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On the minimization of the global variance in the 1‐Reduced local‐energy matrix
Author(s) -
Thomas Gerald F.
Publication year - 1986
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.560290424
Subject(s) - normalization (sociology) , matrix (chemical analysis) , variance (accounting) , mathematics , minification , energy (signal processing) , wave function , physics , quantum mechanics , statistics , mathematical optimization , materials science , accounting , sociology , anthropology , business , composite material
By minimizing the global variance in the 1‐reduced local‐energy matrix E 1 ( X 1 ; X 1 ′), subject to the normalization of the 1‐reduced density matrix ρ 1 ( X 1 ; X 1 ′), one derives an integral matrix equation for E 1 ( X 1 ; X 1 ′) as a functional of ρ 1 ( X 1 ; X 1 ′) at the location ( X 1 ; X 1 ′) of an arbitrary member of an N (≥ 2)‐particle system. The implications for the possible local improvement in the accuracy of approximate wave functions through the imposition of global constraints are briefly discussed.