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A study of Löwdin's criterion for completeness of basis sets
Author(s) -
Leopold J. G.,
Cohen M.,
Katriel J.
Publication year - 1976
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.560100615
Subject(s) - completeness (order theory) , basis (linear algebra) , mathematics , similarity (geometry) , convergence (economics) , set (abstract data type) , mathematical analysis , computer science , geometry , artificial intelligence , economics , image (mathematics) , programming language , economic growth
Löwdin has formulated a useful criterion for testing the completeness of an expansion basis set. From this criterion one may obtain an incompleteness coefficient for a truncated (finite) basis set. We have investigated the significance of this incompleteness coefficient for some of the basis sets we have used in our recent calculations of bounds to quantum mechanical properties. The similarity of the convergence properties between our bounds and the incompleteness coefficient suggests that Löwdin's criterion is likely to be useful in practice.