Localized Orbitals Research Articles

Periodic Trends in the Stabilization of Actinyls in Their Higher Oxidation States Using Pyrrophen Ligands.

Owing to the prominent existence and unique chemistry of actinyls, their complexation with suitable ligands is of significant interest. The complexation of high-valent actinyl moieties (An = U, Np, Pu and Am) with the acyclic sal-porphyrin analogue called "pyrrophen" (L(1)) and its dimethyl derivative (L(2)) with four nitrogen and two oxygen donor atoms was studied using relativistic density functional theory. Based on the periodic trends, the [UVO2-L(1)/L(2)]1- complexes show shorter bond lengths and higher bond orders that increase across the series of pentavalent actinyl complexes mainly due to the localization of the 5f orbitals. Among the hexavalent complexes, the [UVIO2-L(1)/L(2)] complexes have the shortest bonds. Following the uranyl complex, due to the plutonium turn, the [AmVIO2-L(1)/L(2)] complexes exhibit comparable properties with those of the former. Charge analysis suggests the complexation to be facilitated through ligand-to-metal charge transfer (LMCT) mainly through σ donation. Thermodynamic feasibility of complexation was modeled using hydrated actinyl moieties in aqueous medium and was found to be spontaneous. The dimethylated pyrrophen (L(2)) shows higher magnitudes of thermodynamic parameters indicating increased feasibility compared to the unsubstituted ligand (L(1)). Energy decomposition analysis (EDA) along with extended transition-state-natural orbitals for chemical valence theory (ETS-NOCV) analysis shows that the dominant electrostatic contributions decrease across the series and are counteracted by Pauli repulsion. Slight but considerable covalency is provided to hexavalent actinyl complexes by orbital contributions; this was confirmed by molecular orbital (MO) analysis that suggests strong covalency in americyl (VI) complexes. In addition to the pentavalent and hexavalent actinyl moieties, heptavalent actinyl species of neptunyl, plutonyl, and americyl were studied. Beyond the influence of the charges, the geometric and electronic properties point to the stabilization of neptunyl (VII) in the pyrrophen ligand environment, while the others shift to a lower (+VI) and relatively stable OS on complexation.

Bond formation insights into the Diels-Alder reaction: A bond perception and self-interaction perspective.

The behavior of electrons during bond formation and breaking cannot commonly be accessed from experiments. Thus, bond perception is often based on chemical intuition or rule-based algorithms. Utilizing computational chemistry methods, we present intrinsic bond descriptors for the Diels-Alder reaction, allowing for an automatic bond perception. We show that these bond descriptors are available from localized orbitals and self-interaction correction calculations, e.g., from Fermi-orbital descriptors. The proposed descriptors allow a sparse, simple, and educational inspection of the Diels-Alder reaction from an electronic perspective. We demonstrate that bond descriptors deliver a simple visual representation of the concerted bond formation and bond breaking, which agrees with Lewis' theory of bonding.

Quasi-Free Electron States Responsible for Single-Molecule Conductance Enhancement in Stable Radical

Stable organic radicals, which possess half-filled orbitals in the vicinity of the Fermi energy, are promising candidates for electronic devices. In this Letter, using a combination of scanning-tunneling-microscopy-based break junction (STM-BJ) experiments and quantum transport theory, a stable fluorene-based radical is investigated. We demonstrate that the transport properties of a series of fluorene derivatives can be tuned by controlling the degree of localization of certain orbitals. More specifically, radical 36-FR has a delocalized half-filled orbital resulting in Breit-Wigner resonances, leading to an unprecedented conductance enhancement of 2 orders of magnitude larger than the neutral nonradical counterpart (36-FOH). In other words, conversion from a closed-shell fluorene derivative to the free radical in 36-FR opens an electron transport path which massively enhances the conductance. This new understanding of the role of radicals in single-molecule junctions opens up a novel design strategy for single-molecule-based spintronic devices.

Electronic Structure and Aromaticity of an Unusual Cyclo[18]carbon Precursor, C18 Br6.

