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Kinetic-Energy Density-Functional Theory on a Lattice

MPS-Authors
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Theophilou,  I.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free Electron Laser Science;

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Buchholz,  F.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free Electron Laser Science;

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Eich,  F. G.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free Electron Laser Science;

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Ruggenthaler,  M.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free Electron Laser Science;

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Rubio,  A.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free Electron Laser Science;
Center for Computational Quantum Physics (CCQ), The Flatiron Institute;

Fulltext (public)

acs.jctc.8b00292.pdf
(Publisher version), 2MB

Supplementary Material (public)
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Citation

Theophilou, I., Buchholz, F., Eich, F. G., Ruggenthaler, M., & Rubio, A. (2018). Kinetic-Energy Density-Functional Theory on a Lattice. Journal of Chemical Theory and Computation, 14(8), 4072-4087. doi:10.1021/acs.jctc.8b00292.


Cite as: http://hdl.handle.net/21.11116/0000-0001-B27B-C
Abstract
We present a kinetic-energy density-functional theory and the corresponding kinetic-energy Kohn-Sham (keKS) scheme on a lattice and show that by including more observables explicitly in a density-functional approach already simple approximation strategies lead to very accurate results. Here we promote the kinetic-energy density to a fundamental variable along side the density and show for specific cases (analytically and numerically) that there is a one-to-one correspondence between the external pair of on-site potential and site-dependent hopping and the internal pair of density and kinetic-energy density. Based on this mapping we establish two unknown effective fields, the mean-field exchange-correlation potential and the mean-field exchange-correlation hopping, that force the keKS system to generate the same kinetic-energy density and density as the fully interacting 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 and compare the unknown correlation contributions as well as by comparing self-consistent calculations based on the mean-field exchange for the keKS and the exact-exchange for the KS system, respectively.