Atomic Orbitals Research Articles

From Tin(II) to Tin(IV): Following Solid‐liquid Reactions by Microscopy

AbstractIn order to study the formation of complexes independently from stoichiometry we developed a microscale experiment that allows us to monitor the reaction progress by light microscopy In the present study, the complex formation between SnF2 and 1,10‐phenanthroline (phen) with N,N‐dimethylformamide as solvent was investigated over a period of some weeks. By use of this setup, the formation of three different crystals has been observed, whose compositions and structures were determined by single crystal X‐ray diffraction: 3SnF2⋅ phen, 1, 2SnF2 ⋅ SnF4 ⋅ phen, 2, SnF4 ⋅ phen, 3. While the octahedral fluorine environment of the tin(IV) atoms of 2 and 3 is very regular, the coordination of the tin(II) atoms in 1 and 2 is irregular. Assuming a non‐bonding 5 s electron pair, classical 2c–2e‐ and symmetrical and asymmetrical, hypervalent 3c–4e‐bonds – all based on the orthogonal p atomic orbitals of Sn – an approach to analyze and describe these coordinations in a simple comprehensive way is presented.

Exact-Two-Component Complete Active Space Method with Variational Treatment of Magnetic Field and Spin-Orbit Coupling: Application to X-ray Magnetic Circular Dichroism Spectroscopy.

We introduce an exact-two-component complete active space self-consistent-field (X2C-CASSCF) method formulated under the restricted-magnetic-balance condition. This framework allows for the nonperturbative treatment of static magnetic fields using gauge-including atomic orbitals (GIAOs). The GIAO-X2C-CASSCF methodology effectively captures all microstates within the same 2J + 1-degenerate manifold and their splitting in a static magnetic field, which are not accessible through single-reference-based methods. We also present mathematical recursive expressions for evaluating one-electron relativistic integrals by using GIAOs in the presence of a finite magnetic field. Benchmark studies include oxygen and nitrogen K-edge X-ray magnetic circular dichroism spectroscopy (XMCD) for closed-shell organic compounds, as well as L-edge XMCD spectroscopy for the high-spin open-shell transition metal ion Mn2+ and the tetrahedral Mn(II)O46- complex.

Spin-Hall conductivity and optical characteristics of noncentrosymmetric quantum spin Hall insulators: the case of PbBiI

Quantum spin Hall insulators have attracted significant attention in recent years. Understanding the optical properties and spin Hall effect in these materials is crucial for technological advancements. In this study, we present theoretical analyses to explore the optical properties, Berry curvature and spin Hall conductivity of pristine and perturbed PbBiI using the linear combination of atomic orbitals and the Kubo formula. The system is not centrosymmetric and it is hosting at the same time Rashba spin-splitting and quantized spin Hall conductivity. Our calculations reveal that the electronic structure can be modified using staggered exchange fields and electric fields, leading to changes in the optical properties. Additionally, the spin Berry curvature and spin Hall conductivity are investigated as a function of the energy and temperature. The results indicate that due to the small dynamical spin Hall conductivity, generating an ac spin current in the PbBiI requires the use of external magnetic fields or magnetic materials.

Room-temperature selective cyclodehydrogenation on Au(111) via radical addition of open-shell resonance structures

Cyclodehydrogenation is an important ring-formation reaction that can directly produce planar-conjugated carbon-based nanomaterials from nonplanar molecules. However, inherently high C–H bond energy necessitates a high temperature during dehydrogenation, and the ubiquity of C − H bonds in molecules and small differences in their bond energies hinder the selectivity of dehydrogenation. Here, we report a room-temperature cyclodehydrogenation reaction on Au(111) via radical addition of open-shell resonance structures and demonstrate that radical addition significantly decreases cyclodehydrogenation temperature and further improves the chemoselectivity of dehydrogenation. Using scanning tunneling microscopy and non-contact atomic force microscopy, we visualize the cascade reaction process involved in cyclodehydrogenation and determine atomic structures and molecular orbitals of the planar acetylene-linked oxa-nanographene products. The nonplanar intermediates observed during progression annealing, combined with density functional theory calculations, suggest that room-temperature cyclodehydrogenation involves the formation of transient radicals, intramolecular radical addition, and hydrogen elimination; and that the high chemoselectivity of cyclodehydrogenation arises from the reversibility and different thermodynamics of radical addition step.

