OPTIMAL USE OF THE RECURRENCE RELATIONS FOR THE EVALUATION OF MOLECULAR INTEGRALS OVER CARTESIAN GAUSSIAN-BASIS FUNCTIONS

Abstract

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 K4 region. The resulting FLOPS counts in the K4 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 K4 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 K2 or K0 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.