Short-range Electron Correlation Research Articles

Local-spin-density functional for multideterminant density functional theory

Based on exact limits and quantum Monte Carlo simulations, we obtain, at any density and spin polarization, an accurate estimate for the energy of a modified homogeneous electron gas where electrons repel each other only with a long-range coulombic tail. This allows us to construct an analytic local-spin-density exchange-correlation functional appropriate to new, multideterminantal versions of the density functional theory, where quantum chemistry and approximate exchange-correlation functionals are combined to optimally describe both long- and short-range electron correlations.

Theory of the short-range correlation hole model

While standard ab initio methods have provided a route towards highly accurate calculations of a vast array of chemical properties, the applicability of these methods is limited essentially because the computational effort of a correlated calculation grows very rapidly with the number of atomic basis functions while the accuracy does not. Thus, extensive one-particle basis sets are required for reasonable accuracy and, therefore, only small systems can be treated routinely. A great deal of effort has gone into finding ways to circumvent this difficulty, which has been attributed to the improper description of short-range electron correlation. In a recent paper, we introduced a technique intended to partially correct this improper description by using a local density approximation for the short-range correlation hole. Here, we wish to elaborate on the basic concept in several ways. We introduce a more reliable cut-off procedure, discuss the effects of gradient corrections and show how a Hamiltonian can be constructed. This points the way towards the calculation of properties, gradients, excitation energies and so forth; hiding basis set effects in the Hamiltonian is essential to developing a generally applicable method for molecules.

Collective charge modes in a 1D electron liquid

A new behavior of the collective mode in a 1D electron liquid is found. The charge mode frequency goes to zero when the wave number is close to double Fermi wave number, i.e. the soft mode appears in addition to common long-wave plasmons. This mode is related to dynamic short-range electron correlations, which are adequately described in the frame of the Luttinger model. The soft mode is immanent in 1D and is absent in higher-dimensional systems. The results are valid for both Coulomb and short-range electron–electron interaction.

Long-range and short-range Coulomb correlation effects as simulated by Hartree-Fock, local density approximation, and generalized gradient approximation exchange functionals

Exchange functionals used in density functional theory (DFT) are generally considered to simulate long-range electron correlation effects. It is shown that these effects can be traced back to the self-interaction error (SIE) of approximate exchange functionals. An analysis of the SIE with the help of the exchange hole reveals that both short-range (dynamic) and long-range (nondynamic) electron correlation effects are simulated by DFT exchange where the local density approximation (LDA) accounts for stronger effects than the generalized gradient expansion (GGA). This is a result of the fact that the GGA exchange hole describes the exact exchange hole close to the reference electron more accurately than the LDA hole does. The LDA hole is more diffuse, thus leading to an underestimation of exchange and stronger SIE effects, where the magnitude of the SIE energy is primarily due to the contribution of the core orbitals. The GGA exchange hole is more compact, which leads to an exaggeration of exchange in the bond and the nonbonding region and negative SIE contributions. Partitioning of the SIE into intra-/interelectronic and individual orbital contributions makes it possible to test the performance of a given exchange functional in different regions of the molecule. It is shown that Hartree–Fock exchange always covers some long-range effects via interelectronic exchange while self-interaction-corrected DFT is lacking these effects.

Dynamic correlations of the spinless Coulomb Luttinger liquid

The dynamic density response function, form-factor, and spectral function of a Luttinger liquid with Coulomb electron-electron interaction are studied with the emphasis on the short-range electron correlations. The Coulomb interaction changes dramatically the density response function as compared to the case of the short-ranged interaction. The form of the density response function is smoothing with time, and the oscillatory structure appears. However, the spectral functions remain qualitatively the same. The dynamic form-factor contains the $\delta$-peak in the long-wave region, corresponding to one-boson excitations. Besides, the multi-boson-excitations band exists in the wave-number region near to $2k_F$. The dynamic form-factor diverges at the edges of this band, while the dielectric function goes to zero there, which indicates the appearance of a soft mode. We develop a method to analyze the asymptotics of the spectral functions near to the edges of the multi-boson-excitations band.

Influence of the self-interaction error on the structure of the DFT exchange hole

Approximate density functional theory (DFT) covers long-range non-dynamic electron correlation via the exchange functional while the correlation functional includes just the short-range dynamic electron correlation effects. We show that the self-interaction error of approximate exchange functionals (local density approximation, LDA and others) mimics the long-range correlation effects. For this purpose the exchange hole is investigated at the Hartree–Fock, the LDA, and the self-interaction corrected (SIC)-LDA levels of theory.

