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Communication: Self-interaction correction with unitary invariance in density functional theory
6. J. P. Perdew, “Size-consistency, self-interaction correction, and derivative discontinuity,” in Density Functional Theory of Many-Electron Systems, Advances in Quantum Chemistry Vol. 21, edited by S. B. Trickey (Academic Press, 1990), p. 113.
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34. S. Klüpfel, P. Klüpfel, and H. Jónsson, Phys. Rev. A 84, 050501–R (2011); Figure 1 of this paper shows positive SIC corrections to the GGA(PBE) total energies of atoms heavier than N, from real SIC orbitals. P. Klüpfel plausibly concluded from this that, in a sufficiently stretched diatomic molecule made of two identical heavy atoms, the real SIC orbitals would delocalize, leading to a failure of size-extensivity (public discussion at the CECAM Workshop on Self-Interaction Correction: State of the Art and New Directions, Chester, England, 2011).
37. J. P. Perdew, “Nonlocal density functionals for exchange and correlation,” in Density Functional Theory of Molecules, Clusters and Solids, edited by D. E. Ellis (Kluwer Academic Publishers, 1995).
42. J. P. Perdew, A. Ruzsinszky, J. Sun, and K. Burke, “Gedanken densities and exact constraints in density functional theory,” J. Chem. Phys. (submitted).
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Standard spin-density functionals for the exchange-correlation energy of a many-electron ground state make serious self-interaction errors which can be corrected by the Perdew-Zunger self-interaction correction (SIC). We propose a size-extensive construction of SIC orbitals which, unlike earlier constructions, makes SIC computationally efficient, and a true spin-density functional. The SIC orbitals are constructed from a unitary transformation that is explicitly dependent on the non-interacting one-particle density matrix. When this SIC is applied to the local spin-density approximation, improvements are found for the atomization energies of molecules.
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