Projected Augmented Waves (PAW) motivated mixed basis sets for small molecules (2404.08493v5)

Abstract: The success behind many pseudopotential methods, such as the Projected Augmented Waves (PAW) and the Phillips-Kleinman pseudopotential methods, is that these methods are nearly all electron methods in disguise. For the Phillips-Kleinman and PAW pseudopotential methods we show that there is an explicit all electron reformulation (which is nearly equivalent). In the all electron reformulation, as part of the basis set, there are regular low wavevector basis wave functions (plane waves) and several, specially chosen, high wavevector basis wave functions that are specialized to the atomic environment relevant to nuclei of the substances studied. Using this as motivation, here we propose a new, PAW method motivated, basis set for small molecules, where we use the LO or lo (Localized Orbitals) basis wave functions, and pair them with a Gaussian basis, e.g. Gaussian Type Orbitals (GTO), for a hybrid basis for small molecules. Contracted Gaussian functions are also possible (CGFs). Several different, but related, LO (lo) basis wave functions are considered. We also show how to extend this idea to Slater basis set, Slater type orbitals (STO), instead of GTO orbitals, combined with LO or lo orbitals. This is done using shape functions.