Computational design of magnetic molecules and their environment using quantum chemistry, machine learning and multiscale simulations

Field-Induced Slow Magnetization Relaxation of a Tetrahedral S=2 FeIIS4-Containing Complex

In the work described herein, the spin relaxation properties of the mononuclear tetrahedral S=2 [Fe{(SPiPr2)2N}2] complex (1) were studied by employing static and dynamic magnetic measurements at liquid helium temperatures. In the absence of an external direct current (DC) magnetic field, 1 exhibits fast magnetization relaxation. However, in the presence of external magnetic fields of a few kOe, slow relaxation is induced as monitored by alternating current (AC) magnetic susceptibility measurements up to 10 kHz, in the temperature range 2-5 K. Analysis of the temperature dependence of the corresponding relaxation time reveals contributions by Quantum Tunnelling of Magnetization, and the Direct and Orbach processes in the magnetization relaxation mechanism of 1. The energy barrier, Ueff, of the Orbach process, as determined by this analysis, is compared with that related to the zero-field splitting parameters of 1 which were previously determined by high- frequency and -field electron paramagnetic resonance and Mössbauer spectroscopies.

Unravelling the role of spin-vibrational coupling in designing high-performance pentagonal bipyramidal Dy(iii) single ion magnets

At the cutting edge of high-performance single-molecule magnets (SMMs) lie lanthanide-based complexes, renowned for their potent magnetic anisotropy. SMMs containing one metal centre are defined as single-ion magnets (SIMs). The performance of SMMs is measured generally via the barrier height for magnetisation reversal (Ueff) and blocking temperature (TB), below which the magnetisation is fully frozen. To enhance the Ueff and TB values in lanthanide-based SMMs, the static crystal field splitting of mJ levels has been effectively adjusted through ligand design, leveraging the oblate/prolate ground state 4f electron density shape. However, the maximum fine-tuning achievable through ligand design, known as the axial limit, has already been reached in this class of compounds. This necessitates new design principles to enhance SMM characteristics to better suit end-user applications. Among other avenues that can be explored to improve SMM characteristics, a deeper understanding of spin-phonon coupling is critical to advancing TB values. However, there are only a handful of examples where this has been deciphered. In this work, using a combination of DFT and ab initio CASSCF calculations, we have performed spin-phonon calculations on five classes of pentagonal bipyramidal Dy(iii) SIMs exhibiting TB values in the range of 4.5 K to 36 K ([Dy(bbpen)Br] (1, H2bbpen = N,N'-bis(2-hydroxybenzyl)-N,N'-bis(2-methylpyridyl)ethylenediamine), [Dy(OCMe3)Br(THF)5][BPh4] (2) [Dy(OSiMe3)Br(THF)5] [BPh4] (3), [Dy(LN5)(Ph3SiO)2](BPh4)·CH2Cl2 (4) and [L2Dy(H2O)5][I]3·L2·H2O (5, L = tBuPO(NHiPr)2)). Unlike the method employed elsewhere for the calculation of spin-phonon coupling, in this work, we have employed a set of criteria and intuitively selected vibrational modes to perform the spin-phonon coupling analysis. The approach provided here not only reduces the computational cost significantly but also suggests chemical intuition to improve the performance of this class of compounds. Our calculations reveal that low-energy vibrational modes govern the magnetisation relaxation in these SIMs. A flexible first coordination sphere found on some of the complexes was found to be responsible for low-energy vibrations that flip the magnetisation, reducing the TB values drastically (complexes 2 and 3). On the other hand, a rigid first coordination sphere and a stiff ligand framework move the spin-vibrational coupling that causes the relaxation to lie beyond the secondary coordination sphere, resulting in an increase in TB values. Our calculations also reveal that not only the atoms in the first coordination sphere but also those in the secondary coordination sphere affect the performance of the SMMs. Learning from this exercise, we have undertaken several in silico models based on these vibrations to improve the TB values. Some of these predictions were correlated with literature precedents, offering confidence in the methodology employed. To this end, our comprehensive investigation, involving twenty-three molecules/models and five sets of geometries for pentagonal bipyramidal Dy(iii) single-ion magnets (SIMs), unveils a treasure trove of chemically sound design clues, poised to enhance the TB values in this fascinating molecular realm.

