  The success behind many pseudopotential methods such as Projected Augmented
Waves (PAW) and Phillips-Kleinman pseudopotential methods is that these methods
are all electron methods in disguise. For the Phillips Kleinman and PAW methods
we show that there is an all electron formulation. In the all electron
formulation there are regular low wavevector basis wave functions and several,
specially chosen, high wavevector basis wave functions that are specialized to
the atomic environment. Using this as inspiration here we propose a new, PAW
method inspired, basis set for small molecules, where we use the recently
introduced LO or lo (Localized orbitals) basis set is paired with a Gaussian
basis, Gaussian type orbitals (GTO), for a hybrid basis for small molecules.
Contracted Gaussian functions are also possible (CGFs). 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.
