a EX is the global parameter to scale the exact exchange contribution. Within GAPW and GPW, the one-electron contributions h are computed either referring to Eq. (3) including kinetic energy and pseudo potential contributions or by replacing pseudo potentials with the all-electron nuclear potential operator, relying for both formulations on the conventional density matrix D. As mentioned before, GAPW ground-state electrostatic contributions take into account core compensation charges, thus referring to Eqs. (22, 23, 24, 25).