Generalized density-functional theory: Conquering the 𝑁-representability problem with exact functionals for the electron pair density and the second-order reduced density matrix

Journal of Chemical Sciences

Paul W Ayers1¹  Mel Levy2² 

[1] Department of Chemistry, McMaster University, Hamilton, Ontario L8S 4M1, Canada$$;Department of Physics, North Carolina A&T University; Greensboro NC 27411, USA and Department of Chemistry, Tulane University, New Orleans, LA 70118, USA$$

关键词: Density-functional theory;    𝑁-representability problem;    electron pair density.;   

DOI  :  

来源: Indian Academy of Sciences

【 摘 要 】

Using the constrained search and Legendre-transform formalisms, one can derive ``generalized” density-functional theories, in which the fundamental variable is either the electron pair density or the second-order reduced density matrix. In both approaches, the 𝑁-representability problem is solved by the functional, and the variational principle is with respect to all pair densities (density matrices) that are nonnegative and appropriately normalized. The Legendre-transform formulation provides a lower bound on the constrained-search functional. Noting that experience in density-functional and density-matrix theories suggests that it is easier to approximate functionals than it is to approximate the set of 𝑁-representable densities sheds some light on the significance of this work.

【 授权许可】

Unknown