Low-energy Structures Research Articles

The rule of four: anomalous distributions in the stoichiometries of inorganic compounds

Why are materials with specific characteristics more abundant than others? This is a fundamental question in materials science and one that is traditionally difficult to tackle, given the vastness of compositional and configurational space. We highlight here the anomalous abundance of inorganic compounds whose primitive unit cell contains a number of atoms that is a multiple of four. This occurrence—named here the rule of four—has to our knowledge not previously been reported or studied. Here, we first highlight the rule’s existence, especially notable when restricting oneself to experimentally known compounds, and explore its possible relationship with established descriptors of crystal structures, from symmetries to energies. We then investigate this relative abundance by looking at structural descriptors, both of global (packing configurations) and local (the smooth overlap of atomic positions) nature. Contrary to intuition, the overabundance does not correlate with low-energy or high-symmetry structures; in fact, structures which obey the rule of four are characterized by low symmetries and loosely packed arrangements maximizing the free volume. We are able to correlate this abundance with local structural symmetries, and visualize the results using a hybrid supervised-unsupervised machine learning method.

B63: The Most Stable Bilayer Structure with Dual Aromaticity.

The emergence of a bilayer B48 cluster, which has been both theoretically predicted and experimentally observed, as well as the recent experimental synthesis of bilayer borophene sheets on Ag and Cu surfaces, has generated tremendous curiosity in the bilayer structures of boron clusters. However, the connection between bilayer boron cluster and bilayer borophene remains unknown. By combining a genetic algorithm and density functional theory calculations, a global search for the low-energy structures of the B63 cluster was conducted, revealing that the Cs bilayer structure with three interlayer B-B bonds is the most stable bilayer structure. This structure was further examined in terms of its structural stability, chemical bonding, and aromaticity. Interestingly, the interlayer bonds induce strong electronegativity and robust aromaticity. Furthermore, the dual aromaticity stems from diatropic currents originating from virtual translational transitions for both σ and π electrons. This unprecedent bilayer boron cluster is anticipated to enrich the concept of dual aromaticity and serve as a potential precursor for bilayer borophene.

Spin-orbit coupling induced Van Hove singularity in proximity to a Lifshitz transition in Sr4Ru3O10

Van Hove singularities (VHss) in the vicinity of the Fermi energy often play a dramatic role in the physics of strongly correlated electron materials. The divergence of the density of states generated by VHss can trigger the emergence of phases such as superconductivity, ferromagnetism, metamagnetism, and density wave orders. A detailed understanding of the electronic structure of these VHss is therefore essential for an accurate description of such instabilities. Here, we study the low-energy electronic structure of the trilayer strontium ruthenate Sr4Ru3O10, identifying a rich hierarchy of VHss using angle-resolved photoemission spectroscopy and millikelvin scanning tunneling microscopy. Comparison of k-resolved electron spectroscopy and quasiparticle interference allows us to determine the structure of the VHss and demonstrate the crucial role of spin-orbit coupling in shaping them. We use this to develop a minimal model from which we identify a mechanism for driving a field-induced Lifshitz transition in ferromagnetic metals.

Size effects and electronic properties of zinc-doped boron clusters Zn (n = 1-15).

To gain a deeper understanding of zinc-doped boron clusters, theoretical calculations were performed to investigate the size effects and electronic properties of zinc-doped boron clusters. The study of the electronic properties, spectral characteristics, and geometric structures of Zn (n = 1-15) is of great significance in the fields of semiconductor materials science, material detection, and improving catalytic efficiency. The results indicate that Zn (n = 1-15) clusters predominantly exhibit planar or quasi-planar structures, with the Zn atom positioned in the outer regions of the framework. The second stable structure of Zn is a three-dimensional configuration, indicating that the structures of zinc-doped boron clusters begin to convert from the planar or quasi-planar structures to the 3D configurations. The second low-energy structure of Zn is a novel configuration. Relative stability analyses show that the Zn has better chemical stability than other clusters with a HOMO-LUMO gap of 2.79 eV. Electric charge analysis shows that part electrons on zinc atoms are transferred to boron atoms, and electrons prefer to cluster near the framework. According to the electron localization function, it gets harder to localize electrons as the equivalent face value drops, and it's challenging to see covalent bond formation between zinc and boron atoms. The spectrograms of Zn (n = 1-15) exhibit distinct properties and notable spectral features, which can be used as a theoretical basis for the identification and confirmation of boron clusters doped with single-atom transition metals. The calculations were performed using the ABCluster global search technique combined with density functional theory (DFT) methods. The selected low-energy structures were subjected to geometric optimization and frequency calculations at the PBE0/6-311 G(d) level to ensure structural stability and eliminate any imaginary frequencies. To acquire more precise relative energies, we performed single-point energies calculations for the low-lying isomers of Zn (n = 1-15) at the CCSD(T)/6-311 G(d)//PBE0/6-311 G(d) level of theory. All calculations were performed using Gaussian 09 software. To facilitate analysis, we utilized software tools such as Multiwfn, and VMD.