Metal-Metal Bonding in Tri-Actinide Clusters: A DFT Study of [An3Cl6] z (z = 1-6) and [An3Cl6Cp3] z (z = -2- +3; An = Ac, Th, Pa, U, Np, Pu).

The actinide-actinide bonding in tri-actinide clusters [An₃Cl₆]ᶻ (An = Ac-Pu, z = 1-6) and [An₃Cl₆Cp₃]ᶻ (z =-2-+3; Cp = (η5-C5H5)) is studied using density functional theory. We find 3-centre bonding similar to the tri-thorium cluster [{Th(η⁸-C₈H₈)(μ₃-Cl)₂}₃{K(THF)₂}₂]∞, as we previously reported (Nature 2021, 598, 72-75). The population of 3-centre molecular orbitals (3c-MOs) by zero, one or two electrons correlates with shortening of the An-An bond lengths, which also decrease with increasing actinide atomic number, consistent with the contraction of the actinide valence atomic orbitals. Mulliken analyses indicate that these 3c-MOs predominantly involve An 6d and 5f orbitals. Various methods evidence the presence of An-An bonding in most systems with populated 3c-MOs, including bond orders (Mayer and Wiberg), quantum theory of atoms in molecules metrics (ρ, ∇²ρ, -G/V, H, delocalization indices), electron localization function, and electron density assessments. Additionally, we explore the effect of Cp ligand substitution on uranium complexes, finding that bulkier Cp ligands can induce U-U bond distortions and result in slightly longer U-U bonds. Overall, this study advances our understanding of metal-metal bonding in tri-actinide clusters, highlighting its effects on geometric and electronic structures.

Emerging mixed electronic-ionic conductivity in double perovskite (La2/3Sr1/3)2(Sn1/3Fe1/3Cu1/3)2O6-δ: Phase transitions, structural, optical and dielectric study

We report on the eco-friendly synthesis of a double perovskite compound (La2/3Sr1/3)2(Sn1/3Cu1/3Fe1/3)2O6-δ, attractive for sustainable applications due to its unique structural and conductive properties. The incorporation of Cu2+ (3d9) ions into the B sites of the perovskite structure enhanced octahedral distortion via the Jahn-Teller effect. X-ray crystallography and Rietveld structural analysis revealed a significant deviation in the octahedra of (Cu/Fe)O6 and (Sn/Fe)O6 from the ideal perovskite structure, resulting in a decreased overlap between the atomic orbitals. The material displays a high dielectric constant, evidenced by impedance measurements across varying temperatures and frequencies. The analysis highlighted a considerable influence of the grain intrinsic properties and the grain boundary dynamics on both the conduction mechanism and dielectric relaxation. Notably, the introduction of dopants significantly reduces the bandgap energy to 2.7eV, compared to the 4.3eV of SrSnO3. The bandgap reduction factor measured here is lower than that of other reported double-doped SrSnO3 compounds. At 493K, a transition in DSC measurements suggests a structural change of the conductivity from a purely electronic to an electronic-ionic conductivity. The smaller bandgap and enhanced conductivity, coupled with phase transitions lead to a mixed conductivity making this material particularly effective for the use in energy storage technologies such as supercapacitors and batteries with the aim of improving their capacity and efficiency. Additionally, due to its temperature sensitivity, it also has the potential to be used as a valuable component in sensor applications.

