Interelectronic Repulsion Research Articles

Mott gapping in 3dABO3 perovskites without Mott-Hubbard interelectronic repulsion energy U

The existence of band gaps in Mott insulators such as perovskite oxides with partially filled 3d shells has been traditionally explained in terms of strong, dynamic inter-electronic repulsion codified by the on-site repulsion energy U in the Hubbard Hamiltonian. The success of the "DFT+U approach" where an empirical on-site potential term U is added to the exchange-and correlation Density Functional Theory (DFT) raised questions on whether U in DFT+U represents interelectronic correlation in the same way as it does in the Hubbard Hamiltonian, and if empiricism in selecting U can be avoided. Here we illustrate that ab-initio DFT without any U is able to predict gapping trends and structural symmetry breaking (octahedra rotations, Jahn-Teller modes, bond disproportionation) for all ABO3 3d perovskites from titanates to nickelates in both spin-ordered and spin disordered paramagnetic phases. We describe the paramagnetic phases as a supercell where individual sites can have different local environments thereby allowing DFT to develop finite moments on different sites as long as the total cell has zero moment. We use a recently developed exchange and correlation functional ("SCAN") that is sanctioned by the usual single-determinant, mean-field DFT paradigm with static correlations, but has a more precise rendering of self-interaction cancelation. Our results suggest that strong dynamic electronic correlations are not playing a universal role in gapping of 3d ABO3 Mott insulators, and opens the way for future applications of DFT for studying a plethora of complexity effects that depend on the existence of gaps, such as doping, defects, and band alignment in ABO3 oxides.

Low and high Z asymptotics along atomic isoelectronic sequences: configurations with npn′p open shells

The energy levels corrresponding to configurations that involve two p electrons outside a closed shell, or outside a closed shell plus an additional s-type electron, are revisited. The six levels that arise for two inequivalent p orbitals outside a closed shell can be split into two triples, and , to be referred to as normal and inverted, respectively. While the weighted average energy of the normal triple is higher than that of the inverted triple, they sometimes (but not always) intertwine, i.e. . Examining the relative ordering of the latter two states along isoelectronic sequences, they are (sometimes) found to depend on the nuclear charge, Z. For equivalent p electrons only the normal triple is allowed by the Pauli principle. Effects of configurations that, neglecting relativistic effects, are asymptotically degenerate at , when present, are systematically examined. At the low Z end of the isoelectronic sequence a critical charge, Zc, is approached at which the binding energy of the outermost electron vanishes. For an open shell with two inequivalent p electrons it was shown that , where N is the total number of electrons. The quantum defects of the outermost p electron in the various states formed out of such configurations have been examined, confirming an asymptotic integrality conjecture, , where Np is the number of occupied or partly occupied p orbitals in the remaining electron system. For pairs of states belonging to a common configuration, whose difference of energies is , we consider the ratio versus Z, that typically obtains a maximum at some . Below this maximum the interelectronic repulsion is higher in the lower energy state, since is equal to the difference between these interelectronic repulsions. A common thread of the treatment of the various issues considered is the anchoring of our analyses in the asymptotic behaviour of the features considered as and as .

Nearly flat Chern bands in moiré superlattices

The competition between the kinetic energy of electrons in a crystal and the inter-electron Coulomb repulsion underlies many fascinating phenomena in quantum materials. Superlattices formed from moir\'e patterns in graphene structures have emerged as tunable platforms for such physics. This paper shows that in many graphene moir\'e structures not only are the electronic bands narrow enough for Coulomb interaction to be important, but they are also topologically nontrivial. This setting of a strong correlated partially filled topological band promises to lead to many novel phenomena.

