Short-range Electron Correlation Research Articles

A density-fitting implementation of the density-based basis-set correction method.

This work reports an efficient density-fitting implementation of the density-based basis-set correction (DBBSC) method in the MOLPRO software. This method consists in correcting the energy calculated by a wave-function method with a given basis set by an adapted basis-set correction density functional incorporating the short-range electron correlation effects missing in the basis set, resulting in an accelerated convergence to the complete-basis-set limit. Different basis-set correction density-functional approximations are explored and the complementary-auxiliary-basis-set single-excitation correction is added. The method is tested on a benchmark set of reaction energies at the second-order Møller-Plesset (MP2) level and a comparison with the explicitly correlated MP2-F12 method is provided. The results show that the DBBSC method greatly accelerates the basis convergence of MP2 reaction energies, without reaching the accuracy of the MP2-F12 method but with a lower computational cost.

Basis-set correction based on density-functional theory: Linear-response formalism for excited-state energies.

The basis-set correction method based on density-functional theory consists in correcting the energy calculated by a wave-function method with a given basis set by a density functional. This basis-set correction density functional incorporates the short-range electron correlation effects missing in the basis set. This results in accelerated basis convergences of ground-state energies to the complete-basis-set limit. In this work, we extend the basis-set correction method to a linear-response formalism for calculating excited-state energies. We give the general linear-response equations as well as the more specific equations for configuration-interaction wave functions. As a proof of concept, we apply this approach to the calculations of excited-state energies in a one-dimensional two-electron model system with harmonic potential and a Dirac-delta electron-electron interaction. The results obtained with full-configuration-interaction wave functions expanded in a basis of Hermite functions and a local-density-approximation basis-set correction functional show that the present approach does not help in accelerating the basis convergence of excitation energies. However, we show that it significantly accelerates basis convergences of excited-state total energies.

Electron correlation and short-range dynamics in attosecond angular streaking

We employ the R-matrix with time-dependence method to study attosecond angular streaking of F$^-$. Using this negative ion, free of long-range Coulomb interactions, we elucidate the role of short-range electron correlation effects in an attoclock scheme. Through solution of the multielectron time-dependent Schrodinger equation, we aim to bridge the gap between experiments using multielectron targets, and one-electron theoretical approaches. We observe significant negative offset angles in the photoelectron momentum distributions, despite the short-range nature of the binding potential. We show that the offset angle is sensitive to the atomic structure description of the residual F atom. We also investigate the response of co- and counter-rotating electrons, and observe an angular separation in their emission.

Exchange-Correlation Effects in a Finite-Temperature Quasi-One-Dimensional Electron Gas

The exchange-correlation effects in a finite-temperature quasi-one-dimensional electron gas, using the self-consistent mean-field theory of Singwi, Tosi, Land, and Sjölander have been theoretically investigated. The influence of temperature T is elucidated by calculating different static properties (viz. static structure factor, pair-correlation function, static density susceptibility, and free exchange-correlation energy) and the plasmon excitation spectra over a wide range of T and electron number density. Noticeable dependence on T is found, with an interesting interplay between short-range electron correlations and T. More precisely, the pair-correlation function at small separation and for a given density first becomes stronger (i.e., its value decreases) with increasing T and then weakens monotonically above a critical T, whose value increases with reduction in density. On the other hand, the plasmon energy shows a consistent blue shift with rising T. However, the critical wave vector at which plasmons enter the single electron–hole pair continuum, decreases with T. For highlighting the correction due to short-range correlations, the results have been compared with the predictions of random-phase approximation (RPA). As for the zero-T case, the RPA is found to be reliable only in the high density domain.

Short-Range Electron Correlation Stabilizes Noncavity Solvation of the Hydrated Electron.