Highly efficient magnesium ferrite/graphene nano-heterostructure for visible-light photocatalytic applications: Experimental and first-principles DFT studies

In this research study, the electronic structure of magnesium ferrite/graphene (MFO/Gr) nano-heterostructure for photocatalytic application was studied. The MFO nanoparticles with a median size of 85 nm were composited with Gr sheets using a photo-assisted reduction process. The XRD and SAED results, respectively, showed the spinal crystalline structure of MFO and the hexagonal structure of Gr in MFO/Gr nanocomposite. The XPS results revealed that the orbitals of MFO and Gr atoms interacted with each other, implying a Van der Waals heterojunction nanocomposite. The optical characteristics using UV–Vis diffuse reflectance spectrophotometry (UV–Vis DRS) and photoluminescence (PL) spectra demonstrated a lowering of MFO band gap from 2.05 to 1.84 eV by incorporation of Gr. Furthermore, the photoelectrocatalytic and photocatalytic dye degradation examinations showed a substantial impact of Gr on the photocatalytic activity of MFO nanoparticles: a 28-fold increase in the photocurrent and an 8-fold increase in the dye-degradation rate. The density functional theory (DFT) studies on MFO/Gr heterojunction revealed a considerable hybridization between Gr atoms orbitals (2p orbitals) and MFO atoms orbitals (Mg 3 s and Fe 3d orbitals) in the conduction band, which facilitate the transfer of photo-excited electrons from MFO to Gr. Also, the charge density difference at the MFO/Gr interface led to a polarized field at the interface, which is desirable for hindering photogenerated electron-hole recombination in the MFO/Gr nanocomposite. Along with the experimental results, the DFT results also revealed that the MFO/Gr nano-heterostructure is an excellent candidate for photocatalytic applications such as water splitting using sunlight to produce green hydrogen fuel.

Coordinatively Unsaturated Co Single-Atom Catalysts Enhance the Performance of Lithium-Sulfur Batteries by Triggering Strong d-p Orbital Hybridization.

The catalytic activities displayed by single-atom catalysts (SACs) depend on the coordination structure. SACs supported on carbon materials often adopt saturated coordination structures with uneven distributions because they require high-temperature conditions during synthesis. Herein, bisnitrogen-chelated Co SACs that are coordinatively unsaturated are prepared by integrating a Co complex into a conjugated microporous polymer (CMP-CoN2). Compared with saturated analogues, i.e., tetranitrogen-chelated Co SACs (denoted as CMP-CoN4), CMP-CoN2 exhibits higher electrocatalytic activity in polysulfide conversions due to an enhanced hybridization between the 3d orbitals of the Co atoms and the 3p orbitals of the S atoms in the polysulfide. As a result, sulfur cathodes prepared with CoN2 deliver outstanding performance metrics, including a high specific capacity (1393 mA h g-1 at 0.1 C), a superior rate capacity (673.2 mA h g-1 at 6 C), and a low capacity decay rate (of only 0.045% per cycle at 2 C over 1000 cycles). They also outperform sulfur cathodes that contain CMP-CoN4 or CMPs that are devoid of Co SACs. This work reveals how the catalytic activity displayed by SACs is affected by their coordination structures, and the rules that underpin the structure-activity relationship may be extended to designing electrocatalysts for use in other applications.

Effect of Fluorine Substitution on Magnetizabilities: Insights from Density Functional Theory and Benchmark Coupled-Cluster Calculations.

The quantitative calculation of the magnetizability tensor of fluorine-containing molecules has been a longstanding challenge for quantum chemistry. We report a benchmark study on the effect of fluorine substitution on the magnetizability (both isotropic and anisotropic) of 24 small closed-shell molecules using coupled-cluster (CCSD(T)) theory, large basis sets, and London atomic orbitals. By extrapolation to a complete basis set (CBS) result, we establish the CCSD(T)/CBS limit and take the opportunity to assess the performance of various density functional theory approximations. Correcting for zero-point vibration further allows us to directly compare theory with (gas-phase) experimental data. We revisit Flygare's hypothesis on molecular magnetizabilities, which relates the successive replacement of hydrogen by fluorine atoms to changes in the magnetizability anisotropy. Some exceptions to this hypothesis are documented, and we rationalize these observations on the basis of hybridization on carbon.

