Remarks on the exact energy functional for fermions: an analysis using the Löwdin partitioning technique

A comparison model based in the Löwdin partitioning technique is used to analyse the differences between the wave function and density functional models. This comparison model provides a tool, the Löwdin function f (E), to understand the structure of both theories and its discrepancies in terms of t...

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Detalles Bibliográficos
Autores: Caballero Puig, Marc, Moreira, Ibério de Pinho Ribeiro, Bofill i Villà, Josep M.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2014
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/157303
Acceso en línea:https://hdl.handle.net/2445/157303
Access Level:acceso abierto
Palabra clave:Funcions d'ona
Teoria del funcional de densitat
Wave functions
Density functionals
Descripción
Sumario:A comparison model based in the Löwdin partitioning technique is used to analyse the differences between the wave function and density functional models. This comparison model provides a tool, the Löwdin function f (E), to understand the structure of both theories and its discrepancies in terms of the subjacent mathematical structure and the necessary conditions of variationality required for the energy functional. It is argued that density functional theory (DFT) can be compared to the wave function theory (WFT) using the expressions of f (E) at E = 0. The WFT provides an explicit form of the exact energy functional for a fermion system from the full configuration interaction approach. The DFT can be seen as a special case of Löwdin function that does not satisfy all variational conditions on ρ(r) and also on the EXC[ρ] term. This analysis shows that ignoring the restrictions imposed by the spin and space symmetry requirements of the solutions when making a variational calculation implies that the correlations expressed by the ρ(r) function will be inconsistent with a γ1(r1; r′1) function derivable from a spin and space symmetry adapted wave function Ψ(r1s1, ¿, rnsn), even for a closed-shell system (i.e. an energy minimum that will exhibit the phenomenon of 'overcorrelation'). The comparison scheme also provides a new insight on the variational requirements in order to achieve a consistent description of the molecular electronic structure of both ground and excited states. Some numerical results are reported.