Beyond the RPA and GW methods with adiabatic xc-kernels for accurate ground state and quasiparticle energies

Thomas Olsen*, Kristian Sommer Thygesen, Cristopher E. Patrick, Jefferson E. Bates, Adrienn Ruzsinszky

*Corresponding author for this work

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Abstract

We review the theory and application of adiabatic exchange–correlation (xc)-kernels for ab initio calculations of ground state energies and quasiparticle excitations within the frameworks of the adiabatic connection fluctuation dissipation theorem and Hedin’s equations, respectively. Various different xc kernels, which are all rooted in the homogeneous electron gas, are introduced but hereafter we focus on the specific class of renormalized adiabatic kernels, in particular the rALDA and rAPBE. The kernels drastically improve the description of short-range correlations as compared to the random phase approximation (RPA), resulting in significantly better correlation energies. This effect greatly reduces the reliance on error cancellations, which is essential in RPA, and systematically improves covalent bond energies while preserving the good performance of the RPA for dispersive interactions. For quasiparticle energies, the xc-kernels account for vertex corrections that are missing in the GW self energy. In this context, we show that the short-range correlations mainly correct the absolute band positions while the band gap is less affected in agreement with the known good performance of GW for the latter. The renormalized xc kernels offer a rigorous extension of the RPA and GW methods with clear improvements in terms of accuracy at little extra computational cost.
Original languageEnglish
Article number106
Journaln p j Computational Materials
Volume5
Number of pages23
ISSN2057-3960
DOIs
Publication statusPublished - 2019

Cite this

@article{599b0f8534f64d43975feb6906b007c1,
title = "Beyond the RPA and GW methods with adiabatic xc-kernels for accurate ground state and quasiparticle energies",
abstract = "We review the theory and application of adiabatic exchange–correlation (xc)-kernels for ab initio calculations of ground state energies and quasiparticle excitations within the frameworks of the adiabatic connection fluctuation dissipation theorem and Hedin’s equations, respectively. Various different xc kernels, which are all rooted in the homogeneous electron gas, are introduced but hereafter we focus on the specific class of renormalized adiabatic kernels, in particular the rALDA and rAPBE. The kernels drastically improve the description of short-range correlations as compared to the random phase approximation (RPA), resulting in significantly better correlation energies. This effect greatly reduces the reliance on error cancellations, which is essential in RPA, and systematically improves covalent bond energies while preserving the good performance of the RPA for dispersive interactions. For quasiparticle energies, the xc-kernels account for vertex corrections that are missing in the GW self energy. In this context, we show that the short-range correlations mainly correct the absolute band positions while the band gap is less affected in agreement with the known good performance of GW for the latter. The renormalized xc kernels offer a rigorous extension of the RPA and GW methods with clear improvements in terms of accuracy at little extra computational cost.",
author = "Thomas Olsen and Thygesen, {Kristian Sommer} and Patrick, {Cristopher E.} and Bates, {Jefferson E.} and Adrienn Ruzsinszky",
year = "2019",
doi = "10.1038/s41524-019-0242-8",
language = "English",
volume = "5",
journal = "n p j Computational Materials",
issn = "2057-3960",
publisher = "Nature Publishing Group",

}

Beyond the RPA and GW methods with adiabatic xc-kernels for accurate ground state and quasiparticle energies. / Olsen, Thomas; Thygesen, Kristian Sommer; Patrick, Cristopher E.; Bates, Jefferson E.; Ruzsinszky, Adrienn.

In: n p j Computational Materials, Vol. 5, 106, 2019.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Beyond the RPA and GW methods with adiabatic xc-kernels for accurate ground state and quasiparticle energies

AU - Olsen, Thomas

AU - Thygesen, Kristian Sommer

AU - Patrick, Cristopher E.

AU - Bates, Jefferson E.

AU - Ruzsinszky, Adrienn

PY - 2019

Y1 - 2019

N2 - We review the theory and application of adiabatic exchange–correlation (xc)-kernels for ab initio calculations of ground state energies and quasiparticle excitations within the frameworks of the adiabatic connection fluctuation dissipation theorem and Hedin’s equations, respectively. Various different xc kernels, which are all rooted in the homogeneous electron gas, are introduced but hereafter we focus on the specific class of renormalized adiabatic kernels, in particular the rALDA and rAPBE. The kernels drastically improve the description of short-range correlations as compared to the random phase approximation (RPA), resulting in significantly better correlation energies. This effect greatly reduces the reliance on error cancellations, which is essential in RPA, and systematically improves covalent bond energies while preserving the good performance of the RPA for dispersive interactions. For quasiparticle energies, the xc-kernels account for vertex corrections that are missing in the GW self energy. In this context, we show that the short-range correlations mainly correct the absolute band positions while the band gap is less affected in agreement with the known good performance of GW for the latter. The renormalized xc kernels offer a rigorous extension of the RPA and GW methods with clear improvements in terms of accuracy at little extra computational cost.

AB - We review the theory and application of adiabatic exchange–correlation (xc)-kernels for ab initio calculations of ground state energies and quasiparticle excitations within the frameworks of the adiabatic connection fluctuation dissipation theorem and Hedin’s equations, respectively. Various different xc kernels, which are all rooted in the homogeneous electron gas, are introduced but hereafter we focus on the specific class of renormalized adiabatic kernels, in particular the rALDA and rAPBE. The kernels drastically improve the description of short-range correlations as compared to the random phase approximation (RPA), resulting in significantly better correlation energies. This effect greatly reduces the reliance on error cancellations, which is essential in RPA, and systematically improves covalent bond energies while preserving the good performance of the RPA for dispersive interactions. For quasiparticle energies, the xc-kernels account for vertex corrections that are missing in the GW self energy. In this context, we show that the short-range correlations mainly correct the absolute band positions while the band gap is less affected in agreement with the known good performance of GW for the latter. The renormalized xc kernels offer a rigorous extension of the RPA and GW methods with clear improvements in terms of accuracy at little extra computational cost.

U2 - 10.1038/s41524-019-0242-8

DO - 10.1038/s41524-019-0242-8

M3 - Journal article

VL - 5

JO - n p j Computational Materials

JF - n p j Computational Materials

SN - 2057-3960

M1 - 106

ER -