Chemical Control of Correlated Metals as Transparent Conductors

AbstractCorrelated metallic transition metal oxides offer a route to thin film transparent conductors that is distinct from the degenerate doping of broadband wide gap semiconductors. In a correlated metal transparent conductor, interelectron repulsion shifts the plasma frequency out of the visible region to enhance optical transmission, while the high carrier density of a metal retains sufficient conductivity. By exploiting control of the filling, position, and width of the bands derived from the B site transition metal in ABO3 perovskite oxide films, it is shown that pulsed laser deposition‐grown films of cubic SrMoO3 and orthorhombic CaMoO3 based on the second transition series cation 4d2 Mo4+ have superior transparent conductor properties to those of the first transition series 3d1 V4+‐based SrVO3. The increased carrier concentration offered by the greater bandfilling in the molybdates gives higher conductivity while retaining sufficient correlation to keep the plasma edge below the visible region. The reduced binding energy of the n=4 frontier orbitals in the second transition series materials shifts the energies of oxide 2p to metal nd transitions into the near‐ultraviolet to enhance visible transparency. The A site size‐driven rotation of MoO6 octahedra in CaMoO3 optimizes the balance between plasma frequency and conductivity for transparent conductor performance.

A simple model to calculate total and ionization energies of any atom

An earlier-proposed atomic geometrical model is used to estimate the inter-electronic repulsion in multi-electronic atoms. The model allows calculation of the energies for each shell. The resulting total energies of all atoms in the periodic table differ by less than 1% from Hartree–Fock calculations, except for He, where the difference is 1.8%. However, compared to the experimental total energy values for the first 36 elements, the largest difference is 1.04% for Ne. In this simplified model, the first ionization energies of the alkali metals and alkaline earths proved to be somewhat poor. A modification of the model is proposed to improve these ionization energies, keeping a very good agreement with the experimental average shell energies and with the Hartree–Fock calculations for the total energies.

Crystal Chemistry, Optical Spectroscopy and Crystal Field Calculations of Co3TeO6 and Solid Solutions Co3–xZnxTeO6

Solid solutions Co3–xZnxTeO6 (x = 0–3) were prepared both in polycrystalline and single‐crystalline form using solid state reactions and chemical vapour transport reactions, respectively. Miscibility between the isotypic end members was established over the complete range (C2/c, Z = 12, a ≈ 14.85, b ≈ 8.83, c ≈ 10.34 Å, β ≈ 93°). Crystal structure determinations, performed on basis of single crystal laboratory X‐ray (at 295 K) and synchrotron (at 10 and 100 K) data of Co3TeO6 and selected solid solutions, revealed no structural phase transition and allowed a detailed insight into the Co → Zn substitution mechanism. The coordination polyhedra of the five crystallographically independent M2+ cations are distorted octahedra (for three cations), one distorted tetrahedron and one distorted square pyramid. With increasing Zn content the polyhedral distortions increase, and the preference of the Zn2+ cation for the tetrahedral coordination becomes distinctive. Optical absorption and diffuse reflectance spectroscopy reveal extraordinary strong crystal field absorption effects, over wide x ranges predominantly governed by Co2+ in the single tetrahedral and one strongly acentric distorted octahedral site. Superposition Model crystal field calculations yield intrinsic and power‐law exponent parameters in general agreement with previous data for Co2+. The five cation sites show comparatively high crystal field strengths at generally very low interelectronic repulsion parameters, indicating prominent covalent contribution to Co–O bonding in Co3–xZnxTeO6 solid solutions.

Second-Order Jahn–Teller (SOJT) Structural Distortions in Multiply Bonded Higher Main Group Compounds

The geometrical deviations from planar to folded or from linear to bent structures observed in multiply bonded heavy main group element analogues of ethylene and acetylene are treated from a second-order Jahn–Teller (SOJT) perspective. The structural distortions can be regarded as a consequence of a mixing of the filled highest occupied molecular orbital (HOMO) and an unoccupied orbital (LUMO+1). This mixing stabilizes the HOMO and destabilizes the unoccupied LUMO+1 orbital and produces nonbonding electron density, which causes the geometrical distortion through interelectronic repulsion. This occurs more readily in the heavier species because of their generally weaker bonds, which permit a closer approach and hence greater interaction of the molecular levels. Predicting which geometrical distortion enables the HOMO/LUMO+1 mixing requires knowledge of the symmetries of these frontier orbitals and the symmetry of the distortion. For the undistorted structures the product of the symmetries of the interactin...

