On the exactness of the extended Koopmans` theorem: Resolution of the paradox
Conference
·
OSTI ID:447601
- Tulane Univ., New Orleans, LA (United States)
The generalized Koopmans theorem gives an estimate of the lowest ionization energy of an N-electron system. The approximate lowest ionization energy is obtained as the lowest eigenvalue of a generalized eigenvalue problem. It has been shown that the generalized Koopmans theorem predicts the exact lowest ionization energy for Coulomb systems. However, it has also been shown that in general no eigenvalue of the generalized Koopmans procedure corresponds to an exact ionization energy. This paradox is resolved by demonstrating that the lowest eigenvalue of the generalized Koopmans procedure does, in general, not exist for Coulomb systems. Nevertheless, it will also be shown that the generalized Koopmans approach gives ionization energies which are arbitrary close to the exact lowest ionization energy. The eigenvalues of the extended Koopmans theorem have an accumulation point given by the exact lowest ionization energy.
- OSTI ID:
- 447601
- Report Number(s):
- CONF-960343--
- Country of Publication:
- United States
- Language:
- English
Similar Records
GENERALIZED KOOPMANS' THEOREM
Methods for the calculation of photoionization cross sections using the extended Koopman's Theorem
Communication: Generalization of Koopmans’ theorem to optical transitions in the Hubbard model of graphene nanodots
Journal Article
·
Sat Jul 15 00:00:00 EDT 1961
· Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D
·
OSTI ID:4000230
Methods for the calculation of photoionization cross sections using the extended Koopman's Theorem
Journal Article
·
Fri Dec 31 23:00:00 EST 1976
· Int. J. Quant. Chem., Symp.; (United States)
·
OSTI ID:6759940
Communication: Generalization of Koopmans’ theorem to optical transitions in the Hubbard model of graphene nanodots
Journal Article
·
Tue Jan 13 23:00:00 EST 2015
· Journal of Chemical Physics
·
OSTI ID:22415816