Self-Consistent Field Approach for the Variational Quantum Eigensolver: Orbital Optimization Goes Adaptive.

We present a self-consistent field (SCF) approach within the adaptive derivative-assembled problem-tailored ansatz variational quantum eigensolver (ADAPT-VQE) framework for efficient quantum simulations of chemical systems on near-term quantum computers. To this end, our ADAPT-VQE-SCF approach combines the idea of generating an ansatz with a small number of parameters, resulting in shallow-depth quantum circuits with a direct minimization of an energy expression that is correct to second order with respect to changes in the molecular orbital basis. Our numerical analysis, including calculations for the transition-metal complex ferrocene [Fe (C5H5)2], indicates that convergence in the self-consistent orbital optimization loop can be reached without a considerable increase in the number of two-qubit gates in the quantum circuit by comparison to a VQE optimization in the initial molecular orbital basis. Moreover, the orbital optimization can be carried out simultaneously within each iteration of the ADAPT-VQE cycle. ADAPT-VQE-SCF thus allows us to implement a routine analogous to the complete active space SCF, a cornerstone of state-of-the-art computational chemistry, in a hardware-efficient manner on near-term quantum computers. Hence, ADAPT-VQE-SCF paves the way toward a paradigm shift for quantitative quantum-chemistry simulations on quantum computers by requiring fewer qubits and opening up for the use of large and flexible atomic orbital basis sets in contrast to earlier methods that are predominantly based on the idea of full active spaces with minimal basis sets.

Spin-Vibronic Dynamics in Open-Shell Systems beyond the Spin Hamiltonian Formalism.

Vibronic coupling has a dramatic influence over a large number of molecular processes, ranging from photochemistry to spin relaxation and electronic transport. The simulation of vibronic coupling with multireference wave function methods has been largely applied to organic compounds, and only early efforts are available for open-shell systems such as transition metal and lanthanide complexes. In this work, we derive a numerical strategy to differentiate the molecular electronic Hamiltonian in the context of multireference ab initio methods and inclusive of spin-orbit coupling effects. We then provide a formulation of open quantum system dynamics able to predict the time evolution of the electron density matrix under the influence of a Markovian phonon bath up to fourth-order perturbation theory. We apply our method to Co(II) and Dy(III) molecular complexes exhibiting long spin relaxation times and successfully validate our strategy against the use of an effective spin Hamiltonian. Our study sheds light on the nature of vibronic coupling, the importance of electronic excited states in spin relaxation, and the need for high-level computational chemistry to quantify it.

Stiffness and Atomic-Scale Friction in Superlubricant MoS2 Bilayers.

Molecular dynamics simulations, performed with chemically accurate ab initio machine-learning force fields, are used to demonstrate that layer stiffness has profound effects on the superlubricant state of two-dimensional van der Waals heterostructures. We engineer bilayers of different rigidity but identical interlayer sliding energy surface and show that a 2-fold increase in the intralayer stiffness reduces the friction by a factor of ∼6. Two sliding regimes as a function of the sliding velocity are found. At a low velocity, the heat generated by the motion is efficiently exchanged between the layers and the friction is independent of the layer order. In contrast, at a high velocity, the friction heat flux cannot be exchanged fast enough and a buildup of significant temperature gradients between the layers is observed. In this situation, the temperature profile depends on whether the slider is softer than the substrate.

Unraveling the Contributions to Spin-Lattice Relaxation in Kramers Single-Molecule Magnets.

The study of how spin interacts with lattice vibrations and relaxes to equilibrium provides unique insights into its chemical environment and the relation between electronic structure and molecular composition. Despite its importance for several disciplines, ranging from magnetic resonance to quantum technologies, a convincing interpretation of spin dynamics in crystals of magnetic molecules is still lacking due to the challenging experimental determination of the correct spin relaxation mechanism. We apply ab initio spin dynamics to a series of 12 coordination complexes of Co2+ and Dy3+ ions selected among ∼240 compounds that largely cover the literature on single-molecule magnets and well represent different regimes of spin relaxation. Simulations reveal that the Orbach spin relaxation rate of known compounds mostly depends on the ions' zero-field splitting and little on the details of molecular vibrations. Raman relaxation is instead found to be also significantly affected by the features of low-energy phonons. These results provide a complete understanding of the factors limiting spin lifetime in single-molecule magnets and revisit years of experimental investigations by making it possible to transparently distinguish Orbach and Raman relaxation mechanisms.

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.

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.

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.

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.

Chemisorption of nitronyl-nitroxide radicals on gold surface: an assessment of morphology, exchange interaction and decoherence time.

