Interelectronic Repulsion Research Articles

Theoretical Hints to Optimize Energy Dissipation and Cell–Cell Response in Quantum Cellular Automata Based on Tetrameric and Bidimeric Cells

This article is largely oriented towards the theoretical foundations of the rational design of molecular cells for quantum cellular automata (QCA) devices with optimized properties. We apply the vibronic approach to the analysis of the two key properties of such molecular cells, namely the cell–cell response and energy dissipation in the course of the non-adiabatic switching of the electric field acting on the cell. We consider two kinds of square planar cells, namely cells represented by a two-electron tetrameric mixed valence (MV) cluster and bidimeric cells composed of two one-electron MV dimeric half-cells. The model includes vibronic coupling of the excess electrons with the breathing modes of the redox sites, electron transfer, intracell interelectronic Coulomb repulsion, and also the interaction of the cell with the electric field of polarized neighboring cells. For both kinds of cells, the heat release is shown to be minimal in the case of strong delocalization of excess electrons (weak vibronic coupling and/or strong electron transfer) exposed to a weak electric field. On the other hand, such a parametric regime proves to be incompatible with a strong nonlinear cell–cell response. To reach a compromise between low energy dissipation and a strong cell–cell response, we suggest using weakly interacting MV molecules with weak electron delocalization as cells. From this point of view, bidimeric cells are advantageous over tetrameric ones due to their smaller number of electron transfer pathways, resulting in a lower extent of electron delocalization. The distinct features of bidimeric cells, such as their two possible mutual arrangements (“side-by-side” and “head-to-tail”), are discussed as well. Finally, we briefly discuss some relevant results from a recent ab initio study on electron transfer and vibronic coupling from the perspective of the possibility of controlling the key parameters of molecular QCA cells.

Determination of Uranium Central-Field Covalency with 3d4f Resonant Inelastic X-ray Scattering.

Understanding the nature of metal-ligand bonding is a major challenge in actinide chemistry. We present a new experimental strategy for addressing this challenge using actinide 3d4f resonant inelastic X-ray scattering (RIXS). Through a systematic study of uranium(IV) halide complexes, [UX6]2-, where X = F, Cl, or Br, we identify RIXS spectral satellites with relative energies and intensities that relate to the extent of uranium-ligand bond covalency. By analyzing the spectra in combination with ligand field density functional theory we find that the sensitivity of the satellites to the nature of metal-ligand bonding is due to the reduction of 5f interelectron repulsion and 4f-5f spin-exchange, caused by metal-ligand orbital mixing and the degree of 5f radial expansion, known as central-field covalency. Thus, this study furthers electronic structure quantification that can be obtained from 3d4f RIXS, demonstrating it as a technique for estimating actinide-ligand covalency.

Photoluminescence of Mn2+ in the Borosulfate Zn[B2(SO4)4]:Mn2+ - A Tool to Detect Weak Coordination Behavior of Ligands.

The impact of the surrounding ligand field is successfully exploited in the case of Eu2+ to tune the emission characteristics of inorganic photoactive materials with potential application in e.g., phosphor-converted white light-emitting diodes (pc-wLEDs). However, the photoluminescence of Mn2+ related to intraconfigurational 3d5-3d5 transitions is also strongly dependent on local ligand field effects and has been underestimated in this regard so far. In this work, we want to revive the idea how to electronically tune the emission color of a transition metal ion in inorganic hosts by unusual electronic effects in the metal-ligand bond. The concept is explicitly demonstrated for the weakly coordinating layer-like borosulfate ligand in the Mn(II)-containing solid solutions Zn1-xMnx[B2(SO4)4] (x = 0, 0.03, 0.04, 0.05, 0.10). Zn[B2(SO4)4]:Mn2+ shows orange narrow-band luminescence at 590 nm, which is an unusually short wavelength for octahedrally coordinated Mn2+ and indicates an uncommonly weak ligand field. On the other hand, the analysis of the interelectronic Racah repulsion parameters reveals ionic Mn-O bonds with values close to the Racah parameters of the free Mn2+ ion. Overall, this strategy demonstrates that electronic control of the metal-ligand bond can be a tool to make Mn2+ a potent alternative emitter to Eu2+ for inorganic phosphors.

