Time-dependent density-functional theory for periodic solids: assessment of excitonic exchange–correlation kernels

Byun, Young-Moo; Sun, Jiuyu; Ullrich, Carsten A.

doi:10.1088/2516-1075/ab7b12

Cited by 45 publications

(46 citation statements)

References 149 publications

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“…In finite systems with a confining potential, the response functions tend toward zero outside of the confined region, and this so-called long-range behavior is known to be relatively unimportant in the present context-this is not the case in periodic systems [15,16,53,54]. Therefore, as we demonstrate in this work, forcing the interacting response function to equal the noninteracting response function within some yet undefined outer region does not much alter the derived properties of the interacting response function, such as its optical spectrum.…”

Section: Real-space Truncationmentioning

confidence: 89%

“…The unique f xc , modulo a constant shift (see below), defined in Eq. ( 5) can be considered the physical f xc , and it is this definition of f xc that is assumed in discussions on its various properties and limits [15,16,53,54,60]. To modify this f xc using its gauge freedom changes its underlying structure; for example, setting g = 0 gives f xc spurious long-range behavior, and setting g = h produces an f xc that is not symmetric under interchange of x ↔ x .…”

Section: Gauge Freedommentioning

confidence: 99%

“…is not directly observed in the x → −∞ limit-the atom, whose ground-state density does not decay as quickly, converges toward − f H in both the positive and negative limits (see the Supplemental Material [55]). It is known that the long-range limit of f xc , in both finite and periodic systems, satisfies f xc (ω) → −α(ω) f H [15,16,53,54], where α(ω) is a frequency-dependent constant that reflects dielectric screening in the system. Therefore, one expects α = 1 in finite systems, and at lower frequencies, where the numerical methodology provides a robust long-range limit, our observations are consistent with this, see Fig.…”

Section: Quantum Harmonic Oscillatormentioning

confidence: 99%

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Insights from exact exchange-correlation kernels

2021

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The exact exchange-correlation (xc) kernel f xc (x, x , ω) of linear response time-dependent density functional theory is computed over a wide range of frequencies for three canonical one-dimensional finite systems. Methods used to ensure the numerical robustness of f xc are set out. The frequency dependence of f xc is found to be largely due to its analytic structure, i.e., its singularities at certain frequencies, which are required in order to capture particular transitions, including those of double excitation character. However, within the frequency range of the first few interacting excitations, f xc is approximately ω independent, meaning the exact adiabatic approximation f xc (ω = 0) remedies the failings of the local density approximation and random phase approximation for these lowest transitions. The key differences between the exact f xc and its common approximations are analyzed, and cannot be eliminated by exploiting the limited gauge freedom in f xc . The optical spectrum benefits from using as accurate as possible an f xc and ground-state xc potential, while maintaining exact compatibility between the two is of less importance.

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Section: Real-space Truncationmentioning

confidence: 89%

Section: Gauge Freedommentioning

confidence: 99%

Section: Quantum Harmonic Oscillatormentioning

confidence: 99%

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Insights from exact exchange-correlation kernels

2021

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“…One is achieving a level of accuracy that is on par with that of experiment (approximately 0.1 eV) for a wide range of materials, from narrow band gap semiconductors to wide band gap insulators [41]. The other is doing so nonempirically within a formally exact framework, such that other material properties, from defect energetics [42] to optical absorption [43,44], can be predicted on the same footing. Here, we show that both these issues can be re-solved simultaneously.…”

mentioning

confidence: 99%

Band gaps of crystalline solids from Wannier-localization based optimal tuning of a screened range-separated hybrid functional

Wing,

Ohad,

Haber

et al. 2020

Preprint

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Accurate prediction of fundamental band gaps of crystalline solid state systems entirely within density functional theory is a long standing challenge. Here, we present a simple and inexpensive method that achieves this by means of non-empirical optimal tuning of the parameters of a screened range-separated hybrid functional. The tuning involves the enforcement of an ansatz that generalizes the ionization potential theorem to the removal of an electron in an occupied state described by a localized Wannier function in a modestly sized supercell calculation. The method is benchmarked against experiment for a set of systems ranging from narrow band gap semiconductors to large band gap insulators, spanning a range of fundamental band gaps from 0.2 to 14.2 eV and is found to yield quantitative accuracy across the board, with a mean absolute error of ∼0.1 eV and a maximal error of ∼0.2 eV.

