Accurate optical spectra of solids from pure time-dependent density functional theory

Cavo, Sarah; Berger, J. A.

doi:10.1103/physrevb.101.115109

Cited by 22 publications

(15 citation statements)

References 65 publications

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“… 54 , 163 , 181 , 182 For more strongly correlated systems, or indeed the charge-transfer system above, this is not the case, and the role of the Hxc kernel or the corresponding Δ becomes crucial. 183 − 185 …”

Section: Discontinuities In Excited Finite Systems With An Integer Electron Numbermentioning

confidence: 99%

From Kohn–Sham to Many-Electron Energies via Step Structures in the Exchange-Correlation Potential

Kraisler

Hodgson

Gross

2021

J. Chem. Theory Comput.

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Accurately describing excited states within Kohn–Sham (KS) density functional theory (DFT), particularly those which induce ionization and charge transfer, remains a great challenge. Common exchange-correlation (xc) approximations are unreliable for excited states owing, in part, to the absence of a derivative discontinuity in the xc energy (Δ), which relates a many-electron energy difference to the corresponding KS energy difference. We demonstrate, analytically and numerically, how the relationship between KS and many-electron energies leads to the step structures observed in the exact xc potential in four scenarios: electron addition, molecular dissociation, excitation of a finite system, and charge transfer. We further show that steps in the potential can be obtained also with common xc approximations, as simple as the LDA, when addressed from the ensemble perspective. The article therefore highlights how capturing the relationship between KS and many-electron energies with advanced xc approximations is crucial for accurately calculating excitations, as well as the ground-state density and energy of systems which consist of distinct subsystems.

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Section: Discontinuities In Excited Finite Systems With An Integer Electron Numbermentioning

confidence: 99%

From Kohn–Sham to Many-Electron Energies via Step Structures in the Exchange-Correlation Potential

Kraisler

Hodgson

Gross

2021

J. Chem. Theory Comput.

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“…An accurate ground-state KS potential is required for determining ground-state properties, such as the total energy [10], as well as the optical absorption spectra [11,12], charge-transfer energies [13][14][15] and electron real-time dynamics [16]. As existing approximations within KS theory are unreliable, computationally demanding hybrid density functionals [17,18] are employed to calculate these properties [5,[19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Exact expressions for the height of the interatomic step in the exchange-correlation potential from the derivative discontinuity of the energy

Hodgson

2021

Preprint

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Popular approximations to the exchange-correlation (xc) energy of density functional theory do not yield the spatial 'step' structures in the exact xc potential which are necessary to describe dissociation and electron excitation with the Kohn-Sham (KS) system. Via the discontinuity in the derivative of the xc energy as a function of electron number I derive exact analytic expressions in terms of the KS single-particle energies for the height of the step in the xc potential between a variety of open-and closed-shell atoms within stretched molecules.

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“…As such, computationally expensive methods outside of KS theory must be employed in conjunction with a KS calculation to correct the prediction of the gap, e.g., hybrid density functionals [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] or the GW approximation within many-body perturbation theory [29][30][31][32][33][34]. Calculating accurate gaps at the computational cost of a single KS calculation [35][36][37][38][39] offers the prospect of improved semiconductor, thermoelectric material [10,[40][41][42] and photovoltaic [43][44][45] modeling.…”

Section: Introductionmentioning

confidence: 99%

Exact exchange-correlation potentials for calculating the fundamental gap with a fixed number of electrons

Hodgson,

Wetherell,

Fromager

2020

Preprint

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Capturing the discontinuous shift by ∆ in the exact exchange-correlation (xc) potential is the standard proposal for calculating the fundamental gap, Eg, from the Kohn-Sham (KS) gap, εg, within KS density functional theory (DFT), as Eg = εg + ∆, yet this discontinuity is absent from existing approximations. The 'N -centered' formulation of ensemble DFT artificially maintains a total electron number, N , in order to yield Eg not through a discontinuous shift in the xc potential but via the ensemble-weight derivative of the xc energy. Within the N -centered approach we calculate exact xc potentials for a one-dimensional finite system and show analytically that ∆ can in fact be interpreted as a discontinuous shift in the exact N -centered ensemble xc potential, thereby extending to charged excitations an exact property of uncharged excitations. We show that applying the Levy-Zahariev 'shift-in-potential' procedure in this context relocates the discontinuous shift to the unimportant periphery of the system, so that the exact xc potential in effect is free of discontinuities and thus the inability of a local functional to capture discontinuous behavior is inconsequential.

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Accurate optical spectra of solids from pure time-dependent density functional theory

Cited by 22 publications

References 65 publications

From Kohn–Sham to Many-Electron Energies via Step Structures in the Exchange-Correlation Potential

From Kohn–Sham to Many-Electron Energies via Step Structures in the Exchange-Correlation Potential

Exact expressions for the height of the interatomic step in the exchange-correlation potential from the derivative discontinuity of the energy

Exact exchange-correlation potentials for calculating the fundamental gap with a fixed number of electrons

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