Photolumineszenz von Mn2+ in dem Borosulfat Zn[B2(SO4)4] : Mn2+ – Eine Möglichkeit zum Nachweis schwach koordinierender Liganden

AbstractDer Einfluss des umgebenden Ligandenfelds wird im Fall von Eu2+ erfolgreich genutzt, um die Emission anorganischer photoaktiver Materialien durchzustimmen, die z. B. in phosphor‐konvertierten Weißlicht‐emittierenden Dioden (pc‐wLEDs) Anwendung finden. Allerdings ist auch die Photolumineszenz von Mn2+, die auf intrakonfiguralen 3d5–3d5‐Übergängen basiert, stark von lokalen Ligandenfeldeffekten abhängig. Dieser Aspekt wurde bislang eher vernachlässigt. In der vorliegenden Arbeit wollen wir daher die Idee wieder aufleben lassen, die Emissionsfarbe eines Übergangsmetall‐Ions in anorganischen Wirtsverbindungen durch ungewöhnliche elektronische Effekte in der Metall‐Ligand‐Bindung einzustellen. Das Konzept wird explizit für das schwach koordinierende, schichtartigen Borosulfat‐Anion in den Mn2+‐haltigen festen Lösungen Zn1‐xMnx[B2(SO4)4] (x=0; 0.03; 0.04; 0.05; 0.10) demonstriert. Zn[B2(SO4)4] : Mn2+ zeigt orange Schmalbandlumineszenz bei 590 nm, was eine ungewöhnlich kurze Wellenlänge für oktaedrisch koordiniertes Mn2+ darstellt und auf ein besonders schwaches Ligandenfeld hinweist. Eine Analyse der interelektronischen Racah‐Abstoßungsparameter deutet stark ionische Mn−O‐Bindungen mit Werten nahe der Racah‐Parameter des freien Mn2+‐Ions an. Insgesamt demonstriert diese Strategie, dass elektronische Anpassungen der Metall−Ligand‐Bindung als Instrument genutzt werden können, um Mn2+ zu einem potenten alternativen Emitter anstelle von Eu2+ für anorganische Leuchtstoffe zu machen.

Crystal structure and optical absorption spectra of LiCo(SO4)OH and its remarkable relationship to the Zn-Mn-silicate hodgkinsonite

Crystals of the compound LiCo(SO4)OH were synthesised at low-hydrothermal conditions, and the crystal structure was determined and refined from single crystal X-ray diffraction data. LiCo(SO4)OH crystallises monoclinic, space group P21/c, Z = 4, a = 9.586(2), b = 5.425(1), c = 7.317(1) Å, β = 109.65(1)°, V = 358.3 Å3, wR2 = 0.0485 (2215 unique reflections, 78 variables). The structure is built from chains of edge-sharing, quite strongly bond-length and -angle distorted Co(OH)3O3 octahedra (< Co–O > = 2.126 Å), which are further linked by common corners, hydrogen bonds, and by properly shaped SO4 tetrahedra (< S–O > = 1.476 Å) to sheets parallel (100). These sheets are connected to a three-dimensional framework by sharing corners with distorted LiO4 polyhedra (< Li–O > = 1.956 Å). Apart from the isotypic sulfates of Mn2+ and Fe2+, only the molybdate LiCd(MoO4)OH crystallises isostructural with LiCo(SO4)OH. However, a very close structural relationship exists with the rare mineral hodgkinsonite, Zn2Mn(SiO4)(OH)2, yielding crystal chemically very uncommon topological equivalents of Zn2+ ≡ S6+ and Si4+ ≡ Li+, aside from the expectable substitution Mn2+ ≡ Co2+. Polarised optical absorption spectra of LiCo(SO4)OH reveal that the dominating spin-allowed 4T1(P) band system of Co2+ (d7 configuration) is strongly split up and covers a prominent part (~ 15,500–24,500 cm−1) of the visible spectral range, in accordance with the significant distortion of the Co(OH)3O3 polyhedron. The spectra are interpreted in terms of the Superposition Model of crystal fields, yielding a new set of intrinsic and interelectronic repulsion parameters for Co2+.

