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The extended Koopmans' theorem Fock operator and the generalized overlap amplitude one‐electron operator
Author(s) -
Day Orville W.
Publication year - 1996
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1996)57:3<391::aid-qua12>3.0.co;2-7
Subject(s) - eigenfunction , wave function , operator (biology) , hamiltonian (control theory) , energy operator , quantum mechanics , electron , position operator , physics , fock space , propagator , amplitude , mathematical physics , chemistry , mathematics , energy (signal processing) , quasinormal operator , mathematical analysis , finite rank operator , eigenvalues and eigenvectors , mathematical optimization , biochemistry , repressor , transcription factor , gene , banach space
The wave function of a system may be expanded in terms of eigenfunctions of the N −1 electron Hamiltonian times one‐particle functions known as generalized overlap amplitudes (GOAS). The one‐electron operator whose eigenfunctions are the GOAS is presented, without using an energy‐dependent term as in the one‐particle Green function or propagator approach. It is shown that this operator and the extended Koopmans' theorem (EKT) one‐electron operator are of similar form, but perform complementary roles. The GOA operator begins with one‐electron densities and total energies of N −1 electron states to generate the two‐matrix and total energy of an N ‐electron state. The EKT operator begins with the two‐matrix of an N ‐electron state to generate one‐electron densities and ionization potentials (or approximations thereto) for N −1 electron states. However, whereas the EKT orbitals must be linearly independent, no such restriction applies to the GOAS. © 1996 John Wiley & Sons, Inc.