The hydrated electron, e-(aq), has often served as a model system to understand the influence of condensed-phase environments on electronic structure and dynamics. Despite over 50 years of study, however, the basic structure of e-(aq) is still the subject of controversy. In particular, the structure of e-(aq) was long assumed to be an electron localized within a solvent cavity, in a manner similar to halide solvation. Recently, however, we suggested that e-(aq) occupies a region of enhanced water density with little or no discernible cavity. The potential we developed was only subtly different from those that give rise to a cavity solvation motif, which suggests that the driving forces for noncavity solvation involve subtle electron-water attractive interactions at close distances. This leads to the question of how dispersion interactions are treated in simulations of the hydrated electron. Most dispersion potentials are ad hoc or are not designed to account for the type of close-contact electron-water overlap that might occur in the condensed phase, and where short-range dynamic electron correlation is important. To address this, in this paper we develop a procedure to calculate the potential energy surface between a single water molecule and an excess electron with high-level CCSD(T) electronic structure theory. By decomposing the electron-water potential into its constituent energetic contributions, we find that short-range electron correlation provides an attraction of comparable magnitude to the mean-field interactions between the electron and water. Furthermore, we find that by reoptimizing a popular cavity-forming one-electron model potential to better capture these attractive short-range interactions, the enhanced description of correlation predicts a noncavity e-(aq) with calculated properties in better agreement with experiment. Although much attention has been placed on the importance of long-range dispersion interactions in water cluster anions, our study reveals that largely unexplored short-range correlation effects are crucial in dictating the solvation structure of the condensed-phase hydrated electron.

Dispersion interactions in dimers of inert gases: Investigation by means of explicitly correlated coupled clusters CCSD(F12)(T)

Dispersion interactions in He2, Ne2, and Ar2 dimers are investigated using the explicitly correlated method CCSD(F12)(T) with numerical quadratures. The obtained energies of interaction agree well with the results from highly accurate CCSD(T) calculations described in works in which sets of bonded functions are used. It is shown that in order to attain high accuracy in estimating energies of interaction, the exponential parameter of Slater-type geminals in the CCSD(F12)(T) method must be optimized. The higher accuracy of the values of C 6 asymptotic coefficients found using the CCSD(F12)(T) method instead of the conventional CCSD(T) approach is established, demonstrating the importance of considering short-range electron correlation effects in asymptotic regions of potential surfaces where the interaction between atoms is of a long-range dispersion nature.

Towards numerically accurate many-body perturbation theory: short-range correlation effects.

The example of the uniform electron gas is used for showing that the short-range electron correlation is difficult to handle numerically, while it noticeably contributes to the self-energy. Nonetheless, in condensed-matter applications studied with advanced methods, such as the GW and random-phase approximations, it is common to neglect contributions due to high-momentum (large q) transfers. Then, the short-range correlation is poorly described, which leads to inaccurate correlation energies and quasiparticle spectra. To circumvent this problem, an accurate extrapolation scheme is proposed. It is based on an analytical derivation for the uniform electron gas presented in this paper, and it provides an explanation why accurate GW quasiparticle spectra are easy to obtain for some compounds and very difficult for others.

COMPARATIVE INVESTIGATION OF THE EFFECT OF TYPE OF DENSITY FUNCTIONAL IN THE DETERMINATION OF GEOMETRICAL PARAMETERS IN ACuCOMPLEX

The effects of short-range electron correlation, long-range electron exchange, local and nonlocal parts of density, higher order gradients of density, and adding some percentage of Hartree–Fock exchange to the functional on the prediction of geometrical parameters were investigated. A copper complex namely 1,2-bis(1,4,7-triaza-1-cyclononyl) ethane copper (II) with Jahn–Teller distortion in octahedral geometry was used to evaluate the performance of 50 commonly available density functionals. The standard 3-21G basis set was used for all light elements, while pseudo potential LANL2DZ was used for the copper atom. The best bond lengths and bond angles were obtained using M05-2x and OP functionals respectively. Also in order to more accurate survey the performance of B3LYP, we used this functional with two all-electron basis sets (6-31G and 3-21G) and three basis sets involving effective core potentials (LANL2DZ/3-21G, LANL2DZ, and LACVP).