Atomic orbitals modulated dual functional bimetallic phosphides derived from MOF on MOF structure for boosting high efficient overall water splitting

The electronic modulation characteristics of efficient metal phosphide electrocatalysts can be utilized to tune the performance of oxygen evolution reaction (OER). However, improving the overall water splitting performance remains a challenging task. By building metal organic framework (MOF) on MOF heterostructures, an efficient strategy for controlling the electrical structure of MOFs was presented in this study. ZIF-67 was in-situ synthesized on MIL-88 (Fe) using a two-step self-assembly method, followed by low-temperature phosphorization to ultimately synthesize FeP-CoP3 bimetallic phosphides. By combining atomic orbital theory and theoretical calculations (density functional theory), the results reveal the successful modulation of electronic orbitals in FeP-CoP3 bimetallic phosphides, which are synthesized from MOF on MOF structure. The synergistic impact of the metal center Co species and the phase conjugation of both kinds of MOFs are responsible for this regulatory phenomenon. Therefore, the catalyst demonstrates excellent properties, demonstrating HER 81 mV (η10) in a 1.0 mol L−1 KOH solution and OER 239 mV (η50) low overpotentials. The FeP-CoP3 linked dual electrode alkaline batteries, which are bifunctional electrocatalysts, have a good electrocatalytic ability and may last for 50 h. They require just 1.49 V (η50) for total water breakdown. Through this technique, the electrical structure of electrocatalysts may be altered to increase catalytic activity.

Assessment of the exchange-hole dipole moment dispersion correction for the energy ranking stage of the seventh crystal structure prediction blind test.

The seventh blind test of crystal structure prediction (CSP) methods substantially increased the level of complexity of the target compounds relative to the previous tests organized by the Cambridge Crystallographic Data Centre. In this work, the performance of density-functional methods is assessed using numerical atomic orbitals and the exchange-hole dipole moment dispersion correction (XDM) for the energy-ranking phase of the seventh blind test. Overall, excellent performance was seen for the two rigid molecules (XXVII, XXVIII) and for the organic salt (XXXIII). However, for the agrochemical (XXXI) and pharmaceutical (XXXII) targets, the experimental polymorphs were ranked fairly high in energy amongst the provided candidate structures and inclusion of thermal free-energy corrections from the lattice vibrations was found to be essential for compound XXXI. Based on these results, it is proposed that the importance of vibrational free-energy corrections increases with the number of rotatable bonds.

Very-Large-Scale GPU-Accelerated Nuclear Gradient of Time-Dependent Density Functional Theory with Tamm-Dancoff Approximation and Range-Separated Hybrid Functionals.

Modern graphics processing units (GPUs) provide an unprecedented level of computing power. In this study, we present a high-performance, multi-GPU implementation of the analytical nuclear gradient for Kohn-Sham time-dependent density functional theory (TDDFT), employing the Tamm-Dancoff approximation (TDA) and Gaussian-type atomic orbitals as basis functions. We discuss GPU-efficient algorithms for the derivatives of electron repulsion integrals and exchange-correlation functionals within the range-separated scheme. As an illustrative example, we calculate the TDA-TDDFT gradient of the S1 state of a full-scale green fluorescent protein with explicit water solvent molecules, totaling 4353 atoms, at the ωB97X/def2-SVP level of theory. Our algorithm demonstrates favorable parallel efficiencies on a high-speed distributed system equipped with 256 Nvidia A100 GPUs, achieving >70% with up to 64 GPUs and 31% with 256 GPUs, effectively leveraging the capabilities of modern high-performance computing systems.

Modulating dual carrier-transfer channels and band structure in carbon nitride to amplify ROS storm for enhanced cancer photodynamic therapy

Graphite carbon nitride (CN) eliminates cancer cells by converting H2O2 to highly toxic •OH under visible light. However, its in vivo applications are constrained by insufficient endogenous H2O2, accumulation of OH− and finite photocarriers. We designed Fe/NV-CN, co-modified CN with nitrogen vacancies (NV) and ferric ions (Fe3+). NV and Fe3+, not only adjust the band structure of CN through quantum confinement effect and the altered coupled oscillations of atomic orbitals to facilitates •OH production by oxidizing OH−, but also construct dual carrier-transfer channels for electrons and holes to respective active sites by introducing stepped electrostatic potential and shortening three-electron bonds, thereby involving more carriers in •OH production. Fe/NV-CN, the novel reactor, effectually produces vast •OH under illumination by expanding OH− as the raw material of •OH and augmenting carriers at active sites, which induces cancer cell apoptosis by disrupting mitochondrial function for significant shrinkage of Cal27 cell-induced tumor under illumination. This work provides not only an effective photosensitizer avoiding the accumulation of OH− for cancer therapy but also a novel strategy by constructing dual carrier-transfer channels on semiconductor photosensitizers for improving the therapeutic effect of photodynamic therapy.