Herein, the electronic structure and bonding character of the stable cyclo[18]carbon (C18 ) precursor, C18 Br6 , are thoroughly characterized by molecular orbital (MO), density of states (DOS), bond order (BO), and interaction region indicator (IRI) analyses. The delocalization characters of out-of-plane and in-plane π-electrons (labeled as πout - and πin -electrons, respectively) in bonding regions were examined using localized orbital locator (LOL) and electron localization function (ELF). The aromaticity was investigated, studying the molecular magnetic response to external magnetic field by computing the magnetically induced current density (Jind ), iso-chemical shielding surface (ICSS), anisotropy of the induced current density (AICD), and the induced magnetic field (Bind ). All these analyses indicate that C18 Br6 is a globally aromatic species with lower aromaticity than C18 , and the blocking of in-plane π-conjugation (labeled as πin -conjugation) by the presence of -Br substituents in it is the underlying cause for the weakening of molecular aromaticity.

Local N-electron valence state perturbation theory using pair-natural orbitals based on localized virtual molecular orbitals.

Second-order N-electron valence state perturbation theory (NEVPT2) is an exactly size-consistent and intruder-state-free multi-reference theory. To accelerate the NEVPT2 computation, Guo and Neese combined it with the local pair-natural orbital (PNO) method using the projected atomic orbitals (PAOs) as the underlying local basis [Guo et al., J. Chem. Phys. 144, 094111 (2016)]. In this paper, we report the further development of the PNO-NEVPT2 method using the orthonormal and non-redundant localized virtual molecular orbitals (LVMOs) instead of PAOs. The LVMOs were previously considered to perform relatively poor compared to PAOs because the resulting orbital domains were unacceptably large. Our prior work, however, showed that this drawback can be remedied by re-forming the domain construction scheme using differential overlap integrals [Saitow et al., J. Chem. Phys. 157, 084101 (2022)]. In this work, we develop further refinements to enhance the feasibility of using LVMOs. We first developed a two-level semi-local approach for screening out so-called weak-pairs to select or truncate the pairs for PNO constructions more flexibly. As a refinement specific to the Pipek-Mezey localization for LVMOs, we introduced an iterative scheme to truncate the Givens rotations using varying thresholds. We assessed the LVMO-based PNO-NEVPT2 method through benchmark calculations for linear phenyl alkanes, which demonstrate that it performs comparably well relative to the PAO-based approach. In addition, we evaluated the Co-C bond dissociation energies for the cobalamin derivatives composed of 200 or more atoms, which confirms that the LVMO-based method can recover more than 99.85% of the canonical NEVPT2 correlation energy.

Solvent effect on molecular, electronic parameters, topological analysis and Fukui function evaluation with biological studies of imidazo [1, 2-a] pyridine-8-carboxylic acid

Imidazo [1, 2-a] pyridine-8-carboxylic acid, an aromatic molecule, was examined in the current investigation applying the DFT approach exercising 6–311 ++G(d,p) as a source level. The heading molecule's solvation effects, structural characterization and biological characteristics have been discussed using DFT techniques. The accuracy of the frontier molecular orbital theory is contrasted with electronic effects in gas and solvents including water, DMSO, acetone and acetonitrile. Fukui functions together with Molecular electrostatic potential maps were employed to find responsive locations. Scrutinizations of the UV–Visible spectra have been performed through the assistance of the TD-DFT methodology (IEFPCM standard). Computational NBO and NLO investigations were used to determine the chemical's stability and optical characteristics. Among the solvents chosen, the highest value of dipole moment is observed for water (3.89416). Topological inquiries such as Reduced Density Gradient (RDG) along with Localised Orbital Locator (LOL) and Electron Localisation Function (ELF) were achieved and reported using the multiwave function in gas and solvent phases. Drug similarity and ADMET predictions were utilised to ascertain the viability of the compound for its drug candidature. The docking studies were used to look into the interactions of the ligand with appropriate protein targets, indicating that title compound could be used as an anti-inflammatory drug which helps relieve pain from conditions like arthritis, muscle sprains or bone fractures. They also help reduce inflammation, lower fevers, and prevent blood from clotting. Anti-inflammatory protein targets (2VDY, 3CFQ, 3CMF) were used in a molecular docking technique and the parameters associated with those targets were bestowed. Furthermore, Ramachandran charts has been projected to verify the consistency of the targeted proteins.

Symmetrization of Localized Molecular Orbitals.

