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A minimum principle for molecular systems allowing the use of discontinuous wave functions
Author(s) -
Hall G. G.,
Hyslop J.,
Rees D.
Publication year - 1970
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.560040103
Subject(s) - classification of discontinuities , generalization , upper and lower bounds , wave function , energy (signal processing) , potential energy , physics , mathematics , mathematical analysis , quantum mechanics
In this paper the minimum principle proposed for atomic systems by Hall, Hyslop and Rees [1] is generalized to molecules. It is shown that this generalization retains the advantage of admitting the use of a larger class of trial wave functions, for example those with discontinuities, than is possible in the usual minimum energy principle. The further advantage that the upper bounds obtained by this treatment are always at least as good as those of the Rayleigh‐Ritz method is also preserved. The theory is applied to the H 2 +ion, potential energy curves are obtained for various “cut‐off” wave functions, and the equilibrium internuclear distance is calculated. The optimization of the “cut‐off” region so that the upper bound is minimized is also discussed.