Local-spin-density functional for multideterminant density functional theory

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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“…Finally, we note that we have found the same convergence behavior with the short-range exchange-correlation LDA density functional of Ref. 83.…”

Section: A Convergence Of the Wave Functionsupporting

confidence: 55%

Basis convergence of range-separated density-functional theory

Franck

Mussard

Luppi

et al. 2015

The Journal of Chemical Physics

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“…Similar to the Coulomb case, density functional approximations (DFAs), such as the local density approximation (LDA) and generalized-gradient approximations (GGAs), to the exchangecorrelation (XC) energy functional for a given f (r) are needed in the corresponding KS-DFT [25,26]. Here, the LDA exchange energy functional for the erf interaction is obtained by subtracting the LDA exchange energy functional for the erfc interaction [27] from the LDA exchange energy functional for the Coulomb interaction [28], whereas the LDA correlation energy functional for the erfc interaction is obtained by subtracting the LDA correlation energy functional for the erf interaction [29] from the LDA correlation energy functional for the Coulomb interaction [30]. In addition, as the Perdew-Burke-Ernzerhof (PBE) XC energy functional (i.e., a popular GGA) for the Coulomb interaction [31] and its variant for the erfc interaction [32] are both available, their difference gives the PBE XC energy functional for the erf interaction.…”

Section: Model Systems and Computational Detailsmentioning

confidence: 99%

The van der Waals interactions in rare-gas dimers: the role of interparticle interactions

Chen

Hui

Chai

2016

Phys. Chem. Chem. Phys.

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We investigate the potential energy curves of rare-gas dimers with various ranges and strengths of interparticle interactions (nuclear-electron, electron-electron, and nuclear-nuclear interactions).Our investigation is based on the highly accurate coupled-cluster theory associated with those interparticle interactions. For comparison, the performance of the corresponding Hartree-Fock theory, second-order Møller-Plesset perturbation theory, and density functional theory is also investigated.Our results reveal that when the interparticle interactions retain the long-range Coulomb tails, the nature of van der Waals interactions in the rare-gas dimers remains similar. By contrast, when the interparticle interactions are sufficiently short-range, the conventional van der Waals interactions in the rare-gas dimers completely disappear, yielding purely repulsive potential energy curves.

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“…where ǫ sr xc,unif (n) = ǫ xc,unif (n) − ǫ lr xc,unif (n) is the complement short-range exchange-correlation energy per particle obtained from the exchange-correlation energy per particle of the standard uniform electron gas (UEG), ǫ xc,unif (n), [66,67] and the exchange-correlation energy per particle of a UEG with the long-range electronelectron interaction, ǫ lr xc,unif (n), as parametrized from quantum Monte Carlo calculations by Paziani et al [68] (see Ref. 46 for a discussion about the corresponding kernel).…”

Section: Computational Detailsmentioning

confidence: 99%

Assessment of range-separated time-dependent density-functional theory for calculating C6 dispersion coefficients

Toulouse¹,

Rebolini²,

Gould³

et al. 2013

The Journal of Chemical Physics

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We assess a variant of linear-response range-separated time-dependent density-functional theory (TDDFT), combining a long-range Hartree-Fock (HF) exchange kernel with a short-range adiabatic exchange-correlation kernel in the local-density approximation (LDA) for calculating isotropic C6 dispersion coefficients of homodimers of a number of closed-shell atoms and small molecules. This range-separated TDDFT tends to give underestimated C6 coefficients of small molecules with a mean absolute percentage error of about 5%, a slight improvement over standard TDDFT in the adiabatic LDA which tends to overestimate them with a mean absolute percentage error of 8%, but close to time-dependent Hartree-Fock which has a mean absolute percentage error of about 6%. These results thus show that introduction of long-range HF exchange in TDDFT has a small but beneficial impact on the values of C6 coefficients. It also confirms that the present variant of rangeseparated TDDFT is a reasonably accurate method even using only a LDA-type density functional and without adding an explicit treatment of long-range correlation.

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Local-spin-density functional for multideterminant density functional theory

Cited by 122 publications

References 62 publications

Basis convergence of range-separated density-functional theory

Basis convergence of range-separated density-functional theory

The van der Waals interactions in rare-gas dimers: the role of interparticle interactions

Assessment of range-separated time-dependent density-functional theory for calculating C6 dispersion coefficients

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