Extreme softening of Vanderbilt pseudopotentials: General rules and case studies of first-row and d-electron elements

We demonstrate the general ability of an extreme softening of non-normconse rving Vanderbilt pseudopotentials. We discuss the important case of first-r ow elements and elements containing core d electrons. Explicitly, such extr emely soft pseudopotentials are constructed for carbon, hydrogen, nitrogen, and gallium, the d electrons of which have to be treated as valence electr ons. Using a plane-wave basis with cutoff energies between 13 and 16 Ry we observe no loss of accuracy compared to very hard and accurate pseudopotent ials working at cutoff energies between 60 and 110 Ry.