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Optimal use of the recurrence relations for the evaluation of molecular integrals over Cartesian Gaussian basis functions
Author(s) -
Ryu Ungsik,
Kim Myeongcheol,
Lee Yoon Sup
Publication year - 1993
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540140107
Subject(s) - flops , angular momentum , gaussian , recurrence relation , mathematics , basis (linear algebra) , momentum (technical analysis) , rank (graph theory) , tree (set theory) , cartesian coordinate system , physics , algorithm , combinatorics , computer science , quantum mechanics , geometry , parallel computing , finance , economics
We consider the tree search problem for the recurrence relation that appears in the evaluation of molecular integrals over Cartesian Gaussian basis functions. A systematic way of performing tree search is shown. By applying the result of tree searching to the LRL2 method of Lindh, Ryu, and Liu (LRL) ( J. Chem. Phys. , 95 , 5889 1991), which is an auxiliary function‐based method, we obtain significant reductions of the floating point operations (FLOPS) counts in the K 4 region. The resulting FLOPS counts in the K 4 region are comparable up to [ dd | dd ] angular momentum cases to the LRL1 method of LRL, currently the method requiring least FLOPS for [ dd | dd ] and higher angular momentum basis functions. For [ ff | ff ], [ gg | gg ], [ hh | hh ], and [ ii | ii ] cases, the required FLOPS are 24, 40, 51, and 59%, respectively, less than the LRL1 method in the K 4 region. These are the best FLOPS counts available in the literature for high angular momentum cases. Also, there will be no overhead in either the K 2 or K 0 region in implementing the present scheme. This should lead to more efficient codes of integral evaluations for higher angular momentum cases than any other existing codes. © 1993 John Wiley & Sons, Inc.