On extending Kohn-Sham density functionals to systems with fractional number of electrons

Journal Article · Mon Jun 05 00:00:00 EDT 2017 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4982951· OSTI ID:1474043

Li, Chen  ^[1]; Lu, Jianfeng  ^[2]; Yang, Weitao ^[3]

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1. Duke Univ., Durham, NC (United States). Dept. of Chemistry
2. Duke Univ., Durham, NC (United States). Dept. of Chemistry, Dept. of Mathematics and Dept. of Physics
3. Duke Univ., Durham, NC (United States). Dept. of Chemistry and Dept. of Physics; South China Normal Univ., Guangzhou (China). Key Lab. of Theoretical Chemistry of Environment

Here, we analyze four ways of formulating the Kohn-Sham (KS) density functionals with a fractional number of electrons, through extending the constrained search space from the Kohn-Sham and the generalized Kohn-Sham (GKS) non-interacting $$\mathcal{v}$$-representable density domain for integer systems to four different sets of densities for fractional systems. In particular, these density sets are (I) ensemble interacting N-representable densities, (II) ensemble non-interacting N-representable densities, (III) non-interacting densities by the Janak construction, and (IV) non-interacting 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 v-representable 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.

• Research Organization: Energy Frontier Research Centers (EFRC) (United States). Center for Complex Materials from First Principles (CCM); Temple Univ., Philadelphia, PA (United States); Duke Univ., Durham, NC (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)
• Grant/Contract Number: SC0012575; CHE-13-62927; DMS-14-54939
• OSTI ID: 1474043
• Alternate ID(s): OSTI ID: 1365425
• Journal Information: Journal of Chemical Physics, Vol. 146, Issue 21; ISSN 0021-9606
• Publisher: American Institute of Physics (AIP)
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
74 ATOMIC AND MOLECULAR PHYSICS
density-matrix
Kohn-Sham equation
Slater determinant
local density approximations
Hilbert space
density functional theory
Aufbau principle
correlation-consistent basis sets
self consistent field methods
statistical thermodynamics