Local approximation of the correlation energy functional in the density matrix functional theory

A local approximation formula of the correlation energy functional E(c) in terms of the first-order reduced density matrix (1-RDM) is presented. With the contracted Schr?dinger equation the principal dependence of E(c) on the natural occupation numbers n(i) is identified. Using the effective mass theory, E(c) is expressed as a functional of the local density and the local variable, J = SUM (i)[square root of (n(i)(1-n(i))] /phi(i)/(2), where phi(i) are the natural spin orbitals. This local approximation satisfies the homogeneous coordinate scaling relation, gives the exact result for a one-electron system, and is almost free from the exchange energy error. It reproduced about 90% of the correlation energies of atoms and molecules.     

Electron correlation effects on Compton profiles of copper in the GW approximation

The Compton profiles (CPs) of copper are calculated by the GW approximation with FLAPW basis sets on the LDA. In the quasiparticle band structure in the GW approximation, the width of fully occupied 3d valence band which is overestimated in the LDA, is in good agreement with experimental observation. The dynamical screening effects are important for band width narrowing. The occupation number densities are evaluated from the spectral function calculation within the GW calculations. The CPs obtained using these GW calculations successfully reproduce experimental results.     

Electron correlation effects on magnetic Compton profiles of nickel in the GW approximation

The magnetic Compton profiles (MCPs) of 3d transition metal nickel are calculated by the GW approximation with FLAPW basis sets on the LSDA. The 3d valence band width narrowing, which is ascribed to the dynamical screening effects, contributes to eliminate an anomalous peak at 0.7 a.u. in the 〈110〉 direction, and also to diminish the excessive estimation of the Umklapp effects, in the LSDA MCPs. These are in good agreement with experimental observation.     

Local density approximation in site-occupation embedding theory

ABSTRACT

Site-occupation embedding theory (SOET) is a density functional theory (DFT)-based method which aims at modelling strongly correlated electrons. It is in principle exact and applicable to model and quantum chemical Hamiltonians. The theory is presented here for the Hubbard Hamiltonian. In contrast to conventional DFT approaches, the site (or orbital) occupations are deduced in SOET from a partially interacting system consisting of one (or more) impurity site(s) and non-interacting bath sites. The correlation energy of the bath is then treated implicitly by means of a site-occupation functional. In this work, we propose a simple impurity-occupation functional approximation based on the two-level (2L) Hubbard model which is referred to as two-level impurity local density approximation (2L-ILDA). Results obtained on a prototypical uniform eight-site Hubbard ring are promising. The extension of the method to larger systems and more sophisticated model Hamiltonians is currently in progress.     

Local density approximation in effective density-dependentαN-interactions

Different forms of a local density approximation (LDA) in effective density-dependent αN-interactions are compared in single-folding optical model analyses of elastic α particle scattering by^{40, 42, 44, 48}Ca atE _α=104 MeV and by⁴⁰Ca atE _α=140 MeV. It is shown that the form of the LDA considerably influences the results on folded optical potentials. A variable form of the LDA is suggested and discussed which includes previous forms as limiting cases. The new form leads to better fits to the data and to full consistency with the best available “model-independent” optical potentials.     

Nonlocal density functional theory of solids: Applications of the weighted density approximation to silicon

Using the density functional formalism together with the weighted density approximation (WDA), we have carried out selfconsistent bandstructure studies of bulk Si in order to identify the influences of different WDA potentials and different pair correlation functions on the electronic spectrum. Improvements of band energies due to consideration of nonlocalities in exchange and correlation energy depend very sensitively on the particular correlation function used. For the prototype semiconductor Si, only one of the six WDA versions tested seems useful.     

Fourier transformed Compton profiles of semiconductors

The Fourier transformed Compton profiles of several semiconductors are calculated by using a set of realistic Wannier functions. The results obtained in silicon, where experimental information exists, are used to test the one-electron approximation. The study of a series of semiconductors shows the effect of their electronic structure on the Compton scattering.     

Molecular Compton profiles from SCF-MO wavefunctions

Compton profiles are derived from ab initio SCF-MO wavefunctions calculated for cyclopropane, propene, aziridine, ethanimine, ethenamine, oxirane, acetaldehyde and formamide using Dunning's gaussian orbital basis. Good agreement with the experimental profile is found for formamide. The differences between the profiles for the cyclic and acyclic isomers are only slightly larger than the experimental accuracy that can presently be achieved. The cyclic compounds have slightly broader profiles and there are no significant differences arising from strain. Comparison with profiles derived from localized orbital contributions indicate that the localized orbital approach is essentially valid for these systems.     