Nanostructured Design Cathode Materials for Magnesium-Ion Batteries

Energy is undeniably one of the most fundamental requirements of the current generation. Solar and wind energy are sustainable and renewable energy sources; however, their unpredictability points to the development of energy storage systems (ESSs). There has been a substantial increase in the use of batteries, particularly lithium-ion batteries (LIBs), as ESSs. However, low rate capability and degradation due to electric load in long-range electric vehicles are pushing LIBs to their limits. As alternative ESSs, magnesium-ion batteries (MIBs) possess promising properties and advantages. Cathode materials play a crucial role in MIBs. In this regard, a variety of cathode materials, including Mn-based, Se-based, vanadium- and vanadium oxide-based, S-based, and Mg2+-containing cathodes, have been investigated by experimental and theoretical techniques. Results reveal that the discharge capacity, capacity retention, and cycle life of cathode materials need improvement. Nevertheless, maintaining the long-term stability of the electrode-electrolyte interface during high-voltage operation continues to be a hurdle in the execution of MIBs, despite the continuous research in this field. The current Review mainly focuses on the most recent nanostructured-design cathode materials in an attempt to draw attention to MIBs and promote the investigation of suitable cathode materials for this promising energy storage device.

Machine Learning Prediction of the Experimental Transition Temperature of Fe(II) Spin-Crossover Complexes

Spin-crossover (SCO) complexes are materials that exhibit changes in the spin state in response to external stimuli, with potential applications in molecular electronics. It is challenging to know a priori how to design ligands to achieve the delicate balance of entropic and enthalpic contributions needed to tailor a transition temperature close to room temperature. We leverage the SCO complexes from the previously curated SCO-95 data set [Vennelakanti et al. J. Chem. Phys. 159, 024120 (2023)] to train three machine learning (ML) models for transition temperature (T1/2) prediction using graph-based revised autocorrelations as features. We perform feature selection using random forest-ranked recursive feature addition (RF-RFA) to identify the features essential to model transferability. Of the ML models considered, the full feature set RF and recursive feature addition RF models perform best, achieving moderate correlation to experimental T1/2 values. We then compare ML T1/2 predictions to those from three previously identified best-performing density functional approximations (DFAs) which accurately predict SCO behavior across SCO-95, finding that the ML models predict T1/2 more accurately than the best-performing DFAs. In addition, we study ML model predictions for a set of 18 SCO complexes for which only estimated T1/2 values are available. Upon excluding outliers from this set, the RF-RFA RF model shows a strong correlation to estimated T1/2 values with a Pearson's r of 0.82. In contrast, DFA-predicted T1/2 values have large errors and show no correlation to estimated T1/2 values over the same set of complexes. Overall, our study demonstrates slightly superior performance of ML models in comparison with some of the best-performing DFAs, and we expect ML models to improve further as larger data sets of SCO complexes are curated and become available for model training.

Contribution of molecular structures and quantum chemistry technique to root concentration factor: An innovative application of interpretable machine learning

Root concentration factor (RCF) is a significant parameter to characterize uptake and accumulation of hazardous organic contaminants (HOCs) by plant roots. However, complex interactions among chemicals, plant roots and soil make it challenging to identify underlying mechanisms of uptake and accumulation of HOCs. Here, nine machine learning techniques were applied to investigate major factors controlling RCF based on variable combinations of molecular descriptors (MD), MACCS fingerprints, quantum chemistry descriptors (QCD) and three physicochemical properties related to chemical-soil-plant system. Compared to models with variables including MACCS fingerprints or solitary physicochemical properties, the XGBoost-6 model developed by the variable combination of MD, QCD and three physicochemical properties achieved the most remarkable performance, with R2 of 0.977. Model interpretation achieved by permutation variable importance and partial dependence plots revealed the vital importance of HOCs lipophilicity, lipid content of plant roots, soil organic matter content, the overall deformability and the molecular dispersive ability of HOCs for regulating RCF. The integration of MD and QCD with physicochemical properties could improve our knowledge of underlying mechanisms regarding HOCs accumulation in plant roots from innovative structural perspectives. Multiple variables combination-oriented performance improvement of model can be extended to other parameters prediction in environmental risk assessment field.