We present a novel algorithm for (i) detecting approximate symmetries inherently present among spatially localized molecular orbitals and (ii) enforcing these in numerically exact manners by means of unitary optimization techniques. The vast potential of our algorithm to compress a full set of molecular orbitals into only a minimal set of symmetry-unique orbitals is demonstrated, starting from localized bases of either Pipek-Mezey or Foster-Boys orbitals. Comparisons of results based on either of these two localization procedures indicate that Foster-Boys molecular orbitals can be spanned by a smaller number of symmetry-unique orbitals on average, making these outstanding candidates for the exploitation of general, (non-)Abelian point-group symmetries in a range of local correlation methods. As an illustration of said compressibility, our algorithm is capable of identifying a mere 14 symmetry-unique orbitals for the buckminsterfullerene in the highly symmetric Ih molecular point group, corresponding to only 1.7% of its total 840 molecular orbitals in a standard double-ζ basis set. The present work thus marks an important advancement in the exploitation of point-group symmetry within local correlation methods, for which the appropriate adaption of symmetry uniqueness among orbitals has the potential to yield unprecedented speed-ups.

Photoabsorption of Microhydrated Naphthalene and Its Cyano-Substituted Derivatives: Probing Prereactive Models for Photodissociation in Molecular Clouds.

We investigate the photoionization pathways of naphthalene, 1-cyanonaphthalene, and 2-cyanonaphthalene upon complexation with the water dimer, aiming to understand the photodissociation process under conditions of the interstellar medium (ISM). We analyze the intermolecular bonding pattern, equilibrium rotational properties, energy complexation, far-IR spectra, and ionic trends of the possible photoproducts using dispersion-corrected density functional theory (DFT-D) and time-dependent DFT (TD-DFT). For the different configurations, we evaluate the possible charge-transfer (CT) excitations near the photoionization limit. Our results indicate that, in high-radiation regions of the ISM (>8.0 eV), CT excitations occur from localized occupied molecular orbitals (MOs) in the aromatic molecules to mixed unoccupied MOs in the complexes, favoring cationic aromatic species in these conditions. We notice that the photoabsorption spectra depend on the type of intermolecular interaction (H-bonds or O-H···π bonds) in the complexes, as well as the presence and position (1 or 2) of the cyano-functional group in naphthalene. For hydrated naphthalene, the O-H···π complexes assume a more relevant role for photodissociation. In the case of the cyano-substituted derivatives, the H-bonded structures are more favorable to be considered as prereactive models. However, the cyano group at position 2 indicates that CT excitations toward the water dimer are more likely to occur.

Rare-earth control of phase transitions in infinite-layer nickelates.

Perovskite nickelates RNiO3 (R = rare-earth ion) exhibit complex rare-earth ion dependent phase diagram and high tunability of various appealing properties. Here, combining first- and finite-temperature second-principles calculations, we explicitly demonstrate that the superior merits of the interplay among lattice, electron, and spin degrees of freedom can be passed to RNiO2, which recently gained significant interest as superconductors. We unveil that decreasing the rare-earth size directly modulates the structural, electronic, and magnetic properties and naturally groups infinite-layer nickelates into two categories in terms of the Fermi surface and magnetic dimensionality: compounds with large rare-earth sizes (La, Pr) closely resemble the key properties of CaCuO2, showing quasi-two-dimensional (2D) antiferromagnetic (AFM) correlations and strongly localized orbitals around the Fermi level; the compounds with small rare-earth sizes (Nd-Lu) are highly analogous to ferropnictides, showing three-dimensional (3D) magnetic dimensionality and strong dispersion of electrons at the Fermi level. Additionally, we highlight that RNiO2 with R = Nd-Lu exhibit on cooling a structural transition with the appearance of oxygen rotation motion, which is softened by the reduction of rare-earth size and enhanced by spin-rotation couplings. The rare-earth control of dispersion and structural phase transition might be the key factors differentiating the distinct upper critical field and resistivity in different compounds. The established original phase diagram summarizing the temperature and rare-earth controlled structural, electronic, and magnetic transitions in RNiO2 compounds provides rich structural and chemical flexibility to tailor the superconducting property.

Modifications of Tanabe-Sugano d6 Diagram Induced by Radical Ligand Field: Ab Initio Inspection of a Fe(II)-Verdazyl Molecular Complex.

