A new algorithm for the evaluation of two-electron repulsion integrals optimized for high contraction degrees is derived. Both the segmented and general contraction versions of the algorithm show significant theoretical performance gains over the asymptotically fastest algorithms published in the literature so far. A preliminary implementation of the algorithm shows good agreement with the theoretical results and demonstrates substantial average speedups in the evaluation of two-electron repulsion integrals over commonly used basis sets with varying degrees of contraction with respect to a mature, highly optimized quantum chemical code.
Received 22 August 2012Accepted 16 November 2012Published online 19 December 2012
This work has been partially funded by the EU Commission (Contract No. INFSO-RI-261523) under the ScalaLife collaboration.
Article outline: I. INTRODUCTION II. THEORY A. Definitions and notations B. PRISM algorithm for the evaluation of ERIs: CCTTT path C. The K4+MIRROR algorithm 1. Application of the K4 contraction for ERIs involving Pople style basis sets 2. Application of the K4 contraction for ERIs over general contraction type basis sets III. RESULTS AND DISCUSSION A. Theoretical performance of the K4+MIRROR algorithm B. Experimental performance of the K4+MIRROR algorithm IV. CONCLUSIONS AND FUTURE WORK
9.Computational cost of ERIs evaluation is typically measured using floating point operations (FLOP) metric. Commonly, this cost is decomposed into three contributions, i.e., Cost = xK4 + yK2 + z, where first contribution is the computational cost of innermost over primitive CGFs, second contribution is the computational cost of outer loop over half-contracted intermediate integrals, and third contribution is the computational cost of outermost loop over contracted integrals, K is the degree of contraction of Gaussian functions forming batch of ERIs which, for the sake of simplicity, is considered to be the same for all the contracted Gaussian functions involved.
10.P. M. W. Gill, M. Head-Gordon, and J. A. Pople, Int. J. Quantum Chem.36, 269 (1989).