A DFT-based theoretical model for the calculation of spectral profiles of lanthanide M4,5-edge x-ray absorption.

This presentation reports the theoretical study of 3d core-electron excitation in lanthanide compounds in terms of electronic structure effects and optical properties. The calculations are done at the Density-Functional Theory (DFT) level complemented with an effective Hamiltonian based on ligand-field theory. The strategy consists of obtaining from DFT a totally symmetric density, where an active subspace is set up that forms the basis of the fivefold 3d and sevenfold 4f atomic orbitals of the lanthanide ion. This active subspace is defined with the fractional occupation of electrons, which represents open-shell species with the composite configuration 3d94fn+1. Based on the ligand-field analysis of the DFT results, the multiplet energies and ligand-field effects associated with the configuration 3d94fn+1 are evaluated; and the X-ray absorption spectra are simulated in terms of the intra-atomic 4fn → 3d94fn+1 electron transitions within the electric-dipole approximation. Examples for application are proposed taking into consideration the isolated trivalent lanthanides ions and compounds Cs2NaPrX6, with X = F, Cl, and Br. The results are compared with available experimental data, where a good agreement is qualitatively achieved. Also, the screening of the inter-electron repulsion and spin-orbit coupling interaction is numerically obtained that allows one to establish a fully non-empirical treatment of the 3d core-electron excitation, which can be valuable in the characterization and modeling of the spectral profiles of lanthanide M4,5-edge X-ray absorption spectroscopy. The enclosed theoretical model, which is being implemented in the Amsterdam Density Functional (ADF) suite of programs, is computationally economic and can be applied to any lanthanide system without limitations in terms of the size of the matrix elements of the effective Hamiltonian or the coordination symmetry of the lanthanide center.

Uranium(III)-carbon multiple bonding supported by arene \u03b4-bonding in mixed-valence hexauranium nanometre-scale rings

Despite the fact that non-aqueous uranium chemistry is over 60 years old, most polarised-covalent uranium-element multiple bonds involve formal uranium oxidation states IV, V, and VI. The paucity of uranium(III) congeners is because, in common with metal-ligand multiple bonding generally, such linkages involve strongly donating, charge-loaded ligands that bind best to electron-poor metals and inherently promote disproportionation of uranium(III). Here, we report the synthesis of hexauranium-methanediide nanometre-scale rings. Combined experimental and computational studies suggest overall the presence of formal uranium(III) and (IV) ions, though electron delocalisation in this Kramers system cannot be definitively ruled out, and the resulting polarised-covalent U = C bonds are supported by iodide and δ-bonded arene bridges. The arenes provide reservoirs that accommodate charge, thus avoiding inter-electronic repulsion that would destabilise these low oxidation state metal-ligand multiple bonds. Using arenes as electronic buffers could constitute a general synthetic strategy by which to stabilise otherwise inherently unstable metal-ligand linkages.

Singlet vs. triplet interelectronic repulsion in confined atoms

Hund’s multiplicity rule invariably holds for the ground configurations of few-electron atoms as well as those of multi-electron quantum dots. However, the ordering of the corresponding interelectronic repulsions exhibits a reversal in the former but not in the latter system, upon varying the system parameters. Here, we investigate the transition between these two types of behaviour by studying few-electron atoms confined in spherical cavities. “Counter-intuitive” ordering of the interelectronic repulsions is confirmed when the nuclear charge is low enough and the cavity radius is large enough.

