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On the approximation of potential‐energy functions for two‐center systems
Author(s) -
Barnsley Michael F.,
Aguilar Jacques G.
Publication year - 1978
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.560130509
Subject(s) - eigenvalues and eigenvectors , bounding overwatch , function (biology) , potential energy , energy (signal processing) , mathematics , center (category theory) , physics , quantum mechanics , chemistry , computer science , evolutionary biology , artificial intelligence , biology , crystallography
Let E ( R ) be a potential‐energy function for a neutral or ionic diatom in the Born‐Oppenheimer approximation. Then the approximation of E ( R ) for 0 < R < ∞ starting from finite and typically small sets of given information is considered. The approach is based on the fact that the scaled potential curves F ( R ) = R 2 E ( R ) derive from an eigenvalue problem which depends linearly on R . The nature of the curves F ( R ) is examined in detail. The results include the discovery of various approximants, some of which display rigorous bounding properties and others, closely related, whose behavior with respect to the approximated function appears to be predictable.