Large scale electronic structure calculations require modern high performance computing (HPC) resources and, as important, mature HPC applications that can make efficient use of those. Real-space grid-based applications of Density Functional Theory (DFT) using the Projector Augmented Wave method (PAW) can give the same accuracy as DFT codes relying on a plane wave basis set but exhibit an improved scalability on distributed memory machines. The projection operations of the PAW Hamiltonian are known to be the performance critical part due to their limitation by the available memory bandwidth. We investigate on the utility of a 3D factorizable basis of Hermite functions for the localized PAW projector functions which allows to reduce the bandwidth requirements for the grid representation of the projector functions in projection operations. Additional on-the-fly sampling of the 1D basis functions eliminates the memory transfer almost entirely. For an quantitative assessment of the expected memory bandwidth savings we show performance results of a first implementation on GPUs. Finally, we suggest a PAW generation scheme adjusted to the analytically given projector functions.
Spherical Gaussians can be expressed as linear combinations of the appropriate Cartesian Gaussians. General expressions for the transformation coefficients are given. Values for the transformation coefficients are tabulated up to h-type functions. © 1995 John Wiley & Sons, Inc. Recurrence expressions are derived for various types of molecular integrals over Cartesian Gaussian functions by the use of the recurrence formula for three‐center overlap integrals. A number of characteristics inherent in the recursive formalism allow an efficient scheme to be developed for molecular integral computations. With respect to electron repulsion integrals and their derivatives, the present scheme with a significant saving of computer time is found superior to other currently available methods. A long innermost loop incorporated in the present scheme facilitates a fast computation on a vector processing computer.