Influence of compositional variation on structural, optical and EPR studies of undoped and Mn2+ doped lithium sodium zinc pyrophosphates (LNZP)

The structural and spectroscopic characteristics of Mn2+ in LiNaZnP2O5 (LNZP) nanophosphors were prepared by solid state synthesis and investigated. Diffraction of X-rays confirms that the material gets crystallized in orthorhombic phase with Cmcm space group. The average crystallite size for the prepared sample was found to be 28.02 nm and with increase in Mn2+ ions concentration, a systematic decrease in the crystallite size is observed. The microstructure shows that the agglomerated particles consists of irregular shapes for the undoped sample. By increasing the Mn2+concentration, the particles appear as flower-like structure. The EDS pattern showed the elemental compositions of sodium, zinc, phosphor, oxygen and manganese. By using optical absorption spectra, a number of spin-forbidden d-d bands at a range around 390, 420, 465 and 555 nm and corresponding bands were assigned to the transitions 6A­1g (S) → 4T2g (D) (390 nm), 6A1g (S) → 4T2g (G) (465 nm), 6A1g (S) → 4T1g (G) (555 nm) and the band observed around 420 nm was assigned to the transition 6A1g (S) → 4A1g (G) + 4Eg (G) which are characteristics of octahedral site symmetry for Mn2+. Electron spin resonance spectra for undoped LNZP (no spectrum) and Mn2+ doped LNZP nanophosphors were analyzed. The crystal field, interelectronic repulsion and spin-Hamiltonian parameters are evaluated and site symmetry of Mn2+ ions is ascribed as octahedral sites having ligands

On the Study of Racah Parameter B for Nickel (II) and Cobalt (II) Compounds

The ligand field strength (Dq) and interelectronic repulsion (B) have been calculated for nickel (II) and cobalt (II) compounds by Underhill and Billing [1] based on v2 and v3 values. They solved the quadratic equation 340(Dq2-18(v2+v3) Dq+ v2 v3=0 in Dq for octahedral. Then, the B value was determined using the equation v2+ v3−30Dq−15B=0. But, the first equation has real and imaginary solutions and it’s difficult to determine the imaginary one. In addition, in many cases there is no solution of this equation as well as in the case of CoO (d7 oct.). For octahedral, the above two equations can be considered as a system of two equations with two unknowns which can be solved if we have v2 and v3 values and vice versa. Similarly, for tetrahedral, the former two equations also can be solved for Dq and B. Using Newton–Raphson iterations, Dq and B values are exactly determined for octahedral and tetrahedral systems. The obtained values of Dq and B were compared with those previously reported.

Spectroscopic study of synthetic hydrothermal Fe3+-bearing beryl

A synthetic hydrothermal beryl Fe-4-51, investigated previously by Taran and Rossman (Am Miner 86:973–980, 2001), was additionally studied by microprobe, Mossbauer, optical absorption, Raman and IR spectroscopy. For comparison, polarized spectra of natural blue aquamarine and Cr3+, Fe3+-bearing alexandrite, both from Brazil, are also presented. Fe-4-51 is a nearly pure Fe3+-bearing beryl, with a homogeneous composition as shown by electron microprobe. Averaging over 22 points gives a formula of Be3.07(Al1.94, $${\text{Fe}}_{{{\text{0.07}}}}^{{{\text{3}}+}}$$ )Σ=2.01Si5.95O18, with Fe3+ replacing Al3+ in the octahedral site of the structure. The Mossbauer spectrum is dominated by a broad disordered pattern with beryl-suitable parameters; for Fe2+, IS = 1.21 mm/s, QS = 2.71 mm/s, area ≈ 5% and for Fe3+, IS = 0.34 mm/s, QS = 0.71 mm/s, and area ≈ 67%—are distinguished overlying a broad disordered continuum. The optical absorption spectrum is typical of octahedral Fe3+. From it, the crystal field strength Dq is derived as ~ 1520 cm−1 and the values of Racah parameters of interelectronic repulsion B and C are found to be 665 and 3415 cm−1, respectively. This rather low B value, compared with that of a free Fe3+ ion, 814 cm−1, suggests a comparatively high degree of covalency in the octahedral Fe3+–O bond. Infrared spectra show the presence of channel H2O of both I and II structural type in comparable quantities, about 0.5 and 1 mass%, respectively. Raman data show the expected five bands in the energy range from 300 to 1200 cm−1.

