Gradient Expansions for the Large-Coupling Strength Limit of the Møller–Plesset Adiabatic Connection

Daas, Timothy J.; Kooi, Derk P.; Grooteman, Arthur J. A. F.; Seidl, Michael; Gori‐Giorgi, Paola

doi:10.1021/acs.jctc.1c01206

Cited by 17 publications

(36 citation statements)

References 56 publications

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“…or about 9.38 mHa. The presence of such a logarithmic term in the GEA for atoms was very recently noticed in [31], and could be inferred from earlier work (see Appendix A of [11]).…”

supporting

confidence: 54%

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Leading correction to the local density approximation for exchange in large-$Z$ atoms

Argaman¹,

Redd²,

Cancio³

et al. 2022

Preprint

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The large-Z asymptotic expansion of atomic exchange energies has been useful in determining exact conditions for corrections to the local density approximation in density functional theory. We find that the necessary correction is fit well with a leading ZlnZ term, and find its coefficient numerically. The gradient expansion approximation also displays such a term, but with a substantially smaller coefficient. Analytic results in the limit of vanishing interaction with hydrogenic orbitals (a Bohr atom) are given, leading to the conjecture that the true coefficients for all atoms are precisely 2.7 times larger than their gradient expansion counterpart. Combined with the hydrogen atom result, this yields an analytic expression for the exchange-energy correction which is accurate to ∼ 5% for all Z.

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“…or about 9.38 mHa. The presence of such a logarithmic term in the GEA for atoms was very recently noticed in [31], and could be inferred from earlier work (see Appendix A of [11]).…”

supporting

confidence: 54%

“…This research was supported by the NSF (CHE 1856165). We thank Paola Gori-Giorgi for communicating a preprint of [31] and for the ensuing valuable discussions, and John Snyder for unpublished notes.…”

mentioning

confidence: 99%

Leading correction to the local density approximation for exchange in large-$Z$ atoms

Argaman¹,

Redd²,

Cancio³

et al. 2022

Preprint

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show abstract

“…11, the use of W KS ∞ with the HF density greatly worsens the performances of the ACMs considered, supporting the view that an improvement of their performances on real molecules might follow from using the approximation for the HF strong-interaction ingredient that has recently become available. 44 Given that the exchange energy term is absent from the Hubbard model setting, we have limited our analyses to the correlation part of the energy. Nonetheless, our conclusions on how the HF and KS methods compare from a formal point of view should not vary much by an inclusion of the exchange energy.…”

Section: Discussionmentioning

confidence: 99%

“…Whereas W KS ∞ has been known for quite a long time, 27 and an excellent approximation to it in the form of a gradient expansion has been developed since, 43 W HF ∞ has been introduced only recently, 35 and gradient expansion approximations to it have just been devised. 44 The mixed LB functional thus obtained is used as a correction to the HF energy. Its performance for the Hubbard dimer is shown in Fig.…”

Section: Performance Of the Lb And Spl Functionals For The Hubbard Dimermentioning

confidence: 99%

Comparing correlation components and approximations in Hartree-Fock and Kohn-Sham theories via an analytical test case study

Giarrusso,

Pribram-Jones

2022

Preprint

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The asymmetric Hubbard dimer is a model that allows for explicit expressions of the Hartree-Fock (HF) and Kohn-Sham (KS) states as analytical functions of the external potential, ∆v, and of the interaction strength, U. We use this unique circumstance to establish a rigorous comparison between the individual contributions to the correlation energies stemming from the two theories in the {U, ∆v} parameter space. Within this analysis of the Hubbard dimer, we observe a change in the sign of the HF kinetic correlation energy, compare the indirect repulsion energies, and derive an expression for the 'traditional' correlation energy, i.e. the one that corrects the HF estimate, in a pure siteoccupation function theory spirit [Eq. ( 43)]. Next, we test the performances of the Liu-Burke and the Seidl-Perdew-Levy functionals, which model the correlation energy based on its weak-and strong-interaction limit expansions and can be used for both the traditional and the KS correlation energies. Our results show that, in the Hubbard dimer setting, they typically work better for the HF reference, despite having been originally devised for KS. These conclusions are somewhat in line with prior assessments of these functionals on various chemical data sets. However, the Hubbard dimer model allows us to show the extent of the error that may occur in using the strong-interaction ingredient for the KS reference in place of the one for the HF reference, as has been carried out in most of the prior assessments.

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“…64,65 There have been various approaches to regularize MP2 by an approximate treatment of higher-order screening effects, either using empirical 34,[66][67][68][69][70][71][72][73][74][75] or diagrammatically motivated modifications 38,[76][77][78] or attacking the problem from a DFT perspective. 79,80 Starting from the opposite direction, there have been many attempts to correct the RPA correlation energy expression by adding additional terms to improve the description of short-range correlation. This includes range-separation based approaches, [81][82][83][84][85][86][87][88][89][90] or augmentations by singles contributions.…”

Section: Introductionmentioning

confidence: 99%

Assessment of the second-order statically screened exchange correction to the random phase approximation for correlation energies

Förster

2022

Preprint

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With increasing inter-electronic distance, the screening of the electron-electron interaction by the presence of other electrons becomes the dominant source of electron correlation. This effect is described by the random phase approximation (RPA) which is therefore a promising method for the calculation of weak interactions. The success of the RPA relies on the cancellation of errors, which can be traced back to the violation of the crossing symmetry of the 4-point vertex, leading to strongly overestimated total correlation energies. By addition of second-order screened exchange (SOSEX) to the correlation energy, this issue is substantially reduced. In the adiabatic connection (AC) SOSEX formalism, one of the two electron-electron interaction lines in the second-order exchange term is dynamically screened. A related SOSEX expression in which both electron-electron interaction lines are statically screened is obtained from the G3W 2 contribution to the electronic self-energy. In contrast to AC-SOSEX, the evaluation of this correlation energy expression does not require an expensive numerical frequency integration and is therefore advantageous from a computational perspective. We compare the accuracy of both RPA+SOSEX variants for the calculation of the interaction 1

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Gradient Expansions for the Large-Coupling Strength Limit of the Møller–Plesset Adiabatic Connection

Cited by 17 publications

References 56 publications

Leading correction to the local density approximation for exchange in large-$Z$ atoms

Leading correction to the local density approximation for exchange in large-$Z$ atoms

Comparing correlation components and approximations in Hartree-Fock and Kohn-Sham theories via an analytical test case study

Assessment of the second-order statically screened exchange correction to the random phase approximation for correlation energies

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