Effect of short-range electron correlations in dynamic transport in a Luttinger liquid

The density operator in the Luttinger model consists of two components, one of which describes long-wave fluctuations and the other is related to the rapid oscillations of the charge-density-wave (CDW) type, caused by short-range electron correlations. It is commonly believed that the conductance is determined by the long-wave component. The CDW component is considered only when an impurity is present. We investigate the contribution of this component to the dynamic density response of a Luttinger liquid free from impurities. We show that the conventional form of the CDW density operator does not conserve the number of particles in the system. We propose the corrected CDW density operator devoid of this shortcoming and calculate the dissipative conductance in the case when the one-dimensional conductor is locally disturbed by a conducting probe. The contribution of the CDW component to conductance is found to dominate over that of the long-wave component in the low-frequency regime.

The continuum theory of delocalized and self-trapped polarons and bipolarons in solids

The continuum theory of delocalized (D) and self-trapped (S) polarons and bipolarons is developed within the adiabatic approximation and the direct variational approach. The role of each taken separately and the combined effects of the short- and long-range electron-lattice interactions as well as election correlations in the formation of D- and S-polarons and bipolarons is considered in detail. It is shown that the simultaneous accounting of these effects leads to increasing the ratio of the binding energy of a D-bipolaron to double the energy of a D-polaron to 0.372 at ε ∞/ ε 0 → 0 and to a noticeable expansion of the existence regions ( ε ∞/ ε 0 ⩽ 0.16) of these bipolarons. Numerical results show that the short-range electron-lattice interaction and electron correlation also play an important role in the formation of the S-bipolarons. The possible relations of the D- and S-bipolarons to superconductivity in high-temperature and other superconductors are considered.

Two-electron self-consistent-field study of 2kF broken-symmetry states in correlated monatomic and diatomic Peierls-Hubbard chains.

The two-electron-self-consistent-field (SCF2) approach in which the wave function is constructed from spin-unrestricted geminals (UG's) optimized variationally is developed. It combines restricted-geminal (RG)-SCF2 and unrestricted Hartree-Fock methods, thus accounting for both short-range (intrapair) and long-range electron correlations. On this basis ground-state properties of the extended half-filled Peierls-Hubbard chains are calculated in a wide range of site-energy modulation \ensuremath{\alpha} and on-site electron-electron repulsion U. Treating a generalized-Peierls transition in slight-to-strong correlation regimes within the same framework, the electronic-Peierls and spin-Peierls transition areas can be conventionally differentiated by bifurcation points in which UG-SCF2 solutions separate from RG solutions. The corresponding phase diagram in the U-\ensuremath{\alpha} plane is obtained. For the monatomic (\ensuremath{\alpha}=0) chain, the predicted dimerization amplitude is in a good agreement with the earlier Peierls and spin-Peierls calculations. For the diatomic strongly correlated chain, dimerization sharply rises with \ensuremath{\alpha} at the bifurcation point ${\mathrm{\ensuremath{\alpha}}}_{0}$ and then rapidly drops near \ensuremath{\alpha}=U/2; a property that can be related to phase transitions in some donor-acceptor molecular crystals.

Electron correlations in a double-quantum-well structure.

The electron correlation effect in a double-quantum-well structure is investigated. The local-field correction and static structural factors are calculated for these structures. It is found that the static structural factors show an anomalous behavior at small q due to the coupled quantum-well-plasma excitation and the interlayer structural factor is negative at large q. We also found that the long-wavelength acoustic plasma mode is further softened due to short-range electron correlations. The minimum critical well separation for this mode to exist increases by an amount \ensuremath{\sim}1/${\mathit{k}}_{\mathit{f}1}$, where ${\mathit{k}}_{\mathit{f}1}$ is the Fermi wave vector of the well with higher electron concentration.

Dynamic structure of electrons in Al metal studied by inelastic x-ray scattering.

The dynamic structure factor S(q,\ensuremath{\omega}) of electrons in single-crystal Al metal was measured with 1.4-eV resolution by means of inelastic x-ray-scattering spectroscopy for q parallel to [100] and for q parallel to [110] with 0.37q2.06 a.u. using synchrotron radiation from DORIS storage ring. The overall shape of the experimental dynamic structure factors is in agreement with jellium calculations which extend the random-phase approximation by taking into account both local-field corrections and the influence of the momentum-dependent lifetime of the quasiparticles. Besides some q-orientation-dependent fine structure, the S(q,\ensuremath{\omega}) spectra for qg1.1 a.u. exhibit a q-orientation-independent double-peak or one-peak--one-shoulder fine structure. Whereas the q-orientation-dependent fine structure can be attributed to ion-lattice-induced indentations in the electron-hole excitation continuum due to Bragg reflections, the origin of the q-orientation-independent fine structure could not be clarified definitively. The most probable explanation of this fine structure which is based on semiquantitative agreement with model calculations is the shifting down of unoccupied d-like bands due to the lack of d core-state orthogonalization. Alternative interpretations on the basis of special features of the short-range electron correlations (lifetime effects, multiple-pair excitation, plasmaron ground state) have either failed or have been left on the level of qualitative and somewhat speculative arguments.

