Electron pairing in one‐dimensional anharmonic crystal lattices

We show that when anharmonicity is added to the electron–phonon interaction it facilitates electron pairing in a localized state. Such localized state appears as singlet state of two electrons bound with the traveling local lattice soliton distortion, which survives when Coulomb repulsion is included. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Superconductivity from repulsive electronic correlations on alternant cuprate and iron‐based lattices

A key question in the theory of high‐temperature superconductivity is whether off‐diagonal long‐range order can be induced wholly or in large part by repulsive electronic correlations. Electron pairs on cuprate and the iron‐based pnictide and chalcogenide alternant lattices may interact with a strong short‐range Coulomb repulsion and much weaker longer range attractive tail. Here, we show that such interacting electrons can cooperate to produce a superconducting state in which time‐reversed electron pairs effectively avoid the repulsive part but reside predominantly in the attractive region of the potential. The alternant lattice structure is a key feature of such a stabilization mechanism leading to the occurrence of high‐temperature superconductivity with or sign alternating s‐wave or s± condensate symmetries. © 2013 Wiley Periodicals, Inc.     

Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Correlation between large polarons in molecular chains

We studied few extra electrons in a molecular chain with respect of electron-phonon coupling in the adiabatic approximation. It is shown that the lowest state of two extra electrons in a chain corresponds to the singlet bisoliton state with one deformational potential well. Two electrons with parallel spins form a localised triplet state, which corresponds to the two-hump charge distribution function. Three extra electrons form an almost independent nonlinear superposition of a soliton and bisoliton states. In the case of four electrons, the two almost independent bisolitons are formed. These two states tend to separate in the chain at the maximal distance due to the Fermi repulsion, accounted for in the zero-order adiabatic approximation. This repulsion is partly compensated by the attraction between the solitons due to their exchange with virtual phonons, described by the non-adiabatic part of the Hamiltonian. The formation of solitons is characterised by the appearance of the bound soliton and bisoliton levels in the forbidden energy band. This constitutes the qualitative difference of the large polaron (soliton) states from the almost free electron states and small polaron states.     

High‐temperature superconductivity and long‐range order in strongly correlated electronic systems

A selective review of the question of how repulsive electron correlations might give rise to off‐diagonal long‐range order (ODLRO) in high‐temperature superconductors is presented. The article makes detailed explanations of the relevance to superconductivity of reduced electronic density matrices and how these can be used to understand whether ODLRO might arise from Coulombic repulsions in strongly correlated electronic systems. Time‐reversed electron pairs on alternant Cuprate and the iron‐based pnictide and chalcogenide lattices may have a weak long‐range attractive tail and much stronger short‐range repulsive Coulomb interaction. The long‐range attractive tail may find its origin in one of the many suggested proposals for high‐T_c superconductivity and thus has an uncertain origin. A phenomenological Hamiltonian is invoked whose model parameters are obtained by fitting to experimental data. A detailed summary is given of the arguments that such interacting electrons can cooperate to produce a superconducting state in which time‐reversed pairs of electrons effectively avoid the repulsive hard‐core of the Coulomb interaction but reside on average in the attractive well of the long‐range potential. Thus, the pairing of electrons itself provides an enhanced screening mechanism. The alternant lattice structure is the key to achieving robust high‐temperature superconductivity with dx²‐y² or sign alternating s‐wave or s± condensate symmetries in cuprates and iron‐based compounds. Some attention is also given to the question first raised by Leggett as to where the Coulombic energy is saved in the superconducting transition in cuprates. A mean‐field‐type model in which the condensate density serves as an order parameter is discussed. Many of the observed trends in the thermal properties of cuprate superconductors are reproduced giving strong support for the proposed model for high‐temperature superconductivity in such strongly correlated electronic systems. © 2015 Wiley Periodicals, Inc.     

Site‐Directed,On‐Surface Assembly of DNA Nanostructures

Two‐dimensional DNA lattices have been assembled from DNA double‐crossover (DX) motifs on DNA‐encoded surfaces in a site‐specific manner. The lattices contained two types of single‐stranded protruding arms pointing into opposite directions of the plane. One type of these protruding arms served to anchor the DNA lattice on the solid support through specific hybridization with surface‐bound, complementary capture oligomers. The other type of arms allowed for further attachment of DNA‐tethered probe molecules on the opposite side of the lattices exposed to the solution. Site‐specific lattice assembly and attachment of fluorophore‐labeled oligonucleotides and DNA–protein conjugates was demonstrated using DNA microarrays on flat, transparent mica substrates. Owing to their programmable orientation and addressability over a broad dynamic range from the nanometer to the millimeter length scale, such supramolecular architecture might be used for presenting biomolecules on surfaces, for instance, in biosensor applications.     

