Unitary Transform between Radial and Cartesian Representation of the Spherical Harmonic Oscillator Basisdoi:10.26165/JUELICH-DATA/MWHIW5Jülich DATA2021-05-041Baumeister, Paul F., 2021, "Unitary Transform between Radial and Cartesian Representation of the Spherical Harmonic Oscillator Basis", https://doi.org/10.26165/JUELICH-DATA/MWHIW5, Jülich DATA, V1Unitary Transform between Radial and Cartesian Representation of the Spherical Harmonic Oscillator Basisdoi:10.26165/JUELICH-DATA/MWHIW5Baumeister, Paul F.Jülich DATABaumeister, Paul F.Baumeister, Paul F.2021-05-04ChemistryMathematical SciencesPhysicsspherical harmonic oscillatorThe spherical harmonic oscillator is one of the most basic quantum mechanical problems with known analytical solutions in two representations: Radial and Cartesian. This data file provides the coefficient of the unitary transformation connecting the two representations.The matrix elements are limited at \nu = 9, however the generator code is includedCC0 Waiver10.1145/3324989.3325717@inproceedings{10.1145/3324989.3325717, author = {Baumeister, Paul F. and Tsukamoto, Shigeru}, title = {Analytical PAW Projector Functions for Reduced Bandwidth Requirements}, year = {2019}, isbn = {9781450367707}, publisher = {Association for Computing Machinery}, address = {New York, NY, USA}, url = {https://doi.org/10.1145/3324989.3325717}, doi = {10.1145/3324989.3325717}, abstract = {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.}, booktitle = {Proceedings of the Platform for Advanced Scientific Computing Conference}, articleno = {7}, numpages = {11}, keywords = {Density Functional Theory, Radial grid, GPUs, Real-Space grid, Cartesian grid, Projector Augmented Wave method, Many-core}, location = {Zurich, Switzerland}, series = {PASC '19} }sho_unitary.datinteger coefficients for non-zero matrix elements up to \nu = 9text/x-fixed-fieldsho_unitary.F90generator code (Fortran 90)application/octet-streamsho_unitary.pdfTheory documentapplication/pdfsho_unitary.texTheory document sourceapplication/x-tex