Chemistry in one dimension

Loos, Pierre‐François; Ball, Caleb J.; Gill, Peter M. W.

doi:10.1039/c4cp03571b

Cited by 19 publications

(29 citation statements)

References 120 publications

(180 reference statements)

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“…The exact results have been obtained with a James-Coolidge-type (JC) expansion. 97,128 Although the error in the SBLDA correlation energy is still significant, we observe a clear improvement for all bond lengths compared to LDA. This result is encouraging given the simplicity of the SBLDA functional.…”

Section: Dissociating H2mentioning

confidence: 79%

Symmetry-broken local-density approximation for one-dimensional systems

2016

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Within density-functional theory, the local-density approximation (LDA) correlation functional is typically built by fitting the difference between the near-exact and Hartree-Fock (HF) energies of the uniform electron gas (UEG), together with analytic perturbative results from the high-and low-density regimes. Near-exact energies are obtained by performing accurate diffusion Monte Carlo calculations, while HF energies are usually assumed to be the Fermi fluid HF energy. However, it has been known since the seminal work of Overhauser that one can obtain lower, symmetry-broken (SB) HF energies at any density. Here, we have computed the SBHF energies of the one-dimensional UEG and constructed a SB version of the LDA (SBLDA) from the results. We compare the performance of the LDA and SBLDA functionals when applied to one-dimensional systems, including atoms and molecules. Generalization to higher dimensions is also discussed.

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Section: Dissociating H2mentioning

confidence: 79%

Symmetry-broken local-density approximation for one-dimensional systems

2016

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“…Thus, for 1‐jellium, Fogler found

e_{normalH normalF}^{normalF normalF} ((), r_{s}) = \frac{{normalπ}^{2}}{24 r_{s}^{2}} - \frac{1}{2} \frac{normalln r_{s}}{r_{s}} + \frac{2 normalln ((), normalπ false/ 2) - 3 + 2 γ}{4 r_{s}},

where γ is the Euler–Mascheroni constant . Furthermore, because the paramagnetic and ferromagnetic states are degenerate in strict 1D systems, we can confine our attention to the latter …”

Section: The High‐density Regimementioning

confidence: 99%

“…42 Furthermore, because the paramagnetic and ferromagnetic states are degenerate in strict 1D systems, we can confine our attention to the latter. [52][53][54][55][56][57]…”

Section: Hartree-fock Energymentioning

confidence: 99%

The uniform electron gas

Loos

Gill

2016

WIREs Comput Mol Sci

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The uniform electron gas or UEG (also known as jellium) is one of the most fundamental models in condensed-matter physics and the cornerstone of the most popular approximation-the local-density approximation-within densityfunctional theory. In this article, we provide a detailed review on the energetics of the UEG at high, intermediate, and low densities, and in one, two, and three dimensions. We also report the best quantum Monte Carlo and symmetrybroken Hartree-Fock calculations available in the literature for the UEG and discuss the phase diagrams of jellium.

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“…13,27,30 Here, we show how to use these FUEGs to create a new type of exchange functionals applicable to any type of systems. We have already successfully applied this strategy to one-dimensional systems, 28,31,32 for which we have created a correlation functional based on this idea. 25,26 Moreover, we show that these alternative second-rung functionals can be easily coupled to GGA functionals to form a new family of third-rung MGGA functionals.…”

Section: Introductionmentioning

confidence: 99%

Exchange functionals based on finite uniform electron gases

Loos

2017

The Journal of Chemical Physics

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We show how one can construct a simple exchange functional by extending the wellknow local-density approximation (LDA) to finite uniform electron gases. This new generalized local-density approximation (GLDA) functional uses only two quantities: the electron density ρ and the curvature of the Fermi hole α. This alternative "rung 2" functional can be easily coupled with generalized-gradient approximation (GGA) functionals to form a new family of "rung 3" meta-GGA (MGGA) functionals that we INTRODUCTIONDue to its moderate computational cost and its reasonable accuracy, Kohn-Sham (KS) density-functional theory 1,2 (DFT) has become the workhorse of electronic structure calculations for atoms, molecules and solids. 3 To obtain accurate results within DFT, one only requires the exchange and correlation functionals, which can be classified in various families depending on their physical input quantities. 4,5 These various types of functionals are classified by the Jacob's ladder of DFT 6,7 (see Fig. 1). The local-density approximation (LDA) sits on the first rung of the Jacob's ladder and only uses as input the electron density ρ. The generalized-gradient approximation (GGA) corresponds to the second rung and adds the gradient of the electron density ∇ρ as an extra ingredient. The third rung is composed by the so-called meta-GGA (MGGA) functionals 8 which uses, in addition to ρ and ∇ρ, the kinetic energy density τ = occ i |∇ψ i | 2 (where ψ i is an occupied molecular orbital). The infinite uniform electron gas (IUEG) or jellium 9-13 is a much studied and wellunderstood model system, and hence a logical starting point for local exchange-correlation approximations. 14-22 Though analytical models are scarce, we have recently discovered an entire new family of analytical models that one can use to develop new exchange and correlation functionals within DFT. 23-29 Indeed, we have shown that, by constraining n electrons on a surface of a three-dimensional sphere (or 3-sphere), one can create finite uniform electron gases (FUEGs). 13,27,30 Here, we show how to use these FUEGs to create a new type of exchange functionals applicable to any type of systems. We have already successfully applied this strategy to one-dimensional systems, 28,31,32 for which we have created a correlation functional based on this idea. 25,26 Moreover, we show that these alternative second-rung functionals can be easily coupled to GGA functionals to form a new family of third-rung MGGA functionals. Unless otherwise stated, we use atomic units throughout. II. THEORYWithin DFT, one can write the total exchange energy as the sum of its spin-up (σ = ↑) and spin-down (σ = ↓) contributions:2 Hartree Rung 1:Rung 2:Rung 2 : whereand ρ σ is the electron density of the spin-σ electrons. Although, for sake of simplicity, we sometimes remove the subscript σ, we only use spin-polarized quantities from hereon.The first-rung LDA exchange functional (or D30 33 ) is based on the IUEG 13 and readswhere3 A GGA functional (second rung) is defined aswhere F GGA x is th...

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Chemistry in one dimension

Cited by 19 publications

References 120 publications

Symmetry-broken local-density approximation for one-dimensional systems

Symmetry-broken local-density approximation for one-dimensional systems

The uniform electron gas

Exchange functionals based on finite uniform electron gases

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