Rapid and Accurate Prediction of the Axial Magnetic Anisotropy in Cobalt(II) Complexes Using a Machine-Learning Approach

Estimating the magnetic anisotropy for single-ion magnets is complex due to its multireference nature. This study demonstrates that deep neural networks (DNNs) can provide accurate axial magnetic anisotropy (D) values, closely matching the complete-active-space self-consistent-field (CASSCF) quality using density functional theory (DFT) data. We curated an 86-parameter database (UFF1) with electronic data from over 33000 cobalt(II) compounds. The DNN achieved an R2 of 0.906 and a mean absolute error of 18.1 cm-1 in comparison to reference CASSCF D values. Remarkably, it is 11 times more accurate than DFT methods and 7700 times faster. This approach hints at DNNs predicting the anisotropy in larger molecules, even when trained on smaller ligands.

Noncanonical Condensation of Nucleic Acid Chains by Hydrophobic Gold Nanocrystals

Nucleic acid condensates are essential for various biological processes and have numerous applications in nucleic acid nanotechnology, gene therapy, and mRNA vaccines. However, unlike the in vivo condensation that is dependent on motor proteins, the in vitro condensation efficiency remains to be improved. Here, we proposed a hydrophobic interaction-driven mechanism for condensing long nucleic acid chains using atomically precise hydrophobic gold nanoclusters (Au NCs). We found that hydrophobic Au NCs could condense long single-stranded DNA or RNA to form composites of spherical nanostructures, which further assembled into bead-shaped suprastructures in the presence of excessive Au NCs. Thus, suprastructures displayed gel-like behaviors, and Au NCs could diffuse freely inside the condensates, which resemble the collective motions of condensin complexes inside chromosomes. The dynamic hydrophobic interactions between Au NCs and bases allow for the reversible release of nucleic acids in the presence of mild triggering agents. Our method represents a significant advancement toward the development of more efficient and versatile nucleic acid condensation techniques.

Ab initio prediction of key parameters and magneto-structural correlation of tetracoordinated lanthanide single-ion magnets

Single-molecule magnets (SMMs) have great potential in becoming revolutionary materials for micro-electronic devices. As one type of SMM and holding the performance record, lanthanide single-ion magnets (Ln-SIMs) stand at the forefront of the family. Lowering the coordination number (CN) is an important strategy to improve the performance of Ln-SIMs. Here, we report a theoretical study on a typical group of low-CN Ln-SIMs, i.e., tetracoordinated structures. Our results are consistent with those of experiments and they identify the same three best Ln-SIMs via a concise criterion, i.e., the co-existence of long τ_QTM and high U_eff. Compared to the record-holding dysprosocenium systems, the best SIMs here possess τ_QTM values that are shorter by several orders of magnitude and U_eff values that are lower by ∼1000 Kelvin (K). These are important reasons for the fact that the tetracoordinated Ln-SIMs are clearly inferior to dysprosocenium. A simple but intuitive crystal-field analysis leads to several routes to improve the performance of a given Ln-SIM, including compression of the axial bond length, widening the axial bond angle, elongation of the equatorial bond length and usage of weaker equatorial donor ligands. Although these routes are not brand-new, the most efficient option and the degree of improvement resulting from it are not known in advance. Consequently, a theoretical magneto-structural study, covering various routes, is carried out for the best Ln-SIM here and the most efficient route is shown to be widening the axial ∠O-Dy-O angle. The most optimistic case, having a ∠O-Dy-O of 180°, could have a τ_QTM (up to 10³ s) and U_eff (∼2400 K) close to those of the record-holders. Subsequently, a blocking temperature (T_B) of 64 K is predicted to be possible for it. A more practical case, with ∠O-Dy-O being 160°, could have a τ_QTM of up to 400 s, U_eff of around 2200 K and the possibility of a T_B of 57 K. Although having an inherent precision limit, these predictions provide a guide to performance improvement, starting from an existing system.

