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Evaluation of integrals over STOs on different centers and the complementary convergence characteristics of ellipsoidal‐coordinate and zeta‐function expansions
Author(s) -
Kennedy H. L.,
Zhao Y.
Publication year - 1999
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(1999)71:1<1::aid-qua1>3.0.co;2-6
Subject(s) - convergence (economics) , ellipsoid , spherical harmonics , function (biology) , atomic orbital , mathematics , mathematical analysis , physics , electron , quantum mechanics , astronomy , evolutionary biology , economics , biology , economic growth
One‐electron integrals over three centers and two‐electron integrals over two centers, involving Slater‐type orbitals (STOs), can be evaluated using either an infinite expansion for 1/ r 12 within an ellipsoidal‐coordinate system or by employing a one‐center expansion in spherical‐harmonic and zeta‐function products. It is shown that the convergence characteristics of both methods are complimentary and that they must both be used if STOs are to be used as basis functions in ab initio calculations. To date, reports dealing with STO integration strategies have dealt exclusively with one method or the other. While the ellipsoidal method is faster, it does not always converge to a satisfactory degree of precision. The zeta‐function method, however, offers reliability at the expense of speed. Both procedures are described and the results of some sample calculation presented. Possible applications for the procedures are also discussed. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 1–13, 1999