Reference electronic structure calculations in one dimension

We study model one-dimensional chemical systems (representative of their three-dimensional counterparts) using the strictly-correlated electrons (SCE) functional, which, by construction, becomes asymptotically exact in the limit of infinite coupling strength. The SCE functional has a highly non-local dependence on the density and is able to capture strong correlation within KohnSham theory without introducing any symmetry breaking. Chemical systems, however, are not close enough to the strong-interaction limit so that, while ionization energies and the stretched H2 molecule are accurately described, total energies are in general way too low. A correction based on the exact next leading order in the expansion at infinite coupling strength of the Hohenberg-Kohn functional largely improves the results.

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“…22 . For the H 2 potential energy curve, we have also carried out full CI calculations on a numerical grid.…”

Section: Comparison With Other Approachesmentioning

confidence: 99%

“…For this reason, we consider here a simple one-dimensional model that has recently been shown to be a useful laboratory to test functionals for chemical problems, 21,22 offering a reasonably close de-scription of the three-dimensional counterparts and being computationally much less demanding.…”

Section: Introductionmentioning

confidence: 99%

Exchange–correlation functionals from the strong interaction limit of DFT: applications to model chemical systems

Malet

Mirtschink

Giesbertz

et al. 2014

Phys. Chem. Chem. Phys.

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“…[26][27][28] However, all these authors eschewed the Coulomb operator 1/|x| because of its strong divergence at x = 0. For example, Burke and coworkers 23,24 used a softened version of the Coulomb operator 1/ √ x 2 + 1 to study 1D chemical systems, such as light atoms (H, He, Li, Be, . .…”

Section: D Chemistrymentioning

confidence: 99%

Chemistry in one dimension

Loos

Ball

Gill

2015

Phys. Chem. Chem. Phys.

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We report benchmark results for one-dimensional (1D) atomic and molecular systems interacting via the Coulomb operator |x| −1 . Using various wavefunction-type approaches, such as Hartree-Fock theory, second-and third-order Møller-Plesset perturbation theory and explicitly correlated calculations, we study the ground state of atoms with up to ten electrons as well as small diatomic and triatomic molecules containing up to two electrons. A detailed analysis of the 1D helium-like ions is given and the expression of the high-density correlation energy is reported. We report the total energies, ionization energies, electron affinities and other interesting properties of the many-electron 1D atoms and, based on these results, we construct the 1D analog of Mendeleev's periodic table. We find that the 1D periodic table contains only two groups: the alkali metals and the noble gases. We also calculate the dissociation curves of various 1D diatomics and study the chemical bond in H + 2 , HeH 2+ , He 3+ 2 , H 2 , HeH + and He 2+ 2 . We find that, unlike their 3D counterparts, 1D molecules are primarily bound by one-electron bonds. Finally, we study the chemistry of H + 3 and we discuss the stability of the 1D polymer resulting from an infinite chain of hydrogen atoms.

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“…[167][168][169][170][171] However, because the Coulomb potential diverges in one-dimension, and a soft-Coulomb potential shall be used instead, [172][173][174][175] the real physical meaning of this density scaling is rather ambiguous. For this reason, it has never been considered in meta-GGA development; despite it is a possible constraint at this level.…”

Section: Two-dimensional Density Scalingmentioning

confidence: 99%

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

Sala

Fabiano

Constantin

2016

Int J of Quantum Chemistry

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We present the theory of semilocal exchange-correlation (XC) energy functionals which depend on the Kohn-Sham kinetic energy density (KED), including the relevant class of meta-generalized gradient approximation (meta-GGA) functionals. Thanks to the KED ingredient, meta-GGA functionals can satisfy different exact constraints for XC energy and can be made one-electron selfcorrelation free. This leads to a better accuracy over a wider range of properties with respect to GGAs, often reaching the accuracy of hybrid functionals, but at much reduced computational cost.An extensive survey of the relevant literature on existing KED dependent XC functionals is provided, considering nonempirical, semi-empirical, and fully empirical ones. A deeper analysis and a wide benchmark are presented for functionals derived considering only exact constraints and parameters obtained from model and/or atomic systems. K E Y W O R D Sdensity functional theory, kinetic energy, meta-GGA | I N T R O D U C T I O NKohn-Sham (KS)-density functional theory (DFT) [1][2][3][4][5] is nowadays one of the most popular computational approaches in quantum chemistry, solid-state physics, and materials science. [6][7][8][9][10][11] While the ground-state description of a real system of interacting electrons requires a complicate N-electron wavefunction, in KS-DFT this is mapped onto an auxiliary system of noninteracting electrons having the same ground-state density, which can be easily described using N single-particle KS orbitals. [1,2] The correspondence between the many-electron problem and the KS system is in principle exact [1,3] and it is based on the so called exchange-correlation (XC) energy functional, which collects all the quantum electron-electron interaction terms beyond the Hartree one. [12] Within the constrained-search formalism, [13] the XC energy functional is:E xc ½q 5 min W!q hWjT 1V ee jWi2T s ½q 2J½q 5E x ½q 1U c ½q 1T c ½q ;(1) where W is an N-electron ground-state wavefunction yielding the electron density q,T is the kinetic energy (KE) operator,V ee is the electron-electron interaction operator, T s is the KE of the noninteracting system, J is the Coulomb energy, E x is the exact exchange energy, and U c and T c represent, respectively, the potential and the kinetic contributions to the DFT correlation energy E c 5U c 1T c . The important point of Equation1 is that it is an universal functional of the electron density. However, its explicit functional form is not known, and any practical realization of KS-DFT is based on an approximated XC functional. The latter determines in practice the overall accuracy of the KS-DFT calculation.The study of the exact properties of the XC energy functional as well as the development of new and improved approximations have been hot research topics in DFT for more than three decades, and a large number of XC approximations has been proposed. [12,14,15] The different XC functionals are usually classified, according to their complexity, on the so called Jacob's ladder of DFT [14,16] whic...

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Reference electronic structure calculations in one dimension

Cited by 76 publications

References 53 publications

Exchange–correlation functionals from the strong interaction limit of DFT: applications to model chemical systems

Exchange–correlation functionals from the strong interaction limit of DFT: applications to model chemical systems

Chemistry in one dimension

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

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