Convergence of the orbital expansion in a correlated system: A test study on positronium

Positronium, the bound state of an electron and a positron, is an exactly soluble quantum system, similar to a light isotope of hydrogen. It can be studied using the finite basis quantum chemistry codes developed for atoms and molecules. In fact, positronium can be mimicked by two electrons with opposite spins, in the absence of any nucleus and having the sign of the Coulomb interaction reversed. The exact wave function has a cusp in the points of coalescence of the two particles (a “Coulomb peak”), and this fact makes the convergence of the total energy, as a function of the basis set size, extremely slow. For this reason, positronium can be used to test the convergence properties of the quantum chemistry methods used to describe the dynamic correlation. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

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     

Can electrons attract one another?

Electrons are believed to avoid one another in space (correlation) due to the Coulomb repulsion and/or the Pauli exclusion principle. It is shown, using examples of two-electron systems, that indeed the mean electron-electron distance increases in case of the ground electronic state as compared to the independent electron model. It is demonstrated however that there exist excited states, often of low energy, in which the electrons, while having a lot of free physical space (with nuclei being absent), choose to be close to each other in their motion (“anticorrelation”), as if they mutually attracted one another. The source of this effect, quantummechanical in nature, is the orthogonality of the eigenfunctions, that forces the electronic wave functions to differ widely, even at the price of short electron-electron distances. There are also excited states with a mixed behaviour, with complex and often intriguing correlation-anticorrelation patterns.     

Evaluation of screened nuclear attraction and electron repulsion molecular integrals over Gaussian basis functions

Analytical solutions to the Yukawa-like screened Coulomb nuclear attraction and electron repulsion molecular basic integrals, as well as to the basic integrals required to compute the virial coefficient, over Gaussian basis functions, are derived and cast into a practical closed form, suitable to interface with modern codes for the calculation of molecular electronic structure. © 1997 John Wiley & Sons, Inc.     

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.     

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.     

Parallelization of three-center electron repulsion integrals

The parallelization of the three-center electron repulsion integrals arising from the variational fitting of the Coulomb potential is presented. A scheme for dynamical load balancing of the corresponding loop structure is discussed. The implementation in the density functional theory program deMon using the message passing interface is described. The efficiency of the parallelization is analyzed by selected benchmark calculations     

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.     

Theory for the optical properties of small Hg n clusters

The static and dynamical polarizabilities of the Hg-dimer are calculated by using a Hubbard Hamiltonian to describe the electronic structure. The Hamiltonian is diagonalized exactly within a subspace of second-quantized electronic states from which only multiply ionized atomic configurations have been excluded. With this approximation we can describe the most important electronic transitions including the effect of charge fluctuations. We analyze the polarizability as a function of the intraatomic Coulomb interaction which represents the repulsion between electrons. We obtain that this interaction results in strong electronic correlations in the excited states and increases the first excitation energy of the dimer by 0.8 eV in comparison to a calculation which neglects correlations, resulting in a better agreement with the experiment.     

The Coulomb Hole of the Ne Atom

We analyze the Coulomb hole of Ne from highly-accurate CISD wave functions obtained from optimized even-tempered basis sets. Using a two-fold extrapolation procedure we obtain highly accurate results that recover 97 % of the correlation energy. We confirm the existence of a shoulder in the short-range region of the Coulomb hole of the Ne atom, which is due to an internal reorganization of the K-shell caused by electron correlation of the core electrons. The feature is very sensitive to the quality of the basis set in the core region and it is not exclusive to Ne, being also present in most of second-row atoms, thus confirming that it is due to K-shell correlation effects.     

Unpaired electrons at the second‐order reduced density matrix level: Covalent bonding,and coulomb and fermi correlations in closed shell systems

The usual one‐electron populations in atomic orbitals of closed shell systems are split into unpaired and paired at the (spin‐dependent) second‐order reduced density matrix level. The unpaired electron in an orbital is defined as the “simultaneous occurrence of an electron and an electron hole of opposite spins in the same spatial orbital,” which for simplicity is called “electropon.” The electropon population in a given orbital reveals whether and to what degree the Coulomb correlations, and hence, the chemical bonding between this orbital and the remaining orbitals of the system are globally favorable or unfavorable. The interaction of two electropons in two target orbitals reveals the quality (favorable or unfavorable) and the strength of the covalent bonding between these orbitals; this establish a bridge between the notion of “unpaired electrons” and the traditional covalent structure of valence‐bond (VB) theory. Favorable/unfavorable bonding between two orbitals is characterized by the positive/negative (Coulomb) correlation of two electropons of opposite spins, or alternatively, by the negative/positive (Fermi) correlation of two parallel spin electropons. A spin‐free index is defined, and the relationship between the electropon viewpoint for chemical bonding and the well‐known two‐electron Coulomb and Fermi correlations is established. Benchmark calculations are achieved for ethylene, hexatriene, benzene, pyrrole, methylamine, and ammonia molecules on the basis of physically meaningful natural orbitals. The results, obtained in the framework of both orthogonal and nonorthogonal population analysis methods, provide the same conceptual pictures, which are in very good agreement with elementary chemical knowledge and VB theory. © 2013 Wiley Periodicals, Inc.     