A combined Tof-SIMS, XPS and STM characterization has been performed to study the deposition of a sulphur-functionalized nitronyl nitroxide radical on Au(111) clearly demonstrating the chemisorption of intact molecules. Continuous -wave EPR characterization showed that the radical molecules maintain their paramagnetic character. Pulsed EPR measurements allowed to determine the decoherence time of the nanostructure at 80 K, which turned out to be comparable to the one measured in frozen solution and longer than previously reported for many radicals and other paramagnetic molecules at much lower temperatures. Furthermore, we conducted a state-of-the-art ab initio molecular dynamics study, suggesting different possible scenarios for chemisorption geometries and predicting the energetically favoured geometry. Calculation of the magnetic properties indicates a partial non-innocent role of the gold surface in determining the magnetic interactions between radicals in packed structures. This suggests that the observed EPR spectrum is to be attributed to low-density domains of disordered radicals interacting via dipolar interactions.

Contrast-induced encephalopathy mimicking total anterior circulation stroke: a case report and review of the literature.

INTRODUCTION: Contrast-induced encephalopathy is a rare and usually reversible entity due to the administration of iodinated contrast. Clinical manifestations include cortical blindness, encephalopathy, seizures and focal neurological deficits. METHODS: We report the case of a 56-year-old woman who developed global aphasia and right hemiplegia after a cerebral angiography performed for a subarachnoid haemorrhage. A prompt brain MRI resulted negative, while CT scan revealed left cerebral oedema with the cerebral sulci effacement. Complete recovery was observed in 10 days. DISCUSSION: Diagnosis of contrast-induced encephalopathy requires a temporal correlation between neurological dysfunction and administration of iodinated contrast. Usually, the symptomatology is transient with a full recovery within 48-72 h. The most common symptom is cortical blindness, while other symptoms have been rarely reported. Only 20 cases previously reported global aphasia and/or hemiplegia or mimed anterior circulation strokes. Prompt brain neuroimaging is essential in order to exclude an alternative diagnosis that requires a distinct therapeutic approach.

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.

Multiple spin-phonon relaxation pathways in a Kramer single-ion magnet.

We present a first-principles investigation of spin-phonon relaxation in a molecular crystal of Co2+ single-ion magnets. Our study combines electronic structure calculations with machine-learning force fields and unravels the nature of both the Orbach and the Raman relaxation channels in terms of atomistic processes. We find that although both mechanisms are mediated by the excited spin states, the low temperature spin dynamics is dominated by phonons in the THz energy range, which partially suppress the benefit of having a large magnetic anisotropy. This study also determines the importance of intra-molecular motions for both the relaxation mechanisms and paves the way to the rational design of a new generation of single-ion magnets with tailored spin-phonon coupling.

The Limit of Spin Lifetime in Solid-State Electronic Spins.

The development of spin qubits for quantum technologies requires their protection from the main source of finite-temperature decoherence: atomic vibrations. Here we eliminate one of the main barriers to the progress in this field by providing a complete first-principles picture of spin relaxation that includes up to two-phonon processes. Our method is based on machine learning and electronic structure theory and makes the prediction of spin lifetime in realistic systems feasible. We study a prototypical vanadium-based molecular qubit and reveal that the spin lifetime at high temperature is limited by Raman processes due to a small number of THz intramolecular vibrations. These findings effectively change the conventional understanding of spin relaxation in this class of materials and open new avenues for the rational design of long-living spin systems.

The Origin of Magnetic Anisotropy and Single-Molecule Magnet Behavior in Chromium(II)-Based Extended Metal Atom Chains.

Chromium(II)-based extended metal atom chains have been the focus of considerable discussion regarding their symmetric versus unsymmetric structure and magnetism. We have now investigated four complexes of this class, namely, [Cr3(dpa)4X2] and [Cr5(tpda)4X2] with X = Cl- and SCN- [Hdpa = dipyridin-2-yl-amine; H2tpda = N2,N6-di(pyridin-2-yl)pyridine-2,6-diamine]. By dc/ac magnetic techniques and EPR spectroscopy, we found that all these complexes have easy-axis anisotropies of comparable magnitude in their S = 2 ground state (|D| = 1.5-1.8 cm-1) and behave as single-molecule magnets at low T. Ligand-field and DFT/CASSCF calculations were used to explain the similar magnetic properties of tri- versus pentachromium(II) strings, in spite of their different geometrical preferences and electronic structure. For both X ligands, the ground structure is unsymmetric in the pentachromium(II) species (i.e., with an alternation of long and short Cr-Cr distances) but is symmetric in their shorter congeners. Analysis of the electronic structure using quasi-restricted molecular orbitals (QROs) showed that the four unpaired electrons in Cr5 species are largely localized in four 3d-like QROs centered on the terminal, "isolated" Cr2+ ion. In Cr3 complexes, they occupy four nonbonding combinations of 3d-like orbitals centered only on the two terminal metals. In both cases, then, QRO eigenvalues closely mirror the 3d-level pattern of the terminal ions, whose coordination environment remains quite similar irrespective of chain length. We conclude that the extent of unpaired-electron delocalization has little impact on the magnetic anisotropy of these wire-like molecular species.

How do phonons relax molecular spins?