Competition between Water-Water Hydrogen Bonds and Water-π Bonds in Pyrene-Water Cluster Anions.

We present infrared spectra and density functional theory calculations of hydrated pyrene anion clusters with up to four water molecules. The experimental spectra were acquired by using infrared Ar messenger photodissociation spectroscopy. Water molecules form clusters on the surface of the pyrene, forming hydrogen bonds with the π-system. The structures of the water clusters and their interaction with the π-system are encoded in OH stretching vibrational modes. We find that the interactions between water molecules are stronger than the interactions between water molecules and the π-system. While all clusters show multiple conformers, three- and four-membered rings are the lowest energy structures in the larger hydrates.

First-principles analysis of the local atomic environment in calcium lanthanum sulfide ceramics

Density functional theory is utilized to investigate the energetics and mechanisms of sulfur loss across different stoichiometries of La2S3:CaS ceramics. These atomistic results reveal that the local atomic environment around each sulfur atom, consisting of six cation sites, can be used to predict the vacancy formation energy of the atom. Three nominal compositions are considered, 50:50, 65:35, and 90:10 La2S3:CaS, for two different atomic configurations, La2S3-like and La3S4-like. Relations were developed utilizing multivariable linear models. It is shown that the number of cation vacancies and lanthanum atoms in the local environment are among the most important factors in determining the energetics of a sulfur vacancy. Bader charge analysis reveals this is related to the degree of localization of charge change around the vacancy site and how close to the preferred oxidation states the lanthanum is. Results also suggest that while defect-free La2S3-like structures are energetically favorable, once a critical vacancy content is reached, the La3S4-like structure becomes the lower energy structure, which agrees qualitatively with recent experimental observations. This has important implications on how defect content and stoichiometry in this system are related. These findings also provide useful guidance on how these materials might best be processed.

Systematic high-throughput exploration of quaternary M′2M″AlB4 phases

A desired prerequisite when performing a quantum mechanical calculation is to have an initial idea of the atomic positions within an approximate crystal structure. The atomic positions combined should result in a system located in, or close to, an energy minimum. Designing low-energy structures for large multi-component systems is, however, often a challenging task as the degrees of freedom are close to infinite. The low-energy basins of (M′xM″1-x)3AlB4 material systems are herein explored by combining cluster expansion and crystal structure prediction methodologies with density functional theory calculations. Low-energy structures are specifically found at the (M′1/3M″2/3)3AlB4 composition, and this for multiple crystal symmetries. A subsequent high-throughput phase stability search was performed considering the identified low-energy structures at the (M′1/3M″2/3)3AlB4 composition where M′ and M″ were alloyed with Sc, Y, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W, Mn, Fe, and Co for both ordered and disordered structures. Nine quaternary phases were predicted stable with five of these favoring structures with M-sites in the form of a simulated solid solution.

Accelerating Structural Optimization through Fingerprinting Space Integration on the Potential Energy Surface.

Structural optimization has been a crucial component in computational materials research, and structure predictions have relied heavily on this technique, in particular. In this study, we introduce a novel method that enhances the efficiency of local optimization by integrating extra fingerprint space into the optimization process. Our approach utilizes a mixed energy concept in the hyper potential energy surface (PES), combining real energy and a newly introduced fingerprint energy derived from the symmetry of the local atomic environment. This method strategically guides the optimization process toward high-symmetry, low-energy structures by leveraging the intrinsic symmetry of the atomic configurations. The effectiveness of our approach was demonstrated through structural optimizations of silicon, silicon carbide, and Lennard-Jones cluster systems. Our results show that the fingerprint space biasing technique significantly enhances the performance and probability of discovering energetically favorable, high-symmetry structures as compared to conventional optimizations. The proposed method is anticipated to streamline the search for new materials and facilitate the discovery of novel energetically favorable configurations.

