Efficient Total Energy Calculations from Self-Energy Models

Sánchez-Friera, P.; Godby, R. W.

doi:10.1103/physrevlett.85.5611

Cited by 33 publications

(24 citation statements)

References 22 publications

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“…The factor α in front of the Hartree-Fock exact-exchange term is equivalent to a constant static screening function. Alternatively a more complex screening function can be chosen as in the screenedexchange (sX-LDA) approach [17,28,115,116], the -GKS Σ scheme [117] or the Heyd-Scuseria-Ernzerhof (HSE) functional [25][26][27]. An appealing feature of the hy- 18 Some hybrid schemes introduce additional parameters for mixing different portions of the local-spin density (LSD) functional with GGA exchange and correlation in the DFT xc E term [21].…”

Section: Discussionmentioning

confidence: 99%

Exciting prospects for solids: Exact‐exchange based functionals meet quasiparticle energy calculations

Rinke¹,

Qteish

Neugebauer

et al. 2008

Physica Status Solidi (b)

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1 Introduction Density functional theory (DFT) has contributed significantly to our present understanding of a wide range of materials and their properties. As quantummechanical theory of the density and the total energy, it provides an atomistic description from first principles and is, in the local-density or generalized gradient approximation (LDA and GGA), applicable to polyatomic systems containing up to several thousand atoms. However, a combination of three factors limits the applicability of LDA and GGA to a range of important materials and interesting phenomena. They are approximate (jellium-based) exchange-correlation functionals, which suffer from incomplete cancellation of artificial self-interaction and lack the discontinuity of the exchange-correlation potential with respect to the number of electrons. As a consequence the Kohn-Sham (KS) single-particle eigenvalue band gap for semiconductors and insulators underestimates the quasiparticle band gap as measured by the difference of ionisation energy (via photoemission spectroscopy (PES)) and electron affinity (via inverse PES (IPES)). This reduces the predictive power for materials whose band gap is not know from experiment and poses a problem for calculations

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Section: Discussionmentioning

confidence: 99%

Exciting prospects for solids: Exact‐exchange based functionals meet quasiparticle energy calculations

Rinke¹,

Qteish

Neugebauer

et al. 2008

Physica Status Solidi (b)

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“…in the QP representation [26] for the case of the ground state. The crucial points here are that the energy dependence of the self-energy appears in the same way in both Eqs.…”

Section: Basic Theorymentioning

confidence: 99%

A simple derivation of the exact quasiparticle theory and its extension to arbitrary initial excited eigenstates

Ohno

Ono

Isobe

2017

The Journal of Chemical Physics

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The quasiparticle (QP) energies, which are minus of the energies required by removing or produced by adding one electron from/to the system, corresponding to the photoemission or inverse photoemission (PE/IPE) spectra, are determined together with the QP wave functions, which are not orthonormal and even not linearly independent but somewhat similar to the normal spin orbitals in the theory of the configuration interaction, by self-consistently solving the QP equation coupled with the equation for the self-energy. The electron density, kinetic and all interaction energies can be calculated using the QP wave functions. We prove in a simple way that the PE/IPE spectroscopy and therefore this QP theory can be applied to an arbitrary initial excited eigenstate. In this proof, we show that the energy-dependence of the self-energy is not an essential difficulty, and the QP picture holds exactly if there is no relaxation mechanism in the system. The validity of the present theory for some initial excited eigenstates is tested using the one-shot GW approximation for several atoms and molecules. * ohno@ynu.ac.jp

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“…This is related to ongoing efforts 43 to compute accurate total energies from self-consistent 1-electron Green's functions. Specifically, the HSE functional can be interpreted as the GalitskiiMigdal formula 44 applied to the frequency-independent COHSEX self-energy in Eq. (8) to calculate an exchangecorrelation energy,…”

Section: B G3/99 Formation Energiesmentioning

confidence: 99%

Analysis of the Heyd-Scuseria-Ernzerhof density functional parameter space

Moussa¹,

Schultz²,

Chelikowsky³

2012

The Journal of Chemical Physics

151

143

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The Heyd-Scuseria-Ernzerhof (HSE) density functionals are popular for their ability to improve the accuracy of standard semilocal functionals such as Perdew-Burke-Ernzerhof (PBE), particularly for semiconductor band gaps. They also have a reduced computational cost compared to hybrid functionals, which results from the restriction of Fock exchange calculations to small inter-electron separations. These functionals are defined by an overall fraction of Fock exchange and a length scale for exchange screening. We systematically examine this two-parameter space to assess the performance of hybrid screened exchange (sX) functionals and to determine a balance between improving accuracy and reducing the screening length, which can further reduce computational costs. Three parameter choices emerge as useful: "sX-PBE" is an approximation to the sX-LDA screened exchange density functionals based on the local density approximation (LDA); "HSE12" minimizes the overall error over all tests performed; and "HSE12s" is a range-minimized functional that matches the overall accuracy of the existing HSE06 parameterization but reduces the Fock exchange length scale by half. Analysis of the error trends over parameter space produces useful guidance for future improvement of density functionals.

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Efficient Total Energy Calculations from Self-Energy Models

Cited by 33 publications

References 22 publications

Exciting prospects for solids: Exact‐exchange based functionals meet quasiparticle energy calculations

Exciting prospects for solids: Exact‐exchange based functionals meet quasiparticle energy calculations

A simple derivation of the exact quasiparticle theory and its extension to arbitrary initial excited eigenstates

Analysis of the Heyd-Scuseria-Ernzerhof density functional parameter space

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