Quantum entanglement between the spin states of a metal center and radical ligands is suggested in an iron(II) [Fe(dipyvd)2]2+ compound (dipyvd = 1-isopropyl-3,5-dipyridil-6-oxoverdazyl). Wave function ab initio (Difference Dedicated Configuration Interaction, DDCI) inspections were carried out to stress the versatility of local spin states. We named this phenomenon excited state spinmerism, in reference to our previous work (see Roseiro et al., ChemPhysChem 2022, e202200478) where we introduced the concept of spinmerism as an extension of mesomerism to spin degrees of freedom. The construction of localized molecular orbitals allows for a reading of the wave functions and projections onto the local spin states. The low-energy spectrum is well-depicted by a Heisenberg picture. A 60 cm-1 ferromagnetic interaction is calculated between the radical ligands with the Stotal = 0 and 1 states largely dominated by a local low-spin SFe = 0. In contrast, the higher-lying Stotal = 2 states are superpositions of the local SFe = 1 (17%, 62%) and SFe = 2 (72%, 21%) spin states. Such mixing extends the traditional picture of a high-field d6 Tanabe-Sugano diagram. Even in the absence of spin-orbit coupling, the avoided crossing between different local spin states is triggered by the field generated by radical ligands. This puzzling scenario emerges from versatile local spin states in compounds which extend the traditional views in molecular magnetism.

Further investigations into a Laplace MP2 method using range separated Coulomb potential and orbital selective virtuals: Multipole correction, OSV extrapolation, and critical assessment.

We report further investigations to aid the development of a Laplace MP2 (second-order Møller Plesset) method with a range separated Coulomb potential partitioned into short- and long-range parts. The implementation of the method extensively uses sparse matrix algebra, density fitting techniques for the short-range part, and a Fourier transformation in spherical coordinates for the long-range part of the potential. Localized molecular orbitals are employed for the occupied space, whereas virtual space is described by orbital specific virtual orbitals (OSVs) associated with localized molecular orbitals. The Fourier transform is deficient for very large distances between localized occupied orbitals, and a multipole expansion for widely separated pairs is introduced for the direct MP2 contribution, which is applicable also to non-Coulombic potentials that do not satisfy the Laplace equation. For the exchange contribution, an efficient screening of contributing localized occupied pairs is employed, which is discussed more completely here. To mitigate errors due to the truncation of OSVs, a simple and efficient extrapolation procedure is used to obtain results close to MP2 for the full basis set of atomic orbitals Using a suitable set of default parameters, the accuracy of the approach is demonstrated. The current implementation of the approach is not very efficient, and the aim of this paper is to introduce and critically discuss ideas that can have more general applicability beyond MP2 calculations for large molecules.

The Electronic Nature of Cationic Group 10 Ylidyne Complexes

We report a broad theoretical study on [(PMe3)3MER]+ complexes, with M = Ni, Pd, Pt, E = C, Si, Ge, Sn, Pb, and R = ArMes, Tbb, (ArMes = 2,6-dimesitylphenyl; Tbb = C6H2-2,6-[CH(SiMe3)2]2-4-tBu). A few years ago, our group succeeded in obtaining heavier homologues of cationic group 10 carbyne complexes via halide abstraction of the tetrylidene complexes [(PMe3)3M=E(X)R] (X = Cl, Br) using a halide scavenger. The electronic structure and the M-E bonds of the [(PMe3)3MER]+ complexes were analyzed utilizing quantum-chemical tools, such as the Pipek–Mezey orbital localization method, the energy decomposition analysis (EDA), and the extended-transition state method with natural orbitals of chemical valence (ETS-NOCV). The carbyne, silylidyne complexes, and the germylidyne complex [(PMe3)3NiGeArMes]+ are suggested to be tetrylidyne complexes featuring donor–acceptor metal tetrel triple bonds, which are composed of two strong π(M→E) and one weaker σ(E→M) interaction. In comparison, the complexes with M = Pd, Pt; E = Sn, Pb; and R = ArMes are best described as metallotetrylenes and exhibit considerable M−E−C bending, a strong σ(M→E) bond, weakened M−E π-components, and lone pair density at the tetrel atoms. Furthermore, bond cleavage energy (BCE) and bond dissociation energy (BDE) reveal preferred splitting into [M(PMe3)3]+ and [ER] fragments for most complex cations in the range of 293.3–618.3 kJ·mol−1 and 230.4–461.6 kJ·mol−1, respectively. Finally, an extensive study of the potential energy hypersurface varying the M−E−C angle indicates the presence of isomers with M−E−C bond angles of around 95°. Interestingly, these isomers are energetically favored for M = Pd, Pt; E = Sn, Pb; and R = ArMes over the less-bent structures by 13–29 kJ·mol−1.

Decomposing Chemical Space: Applications to the Machine Learning of Atomic Energies.