A comprehensive exploration of structural and electronic properties of molybdenum clusters

Molybdenum clusters, characterized by their unique structure and intriguing catalytic properties, have gained significant attention in recent years. In several existing studies, density functional theory (DFT) methods have been used to find the lowest energy Mo clusters and explore their electronic and magnetic structure. In all cases, with the exception of a single recent study, where a genetic algorithm was employed, initial geometries of the clusters, prior to geometry optimization, were chosen using heuristic approaches based on symmetry considerations and known structures. DFT calculations were performed using different types of pseudopotentials, from soft to hard, and different types of basis sets. However, no comprehensive study has yet been carried out in which a DFT method with the best control on its precision would be complemented by a reliable global minimum search method to find the lowest energy Mo clusters. In this work, we employ a combination of a plane wave-based DFT method and ab initio random structure searching technique to find the lowest energy clusters of up to 10 Mo atoms. In each case, the search has been performed for clusters with different spin multiplicities, which enabled us to explore their magnetic structure. The results are compared for both hard and soft pseudopotentials stressing the importance of treating more electrons explicitly, in agreement with some of the previous studies. For most of the low-energy magnetic structures found, we investigate the distribution of their spin densities, and for all low energy clusters, we confirm their stability by calculating their vibrational structure. For a few smallest clusters, the results of multiconfigurational quantum chemistry calculations are also discussed. Finally, free energies of the Mo clusters, within the quasi-harmonic approximation, are also calculated and discussed.

Nucleon axial-vector form factor and radius from future neutrino experiments

Precision measurements of antineutrino elastic scattering on hydrogen from future neutrino experiments offer a unique opportunity to access the low-energy structure of protons and neutrons. We discuss the determination of the nucleon axial-vector form factor and radius from antineutrino interactions on hydrogen that can be collected at the future Long-Baseline Neutrino Facility and study the sources of theoretical and experimental uncertainties. The projected accuracy would improve existing measurements by 1 order of magnitude and be competitive with contemporary lattice-QCD determinations, potentially helping to resolve the corresponding tension with measurements from (anti)neutrino elastic scattering on deuterium. We find that the current knowledge of the nucleon vector form factors could be one of the dominant sources of uncertainty. We also evaluate the constraints that can be simultaneously obtained on the absolute ν¯μ flux normalization. Published by the American Physical Society 2024

Machine-learning accelerated structure search for ligand-protected clusters.

Finding low-energy structures of ligand-protected clusters is challenging due to the enormous conformational space and the high computational cost of accurate quantum chemical methods for determining the structures and energies of conformers. Here, we adopted and utilized a kernel rigid regression based machine learning method to accelerate the search for low-energy structures of ligand-protected clusters. We chose the Au25(Cys)18 (Cys: cysteine) cluster as a model system to test and demonstrate our method. We found that the low-energy structures of the cluster are characterized by a specific hydrogen bond type in the cysteine. The different configurations of the ligand layer influence the structural and electronic properties of clusters.

Biophysical and nuclear magnetic resonance spectroscopic studies of the binding of baicalein to DNA sequence d(CACGTG)2 and its cytotoxicity evaluation