Generalizing deep learning electronic structure calculation to the plane-wave basis.

Deep neural networks capable of representing the density functional theory (DFT) Hamiltonian as a function of material structure hold great promise for revolutionizing future electronic structure calculations. However, a notable limitation of previous neural networks is their compatibility solely with the atomic-orbital (AO) basis, excluding the widely used plane-wave (PW) basis. Here we overcome this critical limitation by proposing an accurate and efficient real-space reconstruction method for directly computing AO Hamiltonian matrices from PW DFT results. The reconstruction method is orders of magnitude faster than traditional projection-based methods to convert PW results to the AO basis, and the reconstructed Hamiltonian matrices can faithfully reproduce the PW electronic structure, thus bridging the longstanding gap between the AO basis deep learning electronic structure approach and PW DFT. Advantages of the PW methods, such as high accuracy, high flexibility and wide applicability, thus can be all integrated into deep learning electronic structure methods without sacrificing these methods' inherent benefits. This allows for the construction of large-scale and high-fidelity training datasets with the help of PW DFT results towards the development of precise and broadly applicable deep learning electronic structure models.

First-Principles Linear Combination of Atomic Orbitals Calculations of K2SiF6 Crystal: Structural, Electronic, Elastic, Vibrational and Dielectric Properties.

The results of first-principles calculations of the structural, electronic, elastic, vibrational, dielectric and optical properties, as well as the Raman and infrared (IR) spectra, of potassium hexafluorosilicate (K2SiF6; KSF) crystal are discussed. KSF doped with manganese atoms (KSF:Mn4+) is known for its ability to function as a phosphor in white LED applications due to the efficient red emission from Mn⁴⁺ activator ions. The simulations were performed using the CRYSTAL23 computer code within the linear combination of atomic orbitals (LCAO) approximation of the density functional theory (DFT). For the study of KSF, we have applied and compared several DFT functionals (with emphasis on hybrid functionals) in combination with Gaussian-type basis sets. In order to determine the optimal combination for computation, two types of basis sets and four different functionals (three advanced hybrid-B3LYP, B1WC, and PBE0-and one LDA functional) were used, and the obtained results were compared with available experimental data. For the selected basis set and functional, the above-mentioned properties of KSF were calculated. In particular, the B1WC functional provides us with a band gap of 9.73 eV. The dependencies of structural, electronic and elastic parameters, as well as the Debye temperature, on external pressure (0-20 GPa) were also evaluated and compared with previous calculations. A comprehensive analysis of vibrational properties was performed for the first time, and the influence of isotopic substitution on the vibrational frequencies was analyzed. IR and Raman spectra were simulated, and the calculated Raman spectrum is in excellent agreement with the experimental one.

Charge self-consistent dynamical mean field theory calculations in combination with linear combination of numerical atomic orbitals framework based density functional theory

Charge self-consistent dynamical mean field theory calculations in combination with linear combination of numerical atomic orbitals framework based density functional theory

The origin of ferroelectricity in HfO2 from orbital hybridization and covalency

Fluorite-structured HfO2 ferroelectrics exhibit remarkable ferroelectricity owing to the robust thickness scalability, rendering them promising for next-generation ferroelectric memories. Unlike the well-understood perovskite structured ferroelectrics, such as Pb(Zr,Ti)O3, the origin of ferroelectricity in HfO2 remains elusive, which impedes the experimental fabrication of pure and stable ferroelectric orthorhombic phase in films. This study seeks to elucidate its origin by analyzing the covalent nature of local chemical bonding and changes in orbital hybridization and by catching the typical feather of the half-unit-cell spacer/polar layer in the orthorhombic phase. Notably, we find that the differences in the hybridization intensity of the 2s orbitals of two types of O atoms (OI and OII) and 5d orbitals of Hf atoms play a crucial role in inducing ferroelectric distortion. Furthermore, we demonstrate that the intrinsic mechanisms of stress in enhancing the ferroelectricity of HfO2 originate from the modulation of orbital hybridization intensity of the Hf–O bonds. These insights provide a vital theoretical foundation for further exploration of ferroelectric phase transitions and property modulation in HfO2 and similar fluorite-structured ferroelectrics.

