  In the Projector Augmented Wave (PAW) method, a local potential, basis
functions, and projector functions form an All-Electron (AE) basis for valence
wave functions in the application of Density Functional Theory (DFT). The
construction of these potentials, basis functions and projector functions for
each element can be complex, and several codes capable of utilizing the PAW
method have been otherwise prevented from its use by the lack of PAW basis sets
for all atoms. We have developed a procedure that improves the ease and
efficiency of construction of PAW basis sets. An evolutionary algorithm is used
to optimize PAW basis sets to accurately reproduce scattering properties of the
atom and which converge well with respect to the energy cutoff in a planewave
basis. We demonstrate the procedure for the case of Ga with the 4s, 4p, and 3d
electrons treated as valence. Calculations with this Ga PAW basis set are
efficient and reproduce results of linearized augmented plane wave (LAPW)
calculations. We also discuss the relationship between total energy convergence
with respect to the energy cutoff and the magnitude of the matching radius of
the PAW set.
