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Exact ensemble density functional theory for excited states in a model system: investigating the weight dependence of the correlation energy | | Killian Deur
; Laurent Mazouin
; Emmanuel Fromager
; | | Date: |
11 Oct 2016 | | Abstract: | Ensemble density functional theory (eDFT) is an exact time-independent
alternative to time-dependent DFT (TD-DFT) for the calculation of excitation
energies. Despite its formal simplicity and advantages in contrast to TD-DFT
(multiple excitations, for example, can be easily taken into account in an
ensemble), eDFT is not standard which is essentially due to the lack of
reliable approximate exchange-correlation (xc) functionals for ensembles.
Following Burke and coworkers [Phys. Rev. B 93, 245131 (2016)], we propose in
this work to construct an exact eDFT for the nontrivial asymmetric Hubbard
dimer, thus providing more insight into the weight dependence of the ensemble
xc energy in various correlation regimes. For that purpose, an exact analytical
expression for the weight-dependent ensemble exchange energy has been derived.
The complementary exact ensemble correlation energy has been computed by means
of Legendre-Fenchel transforms. Interesting features like discontinuities in
the ensemble xc potential in the strongly correlated limit have been
rationalized by means of a generalized adiabatic connection formalism. Finally,
functional-driven errors induced by ground-state density-functional
approximations have been studied. In the strictly symmetric case or in the
weakly correlated regime, combining ensemble exact exchange with ground-state
correlation functionals gives relatively accurate ensemble energies. However,
in the strongly correlated regime, this approximation leads to highly curved
ensemble energies with negative slope which is unphysical. Using both
ground-state exchange and correlation functionals gives much better results in
that case. In fact, exact ensemble energies are almost recovered in some
density domains. The analysis of density-driven errors is left for future work. | | Source: | arXiv, 1610.3308 | | Services: | Forum | Review | PDF | Favorites | |
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