Orbital mechanism of upright CO activation on Fe(100)

The knowledge of bond activation forms a cornerstone for modern chemistry, wherein symmetry rules of electronic activation lie in the heart of bond activation. However, the question as to how a chemical bond is activated remains elusive. By taking CO activated on Fe(100), herein, we have resolved the long-standing fundamental question; we have found that excitations in the adsorbate feature the bond activation. We essentially have discovered contrasting electronic processes in respective σ and π electron systems of the adsorbed CO molecule. The σ electron system is involved in reversible hidden excitations/deexcitations between two occupied σ orbitals, whereas the π electron system is subject to irreversible π to π* excitations dispersed along the d-band region, which is coupled to the rotational 2π electron couplings depending on the strength of molecule-metal interactions. The σ excitations pertain to the Pauli repulsion mediated quantum nature with energy and entropy marked by the two energy levels, whereas the π to π* excitations fall into a new category of electronic excitations contributing to energy and entropy exchanges in a wide and continuous d-band region. The findings that the internal states of the adsorbate are excited and that fundamental connections between the frontier orbitals and low-lying orbitals are established as the molecule comes to the surface may open up new channels to realize more efficient bond activation and renew our thinking on probing the quantum mechanical nature of bond activation at surfaces with further possible impact on manipulation of orbital activation in femtochemistry and attochemistry.     

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.     

Bending the Curve: Molecular Manifestations of Electron Antisymmetry

As very light fermions, electrons are governed by antisymmetric wave functions that lead to exchange integrals in the evaluation of the energy. Here we use the localized representation of orbitals to decompose the electronic energy in a fashion that isolates the enigmatic exchange contributions and characterizes their distinctive control over electron distributions. The key to this completely general analysis is considering the electrons in groups of three, drawing attention to the curvatures of pair potentials, rather than just their amplitudes and slopes. We show that a positive curvature at short distances is essential for the mutual distancing of electrons and a negative curvature at longer distances is essential to account for the influence of lone pairs on bond torsion. Neither curvature is available in the absence of the exchange contributions. Thus, although exchange energies are much shorter range than Coulomb energies, their influence on molecular geometry is profound and readily understood.     

Pair Function and Structure Factor of an Interacting Electron Liquid

Abstract

Recent work on small angle scattering from liquid metals has caused renewed interest in the electron pair function in the uniform interacting electron liquid, jellium. Therefore we have re-examined this problem, starting from an analysis of the exchange hole, in which the only correlations are due to the Pauli Principle and solely therefore between parallel spin electrons. The pair function g(r) of noninteracting Fermions is expressed in terms of the density of the p-component in the free electron density matrix. This motivates the treatment of the Coulomb repulsion via a potential energy V(r) To close the theory, one must either invoke self-consistency to determine V(r), or relate it to the (direct) correlation function c(r) as in classical liquids. Both methods are briefly considered; the second has the advantage that here the collective plasma oscillations can be introduced through their zero-point energy.     

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.     

Effects of electron correlations in a surface-molecule model for the adiabatic electrochemical electron transfer reactions with allowance for the electrostatic repulsion of electrons on an effective orbital of metal

Within the framework of a surface-molecule model for the adiabatic electrochemical electron transfer reactions, exact expressions for the adiabatic free energy surfaces are obtained and the diagrams of kinetic modes are constructed with allowance made for the electrostatic repulsion between electrons with the opposite spin projection both on the valence orbital of the reactant and on the effective electron orbital of the metal. It is shown that taking into account the electrostatic repulsion on the effective orbital of the metal and the correlation effects connected with it is very substantial for a number of electrochemical electron-transfer reactions and leads not only to an alteration of the activation free energies but also to qualitatively different forms of adiabatic free energy surfaces in some regions of values of the model’s parameters.     

Correlation effects in molecular conductors

The source-sink potential (SSP) model introduced previously [F. Goyer, M. Ernzerhof, and M. Zhuang, J. Chem. Phys. 126, 144104 (2007)] enables one to eliminate the semi-infinite contacts in molecular electronic devices (MEDs) in favor of complex potentials. SSP has originally been derived for independent electrons and extended to interacting two-electron systems subsequently [A. Goker, F. Goyer, and M. Ernzerhof, J. Chem. Phys. 129, 194901 (2008)]. Here we generalize SSP to N-electron systems and consider the impact of electron correlation on the transmission probability. In our correlated method for molecular conductors, the molecular part of the Hu?ckel Hamiltonian of the original SSP is replaced by the Hubbard Hamiltonian. For the contacts, however, the single-electron picture is retained and they are assumed to be spin polarized. Using our method, we study electron transmission in molecular wires, cross-conjugated chains, as well as aromatic systems. We find that, for realistic values of the electron-electron repulsion parameter, correlation effects modify the transmission probability quantitatively, the qualitative features remain. However, we find subtle new effects in correlated MEDs, such as Coulomb drag, that are absent in uncorrelated systems.