Math @ Duke

Publications [#326484] of Jianfeng Lu
Papers Published
 Li, C; Lu, J; Yang, W, On extending KohnSham density functionals to systems with fractional number of electrons.,
Journal of Chemical Physics, vol. 146 no. 21
(June, 2017),
pp. 214109 [doi]
(last updated on 2018/06/21)
Abstract: We analyze four ways of formulating the KohnSham (KS) density functionals with a fractional number of electrons, through extending the constrained search space from the KohnSham and the generalized KohnSham (GKS) noninteracting vrepresentable density domain for integer systems to four different sets of densities for fractional systems. In particular, these density sets are (I) ensemble interacting Nrepresentable densities, (II) ensemble noninteracting Nrepresentable densities, (III) noninteracting densities by the Janak construction, and (IV) noninteracting densities whose composing orbitals satisfy the Aufbau occupation principle. By proving the equivalence of the underlying first order reduced density matrices associated with these densities, we show that sets (I), (II), and (III) are equivalent, and all reduce to the Janak construction. Moreover, for functionals with the ensemble vrepresentable assumption at the minimizer, (III) reduces to (IV) and thus justifies the previous use of the Aufbau protocol within the (G)KS framework in the study of the ground state of fractional electron systems, as defined in the grand canonical ensemble at zero temperature. By further analyzing the Aufbau solution for different density functional approximations (DFAs) in the (G)KS scheme, we rigorously prove that there can be one and only one fractional occupation for the Hartree Fock functional, while there can be multiple fractional occupations for general DFAs in the presence of degeneracy. This has been confirmed by numerical calculations using the local density approximation as a representative of general DFAs. This work thus clarifies important issues on density functional theory calculations for fractional electron systems.


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