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On variational estimates for exchange‐correlation interaction obtained within super‐CI approach to MCSCF approximation
Author(s) -
Gusarov Sergey,
Fedorova Tatiana A.,
Dmitriev Yuri Yu.,
Kovalenko Andriy
Publication year - 2009
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/qua.22007
Subject(s) - hermitian matrix , brillouin zone , formalism (music) , hartree–fock method , quantum mechanics , atomic orbital , configuration interaction , density matrix , singular value decomposition , matrix (chemical analysis) , full configuration interaction , mathematical physics , computational chemistry , mathematics , physics , chemistry , quantum , molecule , art , musical , algorithm , chromatography , visual arts , electron
Variation approximations for the exchange‐correlation interaction are considered which can be obtained when necessary conditions of the generalized Brillouin's theorem are fulfilled. It is done in the post‐Hartree–Fock approach to the electronic structure theories. The corresponding approximations appear within the two‐step Super‐CI self‐consistent procedure of the MCSCF one‐particle optimization. The basic formalism used is in close connection with the formalism of the extended Koopmans' theorem but here the extended Koopmans' matrix itself is calculated in a self‐consistent way. It is based on the singular value decomposition of the Koopmans' matrix. The final hermitian Koopmans' matrix satisfies the conditions of the generalized Brillouin's theorem. It commutes with the density matrix and equations for self‐consistent orbitals are transformed to the generalized Hartree–Fock equations with additional hermitian exchange correlation matrix. This matrix is interpreted as a matrix of the exchange‐correlation interaction. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009