Decay behavior of least-squares coefficients in auxiliary basis expansions

Many quantum chemical methods, both wave function and density based, rely on an expansion of elements of the electron density in an auxiliary basis. However, little is known about the analytical behavior of the expansion coefficients and, in particular, about their rate of decay with distance. We di...

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Bibliographic Details
Published in:The Journal of chemical physics 2005-08, Vol.123 (6), p.061101-061101-4
Main Authors: Gill, P. M. W., Gilbert, A. T. B., Taylor, S. W., Friesecke, G., Head-Gordon, M.
Format: Article
Language:English
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Summary:Many quantum chemical methods, both wave function and density based, rely on an expansion of elements of the electron density in an auxiliary basis. However, little is known about the analytical behavior of the expansion coefficients and, in particular, about their rate of decay with distance. We discuss an exactly solvable model system and characterize the expansion coefficients for various fitting metrics and various dimensionalities of the auxiliary basis. In the case of Coulomb fitting, we find that the decay rate depends critically on the effective dimensionality D of the auxiliary basis, varying from O ( r − 1 ) to O ( r − 3 ) to O ( e − ζ r ) for D = 1 , 2, or 3.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.2000867