Excitations and benchmark ensemble density functional theory for two electrons

Pribram‐Jones, Aurora; Yang, Zeng-hui; Trail, J. R.; Burke, Kieron; Needs, R. J.; Ullrich, Carsten A.

doi:10.1063/1.4872255

Cited by 63 publications

(78 citation statements)

References 66 publications

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“…A first strategy consists in simultaneously optimizing an ensemble of states. Such an ensemble DFT was pioneered by Theophilou [8] and by Gross, Oliveira and Kohn [9] and is still a subject of research [10][11][12][13], but it is hampered by the absence of appropriate approximate ensemble functionals. A second strategy consists in selfconsistently optimizing a single excited state.…”

Section: Introductionmentioning

confidence: 99%

Excited states from range-separated density-functional perturbation theory

et al. 2015

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We explore the possibility of calculating electronic excited states by using perturbation theory along a range-separated adiabatic connection. Starting from the energies of a partially interacting Hamiltonian, a first-order correction is defined with two variants of perturbation theory: a straightforward perturbation theory, and an extension of the Görling-Levy one that has the advantage of keeping the ground-state density constant at each order in the perturbation. Only the first, simpler, variant is tested here on the helium and beryllium atoms and on the dihydrogene molecule. The first-order correction within this perturbation theory improves significantly the total ground-and excited-state energies of the different systems. However, the excitation energies are mostly deteriorated with respect to the zeroth-order ones, which may be explained by the fact that the ionization energy is no longer correct for all interaction strengths. The second variant of the perturbation theory should improve these results but has not been tested yet along the range-separated adiabatic connection.

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Section: Introductionmentioning

confidence: 99%

Excited states from range-separated density-functional perturbation theory

et al. 2015

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“…Indeed, several time-independent DFT approaches for calculating excitation energies exist and are currently being developed. These include ensemble DFT [7][8][9][10][11][12], ∆SCF [13][14][15][16][17] and related methods [18][19][20][21], or perturbation theory [22][23][24][25] along the standard adiabatic connection using the noninteracting Kohn-Sham (KS) Hamiltonian as the zero-order Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

Calculating excitation energies by extrapolation along adiabatic connections

et al. 2015

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In this paper, an alternative method to range-separated linear-response time-dependent densityfunctional theory and perturbation theory is proposed to improve the estimation of the energies of a physical system from the energies of a partially interacting system. Starting from the analysis of the Taylor expansion of the energies of the partially interacting system around the physical system, we use an extrapolation scheme to improve the estimation of the energies of the physical system at an intermediate point of the range-separated or linear adiabatic connection where either the electron-electron interaction is scaled or only the long-range part of the Coulomb interaction is included. The extrapolation scheme is first applied to the range-separated energies of the helium and beryllium atoms and of the hydrogen molecule at its equilibrium and stretched geometries. It improves significantly the convergence rate of the energies toward their exact limit with respect to the range-separation parameter. The range-separated extrapolation scheme is compared with a similar approach for the linear adiabatic connection, highlighting the relative strengths and weaknesses of each approach.

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“…Recent strides by Pernal and coworkers [20,21], Fromager and coworkers [22,23], and others attempt to create a useful practical alternative to TDDFT, but the difficulty remains in finding accurate low-cost approximations. EDFT usually requires running several different self-consistent ensemble calculations to extract several low-lying excitations.Here we (a) derive a formula from EDFT to correct a KS orbital energy difference into an exact excitation energy, without doing any self-consistent ensemble calculations, (b) argue that its computational cost should typically be less than either standard TDDFT or EDFT, (c) calculate this correction using the symmetryeigenstate Hartree-exchange (SEHX) approximation [24][25][26] for atoms, demonstrating its accuracy relative to standard TDDFT, and (d) show that SEHX estimates double excitations.EDFT is a formally exact and variational excited-state method [15][16][17]. Let E i be the electronic energy levels, i = 0, 1, ..., each with degeneracy g i .…”

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confidence: 99%

Direct Extraction of Excitation Energies from Ensemble Density-Functional Theory

et al. 2017

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A very specific ensemble of ground and excited states is shown to yield an exact formula for any excitation energy as a simple correction to the energy difference between orbitals of the KohnSham ground state. This alternative scheme avoids either the need to calculate many unoccupied levels as in time-dependent density functional theory (TDDFT) or the need for many self-consistent ensemble calculations. The symmetry-eigenstate Hartree-exchange (SEHX) approximation yields results comparable to standard TDDFT for atoms. With this formalism, SEHX yields approximate double-excitations, which are missed by adiabatic TDDFT.The Hohenberg-Kohn (HK) theorem [1-4] of groundstate density-functional theory (DFT) [1,5] has several parts. The most-used in practice is the establishment of an exact density functional, F [n], whose minimum yields the exact ground-state density and energy of a given system. Almost all practical calculations use the KohnSham (KS) scheme [5] to minimize F with an approximation to the small exchange-correlation contribution, E XC [n]. In fact, many properties of interest in a modern chemical or materials calculation can be extracted from knowledge of the ground-state energy as a function of nuclear coordinates, or in response to a perturbing field.However, except under very special circumstances, most optical excitation frequencies cannot be deduced. Hence there has always been interest in extending ground-state DFT to include such excitations. Moreover, another part of the HK theorem guarantees that such frequencies (and all properties) are indeed functionals of the ground-state density. In recent years, linearresponse time-dependent DFT (TDDFT) [6][7][8][9][10] has become a popular route for extracting low-lying excitation energies of molecules, because of its unprecedented balance of accuracy with computational speed [11]. For significantly sized molecules, more CPU time will be expended on a geometry optimization than a single TDDFT calculation on the optimized geometry.However, while formally exact, TDDFT with standard approximations is far from perfect. If the unknown exchange-correlation (XC) kernel of TDDFT is approximated by its zero-frequency (and hence ground-state) limit, no multiple excitations survive [11]. While a useful work-around exists for cases where a double is close to a single excitation [12,13], there is as yet no simple and efficient general procedure for extracting double excitations within adiabatic TDDFT [14].Ensemble DFT (EDFT) [15,16] applies the principles of ground-state DFT to a convex ensemble of the lowest M levels of a system, for which a KS system can be defined [17]. EDFT is formally exact, but practical calculations require approximations, and initial attempts yielded disappointing results [18]. Accuracy is greatly improved when so-called "ghost interactions" between distinct states are removed from the approximations [19]. EDFT remains an active research area because, being variational, it should not suffer from some of the limitations of standard TDDFT. Rece...

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Excitations and benchmark ensemble density functional theory for two electrons

Cited by 63 publications

References 66 publications

Excited states from range-separated density-functional perturbation theory

Excited states from range-separated density-functional perturbation theory

Calculating excitation energies by extrapolation along adiabatic connections

Direct Extraction of Excitation Energies from Ensemble Density-Functional Theory

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