Erratum: Rates of convergence of the partial-wave expansions of atomic correlation energies [J. Chem. Phys. <b>96</b>, 4484 (1992)]

Kutzelnigg, Werner; Morgan, John D.

doi:10.1063/1.463358

Cited by 187 publications

(299 citation statements)

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“…It has been theoretically shown that, for the ground-state of the helium atom, the partial-wave expansion of the energy calculated by second-order perturbation theory or by full configuration interaction (FCI) converges as L −3 where L in the maximal angular momentum of the expansion [36][37][38][39][40]. Furthermore, this result has been extended to arbitrary atoms in second-order perturbation theory [41,42]. This has motivated the proposal of a scheme for extrapolating the correlation energy to the complete-basis-set (CBS) limit based on a X −3 power-law dependence of the correlation energy on the cardinal number X of the Dunning hierarchical basis sets [43,44].…”

Section: Introductionmentioning

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: Introductionmentioning

confidence: 99%

“…Here and in the rest of this section, we consider only the dependence of the wave function on r 12 and we restrict ourselves to the most common case of the two electrons being in a natural-parity singlet state [41] for which Ψ(0) = 0. The function…”

Section: A Coulomb Interactionmentioning

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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“…As such, there is much literature for how this limit is approached for molecular basis sets, and it has been shown both analytically and numerically that this limit is approached in X, the cardinal number of the basis set, as 1/X 3 (Ref. 45).…”

Section: A Basis Set Incompleteness Errormentioning

confidence: 99%

Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models

Shepherd

Booth

Alavi

2012

The Journal of Chemical Physics

107

143

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Using the homogeneous electron gas (HEG) as a model, we investigate the sources of error in the 'initiator' adaptation to Full Configuration Interaction Quantum Monte Carlo (i -FCIQMC), with a view to accelerating convergence. In particular we find that the fixed shift phase, where the walker number is allowed to grow slowly, can be used to effectively assess stochastic and initiator error. Using this approach we provide simple explanations for the internal parameters of an i -FCIQMC simulation. We exploit the consistent basis sets and adjustable correlation strength of the HEG to analyze properties of the algorithm, and present finite basis benchmark energies for N = 14 over a range of densities 0.5 ≤ rs ≤ 5.0 a.u. A single-point extrapolation scheme is introduced to produce complete basis energies for 14, 38 and 54 electrons. It is empirically found that, in the weakly correlated regime, the computational cost scales linearly with the plane wave basis set size, which is justifiable on physical grounds. We expect the fixed shift strategy to reduce the computational cost of many i -FCIQMC calculations of weakly correlated systems. In addition, we provide benchmarks for the electron gas, to be used by other quantum chemical methods in exploring periodic solid state systems.

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“…[98][99][100][101] However, the DFT (and HF) methods converge significantly faster (exponential with respect to basis set size), [102,103] and hence the basis set requirements are obviously different. It also bears mentioning that DFT correlates all electrons, but most post-HF methods and the basis sets designed for them use a frozen-core approximation.…”

Section: Polarization Consistent Basis Setsmentioning

confidence: 99%

Gaussian basis sets for molecular applications

Hill¹

2012

Int J of Quantum Chemistry

185

155

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The choice of basis set in quantum chemical calculations can have a huge impact on the quality of the results, especially for correlated ab initio methods. This article provides an overview of the development of Gaussian basis sets for molecular calculations, with a focus on four popular families of modern atom-centered, energy-optimized bases: atomic natural orbital, correlation consistent, polarization consistent, and def2. The terminology used for describing basis sets is briefly covered, along with an overview of the auxiliary basis sets used in a number of integral approximation techniques and an outlook on possible future directions of basis set design.

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Erratum: Rates of convergence of the partial-wave expansions of atomic correlation energies [J. Chem. Phys. 96, 4484 (1992)]

Cited by 187 publications

References 0 publications

Basis convergence of range-separated density-functional theory

Basis convergence of range-separated density-functional theory

Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models

Gaussian basis sets for molecular applications

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