We apply a number of atomic decomposition schemes across the standard QM7 data set─a small model set of organic molecules at equilibrium geometry─to inspect the possible emergence of trends among contributions to atomization energies from distinct elements embedded within molecules. Specifically, a recent decomposition scheme of ours based on spatially localized molecular orbitals is compared to alternatives that instead partition molecular energies on account of which nuclei individual atomic orbitals are centered on. We find these partitioning schemes to expose the composition of chemical compound space in very dissimilar ways in terms of the grouping, binning, and heterogeneity of discrete atomic contributions, e.g., those associated with hydrogens bonded to different heavy atoms. Furthermore, unphysical dependencies on the one-electron basis set are found for some, but not all of these schemes. The relevance and importance of these compositional factors for training tailored neural network models based on atomic energies are next assessed. We identify both limitations and possible advantages with respect to contemporary machine learning models and discuss the design of potential counterparts based on atoms and the intrinsic energies of these as the principal decomposition units.

Electronic band structure and optical properties of Li2In2GeSe6 crystal

We present results of a complex experimental and theoretical study of peculiarities of the electronic structure and optical constants of Li2In2GeSe6 compound crystallizing in monoclinic non-centrosymmetric space group Cc. In particular, we have measured the XPS spectra of core-level and valence electrons of atoms composing a high optical quality Li2In2GeSe6 crystal for both pristine and treated with middle-energy Ar+ ions surfaces. Furthermore, the XPS spectrum as measured for the valence-band range of the Li2In2GeSe6 crystal is compared with the total density of states (DOS) theoretically calculated within a density functional theory (DFT) framework as implemented in the augmented plane wave plus local orbitals (APW+lo) method. The present theoretical APW+lo results reveal a very good agreement regarding the shapes and energy positions of main features of the theoretical total DOS curve and the experimental XPS spectrum when the first-principles DFT calculations are made using the modified Becke-Johnson (mBJ) functional in the form of Tran-Blaha and involving the Hubbard correction parameter U treated for highly correlated In 4d electrons (TB-mBJ+U approach). This technique gives also band gap value of 2.26 eV, which is in good agreement with that experimentally measured for this compound. The present TB-mBJ calculations indicate that, at the top and in the upper region of the valence band, Se 4p states make the biggest contributions; the central region is formed mainly by Ge 4p states, while In 5s states dominate at the bottom and in the lower portion of the Li2In2GeSe6 valence band. With respect to peculiarities of filling the valence band by Se(Ge) 4p states, the present calculations are verified experimentally. Furthermore, the optical properties of Li2In2GeSe6 are studied theoretically in detail employing the TB-mBJ+U technique.

Efficient Narrowband Circularly Polarized Light Emitters Based on 1,4-B,N-embedded Rigid Donor-Acceptor Helicenes.

Narrow-band emission is essential for applicable circularly polarized luminescence (CPL) active materials in ultrahigh-definition CP-OLEDs. One of the most promising classes of CPL active molecules, helicenes, however, typically exhibit broad emission with a large Stokes shift. We present, herein, a design strategy capitalizing on intramolecular donor-acceptor interactions between nitrogen and boron atoms to address this issue. 1,4-B,N-embedded configurationally stable single- and double helicenes were synthesized straightforwardly. Both helicenes show unprecedentedly narrow fluorescence and CPL bands (full width at half maximum between 17-28 nm, 0.07-0.13 eV) along with high fluorescence quantum yields (72-85 %). Quantum chemical calculations revealed that the relative localization of the natural transition orbitals, mainly on the rigid core of the molecule, and small values of root-mean-square displacements between S0 and S1 state geometries, contribute to the narrower emission.

Efficient Narrowband Circularly Polarized Light Emitters Based on 1,4‐B,N‐embedded Rigid Donor–Acceptor Helicenes

AbstractNarrow‐band emission is essential for applicable circularly polarized luminescence (CPL) active materials in ultrahigh‐definition CP‐OLEDs. One of the most promising classes of CPL active molecules, helicenes, however, typically exhibit broad emission with a large Stokes shift. We present, herein, a design strategy capitalizing on intramolecular donor‐acceptor interactions between nitrogen and boron atoms to address this issue. 1,4‐B,N‐embedded configurationally stable single‐ and double helicenes were synthesized straightforwardly. Both helicenes show unprecedentedly narrow fluorescence and CPL bands (full width at half maximum between 17–28 nm, 0.07–0.13 eV) along with high fluorescence quantum yields (72–85 %). Quantum chemical calculations revealed that the relative localization of the natural transition orbitals, mainly on the rigid core of the molecule, and small values of root‐mean‐square displacements between S0 and S1 state geometries, contribute to the narrower emission.

