Kinetic-Energy Density-Functional Theory on a Lattice

Journal Of Chemical Theory And Computation 14 (8), 4072 - 4087 (2018)

Kinetic-Energy Density-Functional Theory on a Lattice

Iris Theophilou,Florian Buchholz,F. G. Eich,Michael Ruggenthaler, Angel Rubio

We present a kinetic-energy density-functionaltheory and the corresponding kinetic-energy Kohn−Sham(keKS) scheme on a lattice and show that, by including moreobservables explicitly in a density-functional approach, alreadysimple approximation strategies lead to very accurate results.Here, we promote the kinetic-energy density to a fundamentalvariable alongside the density and show for specific cases(analytically and numerically) that there is a one-to-onecorrespondence between the external pair of on-site potentialand site-dependent hopping and the internal pair of densityand kinetic-energy density. On the basis of this mapping, weestablish two unknown effectivefields, the mean-fieldexchange-correlation potential and the mean-field exchange-correlation hopping, which force the keKS system to generate the same kinetic-energy density and density as the fullyinteracting one. We show, by a decomposition based on the equations of motions for the density and the kinetic-energy density,that we can construct simple orbital-dependent functionals that outperform the corresponding exact-exchange Kohn−Sham(KS) approximation of standard density-functional theory. We do so by considering the exact KS and keKS systems andcomparing the unknown correlation contributions as well as by comparing self-consistent calculations based on the mean-fieldexchange (for the effective potential) and a uniform (for the effective hopping) approximation for the keKS and the exact-exchange approximation for the KS system, respectively.

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Financial support from the European Research Council (ERC- 2015-AdG-694097), by the European Unions H2020 program under GA no. 676580 (NOMAD), is acknowledged. F.G.E. has received funding from the European Unions Framework Programme for Research and Innovation Horizon 2020 (2014−2020) under the Marie Skłodowska-Curie Grant agreement no. 701796.

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