Premium
Evaluation of the alpha‐function for large parameter values
Author(s) -
Jones H. W.,
Jain J. L.
Publication year - 1996
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/(sici)1097-461x(1996)60:7<1257::aid-qua6>3.0.co;2-y
Subject(s) - atomic orbital , function (biology) , displacement (psychology) , exponential function , mathematical analysis , constant (computer programming) , rule of thumb , mathematics , physics , quantum mechanics , algorithm , computer science , evolutionary biology , biology , psychology , psychotherapist , programming language , electron
In carrying out our plan for doing multicenter molecular integrals over Slater‐type orbitals, it is necessary to evaluate the Löwdin α‐function over a grid from the origin of the coordinate system to the displacement distance of the center of the orbital. A previous article obtained excellent results by expanding the exponentials in the α‐function, for both interior and exterior regions. However, if the displacement distance multiplied by the screening constant, i.e., the ζ a parameter, is larger than 16, we suggest that it may be more efficient in time and storage if we use the closed formula for the α‐function for values of the radial distance r greater than 8. This remarkable rule of thumb was tested for a variety of orbitals up to ζ a =64 and one to ζ a =128. Also, in the exterior region, the formula may always be used if ζ a ≥16. This strategy necessitates using the formula in quadruple precision arithmetic. © 1996 John Wiley & Sons, Inc.