Bounding [AnO2]2+ (An = U, Np) covalency by simulated O K-edge and An M-edge X-ray absorption near-edge spectroscopy.

Restricted active space simulations are shown to accurately reproduce and characterise both O K-edge and U M4,5-edge spectra of uranyl in excellent agreement with experimental peak positions and are extended to the Np analogue. Analysis of bonding orbital composition in the ground and O K-edge core-excited states demonstrates that metal contribution is underestimated in the latter. In contrast, An M4/5-edge core-excited states produce bonding orbital compositions significantly more representative of those in the ground state. Quantum Theory of Atoms in Molecules analysis is employed to explain the discrepancy between K- and M-edge data and demonstrates that the location of the core-hole impacts the pattern of electron localisation in core-excited states. An apparent contradiction to this behaviour in neptunyl is rationalised in terms interelectronic repulsion between the unpaired 5f electron and the excited core-electron.

Functional Properties of Tetrameric Molecular Cells for Quantum Cellular Automata: A Quantum-Mechanical Treatment Extended to the Range of Arbitrary Coulomb Repulsion

We discuss the problem of electron transfer (ET) in mixed valence (MV) molecules that is at the core of molecular Quantum Cellular Automata (QCA) functioning. Theoretical modelling of tetrameric bi-electronic MV molecular square (prototype of basic QCA cell) is reported. The model involves interelectronic Coulomb repulsion, vibronic coupling and ET between the neighboring redox sites. Unlike the majority of previous studies in which molecular QCA have been analyzed only for particular case when the Coulomb repulsion energy significantly exceeds the ET energy, here we do not imply assumptions on the relative strength of these two interactions. Moreover, in the present work we go beyond the adiabatic semiclassical approximation often used in theoretical analysis of such systems in spite of the fact that this approximation ignores such an important phenomenon as quantum tunneling. By analyzing the electronic density distributions in the cells and the ell-cell response functions obtained from a quantum-mechanical solution of a complex multimode vibronic problem we have concluded that such key features of QCA cell as bistability and switchability can be achieved even under failure of the condition of strong Coulomb repulsion provided that the vibronic coupling is strong enough. We also show that the semiclassical description of the cell-cell response functions loses its accuracy in the region of strong non-linearity, while the quantum-mechanical approach provides correct results for this critically important region.

Energy Levels in Pentacoordinate d5 to d9 Complexes

Energy levels of pentacoordinate d5 to d9 complexes were evaluated according to the generalized crystal field theory at three levels of sophistication for two limiting cases of pentacoordination: trigonal bipyramid and tetragonal pyramid. The electronic crystal field terms involve the interelectron repulsion and the crystal field potential; crystal field multiplets account for the spin–orbit interaction; and magnetic energy levels involve the orbital– and spin–Zeeman interactions with the magnetic field. The crystal field terms are labelled according to the irreducible representations of point groups D3h and C4v using Mulliken notation. The crystal field multiplets are labelled with the Bethe notations for the respective double groups D’3 and C’4. The magnetic functions, such as the temperature dependence of the effective magnetic moment and the field dependence of the magnetization, are evaluated by employing the apparatus of statistical thermodynamics as derivatives of the field-dependent partition function. When appropriate, the formalism of the spin Hamiltonian is applied, giving rise to a set of magnetic parameters, such as the zero-field splitting D and E, magnetogyric ratio tensor, and temperature-independent paramagnetism. The data calculated using GCFT were compared with the ab initio calculations at the CASSCF+NEVPT2 level and those involving the spin–orbit interaction.

