New efficient integral algorithms for quantum chemistry

Jaime Axel Rosal Sandberg
KTH, School of Biotechnology (BIO), Theoretical Chemistry and Biology
KTH, 2014


   title={New efficient integral algorithms for quantum chemistry},

   author={Sandberg, Jaime Axel Rosal},



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The contents of this thesis are centered in the developement of new efficient algorithms for molecular integral evaluation in quantum chemistry, as well as new design and implementation strategies for such algorithms aimed at maximizing their performance and the utilization of modern hardware. This thesis introduces the K4+MIRROR algorithm for 2-electron repulsion integrals, a new ERI integral scheme effective for both segmented and general contraction, which surpasses the performance of all previous ERI analytic algorithms published in the literature. The performance of the K4 kernel contraction schemeis further boosted by the use of some new recurrence relations, CDR/AERR family of recurrences, and the algorithms is further refined for spherical GTOs with the also new SKS method. New prescreening methods for two-electron integrals are also derived, allowing a more consistent methodology for discarding negligible ERI batches. This thesis introduces new techniques useful to pack integrals efficiently and better exploit the underlying modern SIMD or stream processing hardware. These algorithms and methods are implemented in a new library, the Echidna Fock Solver, a hybrid parallelized module for computing Coulomb and Exchange matrices which has been interfaced to the Dalton suite of quantum chemistry programs. Self-Consistent Field and Response Theory calculations in Dalton using the new EFS library are substantially accelerated, also enabling for the first time the use of general contraction basis sets as default basis for extended calculations. The thesis further describes the derivation and implementation of an integral algorithm for evaluating the matrix elements needed for the recently introduced QM/CMM method, for which many of the techniques previously derived are also used, along with a suitable prescreening method for the matrix elements. The implementation is also interfaced to the Dalton quantum chemistry program, and used in production calculations. The last chapter of the thesis is devoted to the derivation of a general analytic solution for type-II Effective Core Potential integrals, arguably one of the most troublesome molecular integrals in quantum chemistry. A new recurrence is introduced for the integrals, and a screening method is presented. Based on these results, a new efficient algorithm for computing type-II ECPs is also described.
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