GENERALIZED KOOPMANS' THEOREM

Journal Article · Sat Jul 15 04:00:00 EDT 1961 · Physical Review (U.S.) Superseded in part by Phys.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

DOI:https://doi.org/10.1103/PhysRev.123.420· OSTI ID:4000230

Phillips, J C

Koopmans' theorem states that if the wave function of a many-electron system is approximated by a Slater determinant of Hartree-Fock one-electron wave functions, with one-electron energies defined as the difference in energy of (N + 1)- and N-particle systems, then these one-electron energies are given by the expectation value of the HartreeFock Hamiltonian with respect to the one-electron wave functions. Koopmans' theorem is generalized to include correlation effects by using Hubbard's expression for the total energy of a free-electron gas. The resulting oneelectron Hamiltonian contains in first-order screened exchange. Hubbard's lowest polarization diagram gives, in addition, part of the screened second-order Coulomb interactions, which is small for metallic densities. Collective terms are also obtained. Comparison with the Bohm-Pines Hamiltonian shows a one-to-one correspondence, but with different cutoff functions in each term. Following Hubbard, -the method to include the effects of a periodic potential to first order is extended. The resulting one-electron Hamiltonian provides a convenient and accurate basis for self consistent energy band calculations including exchange and correlation in metals and semiconductors. (auth)

• Research Organization: Univ. of Chicago
• NSA Number: NSA-15-026863
• OSTI ID: 4000230
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 123; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

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