Doublet Ground State in a Vanadium(II) Complex: Redox and Coordinative Noninnocence of Tripodal Ligand Architecture

We report on the geometric and electronic structures of a series of V2+/3+ tren-bridged iminopyridine complexes [tren = tris(2-aminoethyl)amine] that enable the observation of an unexpected doublet ground state for a nominally 3d3 species. Tren undergoes condensation reactions with picolinaldehyde or methyl-6-formylnictonate to form the respective tripodal ligand sets of (py)3tren and (5-CO2Mepy)3tren. The (py)3tren ligand is coordinated to V2+ and V3+ metal centers to form complex salts [1-H](OTf)2 and [1-H](OTf)3, respectively (OTf- = CF3SO3-). For [1-H]2+, strong metal-ligand π-covalency with respect to the V2+ (3d3) and iminopyridine ligands weakens its interelectronic repulsion. For [1-H]3+, the bridgehead nitrogen of the tren scaffold forms a seventh coordinate covalent bond with a V3+ (3d2) metal center. The coordination of (5-CO2Mepy)3tren to a V2+ metal center results in the redox noninnocent and heptacoordinate compound [1-CO2Me](OTf)2 with a doublet (S = 1/2) ground state that we support with magnetic susceptibility and spectroscopy measurements. The complexes are uniformly characterized experimentally with single-crystal X-ray diffraction, electronic absorbance, and electrochemistry, and electronic structures are corroborated by computational techniques. We present a new computational procedure that we term the spin-optimized approximate pair (SOAP) method that enables the visualization and quantification of electron-electron interactions.

Preparation of electrically enhanced forward osmosis (FO) membrane by two-dimensional MXenes for organic fouling mitigation

In this work, a conductive thin film composite forward osmosis (TFC-FO) membrane was firstly prepared via vacuum filtering MXenes nanolayer on the outer surface of polyethersulfone membrane followed by interfacial polymerization in the other side. Moreover, its feasibility of mitigating organic fouling under electric field was evaluated. Results indicated that the addition of MXenes greatly reduced the electric resistance of membrane from 2.1 × 1012 Ω to 46.8 Ω, enhanced the membrane porosity and promoted the membrane performance in terms of the ratio of water flux to reverse salt flux. The modified TFC-FO membrane presented the optimal performance with 0.47 g/m2 loading amount of MXenes. Organic fouling experiments using sodium alginate (SA) and bovine serum albumin (BSA) as representative demonstrated that the introduction of MXenes could effectively enhance the anti-fouling ability of TFC-FO membrane under the electric field of 2 V. The interelectron repulsion hindered organic foulants attaching into membrane surface and thus effectively alleviated the membrane fouling. More importantly, the modified TFC-FO membrane showed good stability during the fouling experiment of 10 h. In all, our work proved that introducing MXenes into the porous layer of support is feasible to alleviate organic fouling of FO membrane.

Influence of manganese ions on elastic and spectroscopic properties of ZnO doped novel calcium fluorophosphate bio active glasses

The glass system 20CaF2-20ZnO-(60-x)P2O5:xMnO with 0 ≤ x ≤ 5.0 was prepared and investigated. The structural changes induced by the addition of MnO in the glass network were explained by using physical, elastic, thermal, chemical durability and spectroscopic studies. Results indicate that with the increase of concentration of MnO content from 1 to 5 mol% the parameters like density, pH of the immersion liquid, elastic moduli and glass characteristic temperatures increases. While the dissociation rate, the Poisson’s ratio and volume per mol decreases and signifying the increased mechanical strength of the prepared glasses. FTIR spectral analysis predicts that all the specific vibrational bands of phosphate bonds like bridging oxygen with phosphorous action, linkages like P-O-P, O-P-O and the crossed linkages like P-O-Mn & P-O-Zn are affected by the incorporation of MnO in the glass matrix. The changes observed in peak positions and intensities of all vibrational bands of IR spectra and optical absorption spectra confirm that manganese ions behaves as a glass former and also as a glass modifier depending on the concentration of MnO. The analysis of the optical absorption spectra of the glasses in particular the crystal field and interelectronic repulsion parameters shows that manganese ions are predominantly occur in the divalent state and occupy tetrahedral sites in the glass matrix when the concentration of MnO in the CaF2-ZnO-P2O5 glasses exceeds 1.0 mol%.

