Landscape of an exact energy functional
Entity
UAM. Departamento de QuímicaPublisher
American Physical SocietyDate
2016-04-26Citation
10.1103/PhysRevA.93.042511
Physical Review A - Atomic, Molecular, and Optical Physics 93.4 (2016): 042511
ISSN
1050-2947 (print); 1094-1622 (online)DOI
10.1103/PhysRevA.93.042511Funded by
We gratefully acknowledge funding from Ramón y Cajal (P.M.-S.) and the Royal Society (A.J.C.). P.M.S. also acknowledges funding from MINECO Grant No. FIS2015-64886-C5-5-PProject
Gobierno de España. FIS2015-64886-C5-5-PEditor's Version
http://dx.doi.org/10.1103/PhysRevA.93.042511Subjects
Energy functional; Electronic structure; Quantum theory; Derivative discontinuity; QuímicaRights
© 2016 American Physical SocietyAbstract
One of the great challenges of electronic structure theory is the quest for the exact functional of density functional theory. Its existence is proven, but it is a complicated multivariable functional that is almost impossible to conceptualize. In this paper the asymmetric two-site Hubbard model is studied, which has a two-dimensional universe of density matrices. The exact functional becomes a simple function of two variables whose three-dimensional energy landscape can be visualized and explored. A walk on this unique landscape, tilted to an angle defined by the one-electron Hamiltonian, gives a valley whose minimum is the exact total energy. This is contrasted with the landscape of some approximate functionals, explaining their failure for electron transfer in the strongly correlated limit. We show concrete examples of pure-state density matrices that are not v representable due to the underlying nonconvex nature of the energy landscape. The exact functional is calculated for all numbers of electrons, including fractional, allowing the derivative discontinuity to be visualized and understood. The fundamental gap for all possible systems is obtained solely from the derivatives of the exact functional
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Google Scholar:Cohen, Aron J.
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Mori Sánchez, Paula
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