Wave-function inspired density functional applied to the H<sub>2</sub>/${{\rm{H}}}_{2}^{+}$ challenge

Zhang, Igor Ying; Rinke, Patrick; Scheffler, Matthias

doi:10.1088/1367-2630/18/7/073026

Cited by 18 publications

(33 citation statements)

References 109 publications

(270 reference statements)

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“…The current construction of DH functionals suffer from the same problem as MP2 for systems with small energy gaps. The other ways of utilizing the information of unoccupied orbitals, e.g., renormalization of the MP2 term (48,49), random phase approximation instead of Tables 1 and 2, respectively. A negative rMaxD or rMaxE indicates a method that is better than MP2 for density or energy, respectively.…”

Section: Discussionmentioning

confidence: 99%

Doubly hybrid density functionals that correctly describe both density and energy for atoms

Zhu

2018

Proc. Natl. Acad. Sci. U.S.A.

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Recently, it was argued [Medvedev MG, et al. (2017) 355:49-52] that the development of density functional approximations (DFAs) is "straying from the path toward the exact functional." The exact functional should yield both exact energy and density for a system of interest; nevertheless, they found that many heavily fitted functionals for molecular energies actually lead to poor electron densities of atoms. They also observed a trend that, for the nonempirical and few-parameter functionals, densities can be improved as one climbs up the first four rungs of the Jacob's ladder of DFAs. The XYG3 type of doubly hybrid functionals (xDHs) represents a less-empirical and fewer-parameter functional on the top fifth rung, in which both the Hartree-Fock-like exchange and the second-order perturbative (MP2-like) correlation are hybridized with the low rung functionals. Here, we show that xDHs can well describe both density and energy for the same atomic set of Medvedev et al., showing that the latter trend can well be extended to the top fifth rung.

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Section: Discussionmentioning

confidence: 99%

Doubly hybrid density functionals that correctly describe both density and energy for atoms

Zhu

2018

Proc. Natl. Acad. Sci. U.S.A.

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“…) retains all the advantages of BGE2 [23] such as size consistency, being one-electron self-interaction-free, and giving the exact H 2 dissociation limit in the minimal basis. Furthermore, sBGE2 improves on BGE2 in the intermediate bonding regime, as is evident from Fig.…”

Section: Fig 1 H2 (A) and Hmentioning

confidence: 99%

“…The screened e ab -coupling of the sBGE2 correlation solves this divergence, which is demonstrated by the good performance of ZRPS for similarly challenging cases, such as the closing energy gaps in the dissociation limit of molecular dimers. Given that the (s)BGE2 correlation is size-extensive [23], the applicability of ZRPS to extended systems is guaranteed. The implementation and further numeric benchmarks of ZRPS for solids are ongoing in our group.…”

Section: Pbe-tsmentioning

confidence: 99%

“…Conversely, the e ab -coupling effect properly describes two-electron (near)-degeneracy correlation, which is important for H 2 dissociation. In our previous work [23] we demonstrated that BGE2 can describe static-correlation by means of a level-shift expansion of the e ab -coupling effect and by showing that BGE2 gives an exact description of the H 2 dissociation limit in a minimal basis.…”

mentioning

confidence: 97%

“…Recently, we proposed a non-empirical level-5 correlation functional that corresponds to the second-order Bethe-Goldstone equation (BGE2) [23] …”