Shannon entropies and Fisher information of K-shell electrons of neutral atoms

We represent the two K-shell electrons of neutral atoms by Hylleraas-type wave function which fulfils the exact behavior at the electron–electron and electron-nucleus coalescence points and, derive a simple method to construct expressions for single-particle position- and momentum-space charge densities, ρ(r) and γ(p) respectively. We make use of the results for ρ(r) and γ(p) to critically examine the effect of correlation on bare (uncorrelated) values of Shannon information entropies (S) and of Fisher information (F) for the K-shell electrons of atoms from helium to neon. Due to inter-electronic repulsion the values of the uncorrelated Shannon position-space entropies are augmented while those of the momentum-space entropies are reduced. The corresponding Fisher information are found to exhibit opposite behavior in respect of this. Attempts are made to provide some plausible explanation for the observed response of S and F to electronic correlation.

Structural influence of mixed transition metal ions on lithium bismuth borate glasses

Lithium bismuth borate glasses containing mixed transition metals having composition 7CoO·23Li2O·20Bi2O3·50B2O3 (CLBB), 7V2O5·23Li2O·20Bi2O3·50B2O3 (VLBB) and x(2CoO·V2O5)·(30 - x)Li2O·20Bi2O3·50B2O3 (x = 0.0 (LBB) and x = 2.0, 5.0, 7.0, 10.0 mol% (CVLBB1-4)) are synthesized via melt quench route. The synthesized compositions are investigated for their physical properties using density (D) and molar volume (Vm), thermal properties by analyzing DSC/TG thermo-graphs, structural properties using IR absorption spectra in the mid-IR range and optical properties using UV–Vis–NIR spectroscopy. The Electron Paramagnetic Resonance (EPR) spectra of vanadyl and cobalt ion have been analyzed to study compositional effects on spin-Hamiltonian parameters. The non linear variations in physical properties depict a strong structural influence of Co/V- oxides on the glassy matrix. The compositional variations in characteristic temperatures (glass transition temperature Tg, glass crystallization temperature Tp and glass melting temperature Tm) reveals that Tg for glass samples CLBB is relatively less than that of pure lithium bismuth borate (LBB) glass sample wherein Tg for sample VLBB is higher than that of LBB. The increase in Tg (as compared with LBB) with an enhanced substitution of mixed transition metal oxides (2CoO·V2O5) shows a progressive structure modification of bismuth borate matrix. These predictions are very well corroborated by corresponding compositional trends of Tp and Tm. FTIR studies reveal that Co2+& VO2+ ions lead to structural rearrangements through the conversion of three-coordinated boron into four coordinated boron and thereby reducing number of non-bridging oxygen atoms. Bismuth is found to exist in [BiO6] octahedral units only, whereas boroxol rings are not present in the glass network. The theoretical values of optical basicity (Λth) and corresponding oxide ion polarizability (αo2−) have also been calculated to investigate oxygen covalency of glass matrix. Trends in both these parameters suggested an increase in ionic bonding on substitution of divalent transition metal cations causing a more bonding compaction in glass structure. The UV–Vis–NIR spectra suggest that cobalt ions exist as Co2+ states in octahedral coordination in glass network. Inter-electronic repulsion parameter and crystal field splitting energy were evaluated to understand the site symmetry around Co2+-ion in glass. X-band EPR spectra suggest that vanadium ions (V4+) exists as VO2+-ions in octahedral coordination with tetragonal compression. Spin Hamiltonian parameters g-values and A-values of VO2+ ions in glass were calculated. For sample CLBB two resonance lines in EPR spectrum attribute to octahedral symmetry around Co2+-ions were observed.

Effect of Co2+ ions on the ligand field, optical, and structural properties of ZnLiB glasses

Glass systems with composition x CoO-(25-x) ZnO-75 Li2B4O7, (where x=0, 0.5, 1, 2 and 3mol%) were prepared by conventional melt-quenching technique. The density and molar volume of the glass systems were determined in order to study their structures. The physical parameters such as ionic concentration, interionic distance, polaron radius, field strength, molar refractivity, and metallization were estimated. The decrease in the optical basicity Ʌth suggests that the covalence of the glass increases. The crystal field (10Dq) and interelectronic repulsion (B, C) parameters were evaluated. FT-IR spectra of the glasses showed vibration modes corresponding to stretching of BO3 and BO4 units. It was found that N4 decreases with increasing the CoO content. This is due to the increased intensity of the vibrational bands associated to BO3 units at the expense of the BO4 units, which led to an increased number of NBOs.