Correlation effects close to the ground state critical charge of the two-electron atom

The critical charge, at which the “first ionization energy” of the ground-state of the two-electron atom vanishes, is evaluated for the radial limit, as well as for the s+p,s+p+d,s+p+d+f and s+p+d+f+g partially angularly correlated variational limits, getting closer and closer to the fully-correlated critical charge. The (counterintuitive) square integrability of the various correlated wave functions at their respective critical charges is deduced by noting that the derivatives of the corresponding binding energies with respect to Z (hence, the expectation values of the interelectronic repulsion) remain non-vanishing upon approaching these critical nuclear charges.

One-dimensional narrow-band conductors

We review one-dimensional lattice models and the corresponding results that describe the low-temperature properties of quasi-one-dimensional lattice systems with long-range interaction. A widely known example is narrow-band low-dimensional conductors with long-range interelectron repulsion. The models deal with particles that live on the one-dimensional host lattice (chain), translation invariant or disordered, and interact via the long-range repulsive potential. The results are presented concerning the translation invariant host chain, in particular: the low-temperature thermodynamics incommensurable ground states and related devil-staircase form of various characteristics as functions of pertinent parameters, the self-localization of particles, a new branch of elementary excitations, etc. In the disordered case, where the sites of the host chain fluctuate randomly around the sites of the periodic chain, the low-temperature thermodynamics and the structure of the ground state are discussed in the framework of a certain model, which we call the cluster model and which seems to be a fairly reasonable approximation for low temperatures and small concentration of particles. Using analytical and numerical tools we analyze the thermodynamics and the ground state of the model. The latter proves to be a sequence of random domains and we study in detail their distribution.

Spectroscopy of structurally disordered hydrated iron fluoridotitanate in the regions of vibrational and electronic excitations

Raman and optical absorption spectra of disordered hydrated iron fluoridotitanate (HITF) single crystal were studied. Temperature transformations of the Raman spectra indicate independent ordering processes of the [TiF6]2− and [Fe(H2O)6]2+ complexes below the structural phase transition. The absorption spectrum in the near-infrared and visible ranges includes transitions from the high spin ground state 5T2 of Fe2+ ion to the excited 5E state and a set of excited triplets. Analysis by Tanabe-Sugano method gives crystal field Dq = 490 cm−1 and Racah parameters B = 340 cm−1 and C = 1904 cm−1. Considerable decrease of B parameter as compared to the free ion value indicates a decrease of interelectron repulsion in the disordered neighborhood of Fe2+ ions.

Anomalous magnetism of uranium(IV)-oxo and -imido complexes reveals unusual doubly degenerate electronic ground states

Anomalous magnetism of uranium(IV)-oxo and -imido complexes reveals unusual doubly degenerate electronic ground states

Rényi, Fisher, Shannon, and their electron correlation tools for two-electron series

Information entropies, such as Rényi, Fisher, and Shannon, are calculated for the 1s2-state of the two-electron series, in position space. It is considered that the exponential cosine screened Coulomb potential (ECSCP) describes the medium. Explicit correlated Hylleraas functions with 3-parameter are used to focus on getting the most distinctive physical features of the inter-electronic repulsion results. In one- and two-electron charge densities, the numerical values of the information entropies and their ratios are calculated. Fisher-Shannon, and Fisher-Rényi information products that measure the electron-electron correlation strength, are calculated and discussed. Also, we used the contour maps and 3D-graphs to visualize how the interplay between inter-electronic repulsion and electrons-nuclear charge interaction determines the variation of information entropies as a function of the nuclear charge and the screening parameter. In this work, an expression for the divergence in Hylleraas coordinates has been derived and the results of the information quantities for two-electron systems with ECSCP have been calculated, in one-and two-electron densities, for the first time.

