Relation between the ultrasoft pseudopotential formalism and the LAPW method

In this work, it is shown how wave functions can be augmented in the framework of Vanderbilt's ultrasoft pseudopotential approach. The augmented wave functions bear a strong resemblance to linear-augmented plane waves. Thus, a very close relation between the ultrasoft pseudopotential and the LAPW methods is found. A detailed analysis of this relationship is carried out that provides some valuable insight into better understanding the efficiency of the ultrasoft pseudopotentials.