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confidence: 99%

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Towards Efficient Orbital-Dependent Density Functionals for Weak and Strong Correlation

et al. 2016

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We present a new paradigm for the design of exchange-correlation functionals in density-functional theory. Electron pairs are correlated explicitly by means of the recently developed second order Bethe-Goldstone equation (BGE2) approach. Here we propose a screened BGE2 (sBGE2) variant that efficiently regulates the coupling of a given electron pair. sBGE2 correctly dissociates H2 and H + 2 , a problem that has been regarded as a great challenge in density-functional theory for a long time. The sBGE2 functional is then taken as a building block for an orbital-dependent functional, termed ZRPS, which is a natural extension of the PBE0 hybrid functional. While worsening the good performance of sBGE2 in H2 and H + 2 , ZRPS yields a remarkable and consistent improvement over other density functionals across various chemical environments from weak to strong correlation.The popularity of density-functional theory in physics, chemistry and materials science stems from the favorable balance between accuracy and computational efficiency offered by semi-local or hybrid approximations to the exchange-correlation (xc) functional. However, certain well-documented failures such as the unsatisfactory prediction of atomization energies, the significant underestimation of weak interactions and reaction barriers and the inability to correctly describe strongly interacting scenarios with pronounced multi-reference character, such as bond dissociation [1-7], limit the predictive power of these functionals in certain cases.Density functionals that depend on the unoccupied as well as the occupied Kohn-Sham orbitals stand on the fifth and currently highest rung of the ladder [8] of density functional approximations. The rapid growth of computational capacity has been boosting the development of practical level-5 functionals over the past ten years. One example is Görling-Levy perturbation theory at 2nd order that corresponds to the exact xc-functional for systems with a linear adiabatic-connection path [4,9]. However, in reality the adiabatic-connection path is not linear and Görling-Levy perturbation theory fails for systems with small energy gaps, where (near)-degeneracy correlation (also known as static correlation) is dominant, as exemplified by molecular dissociation [5][6][7]. The random-phase approximation (RPA) is another example of a level-5 functional. RPA sums up a sequence of "ring diagrams" to infinite order [10] and is remarkably accurate for reaction-barrier heights and weak interactions, but it significantly underestimates atomization energies. It also produces the correct H 2 dissociation limit [11], but fails for H + 2 dissociation due to appreciable self-correlation errors [12,13]. Recently, much effort

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The XYG3 type of doubly hybrid density functionals

2016

WIREs Comput Mol Sci

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Doubly hybrid (DH) functionals have emerged as a new class of density functional approximations (DFAs), which not only have a nonlocal orbital-dependent component in the exchange part, but also incorporate the information of unoccupied orbitals in the correlation part, being at the top rung of Perdew's view of Jacob's ladder in DFAs. This review article focuses on the XYG3 type of DH (xDH) functionals, which use a low rung functional to perform the self-consistent-field calculation to generate orbitals and densities, with which a top rung DH functional is used for final energy evaluation. We will discuss the theoretical background of the xDH functionals, briefly reviewing the adiabatic connection formalism, coordinate scaling relations, and Görling-Levy perturbation theory. General performance of the xDH functionals will be presented for both energies and structures. In particular, we will present the fractional charge behaviors of the xDH functionals, examining the self-interaction errors, the delocalization errors and the deviation from the linearity condition, as well as their effects on the predicted ionization potentials, electron affinities and fundamental gaps. This provides a theoretical rationale for the observed good performance of the xDH functionals.

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Wave-function inspired density functional applied to the H₂/${{\rm{H}}}_{2}^{+}$ challenge

Cited by 18 publications

References 109 publications

Doubly hybrid density functionals that correctly describe both density and energy for atoms

Doubly hybrid density functionals that correctly describe both density and energy for atoms

Towards Efficient Orbital-Dependent Density Functionals for Weak and Strong Correlation

The XYG3 type of doubly hybrid density functionals

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Wave-function inspired density functional applied to the H2/${{\rm{H}}}_{2}^{+}$ challenge

Cited by 18 publications

References 109 publications

Doubly hybrid density functionals that correctly describe both density and energy for atoms

Doubly hybrid density functionals that correctly describe both density and energy for atoms

Towards Efficient Orbital-Dependent Density Functionals for Weak and Strong Correlation

The XYG3 type of doubly hybrid density functionals

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Wave-function inspired density functional applied to the H₂/${{\rm{H}}}_{2}^{+}$ challenge