Category theory and organic electronics

Inorganic semiconductors and conducting polymers are described by band conduction models with delocalized electrons, whereas small-molecule organic compounds are described by hopping conduction between localized molecular orbitals. However, the latter devices can reproduce fully the characteristics of semiconductor devices. Why are they so different and yet so similar? We will try to answer this question using Category theory and considering the meaning of electrical transport in electronic materials. The meaning of the category theory in physics is to consider different mathematical entities under a common mathematical structure.In this paper, the basic idea of category theory is first explained in detail using the example of complex impedance, and then four examples of its application are discussed. The derivation of the Mott-Gurney equation and the negative capacitance in OLED are discussed as examples of solving problems by moving to different categories. After those simple examples of formal rewriting from physical entity to mathematical entity, it is shown that electrical connection and electrical contact lead to direct sums and direct products of conducting states, based on the duality concept. We conclude that small-molecule organic compounds are not a mere branch of semiconductors, but rather equal counterparts of semiconductors in duality that are necessary to clarify the origin of the difference and similarity between organic electronics and semiconductor physics. Finally, by considering the electrical responses of OLEDs and OFETs in the immittance category, we show that they can be described under a common operating dynamic and propose a new operating model for OFETs.

Theoretical Investigation of Diameter Effects and Edge Configuration on the Optical Properties of Graphdiyne Nanotubes in the Presence of Electric Field

In this research, the structural, electronic and optical properties of the armchair (ant) and zigzag (znt) Graphdiyne nanotubes (GDY-NT) with different diameters were studied based on density functional theory (DFT). The computations were done using SIESTA code, based on linear combination of localized atomic orbitals (LCAO) method and the generalized gradient approximation (GGA). The results from the band structure analysis show that all these nanotubes are semiconductor with direct band gap at gamma point. The band gap of the nanotubes is clearly dependent on the nanotube diameter, and by increasing the nanotube diameter, the band gap is decreased. Optical properties such as dielectric function; absorption coefficient, optical conductivity and refractive index were examined and calculated for all samples. The results show that all these functions have an inverse relationship with the nanotube diameter and a direct relationship with the band gap. The effect of applying the external electric field with intensity of 0.1 V/Å, 0.2 V/Å in the direction of x-axis (perpendicular to the nanotube axis) on the structural and electronic features of these nanotubes has been studied and calculated.

Comparative study of first-principles approaches for effective Coulomb interaction strength Ueff between localized f-electrons: Lanthanide metals as an example.

As correlation strength has a key influence on the simulation of strongly correlated materials, many approaches have been proposed to obtain the parameter using first-principles calculations. However, a comparison of the different Coulomb strengths obtained using these approaches and an investigation of the mechanisms behind them are still needed. Taking lanthanide metals as an example, we research the factors that affect the effective Coulomb interaction strength, Ueff, by local screened Coulomb correction (LSCC), linear response (LR), and constrained random-phase approximation (cRPA) in the Vienna Ab initio Simulation Package. The Ueff LSCC value increases from 4.75 to 7.78eV, Ueff LR is almost stable at about 6.0eV (except for Eu, Er, and Yb), and Ueff cRPA shows a two-stage decreasing trend in both light and heavy lanthanides. To investigate these differences, we establish a scheme to analyze the coexistence and competition between the orbital localization and the screening effect. We find that LSCC and cRPA are dominated by the orbital localization and the screening effect, respectively, whereas LR shows the balance of the competition between the two factors. Additionally, the performance of these approaches is influenced by different starting points from the Perdew-Burke-Ernzerhof (PBE) and PBE + U, especially for cRPA. Our results provide useful knowledge for understanding the Ueff of lanthanide materials, and similar analyses can also be used in the research of other correlation strength simulation approaches.

Chemical interactions that govern the structures of metals.

Most metals adopt simple structures such as body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed (HCP) structures in specific groupings across the periodic table, and many undergo transitions to surprisingly complex structures on compression, not expected from conventional free-electron-based theories of metals. First-principles calculations have been able to reproduce many observed structures and transitions, but a unified, predictive theory that underlies this behavior is not yet in hand. Discovered by analyzing the electronic properties of metals in various lattices over a broad range of sizes and geometries, a remarkably simple theory shows that the stability of metal structures is governed by electrons occupying local interstitial orbitals and their strong chemical interactions. The theory provides a basis for understanding and predicting structures in solid compounds and alloys over a broad range of conditions.