Molecular Compton profiles from SCF-MO wavefunctions

This paper considers the dependence of Compton profiles calculated from molecular wavefunctions on the atomic basis set used. For fluoromethane there is no significant difference between profiles calculated with a Slater minimal basis set and with STO-3G, STO-4G and STO-5G sets. A Slater double-zeta set and Dunning's gaussian basis give essentially the same profile and the addition of polarization functions to the Dunning basis has little effect. For methanol, methylamine and ethane there is a significant difference between the STO-3G profiles and those calculated from extended basis sets but again the addition of polarization functions has little effect. The use of Dunning's basis would seem to be adequate for Compton profile calculations for molecules of medium size. As one goes along the series from ethane to fluoromethane the Compton profile becomes broader.     

Computation of interface density profiles by density functional theories: application to the two-dimensional one-component plasma

We derive a density functional theory appropriate for hard wall problems. This formalism and the familiar square gradient theory are tested in the case of the two dimensional, one component plasma. Comparisons with exact (analytic and Monte Carlo) results show that both theories are reasonably accurate for not too strong coupling.     

Compton profiles of trigonal and amorphous selenium

Compton profiles of trigonal and amorphous Selenium were measured with ²⁴¹Am γ-radiation using two crystalline and amorphous samples of identical geometric dimensions. As a result the difference profiles of amorphous and polycrystalline Se are reported and discussed. The valence electron Compton profile of the polycrystalline phase is compared to SCOPW-calculations by Krusius.     

Compton profiles of multiply ionized oxygen atoms

We have calculated Compton profiles of multiply ionized oxygen atoms with electronic configurations 1s^m2sⁿ2p^q, m=1−2,n=0−2,q=0−4. The values of the Compton profiles from the present calculation can be used to determine the doubly differential electron production cross sections in recent ion-atom collision experiments with oxygen ions in the rest frame of the target atoms. The calculations have been performed in impulse approximation using numerical Hartree-Fock wave functions. Compton profiles of neutral oxygen atoms, available in the literature, are in excellent agreement with the present calculation. The variation of Compton profile with the degree of ionization is investigated.     

Atomic Compton profiles within different exchange-only theories

The impulse Compton Profiles (CPs) J(q) and the expectation values for some inert gas atoms (He-Kr) are computed and compared within the Harbola-Sahni (HS), Hartree-Fock (HF) theories and a Self-Interaction-Corrected (SIC) density functional model. The Compton profiles for excited states of helium atom are also calculated. While the calculated CPs are found to generally agree, they differ slightly from one another for small values of the Compton parameter q and are in good agreement for large q values. The expectation values within the three theories are also found to be comparable. The HS formalism is seen to mimic HF reasonably well in the momentum space, establishing the logical consistency of the former. Received: 11 December 1998 / Received in final form: 20 April 1999     

Faddeev random phase approximation applied to molecules

The Faddeev Random Phase Approximation (FRPA) is a Green’s function method which couples collective degrees of freedom to the single particle motion by resumming an infinite number of Feynman diagrams. The Faddeev technique is applied to describe the two-particle-one-hole (2p1h) and two-hole-one-particle (2h1p) Green’s function in terms of non-interacting propagators and kernels for the particle-particle (pp) and particle-hole (ph) interactions. This results in an equal treatment of the intermediary pp and ph channels. In FRPA both the pp and ph phonons are calculated on the random phase approximation (RPA) level. In this work the equations that lead to the FRPA eigenvalue problem are derived. The method is then applied to atoms, small molecules and the Hubbard model, for which the ground state energy and the ionization energies are calculated. Special attention is directed to the RPA instability in the dissociation limit of diatomic molecules and in the Hubbard model. Several solutions are proposed to overcome this problem.     

Compton profiles of metals and Van Hove singularities

The structures of the Compton profiles of metals, as observed by Platzman et al., are tentatively interpreted as Van Hove singularities for Bloch electrons.     

Electron momentum distribution and Compton profiles of europium

The electron momentum distribution and Compton profiles of the rare earth element Eu was measured using HPGe photon detector. The target atoms were excited by means of 59.54 keV gamma rays from Am-241 radioactive source of strength 300 mCi. Elemental foil of uniform aerial density, and purity better than 99.9% was used as target. The data were recorded and analyzed using a 4 K multichannel analyzer. These data duly corrected for instrumental resolution effects, sample absorption, energy dependence of the differential Compton cross-section and double scattering, and compared with theoretical renormalized free atom (RFA) values.     

Compton profiles of liquid and solid lithium metals

Compton profile measurements have been performed on liquid and solid lithium metal using 59.54 keV γ-ray from ²⁴¹Am source. A difference between Compton profiles in both states has been found.