This paper reports the interaction of baicalein with a hexamer nucleic acid sequence d(CACGTG)2, present in the promoter region of various transcription factors, using biophysical techniques and nuclear magnetic resonance spectroscopy. UV–Visible absorption and fluorescence titration data implied partial intercalative binding of baicalein with a binding constant of 105 M−1. Continuous variation analysis using fluorescence data revealed a 1:1 stoichiometry of the baicalein and DNA in the solution. Circular dichroism data displayed a structural change of DNA upon baicalein binding. Thermal denaturing studied using circular dichroism showed that the melting temperature of the system does not significantly vary with the addition of baicalein. The spectral features suggest a partial intercalation of baicalein. Differential scanning calorimetric data exhibited two two-state transitions for alone DNA and its 1:1 complex with subtle changes in the melting temperatures supporting the non-intercalative binding of baicalein. Nuclear magnetic resonance data showed baicalein binding to the region near the C3pG4 base step, evidenced by the intermolecular nuclear overhauser effect cross peaks. Distance restrained molecular dynamics was employed to obtain the lowest energy structure. Biological evaluation of the effect of baicalein displayed excellent apoptotic effect on different cancer cell lines. IC50 values of 72.55, 79.9 and 96.7 µM were obtained in MCF-7, DU-145 and HCT-15 cell lines. The results uphold its chemotherapeutic potential.

Decarbonylation Products of Binuclear Methylphosphinidene Complexes of Cyclopentadienyliron Carbonyls: Triplet and Quintet Structures Are Favored Energetically over Singlet Structures with Iron-Iron Multiple Bonding.

The structures, energetics, and energetically preferred spin states of methylphosphinidene-bridged binuclear cyclopentadienyliron carbonyl complexes MePFe2(CO)nCp2 (n = 4, 3, 2, and 1) related to the experimentally known (μ-RP)Fe2(μ-CO)(CO)2Cp2 (R = cyclohexyl, phenyl, mesityl, and 2,4,6-tBu3C6H2) complexes have been investigated by density functional theory. Singlet structures having a pyramidal pseudotetrahedral phosphorus environment with 18-electron iron configurations are energetically preferred in the tricarbonyl and tetracarbonyl systems MePFe2(CO)nCp2 (n = 4 and 3) with the lowest energy structures of the tricarbonyl very closely resembling the experimentally determined structures. For the more unsaturated dicarbonyl and monocarbonyl systems MePFe2(CO)nCp2 (n = 2 and 1), higher spin state triplet and quintet structures are energetically preferred over singlet structures. These more highly unsaturated structures can be derived from the lowest energy singlet MePFe2(CO)nCp2 (n = 4, 3) by the removal of carbonyl groups. The iron atoms giving up carbonyl groups in their 16- and 14-electron configurations bear the spin density of the unpaired electrons in the higher spin states. The lowest energy singlet structure of the monocarbonyl MePFe2(CO)Cp2, although a relatively high energy isomer, is unusual among the collection of MePFe2(CO)nCp2 (n = 4, 3, 2, and 1) structures by having both the formal Fe=Fe double bond and the four-electron donor MeP unit with the planar phosphorus coordination required to allow each of its iron atoms to attain the favored 18-electron configuration.

Anion Photoelectron Spectroscopy and Quantum Chemistry Calculations of Gas-Phase TaSi17̅ and TaSi18̅ Clusters: Structural Determination, Bonding Characteristics, and Multiplicity of Structural Forms.

This study explores the structures and chemical bonding properties of TaSi17̅ and TaSi18̅ clusters by employing anion photoelectron spectroscopy and theoretical computations. Utilizing CALYPSO and ABCluster programs for initial structure prediction, B3LYP hybrid functional for optimization, and CCSD(T)/def2-TZVPPD level for energy calculations, the research identifies the most stable isomers of these clusters. Key findings include the identification of two coexisting low-energy isomers for TaSi17̅, exhibiting Ta-endohedral fullerene-like cage structures, and the lowest-energy structures of TaSi17̅ and TaSi18̅ anions can be considered as derived from the TaSi16̅ superatom cluster. The study enhances the understanding of group 14 element chemistry and guides the design of novel inorganic metallic compounds, potentially impacting materials science.

