Variational calculations on the helium isoelectronic sequence

Freund, David; Huxtable, Barton D.; Morgan, John D.

doi:10.1103/physreva.29.980

Cited by 272 publications

(108 citation statements)

References 22 publications

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“…For the case of the Coulomb interaction, an essentially exact curve has been calculated with a highly accurate 418-term Hylleraas-type wave function [73][74][75]. For comparison, we also show the results obtained with the single-determinant HF and RSH wave functions (with the cc-pV6Z basis) which just give horizontal lines since they do not depend on θ.…”

Section: A Convergence Of the Wave Functionmentioning

confidence: 99%

“…(measured from the nucleus) and the position of the second electron is varied on a circle at the same distance of the nucleus, r 2 = (0.5 cos θ, 0.5 sin θ, 0.). For the Coulomb interaction, we compare with the essentially exact curve obtained with a highly accurate 418-term Hylleraas-type wave function [73][74][75]. The curve of Ψ lr,µ (r 1 , r 2 ) as a function of θ reveals the angular correlation between the electrons [82].…”

Section: A Convergence Of the Wave Functionmentioning

confidence: 99%

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Basis convergence of range-separated density-functional theory

Franck

Mussard

Luppi

et al. 2015

The Journal of Chemical Physics

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Range-separated density-functional theory is an alternative approach to Kohn-Sham densityfunctional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components, and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the oneelectron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with the cardinal number X of the Dunning basis sets cc-p(C)VXZ, and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.

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Section: A Convergence Of the Wave Functionmentioning

confidence: 99%

Section: A Convergence Of the Wave Functionmentioning

confidence: 99%

Basis convergence of range-separated density-functional theory

Franck

Mussard

Luppi

et al. 2015

The Journal of Chemical Physics

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“…The non-interacting Kohn-Sham kinetic energy functional T s , the exchange functional E x , the correlation functional E c , and their sum E xc for the ensemble n = (1 − w) n 1 + w n 2 formed by the N = 1 and N = 2 densities of the He atom series, as a function of the weight w. All quantities are very accurate, calculated from the variational wavefunctions of Ref. [19] (see also [20] and [21]), and are reported in Hartree atomic units.…”

Section: Fractional Number Of Electronsmentioning

confidence: 99%

Degeneracy and size consistency in electronic density functional theory

Gori‐Giorgi¹,

Savin²

2008

J. Phys.: Conf. Ser.

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The electronic structure calculations based upon energy density functionals are highly successful and widely used both in solid state physics and quantum chemistry. Moreover, the Hohenberg-Kohn theorems and the Kohn-Sham method provide them with a firm basis. However, several basic issues are not solved, and hamper the progress to achieve high accuracy.In this paper we focus on the conceptual problem of size consistency, basing our analysis on the non-intensive character of the (spin) electronic density in the presence of degeneracy. We also briefly discuss some of the issues concerning fractional electron numbers from the same point of view, analyzing the behavior of the exact functionals for the He and the Hooke's atom series when the number of electrons fluctuates between one and two.• to provide reasonable error estimates;• to allow systematic improvement, meaning that one knows how to reduce the errors by means of a well defined procedure.

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“…This assumption seems to be general enough even for the e − e − n cusp where additional logarithmic terms have to be taken into account (cf. [18,19]). …”

Section: Basic Assumptions On the Regularity Of Jastrow Factorsmentioning

confidence: 99%

“…This ansatz was strongly motivated by the highly accurate Hylleraas wavefunctions for two-electron systems (cf. [19]). Such kind of polynomial expansion raises the question for off-diagonal e − n cusps and the behaviour of F (2) at the three-particle e − e − n cusp.…”

Section: Basic Assumptions On the Regularity Of Jastrow Factorsmentioning

confidence: 99%

BestN-term approximation in electronic structure calculations. II. Jastrow factors

2007

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Abstract. We present a novel application of best N -term approximation theory in the framework of electronic structure calculations. The paper focusses on the description of electron correlations within a Jastrow-type ansatz for the wavefunction. As a starting point we discuss certain natural assumptions on the asymptotic behaviour of two-particle correlation functions F (2) near electron-electron and electronnuclear cusps. Based on Nitsche's characterization of best N -term approximation spaces A α q (H 1 ), we prove that F (2) ∈ A α q (H 1 ) for q > 1 and α = 1 q − 1 2 with respect to a certain class of anisotropic wavelet tensor product bases. Computational arguments are given in favour of this specific class compared to other possible tensor product bases. Finally, we compare the approximation properties of wavelet bases with standard Gaussian-type basis sets frequently used in quantum chemistry.

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Variational calculations on the helium isoelectronic sequence

Cited by 272 publications

References 22 publications

Basis convergence of range-separated density-functional theory

Basis convergence of range-separated density-functional theory

Degeneracy and size consistency in electronic density functional theory

BestN-term approximation in electronic structure calculations. II. Jastrow factors

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