In the present paper we consider the shift operator S on the Wiener algebra W (D) of analytic functions on the unit disc D of the complex plane C. A complex number Ξ» is called an extended eigenvalue of S if there exists a nonzero operator A satisfying the equation AS = Ξ»SA. We prove that the set of
On the exactness of extended Koopmans' eigenvalues
β Scribed by B.T. Pickup; J.G. Snijders
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 436 KB
- Volume
- 153
- Category
- Article
- ISSN
- 0009-2614
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β¦ Synopsis
We discuss conditions under which extended Koopmans' eigenvalues become exact ionisatlon potentials. Second-order perturbation theory is used to compare with known expressions involving relaxation contributions to the exact resulls. In two-electron systems all the EK elgenvalues are shown to be exact provided there are no vanishing natural occupancies in the exact reference state. In a finite basis model the EK eigenvalues do not match the exact IPs of the corresponding model Hamiltonian.
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