Comment on the spherical quantum dot with interaction effects

A series of studies of the lowest [Formula: see text] state of a model of a two-electron quantum dot, that consists of a finite spherical well [see, for example, Sivakami et al., Int. J. Mod. Phys. B 24, 5561 (2010)], exhibited a range of interesting applications. However, the quantity of central interest, the expectation value of the interelectronic repulsion (that must be nonnegative) was calculated erroneously, yielding negative values. In the present note, this expectation value is evaluated with respect to the exact first-order perturbation theory wavefunction (the scheme considered in the papers cited above) as well as with respect to a minimal basis set Gaussian variational wavefunction. Reasonable agreement between the two schemes is confirmed, both yielding the expected positive values of the expectation value of the interelectronic repulsion, over the whole range of the relevant parameters.

Atomic vs. quantum dot open shell spectra.

Hund's rules apply to pairs of atomic states which, in the limit of weak interelectronic repulsion, belong to a common configuration. We examine the asymptotic behavior of the energy difference between states belonging to such pairs (ΔE) as a function of the nuclear charge (Z) at both Z→∞ (ignoring relativistic effects) and at Z→Zc, where Zc is the critical charge below which the outermost electron is not bound. We find that the ratio ΔEZ2 is non-monotonic, having a maximum at some intermediate value of Z. This non-monotonicity is shown to account for the sign reversal in the difference between the corresponding interelectronic repulsion energies. For analogous open shell systems with confining potentials (such as Hooke's atom or the infinite spherical well), the corresponding function of the energy difference, in terms of which the interelectronic repulsion energy is given as a first derivative with respect to the parameter that characterizes the strength of the one-body potential (such as the harmonic force constant or the well radius, respectively), is monotonic in this parameter. This implies that the relative magnitude of the interelectronic repulsion energies that characterizes the strong one-body limit (usually, the ordering naively expected on the basis of Hund's rule) remains valid along the whole isoelectronic sequence.

On the correlation measure of two-electron systems

We make use of a Hylleraas-type wave function to derive an exact analytical model to quantify correlation in two-electron atomic/ionic systems and subsequently employ it to examine the role of inter-electronic repulsion in affecting (i) the bare (uncorrelated) single-particle position- and momentum-space charge distributions and (ii) corresponding Shannon’s information entropies. The results presented for the first five members in the helium iso-electronic sequence, on the one hand, correctly demonstrate the effect of correlation on bare charge distributions and, on the other hand, lead us to some important results for the correlated and uncorrelated values of the entropies. These include the limiting behavior of the correlated entropy sum (sum of position- and momentum-space entropies) and geometrical realization for the variation of information entropies as a function of Z. We suggest that, rather than the entropy sum, individual entropies should be regarded as better candidates for the measure of correlation.

Molecular and electronic structure of terminal and alkali metal-capped uranium(V) nitride complexes.

Determining the electronic structure of actinide complexes is intrinsically challenging because inter-electronic repulsion, crystal field, and spin–orbit coupling effects can be of similar magnitude. Moreover, such efforts have been hampered by the lack of structurally analogous families of complexes to study. Here we report an improved method to U≡N triple bonds, and assemble a family of uranium(V) nitrides. Along with an isoelectronic oxo, we quantify the electronic structure of this 5f1 family by magnetometry, optical and electron paramagnetic resonance (EPR) spectroscopies and modelling. Thus, we define the relative importance of the spin–orbit and crystal field interactions, and explain the experimentally observed different ground states. We find optical absorption linewidths give a potential tool to identify spin–orbit coupled states, and show measurement of UV···UV super-exchange coupling in dimers by EPR. We show that observed slow magnetic relaxation occurs via two-phonon processes, with no obvious correlation to the crystal field.