium ions. The N-glucopeptide CSF114(Glc) does not affect  tBLMs to a detectable extent.