Site‐Directed,On‐Surface Assembly of DNA Nanostructures

Two‐dimensional DNA lattices have been assembled from DNA double‐crossover (DX) motifs on DNA‐encoded surfaces in a site‐specific manner. The lattices contained two types of single‐stranded protruding arms pointing into opposite directions of the plane. One type of these protruding arms served to anchor the DNA lattice on the solid support through specific hybridization with surface‐bound, complementary capture oligomers. The other type of arms allowed for further attachment of DNA‐tethered probe molecules on the opposite side of the lattices exposed to the solution. Site‐specific lattice assembly and attachment of fluorophore‐labeled oligonucleotides and DNA–protein conjugates was demonstrated using DNA microarrays on flat, transparent mica substrates. Owing to their programmable orientation and addressability over a broad dynamic range from the nanometer to the millimeter length scale, such supramolecular architecture might be used for presenting biomolecules on surfaces, for instance, in biosensor applications.     

Long-range energy transfer and ionization in extended quantum systems driven by ultrashort spatially shaped laser pulses

The processes of ionization and energy transfer in a quantum system composed of two distant H atoms with an initial internuclear separation of 100 atomic units (5.29 nm) have been studied by the numerical solution of the time-dependent Schr?dinger equation beyond the Born-Oppenheimer approximation. Thereby it has been assumed that only one of the two H atoms was excited by temporally and spatially shaped laser pulses at various laser carrier frequencies. The quantum dynamics of the extended H-H system, which was taken to be initially either in an unentangled or an entangled ground state, has been explored within a linear three-dimensional model, including the two z coordinates of the electrons and the internuclear distance R. An efficient energy transfer from the laser-excited H atom (atom A) to the other H atom (atom B) and the ionization of the latter have been found. It has been shown that the physical mechanisms of the energy transfer as well as of the ionization of atom B are the Coulomb attraction of the laser driven electron of atom A by the proton of atom B and a short-range Coulomb repulsion of the two electrons when their wave functions strongly overlap in the domain of atom B.     

Significant reduction of on-site Coulomb energy U due to short-range correlation in an organic Mott insulator.

By carrying out a first-principles T-matrix calculation on multiple scatterings between electrons, we show that the intramolecular electron-electron interaction energy U, of a Mott insulator of the organic radical 1,3,5-trithia-2,4,6-triazapentalenyl (TTTA) is significantly reduced from the naive expectation value of the Coulomb interaction (7.3 eV and 5.3 eV, respectively, for the bare and screened Coulomb interactions) to 2.9 eV due to the short-range correlation. This result together with the intermolecular interaction energy D=1.3 eV explains the experimental optical gap (1.5 eV). The associated two-particle wavefunction clearly shows the Coulomb hole indicating that two electrons with antiparallel spins cannot approach because of the Coulomb repulsion. We also discuss the energetics and magnetics of this system.     

Intact Four‐atom Organic Tetracation Stabilized by Charge Localization in the Gas Phase

Several features distinguish intact multiply charged molecular cations (MMCs) from other species such as monocations and polycations: high potential energy, high electron affinity, a high density of electronic states with various spin multiplicities, and charge‐dependent reactions. However, repulsive Coulombic interactions make MMCs quite unstable, and hence small organic MMCs are currently not readily available. Herein, we report that the isolated four‐atom molecule diiodoacetylene survives after the removal of four electrons via tunneling. We show that the tetracation remains metastable towards dissociation because of the localization (91–95 %) of the positive charges on the terminal iodine atoms, ensuring minimum Coulomb repulsion between adjacent atoms as well as maximum charge‐induced attractive dipole interactions between iodine and carbon. Our approach making use of iodines as the positively charged sites enables small organic MMCs to remain intact.     