Tomonaga–Luttinger liquid in the edge channels of a quantum spin Hall insulator

Quantum spin Hall insulators are two-dimensional materials that host conducting helical electron states strictly confined to the one-dimensional boundaries. These edge channels are protected by time-reversal symmetry against single-particle backscattering, opening new avenues for spin-based electronics and computation. However, the effect of the interelectronic Coulomb repulsion also has to be taken into account, as two-particle scattering is not impeded by topological protection and may strongly affect the edge state conductance. Here, we explore the impact of electronic correlations on highly localized edge states of the unique quantum spin Hall material bismuthene on SiC(0001) (ref. 1). Exploiting the advantage of having an accessible monolayer substrate system, we use STM/STS to visualize the close-to-perfect one-dimensional confinement of the edge channels and scrutinize their suppressed density of states at the Fermi level. On the basis of the observed spectral behaviour and its universal scaling with energy and temperature, we demonstrate the correspondence with a (helical) Tomonaga–Luttinger liquid. In particular, the extracted interaction parameter K is directly relevant to the fundamental question of the temperatures at which the quantized conductance (a hallmark of quantum spin Hall materials) will become obscured by correlations2. Scanning tunnelling microscopy and spectroscopy study of the conductive edge state in a two-dimensional topological insulator reveals the interplay of topology and electronic correlations.

Theoretical insight into the magnetic circular dichroism of uranium N6,7‐edge X‐ray absorption

AbstractWe use ligand‐field density functional theory to determine the electronic structure and to model magnetic circular dichroism in the X‐ray absorption spectroscopy (XAS) of uranium compounds. This study extends earlier work on tetravalent uranium ion, in which a model Hamiltonian was set up in order to study electronic structure with three nonequivalent 4f, 5f, and 6d electrons. In the earlier work, the model Hamiltonian took into consideration the interelectron repulsion, spin‐orbit coupling interaction, and ligand‐field splitting. Uranium N6,7‐edge XAS spectra were calculated on the basis of the 5f2 → 4f135f26d1 electron transition, showing spectral profiles that were mainly dominated by 4f electron spin‐orbit coupling, as well as 6d ligand‐field splitting. Fine structures were also observed due to the interelectronic repulsion between 4f‐5f, 4f‐6d, and 5f‐6d electrons. Here, the theoretical study is extended to take into consideration the presence of an external magnetic field, incorporating into the model Hamiltonian for three‐open‐shell electron configuration a term for Zeeman interaction. Therefore, we are able to model spectra with a left‐circularly and right‐circularly polarized X‐ray, demonstrating evidence of X‐ray magnetic circular dichroism (XMCD) for a tetravalent U4+ ion in the molecular (U(η8‐C8H8)2) complex. The XMCD originates from a ground‐state electronic structure with open‐shell 5f electrons. Furthermore, the present calculation of uranium N6,7‐edge XAS and XMCD spectra also enables the ligand‐field bonding analysis of the coordination compound.

Correlation effects and configuration of a one-dimensional bipolaron

Abstract The aim of the work is to study the structure of a one-dimensional (1D) bipolaron, taking into account three types of correlation effects: such as interelectronic correlations caused by the direct dependence of the wave function on the distance between electrons as well as the one-center and two-center correlations. Gaussian orbitals with exponentially-correlated multipliers were used for variational calculations. It is shown that in the domain of existence of an 1D optical bipolaron – unlike in a 3D system – a two-center bipolaron is formed. The one-center bipolaron configuration becomes energetically favorable as compared to the two-center one for V C ≤ 1.2 (where V C is interelectronic repulsion parameter). This domain corresponds to an acoustical or acousto-optical bipolaron in the strong-coupling limit.

Spectroscopic and mechanical studies of lithium aluminoborate glasses doped with chromium ions

Aluminoborate glasses, doped with chromium ions, were prepared using melt quenching technique. Spectroscopic and mechanical tools were utilized to study the impact of B2O3 substitution with Al2O3 on the structure of the glass system. Infrared spectra uncovered that substitution of B2O3 with Al2O3 causes concealment of non-bridging oxygen NBOs and creation of inflexible AlO4 tetrahedral. The UV–Vis absorption spectra demonstrated a blue-shift of the optical absorption edge with increasing Al2O3 content. The optical band gap was found to increase, while the refractive index diminished with addition of Al2O3 content. The calculated crystalline field Dq, Racah parameters (B and C) and Dq/B indicated the diminishment in inter-electron repulsion with increasing the covalency. In particular, a value of Dq/B larger than 2.3 assures that chromium ions are in strong ligand field sites. The elastic moduli increase with increasing Al2O3 content, due to the reduction NBOs and, consequently, the increased average bond connectivity.