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“…Importantly, these quantities can be verified through the use of optical absorption spectroscopy or electron energy loss spectroscopy. By transforming those equations into reciprocal space, a theorist would be able to calculate the band structures and other excitation effects for many materials [16,17]. While extended systems are worthwhile to explore and there are numerous parallels to finite systems, we will not spend time exploring this rich ecosystem.…”

Section: Functional Approximations and Time-dependencementioning

confidence: 99%

Applications of model systems to explore exchange-correlation effects in density-functional theory

Pluhar¹

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Density-functional theory (DFT), in its various forms, has become a near ubiquitous form of theoretical research used to benchmark and prototype solutions to many finite and extended state system. This is largely because DFT can both capture the rich physics that is present in these electronic systems, while remaining computationally cost-effective and interpretable. However, DFT also has the requirement that the density functional being used to iteratively converge towards a solution must be accurate and correct. While on the surface such a stipulation seems benign, in practice the density functionals can be overwhelmingly complex and error can be introduced that comes from either the density functional that is chosen or the approximations used to make a system more calculationally tenable. In this work, our focus is on the use of model systems to calculate and determine the usefulness and shortcomings of DFT. By simplifying the underlying system, while also retaining enough physical quantities from real systems, we can focus on how the approximations affect the outcomes that are produced. To begin, we show that charge-transfer dynamics can be described in unique and enlightening ways through the use of the particle-hole map (PHM). Using a one-dimensional, multi-well system, we effectively demonstrate how interesting electron dynamics can be uncovered by applying unitary transformations to the wavefunctions. By spatially localizing the electronic wavefunctions through the Foster-Boys method, which is analogous to Wannier localization in extended systems, the intermediating components of charge transfer systems can be examined to determine their effect on the system-at-large. From the simple one-dimensional system, we could quickly infer real molecular systems that could potentially be examined using the same method to surmise the role charge-transfer intermediaries play in such systems as organic photovoltaics. Beyond electron dynamics, the role of exchange-correlation (xc) scalar potentials and magnetic fields that are features of noncollinear spin Kohn-Sham (KS) and DFT was explored by comparing the exact Schroedinger solution to the KS and DFT approximations. By extending the Hubbard model to four sites, we can both solve the system exactly, while allowing for on-site and nearest-neighbor interactions. We were able to obtain benchmark solutions across a wide range of interaction strengths, determining that there are regimes where the xc magnetic fields play an increasingly larger role as the system becomes more correlated. In fact, there is a regime where the xc magnetic fields become larger than the external magnetic fields that are applied on the system. Through the model system, we could additionally compare the exact solutions against the approximated xc functionals and demonstrate that the weakly correlated regime can be adequately described by the xc functional approximations common to many real-systems. Moving beyond steady state observations, we can also describe time-dependent electron dynamics through real-time TDDFT and use a model system to compare the time-evolution of the exact and KS solutions. By allowing the xc potentials to propagate in real time, we could explore the role the xc torques played during the evolution of a triangular lattice under an applied, time-varying magnetic field. Additionally, by controlling the spin-orbit coupling present in the small model system, we determined that the spin orbit coupling plays a substantial role in keeping the spins more closely aligned with the exact system. In part, this was due to the spin-orbit coupling serving as a time-varying magnetic field, which tended to be larger than the xc potentials that were also present. The trimer can also be quickly and easily expanded with the added spin-orbit coupling and compared to real model systems through computational physics software, such as Octopus.

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Time-dependent density-functional theory for periodic solids: assessment of excitonic exchange–correlation kernels

Cited by 45 publications

References 149 publications

Insights from exact exchange-correlation kernels

Insights from exact exchange-correlation kernels

Band gaps of crystalline solids from Wannier-localization based optimal tuning of a screened range-separated hybrid functional

Applications of model systems to explore exchange-correlation effects in density-functional theory

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