THE MAGNETOVOLUME EFFECT IN STRONG ITINERANT PARAMAGNETS

The results of investigations of the enhanced spin susceptibility of some transition metals and alloys under pressure are reviewed and discussed. The evaluated values of the volume derivative of the interaction parameter d In J/d In V unambiguously confirm the predominant role of the short-range electron correlations in these systems.

QUANTUM HALL EFFECT: WHAT IS REALLY GOING ON AT HALF-FILLING?

This paper reviews the authors' theoretical understanding for the quantum Hall anomalies recently observed at fractional fillings with even denominators, more particularly at filling 1/2, where the electron spins are still fully polarized. After a brief reminder of the basic experimental evidence dip of {rho}{sub xx}, lack of plateau in {rho}{sub xx}, temperature behavior, the author discusses the important role of electron-hole (e-h) symmetry at half-filling. In particular the two alternative possibilities of spontaneous e-h symmetry breaking or non-breaking are discussed along with their physical implications. Hartree-Fock charge density waves are presented as an explicit example of spontaneous e-h symmetry breaking. Next, several different scenarios are discussed for the ground state at half-filling. One, largely discussed in the experimental papers is that of Halperin, involving phase separation. Another is that of Fano et al. where the half-filling ground state is supposed to be incompressible and homogeneous, but deformable. Pursuing further the second scenario, numerical evidence from the recent work of Chen is presented, indicating incompressibility and deformability. This work also demonstrates a rather abrupt switching of short-range electron correlations. Just below half-filling, an electron is typically surrounded by six close-by electrons (like a triangular lattice).

Accurate ab initio calculation on the low-energy elastic scattering of electrons from helium.

The multiconfiguration Hartree-Fock method developed by Saha [Phys. Rev. A 39, 5048 (1989)] to study scattering of electrons from atoms has been applied to the low-energy elastic scattering of electrons from helium atoms. The short-range electron correlation and the long-range dynamical polarization of the target by the scattering electron, which are very important in these calculations, have been taken into account in an accurate ab initio manner through the configuration-interaction procedure. Detailed results for phase shifts, elastic differential, integral-elastic, and momentum-transfer cross sections for electrons elastically scattered from helium are reported for the low and intermediate energies ranging from 0.58 to 50 eV. The present results are compared with accurate experimental measurements and theoretical calculations. It is found that the present multiconfiguration self-consistent-field method produces high-quality results that show excellent agreement with experimental measurements and compare well with other accurate theoretical calculations.

Electron correlation in the Coulomb hole model. Comparison of methods

Methods, based both on the density functional and on the correlation factor, are analyzed by applying them to the correlation energy calculation of two- and four-electron closed shell atoms; so that only the short range electron correlation is considered. The method based on the correlation factor seems to be more promising than those of the density functional. However, in the present state of development, there are some serious deficiencies that limit their application to atomic and molecular calculations.

Elementary excitations in quantum liquids

By 1931 it was already clear that condensed matter was to be a marvelous proving ground for the then newly developed quantum mechanics. The Sommerfeld free electron gas model for a metal; Bloch's theorem; the description of energy bands in solids; the theoretical explanation of why some solids are metals, some insulators, some semiconductors; all these provide eloquent testimony to the ingenuity of the theorist in developing a quantum description of independent electron motion that explained or illuminated experiment. During the succeeding decade, theorists began to examine some consequences of electron–electron interactions. Thus in 1934, when Frederick Seitz and Eugene Wigner developed the first theory of energy bands and cohesion in the alkali metals, they drew upon the pioneering study by Wigner of Coulomb correlations in a quantum plasma (interacting electrons moving in a uniform background of positive charge). In 1937, John Bardeen took into account the screening of ion motions by electrons in his seminal investigation of electron–phonon interactions in metals, while the concept of a pseudopotential to describe the way in which strong short-range electron correlations influence the electron–ion interaction in solids was put forward by H. Hellman in 1936 and independently by Conyers Herring in 1939.

Search for positron annihilation with a single-photon emission

Annihilation of a thermalised positron in a solid can result in the emission of a single photon, accompanied by the recoil of a 'spectator' electron. This decay mode, if observed, would provide a unique method for measuring short-range electron correlations. Both theoretical and experimental results of this process are reported. The theoretical calculations were carried out for different electron densities. For Li the predicted ratio for one-photon events to the familiar two-photon events was in the range of 2*10-9 to 1*10-8. An experimental measurement of this ratio provides an upper limit of 4*10-6.