Electronic excitation in bulk and nanocrystalline alkali halides

The lowest energy excitations in bulk alkali halides are investigated by considering five different excited state descriptions. It is concluded that excitation transfers one outermost halide electron in the fully ionic ground state to the lowest energy vacant s orbital of one closest cation neighbour to produce the excited state termed dipolar. The excitation energies of seven salts were computed using shell model description of the lattice polarization produced by the effective dipole moment of the excited state neutral halogen-neutral metal pair. Ab initio uncorrelated short-range inter-ionic interactions computed from anion wavefunctions adapted to the in-crystal environment were augmented by short-range electron correlation contributions derived from uniform electron-gas density functional theory. Dispersive attractions including wavefunction overlap damping were introduced using reliable semi-empirical dispersion coefficients. The good agreement between the predicted excitation energies and experiment provides strong evidence that the excited state is dipolar. In alkali halide nanocrystals in which each ionic plane contains only four ions, the Madelung energies are significantly reduced compared with the bulk. This predicts that the corresponding intra-crystal excitation energies in the nanocrystals, where there are two excited states depending on whether the halide electron is transferred to a cation in the same or in the neighbouring plane, will be reduced by almost 2 eV. For such an encapsulated KI crystal, it has been shown that the greater polarization in the excited state of the bulk crystal causes these reductions to be lowered to a 1.1 eV-1.5 eV range for the case of charge transfer to a neighbouring plane. For intra-plane charge transfer the magnitude of the polarization energy is further reduced thus causing the excitation in these encapsulated materials to be only 0.2 eV less than in the bulk crystal.

Inelastic scattering of low-energy electrons in liquid water computed from optical-data models of the Bethe surface

Purpose: We provide a short overview of optical-data models for the description of inelastic scattering of low-energy electrons (10–10,000 eV) in liquid water. The effect on the inelastic scattering cross section due to different optical data and extension algorithms is examined with emphasis on some recent developments.Materials and methods: The optical-data method whereby experimental optical data and theoretical extension algorithms are used to describe the dependence of the dielectric response function on energy- and momentum-transfer and obtain the Bethe surface of the material, currently represents the most used method for computing the inelastic scattering of low-energy electrons in condensed media. Two sets of experimental optical data for liquid water obtained from reflectance and inelastic X-ray scattering spectroscopy, respectively, and the extension algorithms of Ritchie, Penn, and Ashley are examined. Recent developments are discussed along with the role of corrections to the random phase approximation (RPA) of electron gas theory. Results: The inelastic scattering cross section in the energy range 200–10,000 eV was found to be rather insensitive (to within 10%) to the choice of optical data or the extension algorithm. In contrast, differences between model calculations increase rapidly below 200 eV with the influence of the extension algorithm being dominant.Conclusion: The choice of the extension algorithm used to extrapolate optical data to finite momentum transfer and obtain the Bethe surface is crucial in modelling the inelastic scattering of electrons with energies below 200 eV. A new set of measurements on the dielectric response function of liquid water beyond the optical limit and the development of extension algorithms that will go beyond RPA by considering the effect of (short-range) electron exchange and correlation should be of some priority.

Resonant Correlation-Induced Optical Bistability in an Electron System on Liquid Helium

We show that electrons on liquid helium display intrinsic bistability of resonant intersubband absorption. The bistability occurs for comparatively weak microwave power. The underlying giant nonlinearity of the many-electron response results from the interplay of the strong short-range electron correlations, the long relaxation time, and the multisubband character of the electron energy spectrum.