The critical role of ultra-low-energy vibrations in the relaxation dynamics of molecular qubits

Improving the performance of molecular qubits is a fundamental milestone towards unleashing the power of molecular magnetism in the second quantum revolution. Taming spin relaxation and decoherence due to vibrations is crucial to reach this milestone, but this is hindered by our lack of understanding on the nature of vibrations and their coupling to spins. Here we propose a synergistic approach to study a prototypical molecular qubit. It combines inelastic X-ray scattering to measure phonon dispersions along the main symmetry directions of the crystal and spin dynamics simulations based on DFT. We show that the canonical Debye picture of lattice dynamics breaks down and that intra-molecular vibrations with very-low energies of 1-2 meV are largely responsible for spin relaxation up to ambient temperature. We identify the origin of these modes, thus providing a rationale for improving spin coherence. The power and flexibility of our approach open new avenues for the investigation of magnetic molecules with the potential of removing roadblocks toward their use in quantum devices.

Machine Learning Predicting Optimal Preparation of Silica-Coated Gold Nanorods for Photothermal Tumor Ablation

Gold nanorods (GNRs) coated with silica shells are excellent photothermal agents with high surface functionality and biocompatibility. Understanding the correlation of the coating process with both structure and property of silica-coated GNRs is crucial to their optimizing preparation and performance, as well as tailoring potential applications. Herein, we report a machine learning (ML) prediction of coating silica on GNR with various preparation parameters. A total of 306 sets of silica-coated GNRs altogether were prepared via a sol-gel method, and their structures were characterized to extract a dataset available for eight ML algorithms. Among these algorithms, the eXtreme gradient boosting (XGboost) classification model affords the highest prediction accuracy of over 91%. The derived feature importance scores and relevant decision trees are employed to address the optimal process to prepare well-structured silica-coated GNRs. The high-throughput predictions have been adopted to identify optimal process parameters for the successful preparation of dumbbell-structured silica-coated GNRs, which possess a superior performance to a conventional cylindrical core-shell counterpart. The dumbbell silica-coated GNRs demonstrate an efficient enhanced photothermal performance in vivo and in vitro, validated by both experiments and time domain finite difference calculations. This study epitomizes the potential of ML algorithms combined with experiments in predicting, optimizing, and accelerating the preparation of core-shell inorganic materials and can be extended to other nanomaterial research.

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.

Data-driven design of molecular nanomagnets

Three decades of research in molecular nanomagnets have raised their magnetic memories from liquid helium to liquid nitrogen temperature thanks to a wise choice of the magnetic ion and coordination environment. Still, serendipity and chemical intuition played a main role. In order to establish a powerful framework for statistically driven chemical design, here we collected chemical and physical data for lanthanide-based nanomagnets, catalogued over 1400 published experiments, developed an interactive dashboard (SIMDAVIS) to visualise the dataset, and applied inferential statistical analysis. Our analysis shows that the Arrhenius energy barrier correlates unexpectedly well with the magnetic memory. Furthermore, as both Orbach and Raman processes can be affected by vibronic coupling, chemical design of the coordination scheme may be used to reduce the relaxation rates. Indeed, only bis-phthalocyaninato sandwiches and metallocenes, with rigid ligands, consistently present magnetic memory up to high temperature. Analysing magnetostructural correlations, we offer promising strategies for improvement, in particular for the preparation of pentagonal bipyramids, where even softer complexes are protected against molecular vibrations.