Twelve outstanding problems in ground-state density functional theory: A bouquet of puzzles

2009/10/31 by T. Gal, Adrienn Ruzsinszky, John P. Perdew +1 · 48 citations
Chemical Engineering · Chemistry · Materials Science · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Applied mathematics #Atom (system on chip) #Catalysis and Oxidation Reactions #Chemistry #Computational chemistry #Computer science #Density functional theory #Functional theory #Ground state #Machine Learning in Materials Science #Mathematics #Orbital-free density functional theory #Physics #Quantum mechanics #Schrödinger equation #Statistical physics #Theoretical physics #Time-dependent density functional theory #cond-mat.mtrl-sci #physics.atom-ph #physics.chem-ph

paper · pdf · doi:10.1016/j.comptc.2010.09.002

published in Computational and Theoretical Chemistry 963(1), 2-6 (Elsevier BV) · 35 pages, to appear in JCP; text made more precise, Aufbau discussed, T_s derivative discontinuities given too, two Appendices added

arxiv created 2010/07/19 · arxiv updated 2010/11/10 · openalex publication_date 2010/12/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

On the basis of the zero-temperature grand canonical ensemble generalization of the energy E[N,N_s,v,B] for fractional particle N and spin N_s numbers, the energy surface over the (N,N_s) plane is displayed and analyzed in the case of homogeneous external magnetic fields B(r). The (negative of the) left/right-side derivatives of the energy with respect to N, N_up, and N_down give the fixed-N_s, spin-up, and spin-down ionization potentials/electron affinities, respectively, while the derivative of E[N,N_s,v,B] with respect to N_s gives the (signed) half excitation energy to a state with N_s increased (or decreased) by 2. The highest occupied and lowest unoccupied Kohn-Sham spin-orbital energies are identified as the corresponding spin-up and spin-down ionization potentials and electron affinities. The excitation energies to the states with N_s+2, N_s-2, can be obtained as the differences between the lowest unoccupied and the opposite-spin highest occupied spin-orbital energies, if the (N,N_s) representation of the Kohn-Sham spin-potentials is used. The cases where the convexity condition on the energy does not hold are also discussed. Finally, the discontinuities of the energy derivatives and the Kohn-Sham potential are analyzed and related.

Citations

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