Strengths and limitations of the adiabatic exact-exchange kernel for total energy calculations

Hellgren, Maria; Baguet, Lucas

doi:10.1063/5.0146423

Cited by 3 publications

(3 citation statements)

References 63 publications

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“…For this purpose, it is useful to express it in terms of the reducible polarizability, χ. 62 For a system with N electrons in its ground-state, the interaction energy is given by the expectation value of Coulomb interaction operator V ̂in the many-body groundstate…”

Section: Interaction Energy In Terms Of the Polarizabilitymentioning

confidence: 99%

“…Our focus is to find accurate expressions for the interaction energy E inter . For this purpose, it is useful to express it in terms of the reducible polarizability, χ …”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Therefore, the resulting self-energy is always approximate . Nevertheless, using a GW̃ self-energy instead of GW often improves the QP energies. ,, At the same time, the idea is much less explored when it comes to total energies. , Moreover, to the best of our knowledge, a systematic study for both total energy and spectra that would discern the effect of the replacement of the full Γ by a two-argument vertex on one side from the effect of approximations to f xc itself on the other side is still missing.…”

Section: Introductionmentioning

confidence: 99%

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Total Energy beyond GW: Exact Results and Guidelines for Approximations

El-Sahili,

Sottile,

Reining

2024

J. Chem. Theory Comput.

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The total energy and electron addition and removal spectra can, in principle, be obtained exactly from the one-body Green’s function (GF). In practice, the GF is obtained from an approximate self-energy. In the framework of many-body perturbation theory, we derive different expressions that are based on an approximate self-energy, but that yield nevertheless, in principle, the exact exchange–correlation contribution to the total energy for any interaction strength. Response functions play a crucial role, which explains why, for example, ingredients from time-dependent density functional theory can be used to build these approximate self-energies. We show that the key requirement for obtaining exact results is the consistent combination of ingredients. Also when further approximations are made, as it is necessary in practice, this consistency remains the key to obtain good results. All findings are illustrated using the exactly solvable symmetric Hubbard dimer.

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Section: Interaction Energy In Terms Of the Polarizabilitymentioning

confidence: 99%

“…Our focus is to find accurate expressions for the interaction energy E inter . For this purpose, it is useful to express it in terms of the reducible polarizability, χ …”

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Total Energy beyond GW: Exact Results and Guidelines for Approximations

El-Sahili,

Sottile,

Reining

2024

J. Chem. Theory Comput.

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Exact exchange-like electric response from a meta-generalized gradient approximation: A semilocal realization of ultranonlocality

Aschebrock,

Lebeda,

Brütting

et al. 2023

The Journal of Chemical Physics

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We review the concept of ultranonlocality in density functional theory and the relation between ultranonlocality, the derivative discontinuity of the exchange energy, and the static electric response in extended molecular systems. We present the construction of a new meta-generalized gradient approximation for exchange that captures the ultranonlocal response to a static electric field in very close correspondence to exact exchange, yet at a fraction of its computational cost. This functional, in particular, also captures the dependence of the response on the system size. The static electric polarizabilities of hydrogen chains and oligo-acetylene molecules calculated with this meta-GGA are quantitatively close to the ones obtained with exact exchange. The chances and challenges associated with the construction of meta-GGAs that are intended to combine a substantial derivative discontinuity and ultranonlocality with an accurate description of electronic binding are discussed.

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Potential energy surfaces from many-body functionals: Analytical benchmarks and conserving many-body approximations

Lani,

Marzari

2024

Phys. Rev. Research

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We investigate analytically the performance of many-body energy functionals, derived by Klein, Luttinger, and Ward, at different levels of diagrammatic approximations, ranging from second Born, to , to the so-called T matrix, for the calculation of total energies and potential energy surfaces. We benchmark our theoretical results on the extended two-site Hubbard model, which is analytically solvable and for which several exact properties can be calculated. Despite its simplicity, this model displays the physics of strongly correlated electrons: it is prototypical of the H2 dissociation, a notoriously difficult problem to solve accurately for the majority of mean-field-based approaches. We show that both functionals exhibit good to excellent variational properties, particularly in the case of the Luttinger-Ward one, which is in close agreement with fully self-consistent calculations, and we elucidate the relation between the accuracy of the results and the different input one-body Green's functions. Provided that these are wisely chosen, we show how the Luttinger-Ward functional can be used as a computationally inexpensive alternative to fully self-consistent many-body calculations, without sacrificing the precision of the results obtained. Furthermore, in virtue of this accuracy, we argue that this functional can also be used to rank different many-body approximations at different regimes of electronic correlation, once again bypassing the need for self-consistency. Published by the American Physical Society 2024

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Strengths and limitations of the adiabatic exact-exchange kernel for total energy calculations

Cited by 3 publications

References 63 publications

Total Energy beyond GW: Exact Results and Guidelines for Approximations

Total Energy beyond GW: Exact Results and Guidelines for Approximations

Exact exchange-like electric response from a meta-generalized gradient approximation: A semilocal realization of ultranonlocality

Potential energy surfaces from many-body functionals: Analytical benchmarks and conserving many-body approximations

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