Self-interaction correction to density-functional approximations for many-electron systems

We present two related methods for the self-interaction correction of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle

J. P. Perdew; Alex Zunger

2002

Scholarcy highlights

  • ) It follows that, for densities varying slowly enough over space, the LSD and self-interaction-corrected LSD approximations both yield the exact energy per electron
  • A major problem of solid-state theory and quantum chemistry is to understand the behavior of many electrons interacting via Coulomb's law:(All equations are in atomic units, if=m = e'= I.)In the earliest quantum-mechanical theory, Thom-„) as and Fermi replaced the expectation value: y gX da X n(gin(r ) jAs early as 1934, Fermi and Amaldi' observed the failure of Eq to vanish for one-electron systems due to the spurious self-interaction inherent in it, and proposed the first and crudest version of self-interaction correction: where N is the number of electrons in the system
  • We present two related methods for the self-interaction correction of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle
  • Fractional-occupation numbers are allowed in principle, further work on the exchangecorrelation functional is needed before they can be used in practice
  • The most straightforward self- consistent formalism incorporating selfinteraction correction is that of Eq
  • Like the Hartree approximation which it resembles, it is a density-functional theory in the sense of the Hohenberg-Kohn' theorem, it does not fit into the Kohn-Sham scheme
  • Valone'" has proposed that the search in Eq be made over statistical mixtures of antisymmetric N-electron wave functions; if we apply this search in Eq, we find that the definitions of Eqs. and are equivalent, since by Coleman's theorem'" the necessary and sufficient conditions for a Hermitian one-particle density matrix n(r, r') to arise from some statistical mixture of N-fermion wave functions are

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