The exactness of the extended Koopmans’ theorem: A numerical study

Sundholm, Dage; Olsen, Jeppe
March 1993
Journal of Chemical Physics;3/1/1993, Vol. 98 Issue 5, p3999
Academic Journal
The exactness of the extended Koopmans’ theorem has been studied by comparing multiconfiguration Hartree–Fock calculations on Be(1S) with configuration interaction calculations on Be+(2S) performed in the same basis. The lowest ionization potentials calculated as the energy difference between Be and Be+ and those obtained from the extended Koopmans’ theorem approach each other with increased size of the orbital basis. The difference between the ionization potentials obtained in an 11s basis is 0.034 meV (1.2×10-6 a.u.), and in a 12s basis the difference is 0.019 meV (0.7×10-6 a.u.) which shows that the s-limits for the two ionization potentials are equal. Similarly, the sp-, and spd-, and the spdf-limits of the two ionization potentials approach each other in the limit of complete basis of the given irreducible representations, indicating that the extended Koopmans’ theorem is exact for the lowest ionization potential.


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