The coupling between electronic spins and lattice vibrations is fundamental for driving relaxation in magnetic materials. The debate over the nature of spin-phonon coupling dates back to the 1940s, but the role of spin-spin, spin-orbit, and hyperfine interactions has never been fully established. Here, we present a comprehensive study of the spin dynamics of a crystal of Vanadyl-based molecular qubits by means of first-order perturbation theory and first-principles calculations. We quantitatively determine the role of the Zeeman, hyperfine, and electronic spin dipolar interactions in the direct mechanism of spin relaxation. We show that, in a high magnetic field regime, the modulation of the Zeeman Hamiltonian by the intramolecular components of the acoustic phonons dominates the relaxation mechanism. In low fields, hyperfine coupling takes over, with the role of spin-spin dipolar interaction remaining the less important for the spin relaxation.

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.

A unified picture of the covalent bond within quantum-accurate force fields: From organic molecules to metallic complexes' reactivity.

Computational studies of chemical processes taking place over extended size and time scales are inaccessible by electronic structure theories and can be tackled only by atomistic models such as force fields. These have evolved over the years to describe the most diverse systems. However, as we improve the performance of a force field for a particular physical/chemical situation, we are also moving away from a unified description. Here, we demonstrate that a unified picture of the covalent bond is achievable within the framework of machine learning-based force fields. Ridge regression, together with a representation of the atomic environment in terms of bispectrum components, can be used to map a general potential energy surface for molecular systems at chemical accuracy. This protocol sets the ground for the generation of an accurate and universal class of potentials for both organic and organometallic compounds with no specific assumptions on the chemistry involved.

The disclosure of mesoscale behaviour of a 3d-SMM monolayer on Au(111) through a multilevel approach.

Here we present a computational study of a full- and a half-monolayer of a Fe4 single molecule magnet ([Fe4(L)2(dpm)6], where H3L = 2-hydroxymethyl-2-phenylpropane-1,3-diol and Hdpm = dipivaloylmethane, Fe4Ph) on an unreconstructed surface of Au(111). This has been possible through the application of an integrated approach, which allows the explicit inclusion of the packing effects in the classical dynamics to be used in a second step in periodic and non-periodic high level DFT calculations. In this way we can obtain access to mesoscale geometrical data and verify how they can influence the magnetic properties of interest of the single Fe4 molecule. The proposed approach allows to overcome the ab initio state-of-the-art approaches used to study Single Molecule Magnets (SMMs), which are based on the study of one single adsorbed molecule and cannot represent effects on the scale of a monolayer. Indeed, we show here that it is possible to go beyond the computational limitations inherent to the use, for such complex systems, of accurate calculation techniques (e.g. ab initio molecular dynamics) without losing the level of accuracy necessary to gain new detailed insights, hardly reachable at the experimental level. Indeed, long-range and edge effects on the Fe4 structures and their easy axis of magnetization orientations have been evidenced as their different contributions to the overall macroscopic behavior.

Solution structure of a pentachromium(ii) single molecule magnet from DFT calculations, isotopic labelling and multinuclear NMR spectroscopy.

The structure of pentachromium(ii) extended metal atom chain [Cr5(tpda)4Cl2] (2), which behaves as a single molecule magnet at low temperature, was investigated by Density Functional Theory (DFT) calculations and spectroscopic studies without the constraints of a crystal lattice (H2tpda = N2,N6-bis(pyridin-2-yl)pyridine-2,6-diamine). DFT studies both in the gas phase and including CH2Cl2 solvent effects indicate that an unsymmetric structure (C4 point group), with pairs of formally quadruply-bonded metal ions and one terminal metal center, is slightly more stable (2.9 and 3.9 kcal mol-1) than a symmetric structure (D4 point group). Isotopically-labelled samples (2-d8 and 2-d16) have then been prepared to aid in molecular symmetry determination by combined 1H and 2H NMR studies in dichloromethane solution. The spectra are strongly suggestive of a symmetric (D4) framework, indicating fast shuttling between the two unsymmetric forms over the timescale of NMR experiments. Procedures for a high-yield Pd-free synthesis of H2tpda and for site-selective post-synthetic H/D exchange of aromatic H2tpda hydrogens are also reported.

Intra-molecular origin of the spin-phonon coupling in slow-relaxing molecular magnets.

We perform a systematic investigation of the spin-phonon coupling leading to spin relaxation in the prototypical mononuclear single molecule magnet [(tpaPh)Fe]-. In particular we analyze in detail the nature of the most relevant vibrational modes giving rise to the relaxation. Our fully ab initio calculations, where the phonon modes are evaluated at the level of density functional theory and the spin-phonon coupling by mapping post-Hartree-Fock electronic structures onto an effective spin Hamiltonian, reveal that acoustic phonons are not active in the spin-phonon relaxation process of dilute SMMs crystals. Furthermore, we find that intra-molecular vibrational modes produce anisotropy tensor modulations orders of magnitude higher than those associated to rotations. In light of these results we are able to suggest new designing rules for spin-long-living SMMs which go beyond the tailoring of static molecular features but fully take into account dynamical features of the vibrational thermal bath evidencing those internal molecular distortions more relevant to the spin dynamics.