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.
The idea of using the SHO basis has probably not received attention as the related basis set has been found not to converge as rapidly as a set of only Gaussian-type orbitals (GTOs) contracted over a set of different spread parameters @math @cite_10 when used as a basis set for quantum chemistry calculations @cite_16 . Note that the subset of radial SHO states with @math are GTOs.
@cite_16 @cite_10
2078146328 2006144138
Various contracted Gaussian basis sets for atoms up to Kr are presented which have been determined by optimizing atomic self‐consistent field ground state energies with respect to all basis set parameters, i.e., orbital exponents and contraction coefficients. The use of gradient techniques for the development of energy-optimized basis sets has been investigated. The region where the energy surface is approximately quadratic with a positive definite Hessian is found to be very small for large basis sets. However, scaled Newton-Raphson methods prove quite effective even when the starting point is outside this region. The analytic calculation of the Hessian is found to be most efficient in terms of computing time.