https://doi.org/10.1140/epjb/e2018-90109-6
Regular Article
About the relation of electron–electron interaction potentials with exchange and correlation functionals★
1
Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza,
Calle Mariano Esquillor,
50018
Zaragoza, Spain
2
ARAID Foundation,
Av. de Ranillas 1-D,
50018
Zaragoza, Spain
a e-mail: acastro@bifi.es
Received:
1
March
2018
Received in final form:
13
April
2018
Published online: 6
June
2018
We investigate, numerically, the possibility of associating to each approximation to the exchange-and-correlation functional in density-functional theory (DFT), an optimal electron–electron interaction potential for which it performs best. The fundamental theorems of density-functional theory (DFT) make no assumption about the precise form of the electron–electron interaction: to each possible electron–electron interaction corresponds an exchange-and-correlation functional. This fact suggests the opposite question: given some functional of the density, is there any electron–electron interaction for which it is the exact exchange-and-correlation functional? And, if not, what is the interaction for which the functional produces the best results? Within the context of lattice DFT, we study these questions by working on the one-dimensional Hubbard chain. The idea of associating an optimal interaction potential to each approximation to the exchange and correlation functionals suggests, finally, a procedure to optimise parameterised families of functionals: find that one whose associated interaction most closely resembles the real one.
© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2018