A road to a multiconfigurational ensemble density functional theory without ghost interactions

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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“…The REKS method is a multireference extension to ground-state DFT and EDFT (see also [44]), while the others are within standard EDFT.…”

Section: −1 Imentioning

confidence: 99%

Direct Extraction of Excitation Energies from Ensemble Density-Functional Theory

et al. 2017

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“…0 , which is a typical value in range-separated eDFT calculations 31,43 . Interestingly, convergence towards the pure wavefunction theory result (µ → +∞ limit) is essentially reached for µ = 1.0a −1 0 thanks to both ghost-interaction and extrapolation corrections.…”

Section: Discussionmentioning

confidence: 89%

“…In practice, long-range-interacting wavefunctions are usually computed (self-consistently) at the configuration interaction (CI) level 31,40,43 within the weightindependent density functional approximation (WIDFA), which simply consists in substituting in Eqs. (15) and (18) the ground-state (w 0 = 1) short-range xc functional E sr,µ xc [n] (which is approximated by a local or semi-local functional 51,52 ) for the ensemble one.…”

Section: Theorymentioning

confidence: 99%

“…when WIDFA is applied), this is not the case 40,44,48 . In order to correct for GI errors, one can either construct individual state energies 31,43 or use an alternative separation of short-range ensemble exchange and correlation energies, as proposed recently by some of the authors 44 . The first approach will be discussed further in Sec.…”

Section: B Ghost Interaction Correctionmentioning

confidence: 99%

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Combining extrapolation with ghost interaction correction in range-separated ensemble density functional theory for excited states

Alam

Deur

Knecht

et al. 2017

The Journal of Chemical Physics

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The extrapolation technique of Savin [J. Chem. Phys. 140, 18A509 (2014)], which was initially applied to range-separated ground-state-density-functional Hamiltonians, is adapted in this work to ghost-interactioncorrected (GIC) range-separated ensemble density-functional theory (eDFT) for excited states. While standard extrapolations rely on energies that decay as µ −2 in the large range-separation-parameter µ limit, we show analytically that (approximate) range-separated GIC ensemble energies converge more rapidly (as µ −3 ) towards their pure wavefunction theory values (µ → +∞ limit), thus requiring a different extrapolation correction. The purpose of such a correction is to further improve on the convergence and, consequently, to obtain more accurate excitation energies for a finite (and, in practice, relatively small) µ value. As a proof of concept, we apply the extrapolation method to He and small molecular systems (viz. H 2 , HeH + and LiH), thus considering different types of excitations like Rydberg, charge transfer and double excitations. Potential energy profiles of the first three and four singlet Σ + excitation energies in HeH + and H 2 , respectively, are studied with a particular focus on avoided crossings for the latter. Finally, the extraction of individual state energies from the ensemble energy is discussed in the context of range-separated eDFT, as a perspective.

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“…[12] The development of new and more accurate density functionals is a very active research field even today. The importance that functionals satisfy as much constraints as is possible is recognized in a Tutorial Review of Perdew et al [13] Pastorczak and Pernal [14] present progress in ensemble density functional theory. Density functional theory for d-and f-electron materials and compounds is treated by Mattsson and Wills [15] in another Tutorial Review.…”

mentioning

confidence: 99%

Advances in DFT

Nagy

2016

Int J of Quantum Chemistry

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A road to a multiconfigurational ensemble density functional theory without ghost interactions

Cited by 6 publications

References 51 publications

Direct Extraction of Excitation Energies from Ensemble Density-Functional Theory

Direct Extraction of Excitation Energies from Ensemble Density-Functional Theory

Combining extrapolation with ghost interaction correction in range-separated ensemble density functional theory for excited states

Advances in DFT

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