Spin-state transition and spin-polaron physics in cobalt oxide perovskites: ab initio approach based on quantum chemical methods

A fully ab initio scheme based on quantum chemical wavefunction methods is used to investigate the correlated multiorbital electronic structure of a 3d-metal compound, LaCoO3. The strong short-range electron correlations, involving both Co and O orbitals, are treated by multireference techniques. The use of effective parameters such as the Hubbard U and interorbital U′, J terms and the problems associated with their explicit calculation are avoided with this approach. We compute the ordering of the lowest N-particle states in the parent compound and provide new insight into the nature of charge carriers in the hole-doped material. Our results suggest that the transition to a magnetically active state at about 90 K in LaCoO3 involves a high-spin, t2g4eg2 configuration. Additionally, we explain the paramagnetic phase in the low-temperature lightly doped compound through the formation of Zhang–Rice-like oxygen hole states and ferromagnetic clusters.

Self-consistent many-body perturbation theory in range-separated density-functional theory: A one-electron reduced-density-matrix-based formulation

In many cases, density-functional theory (DFT) with current standard approximate functionals offers a relatively accurate and computationally cheap description of the short-range dynamic electron correlation effects. However, in general, standard DFT does not treat the dispersion interaction effects adequately which, on the other hand, can be described by many-body perturbation theory (MBPT). It is therefore of interest to develop a hybrid model which combines the best of both the MBPT and DFT approaches. This can be achieved by splitting the two-electron interaction into long-range and short-range parts; the long-range part is then treated by MBPT and the short-range part by DFT. This work deals with the formulation of a general MBPT-DFT model (i.e., valid for any type of zeroth-order Hamiltonian) based on such a range separation. Applying the Rayleigh-Schr\"odinger formalism in this context, one finds that the generalized Bloch equation becomes self-consistent at each order of perturbation. This complication arises because the short-range part of the energy is a functional of the exact electron density, which is expanded in a perturbation series. In order to address this ``self-consistency problem'' and provide computable orbital-based expressions for any order of perturbation, a general one-electron reduced-density-matrix-based formalism is proposed. Two applications of our general formalism are presented: The derivation of a hybrid second-order M\o{}ller-Plesset-DFT model and the formulation of a range-separated optimized effective potential method based on a hybrid G\"orling-Levy-type MBPT-DFT model.

First principlesT-matrix calculations for Auger spectra of hydrocarbon systems

Auger spectra of hydrocarbon systems ($\mathrm{C}{\mathrm{H}}_{4}$, ${\mathrm{C}}_{2}{\mathrm{H}}_{2}$, ${\mathrm{C}}_{2}{\mathrm{H}}_{4}$, and ${\mathrm{C}}_{6}{\mathrm{H}}_{6}$ molecules) are calculated from the first principles using Green's function method based on the many-body perturbation theory beyond the framework of the density functional theory. The ladder approximation to the two-particle Green's function ($T$ matrix), which describes the short-range electron correlations between two holes or electrons, can accurately determine in a single calculation the whole spectrum of doubly ionized final states of the Auger process. The two-particle eigenvalues and eigenfunctions are determined from the Bethe-Salpeter equation for the $T$ matrix. The obtained results are in good agreement with the experimental data.

Zener Double Exchange from Local Valence Fluctuations in Magnetite

Magnetite (Fe3O4) is a mixed valent system where electronic conductivity occurs on the B site (octahedral) iron sublattice of the spinel structure. Below T(V)=123 K, a metal-insulator transition occurs which is argued to arise from the charge ordering of 2+ and 3+ iron valences on the B sites (Verwey transition). Inelastic neutron scattering measurements show that optical spin waves propagating on the B site sublattice (approximately 80 meV) are shifted upwards in energy above T_{V} due to the occurrence of B-B ferromagnetic double exchange in the mixed valent phase. The double exchange interaction affects only spin waves of Delta(5) symmetry, not all modes, indicating that valence fluctuations are slow and the double exchange is constrained by short-range electron correlations above T(V).