Generic multi-particle transverse momentum correlations as a new tool for studying nuclear structure at the energy frontier

The mean transverse momentum of produced particles, [pT]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[p_\ extrm{T} ]$$\\end{document}, and its event-by-event fluctuations give direct access to the initial conditions of ultra-relativistic heavy-ion collisions and help probe the colliding nuclei’s structure. The [pT]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[p_\ extrm{T} ]$$\\end{document} fluctuations can be studied via multi-particle pT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_\ extrm{T}$$\\end{document} correlations; so far, only the lowest four orders have been studied. Higher-order fluctuations can provide stronger constraints on the initial conditions and improved sensitivity to the detailed nuclear structure; however, their direct implementation can be challenging and is still lacking. In this paper, we apply a generic recursive algorithm for the genuine multi-particle pT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_\ extrm{T}$$\\end{document} correlations, which enables the accurate study of higher-order [pT]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[p_\ extrm{T} ]$$\\end{document} fluctuations without heavy computational cost for the first time. With this algorithm, we will examine the power of multi-particle pT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_\ extrm{T}$$\\end{document} correlations through Monte Carlo model studies with different nuclear structures. The impact on the nuclear structure studies, including the nuclear deformation and triaxial structure, will be discussed. These results demonstrate the usefulness of multi-particle pT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_\ extrm{T}$$\\end{document} correlations for studying nuclear structure in high-energy nuclei collisions at RHIC and the LHC, which could serve as a complementary tool to existing low-energy nuclear structure studies.

Visualizing the Low-Energy Electronic Structure of Prototypical Hybrid Halide Perovskite through Clear Band Measurements.

Organic-inorganic hybrid perovskites (OIHPs) are a promising class of materials that rival conventional semiconductors in various optoelectronic applications. However, unraveling the precise nature of their low-energy electronic structures continues to pose a significant challenge, primarily due to the absence of clear band measurements. Here, we investigate the low-energy electronic structure of CH3NH3PbI3 (MAPI3) using angle-resolved photoelectron spectroscopy combined with ab initio density functional theory. We successfully visualize the electronic structure of MAPI3 near the bulk valence band maximum by using a laboratory photon source (He Iα, 21.2 eV) at low temperature and explore its fundamental properties. The observed valence band exhibits a highly isotropic and parabolic band characterized by small effective masses of 0.20-0.21 me, without notable spectral signatures associated with a large polaron or the Rashba effect, subjects that are intensely debated in the literature. Concurrently, our spin-resolved measurements directly disprove the giant Rashba scenario previously suggested in a similar perovskite compound by establishing an upper limit for the Rashba parameter (αR) of 0.28 eV Å. Our results unveil the unusually complex nature of the low-energy electronic structure of OIHPs, thereby advancing our fundamental understanding of this important class of materials.

Use of hybrid molecular simulation techniques for systematic analysis of polyphenols as promising therapeutic agent against SARS-CoV-2

In our current study, we systematically report the four phenol classes via three-layer in silico screening approaches consisting of quantum chemical methods, molecular docking and molecular dynamics simulations. We studied the interactions of main protease (Mpro) and Nsp9 proteins of SARS-CoV-2 with four classes of polyphenolic compounds, where both proteins are crucial for virus replication. The phenols are extensively reported for medicinal applications, as these are antioxidants, anti-parasitic, anti-viral, anti-diabetic and anti-inflammatory compounds. Initial molecular docking study shows that among forty phenolic compounds the L9, L17, L26 and, L32 reveal the best binding energies with Mpro protein. Their values of docking score in terms of binding energy with Mpro protein is ranging from -5.7 to -6.8 kcal.mol−1. While on the other hands, L8, L11, L22 and, L34 exhibit the best docking scores with Nsp9 protein, which are ranging from -5.8 to -6.8 kcal.mol−1. Additionally, the lead compounds (ligands) were studied by quantum chemical methods for their optimized or the lowest energy structures, electronic properties, frontier molecular orbitals (FMOs) as well as molecular electrostatic potentials (MEPs). The global chemical descriptors are also calculated to explain the global reactivity trend for the lead compounds. To mimic the aqueous like environment, we added ions according to the electrostatic potential of the macromolecule, water molecules are being added to create physiologically relevant environment for studying biological molecules. Proteins, nucleic acids, and other biomolecules are typically surrounded by water molecules in biological systems. The addition of water molecules in MD simulations may provide a more accurate representation of their natural environment. The molecular dynamics simulations are performed for the complexes of best-docked lead compounds and for both proteins (Mpro and, Nsp9) over multiple replicate trajectories of 320 ns. The flexibility and stability behavior of the lead compounds in terms of RMSD and RMSF plots are analyzed through MD simulations results. The binding free energy of the best-docked lead compounds with both proteins in terms of Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) analysis are calculated, which are found as -8.79 and -3.97 kcal.mol−1 for Mpro-L32 and Nsp9-L8 complexes, respectively. The pharmacokinetic analysis of the lead compounds are also performed to disclose their ADME (absorption, distribution, metabolism, and excretion) and toxic character using online server pkCSM. This allowed for a comprehensive understanding of how these compounds would behave in the organism, specifically focusing on their ADME properties. We believe that the current study can evoke the interest of scientific community by providing fundamental insights, which will ultimately lead in-vivo and in-vitro analysis to assess the studied phenolic therapeutic inhibitors against the SARS-CoV-2.

