Long-range excitations in time-dependent density functional theory

Maitra, Neepa T.; Tempel, David G.

doi:10.1063/1.2387951

Cited by 59 publications

(60 citation statements)

References 48 publications

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“…[58] as discussed in the previous section, but here the effect is in the correlation potential. The strong frequency-dependence arises in this case because the charge-transfer excitations are a linear combination of single and double-excitations out of the Kohn-Sham ground state [109]: in fact every single excitation, be it local or charge-transfer, out of the HOMO is neardegenerate with a double-excitation where the other electron occupying the HOMO transits to the LUMO at cost exponentially small in R [103]. That this must be the case is evident from Figure 3 in order to avoid states which have "half" an electron excess or deficient on one atom.…”

Section: B Charge-transfer Between Open-shell Fragmentsmentioning

confidence: 99%

Charge transfer in time-dependent density functional theory

Maitra

2017

J. Phys.: Condens. Matter

134

151

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Charge transfer plays a crucial role in many processes of interest in physics, chemistry, and biochemistry. In many applications the size of the systems involved calls for time-dependent density functional theory (TDDFT) to be used in their computational modeling, due to its unprecedented balance between accuracy and efficiency. However, although exact in principle, in practise approximations must be made for the exchange-correlation functional in this theory, and the standard functional approximations perform poorly for excitations which have a long-range charge-transfer component. Intense progress has been made in developing more sophisticated functionals for this problem, which we review. We point out an essential difference between the properties of the exchange-correlation kernel needed for an accurate description of charge-transfer between open-shell fragments and between closed-shell fragments. We then turn to charge-transfer dynamics, which, in contrast to the excitation problem, is a highly non-equilibrium, non-perturbative, process involving a transfer of one full electron in space. This turns out to be a much more challenging problem for TDDFT functionals. We describe dynamical step and peak features in the exact functional evolving over time, that are missing in the functionals currently used. The latter underestimate the amount of charge transferred and manifest a spurious shift in the charge transfer resonance position. We discuss some explicit examples.

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Section: B Charge-transfer Between Open-shell Fragmentsmentioning

confidence: 99%

Charge transfer in time-dependent density functional theory

Maitra

2017

J. Phys.: Condens. Matter

134

151

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“…It is interesting that we have here an example of the form the -dependence of the exchange-correlation kernel may take, and of the effects of this -dependence, which has received considerable attention in the TDDFT case. 8,9,39,40 For all there is an ⑀ 0 ͑͒ = 0 eigenvalue. The line ⑀ 0 ͑͒ = 0 is cut by the ⑀ = line at = 0, yielding the trivial "zero-excitation" solution =0 ͑this solution is better called "trivial" than "erroneous," cf.…”

Section: A the Exact "-Dependent… Equationsmentioning

confidence: 99%

Excitation energies with time-dependent density matrix functional theory: Singlet two-electron systems

Giesbertz

Pernal

Gritsenko

et al. 2009

The Journal of Chemical Physics

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Time-dependent density functional theory in its current adiabatic implementations exhibits three striking failures: ͑a͒ Totally wrong behavior of the excited state surface along a bond-breaking coordinate, ͑b͒ lack of doubly excited configurations, affecting again excited state surfaces, and ͑c͒ much too low charge transfer excitation energies. We address these problems with time-dependent density matrix functional theory ͑TDDMFT͒. For two-electron systems the exact exchange-correlation functional is known in DMFT, hence exact response equations can be formulated. This affords a study of the performance of TDDMFT in the TDDFT failure cases mentioned ͑which are all strikingly exhibited by prototype two-electron systems such as dissociating H 2 and HeH + ͒. At the same time, adiabatic approximations, which will eventually be necessary, can be tested without being obscured by approximations in the functional. We find the following: ͑a͒ In the fully nonadiabatic ͑-dependent, exact͒ formulation of linear response TDDMFT, it can be shown that linear response ͑LR͒-TDDMFT is able to provide exact excitation energies, in particular, the first order ͑linear response͒ formulation does not prohibit the correct representation of doubly excited states; ͑b͒ within previously formulated simple adiabatic approximations the bonding-to-antibonding excited state surface as well as charge transfer excitations are described without problems, but not the double excitations; ͑c͒ an adiabatic approximation is formulated in which also the double excitations are fully accounted for.

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“…Also, double-excitations can be shown to be missing within any adiabatic approximation [96], although frequency-dependent kernels can be constructed that restore them [103]. Charge transfer-type excitations also fail [104].…”

Section: B Tddft Approximationsmentioning

confidence: 99%

Density functional calculations of nanoscale conductance

Koentopp

Chang

Burke

et al. 2008

J. Phys.: Condens. Matter

141

156

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Density functional calculations for the electronic conductance of single molecules are now common. We examine the methodology from a rigorous point of view, discussing where it can be expected to work, and where it should fail. When molecules are weakly coupled to leads, local and gradientcorrected approximations fail, as the Kohn-Sham levels are misaligned. In the weak bias regime, XC corrections to the current are missed by the standard methodology. For finite bias, a new methodology for performing calculations can be rigorously derived using an extension of time-dependent current density functional theory from the Schrödinger equation to a Master equation. Contents

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Long-range excitations in time-dependent density functional theory

Cited by 59 publications

References 48 publications

Charge transfer in time-dependent density functional theory

Charge transfer in time-dependent density functional theory

Excitation energies with time-dependent density matrix functional theory: Singlet two-electron systems

Density functional calculations of nanoscale conductance

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