Boys function evaluation on graphical processing units

Section: Introductionmentioning

confidence: 99%

A fast algorithm for computing the Boys function

Beylkin

Sharma

2021

Optimizing two-electron repulsion integral calculations with McMurchie–Davidson method on graphic processing unit

Tian

Suo

2021

In this article, several optimization methods of two-electron repulsion integral calculations on a graphic processing unit (GPU) are presented. These methods are based on the investigations of the method presented by McMurchie and Davidson (MD). A new Boys function evaluation method for the GPU calculation is introduced. The series summation, the error function, and the finite sum formula method are combined; thus, good performance on the GPU can be achieved. By taking some theoretical study of the McMurchie–Davidson recurrence relations, three major optimization approaches are derived from the deduction of the general term formula for the Hermite expansion coefficient. The three approaches contain a new form of the Hermite expansion coefficients with corresponding recurrence relations, which is more efficient for one-electron integrals and [ss|∗∗] or [∗∗|ss] type two-electron integrals. In addition, a simple yet efficient new recurrence formula for the coefficient evaluation is derived, which is more efficient both in float operations and memory operations than its original one. In average, the new recurrence relation can save 26% float operations and 37% memory operations. Finally, a common sub-expression elimination (CSE) method is implemented. This CSE method is directly generated from some equalities we discovered from the general term formula other than by computer algebra system software. This optimized method achieved up to 3.09 speedups compared to the original MD method on the GPU and up to 92.75 speedups compared to the GAMESS calculation on the central processing unit.

Expansion of multicenter Coulomb integrals in terms of two-center integrals

Kovačević

2022

Three- and four-centre Coulomb integrals in the solid spherical harmonic Gaussian basis are solved by expansion in terms of two-centre integrals. The two-electron Gaussian product rule, coupled with the addition theorem for solid spherical harmonics, reduces four-centre Coulomb integrals into a linear combination of two-centre Coulomb integrals and one-centre overlap integrals. With this approach, three- and four-centre Coulomb integrals can be reduced to the same form of two-centre integrals. Resulting two-centre Coulomb integrals can be further simplified into a simpler form, which can be related to the Boys function. Multi-centre Coulomb integrals are solved hierarchically: simple two-centre Coulomb integrals are used for calculation of more complicated two-centre Coulomb integrals, which are used in the calculation of multicentre integrals.