A pressure-free long-time stable reduced-order model for two-dimensional Rayleigh-Bénard convection.

The present work presents a stable proper orthogonal decomposition (POD)-Galerkin based reduced-order model (ROM) for two-dimensional Rayleigh-Bénard convection in a square geometry for three Rayleigh numbers: 104 (steady state), 3×105 (periodic), and 6×106 (chaotic). Stability is obtained through a particular (staggered-grid) full-order model (FOM) discretization that leads to a ROM that is pressure-free and has skew-symmetric (energy-conserving) convective terms. This yields long-time stable solutions without requiring stabilizing mechanisms, even outside the training data range. The ROM's stability is validated for the different test cases by investigating the Nusselt and Reynolds number time series and the mean and variance of the vertical temperature profile. In general, these quantities converge to the FOM when increasing the number of modes, and turn out to be a good measure of accuracy. However, for the chaotic case, convergence with increasing numbers of modes is relatively difficult and a high number of modes is required to resolve the low-energy structures that are important for the global dynamics.

Machine-Learned Potentials by Active Learning from Organic Crystal Structure Prediction Landscapes.

A primary challenge in organic molecular crystal structure prediction (CSP) is accurately ranking the energies of potential structures. While high-level solid-state density functional theory (DFT) methods allow for mostly reliable discrimination of the low-energy structures, their high computational cost is problematic because of the need to evaluate tens to hundreds of thousands of trial crystal structures to fully explore typical crystal energy landscapes. Consequently, lower-cost but less accurate empirical force fields are often used, sometimes as the first stage of a hierarchical scheme involving multiple stages of increasingly accurate energy calculations. Machine-learned interatomic potentials (MLIPs), trained to reproduce the results of ab initio methods with computational costs close to those of force fields, can improve the efficiency of the CSP by reducing or eliminating the need for costly DFT calculations. Here, we investigate active learning methods for training MLIPs with CSP datasets. The combination of active learning with the well-developed sampling methods from CSP yields potentials in a highly automated workflow that are relevant over a wide range of the crystal packing space. To demonstrate these potentials, we illustrate efficiently reranking large, diverse crystal structure landscapes to near-DFT accuracy from force field-based CSP, improving the reliability of the final energy ranking. Furthermore, we demonstrate how these potentials can be extended to more accurately model structures far from lattice energy minima through additional on-the-fly training within Monte Carlo simulations.

Geometries, Electronic Structures, Bonding Properties, and Stability Strategy of Endohedral Metallofullerenes TM@C28 (TM = Sc−, Y−, La−, Ti, Zr, Hf, V+, Nb+, Ta+)

We performed quantum chemical calculations on the geometries, electronic structures, bonding properties, and stability strategy of endohedral metallofullerenes TM@C28 (TM = Sc−, Y−, La−, Ti, Zr, Hf, V+, Nb+, Ta+). Our calculations revealed that there are three different lowest-energy structures with C2v, C3v, and Td symmetries for TM@C28. The HOMO–LUMO gap of all these structures ranges from 1.35 eV to 2.31 eV, in which [V@C28]+ has the lowest HOMO–LUMO gap of 1.35 eV. The molecular orbitals are mainly composed of fullerene cage orbitals and slightly encapsulated metal orbitals. The bonding analysis on the metal–cage interactions reveals they are dominated by the Coulomb term ΔEelstat and the orbital interaction term ΔEorb, in which the orbital interaction term ΔEorb contributes more than the Coulomb term ΔEelstat. The addition of one or two CF3 groups to [V@C28]+ could increase the HOMO–LUMO gap and further increase the stability of [V@C28]+.