Concept of electrons pairing during the formation of covalent chemical bonds

This research studies the forces acting in an electron pair with antiparallel spins participating in forming a covalent chemical bond between atoms. The first is the force of electrostatic repulsion of electrons. The second is the gravitational attraction of these electrons. The third is the force of electromagnetic attraction between the electron pair. From calculations it follows, that the force of gravitational attraction is negligible, and therefore it is not able to withstand the force of electrostatic repulsion between electrons. However, the force of electromagnetic attraction between a pair of electrons with antiparallel spins turned out to be hundreds of times greater than the force of their electrostatic repulsion. As a result, the formation of stable electron pairs in molecular orbitals becomes possible. Thus, valence electrons of neighboring atoms interact with each other like femto-electromagnets, as a result of which a stable bond is formed between these electrons. Calculations have shown that in hydrogen molecule the force of electrostatic attraction between nuclei and paired electrons of a molecular orbital significantly exceeds the force of electrostatic repulsion of nuclei, which ensures the formation of a strong covalent chemical bond. To form covalent bonds in other molecules, the force of electrostatic attraction between the nuclei and paired electrons of the molecular orbitals must be much greater than the forces of electrostatic repulsion between both the positively charged nuclei and the negatively charged electrons of the atomic orbitals of different atoms.

Artificial Intelligence Modeling of Materials’ Bulk Chemical and Physical Properties

Energies of the atomic and molecular orbitals belonging to one and two atom systems from the fourth and fifth periods of the periodic table have been calculated using ab initio quantum mechanical calculations. The energies of selected occupied and unoccupied orbitals surrounding the highest occupied and lowest unoccupied orbitals (HOMOs and LUMOs) of each system were selected and used as input for our artificial intelligence (AI) software. Using the AI software, correlations between orbital parameters and selected chemical and physical properties of bulk materials composed of these elements were established. Using these correlations, the materials’ bulk properties were predicted. The Q2 correlation for the single-atom predictions of first ionization potential, melting point, and boiling point were 0.3589, 0.4599, and 0.1798 respectively. The corresponding Q2 correlations using orbital parameters describing two-atom systems increased the capability to predict the experimental properties to the respective values of 0.8551, 0.8207, and 0.7877. The accuracy in predicting materials’ bulk properties was increased up to four-fold by using two atoms instead of one. We also present results of the prediction of molecules for materials relevant to energy systems.

Cholesky Decomposition in Spin-Free Dirac-Coulomb Coupled-Cluster Calculations.

We present an implementation for the use of Cholesky decomposition (CD) of two-electron integrals within the spin-free Dirac-Coulomb (SFDC) scheme that enables to perform high-accuracy coupled-cluster (CC) calculations at costs almost comparable to those of their nonrelativistic counterparts. While for nonrelativistic CC calculations, atomic-orbital (AO)-based algorithms, due to their significantly reduced disk-space requirements, are the key to efficient large-scale computations, such algorithms are less advantageous in the SFDC case due to their increased computational cost in that case. Here, molecular-orbital (MO)-based algorithms exploiting the CD of the two-electron integrals allow us to reduce disk-space requirements and lead to computational cost in the CC step that is more or less the same as in the nonrelativistic case. The only remaining overhead in a CD-SFDC-CC calculation is due to the need to compute additional two-electron integrals, the somewhat higher cost of the Hartree-Fock calculation in the SFDC case, and additional cost in the transformation of the Cholesky vectors from the AO to the MO representation. However, these additional costs typically amount to less than 5-15% of the total wall time and are thus acceptable. We illustrate the efficiency of our CD scheme for SFDC-CC calculations on a series of illustrative calculations for the X(CO)4 molecules with X = Ni, Pd, Pt.