Dupré–Blundell model for the Landau diamagnetism applied to electrons gyrating in a crystalline solid

The model developed by Dupré and Blundell for calculating the Landau diamagnetism of free electrons is adapted to the case when the tightly bound electrons in a crystal lattice are submitted to the action of the magnetic field. In particular, the frequency of the electron gyration and the energy change contributing to the nonoscillating part of the diamagnetism are considered for the simple cubic and the body‐centered cubic lattices. The plots of the energy change done versus the position of the Fermi energy in a crystal exhibit much different behavior than a similar plot obtained in the free‐electron case. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

On robust density fitting in molecules and extended systems

Two theorems for robust density fitting are proved: A. For a given electron density, the best robust density fitting approximation to the Coulomb electron repulsion energy results from the unconstrained Coulomb metric fit, B. For infinite periodic systems, the necessary condition for correct long-range behavior of any robust density fitting approximation of the Coulomb electron repulsion energy is the exact reproduction of the number of electrons.     

Antiferromagnetic phase of a 2‐D Wigner crystal

The antiferromagnetic phase of a 2‐D Wigner crystal is investigated, using a localized representation for electrons. In our model, the electrons are located at the lattice sites of a face‐centered square lattice (corresponding to bcc in the 3‐D case). This lattice may be thought of as consisting of two equivalent interpenetrating sublattices. The ground‐state energies of the antiferromagnetic phase of a 2‐D Wigner electron crystal are computed with uniform neutralizing, Gaussian‐type, and Yukawa‐type positive backgrounds in the range of r_s = 5 to 130. The role of correlation energy is suitably taken into account. The possibility of the antiferromagnetic phase of the 2‐D Wigner crystal having a square or circle as the region of occupation in momentum space is also analyzed. The low‐density region favorable for the antiferromagnetic phase of Wigner crystallization is found to be at r_s = 7.0. Our results agree well with experimental and other theoretical results for the 2‐D Wigner crystal. The structure‐dependent Wannier functions, which give proper localized representation for Wigner electrons, are constructed and employed in the calculation for the first time. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Excitation spectrum of Hubbard model with infinite electron repulsion on strip‐type triangular lattices

The estimations of the stability region of the lattice ferromagnetic ground state in the space of model parameters are found. For the triangular lattice strip formed by L segments with the total number of electrons N=L+1 we derived the effective Hamiltonians describing the low‐energy states of the strips and obtained the analytical estimations for above stability region. The possibility of the magnetic transition with the jump of the ground‐state spin between minimal and maximal values has also been shown. For the strip with N=L and an alternating value of the one‐site potential energy, we have obtained the exact relation between electron parameters, which provides the ferromagnetic character of the lattice ground state. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 253–259, 2001     

Electrochemical transistor based on bridge tunneling contact containing two redox groups

The method of kinetic equations was used to show that a bridge tunneling contact containing two redox groups in the sequential configuration immersed into a solution of electrolyte at the room temperature features pronounced transistor properties at a given set of physical system parameters. Valence electrons of redox groups interact strongly with the classical phonon subsystem of the liquid medium. Debye screening of the electric field in the tunneling gap and Coulomb repulsion between electrons in different redox groups are taken into account. The case of nonadiabatic electron transfer both between redox groups and between electrodes and redox groups is considered in the limit of infinitely high Coulomb repulsion between electrons in a redox group. For sufficiently high absolute values of difference δ between unperturbed energy levels of redox groups, the system features voltammetric characteristics typical for a transistor. The amplification effect appears due to a strong dependence of tunneling current on overpotential. The emphasis is upon the peculiaritiespeculiarities of voltammetric characteristics in the case of asymmetric tunneling contacts.     

Na4IrO4: Square‐Planar Coordination of a Transition Metal in d5 Configuration due to Weak On‐Site Coulomb Interactions

Local environments and valence electron counts primarily determine the electronic states and physical properties of transition‐metal complexes. For example, square‐planar coordination geometries found in transition‐metal oxometalates such as cuprates are usually associated with the d⁸ or d⁹ electron configuration. In this work, we address an unusual square‐planar single oxoanionic [IrO₄]^4? species, as observed in Na₄IrO₄ in which Ir^IV has a d⁵ configuration, and characterize the chemical bonding through experiments and by ab initio calculations. We find that the Ir^IV center in ground‐state Na₄IrO₄ has square‐planar coordination geometry because of the weak Coulomb repulsion of the Ir‐5d electrons. In contrast, in its 3d counterpart Na₄CoO₄, the Co^IV center is tetrahedrally coordinated because of strong electron correlation. Na₄IrO₄ may thus serve as a simple yet important example to study the ramifications of Hubbard‐type Coulomb interactions on local geometries.     