The noble gas dimers as a probe of the energetic contributions of dispersion and short-range electron correlation in weakly bound systems

The binding of the noble gas dimers is examined using a theory in which the Hartree–Fock interaction energy is augmented with both a short-range correlation term derived from the theory of a uniform electron-gas plus a dispersion energy damped according to the theory of Jabobi and Csanak. The good agreement between the predicted and experimental binding energies and equilibrium inter-nuclear separations confirms that this approach captures the essential physics of the interaction. A review of other methods confirms the previously reported failures of density functional theory. A further survey shows that fully ab initio variational methods must be taken to the very refined level of coupled cluster theory with a large quadruple or quintuple zeta basis set if they are to achieve greater accuracy than the approach presented here.

London dispersion forces by range-separated hybrid density functional with second order perturbational corrections: The case of rare gas complexes

A satisfactory account of the van der Waals (vdW) (London dispersion) forces is, in general not possible by the Kohn-Sham method using standard local, semilocal generalized gradient approximation (GGA), or meta-GGA density functionals. The recently proposed range-separated hybrid (RSH) approach, supplemented by second order perturbational corrections (MP2) to include long-range dynamic correlation effects, offers a physically consistent, seamless description of dispersion forces. It is based on a rigorous generalization of the Kohn-Sham method, where long-range exchange and correlation effects are treated by wave function methods, while short-range electron exchange and correlation are handled by local or semilocal functionals. The method is tested on a series of rare gas dimers in comparison with standard wave function theory and density functional theory approaches. In contrast to the most successful exchange correlation functionals, which describe at best the vdW minimum, the RSH+MP2 approach is valid also in the asymptotic region and the potential curve displays the correct 1/R(6) behavior at large internuclear separations. In contrast to usual MP2 calculations, the basis set superposition error is considerably reduced, making RSH+MP2 an ideal tool for exploring the potential energy surface of weakly bound molecular complexes.

Short-Range Electron Correlations of CO<SUB>2</SUB> Molecule by First Principles <I>T</I>-Matrix Calculations

In this paper, we obtain the double ionization energy spectra and the two-electron distribution functions from the first principles evaluating the ladder diagrams up to the infinite order (T-matrix) and discuss the short-range electron correlations. The T-matrix, which describes the multiple scattering between electrons (or holes), can accurately represent the short-range repulsive Coulomb interaction. The double ionization energy spectra calculated for the CO2 molecule agree with the corresponding experiments very well. And the two-electron distribution function obtained from the T-matrix clearly shows ‘‘Coulomb hole’’ due to the avoidance of the antiparallel spin electrons confined in a small region. [doi:10.2320/matertrans.48.638]

First principles calculations of double ionization energy spectra and two-electron distribution function using T-matrix theory

Short-range electron correlation plays a very important role in small systems and significantly affects the double ionization energy (DIE) spectra and the two-electron distribution functions of a CO molecule, for example. In our calculations, the local density approximation (LDA) of the density functional theory is chosen as a starting point, the GW approximation (GWA) is performed in a next step, and finally the Bethe–Salpeter equation for the T-matrix, describing the particle–particle ladder diagrams up to the infinite order, is solved via the eigenvalue problem. The calculated DIE spectra, which are directly given by the eigenvalues, reflect the short-range electron correlation and are in good agreement with the experiment. We confirm that the Coulomb hole appears in the two-electron distribution function constructed from the eigenfunction.

Two-electron distribution functions and short-range electron correlations of atoms and molecules by first principles T-matrix calculations

The accurate first principles description of the correlations between electrons has been a topic of interest in molecular physics. We have reported in our previous paper [J. Chem. Phys. 123, 144112 (2005)] that the T matrix, which is the ladder diagrams up to the infinite order, can accurately represent the short-range electron correlations while calculating the double ionization energy spectra of atoms and molecules. In this paper, we calculate the two-electron distribution functions of real systems (Ar, CO, CO(2), and C(2)H(2)) from the eigenvalue equation associated with the Bethe-Salpeter equation for the T matrix by beginning with the local density approximation of the density functional theory and the GW approximation. We found that when the interelectron distance is very small, the Coulomb hole appears between antiparallel spin electrons due to the short-range repulsive Coulomb interaction. The resulting two-electron distribution functions clearly show the Coulomb hole.