New procedure to evaluate aromaticity at the density functional theory,Hartree–Fock,and post‐self‐consistent field levels

The spatial exchange interaction, arising from the exchange‐type two‐electron integrals ( ) between two different groups P and Q, is another driving force for the delocalization of π‐electrons besides orbital charge‐transfer and exchange interactions. We have developed a new combination program for restricted geometry optimization, in which all of the orbital and spatial interactions among isolated groups were excluded from the localized geometry of a conjugated molecule. This was achieved by deleting particular Fock elements and the 15 types of exchange‐type two‐electron integrals, ensuring that the corresponding π‐electrons are completely localized within their respective groups and the π‐orbitals are fully localized. The extra stabilization energy (ESE) of benzene is ?36.3 kcal/mol (B3LYP/6‐31G*), and the level of density functional theory, Hartree–Fock, and post‐self‐consistent field (Møller–Plesset 2, configuration interaction singles and doubles, and singles and doubles coupled‐cluster) and the basis sets have slight effect on the ESE. Based on the comparisons between our procedure, Morokuma's energy decomposition analysis and the block‐localized wave function method, it was confirmed that our program calculates reliable results. The nonaromaticity of acyclic polyenes and antiaromaticity of cyclobutadiene and planar cyclooctatetraene were also estimated. Comparison of the C? C single bond lengths in the ground state with its π‐localized geometries showed that shortening of the single bonds in acyclic polyenes and butadiyne should be attributed to different hybridization, demonstrating that the effect of π‐delocalization on single bonds is so small as to be negligible. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

On‐site correlation of p‐electron in d10 semiconductor zinc oxide

Using GGA+U approach based on the density functional theory, the on‐site correlation and the electronic structure of wurtzite zinc oxide are investigated. By atomic population analysis, the zinc 3d orbital is found to be almost fully filled, but the oxygen 2p orbital is partially filled. So, the zinc oxide can be approximately regarded as a sort of d¹⁰ semiconductor. Similar to that of d⁰ magnets found previously, the on‐site Coulomb repulsion of 2p orbital in such a d¹⁰ system is shown to be also indispensable in addition to that of 3d orbital. As the unconventional on‐site Coulomb repulsion of O 2p is considered, the theoretical results agree with the previous experimental observations satisfactorily. The partial density of states shows significant O? Zn hybridization in the valence band, but it decreases a little as the on‐site correlations are taken into account. © 2013 Wiley Periodicals, Inc.     

On the calculation of arbitrary multielectron molecular integrals over Slater‐type orbitals using recurrence relations for overlap integrals. II. Two‐center expansion method

Using expansion formulas for the charge‐density over Slater‐type orbitals (STOs) obtained by the one of authors [I. I. Guseinov, J Mol Struct (Theochem) 1997, 417, 117] the multicenter molecular integrals with an arbitrary multielectron operator are expressed in terms of the overlap integrals with the same screening parameters of STOs and the basic multielectron two‐center Coulomb or hybrid integrals with the same operator. In the special case of two‐electron electron‐repulsion operator appearing in the Hartree–Fock–Roothaan (HFR) equations for molecules the new auxiliary functions are introduced by means of which basic two‐center Coulomb and hybrid integrals are expressed. Using recurrence relations for auxiliary functions the multicenter electron‐repulsion integrals are calculated for extremely large quantum numbers. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 117–125, 2001     

Effect of Coulomb interaction between the electrons on two-electron redox-mediated tunneling

Two-electron non-adiabatic redox-mediated tunneling through a symmetric electrochemical contact with a bridge molecule having one electron energy level participating in tunneling is considered under ambient conditions. It is shown that the current/overpotential dependence in this system can disclose two distinct or overlapping clear-cut maxima depending on the value of the effective Coulomb repulsion energy. This new effect is due to the opening of the channel for tunneling of second electron with the variation of the electrode potential. The system manifests also a rectification effect in the current/bias voltage curve which depends on the value of the effective Coulomb repulsion energy.