To obtain the exchange-correlation energy accurately it is necessary that outside the core region the real and pseudo wavefunctions be identical so that both wavefunctions generate identical charge densities (see conditions listed above). Generation of a pseudopotential that satisfies
where is the all electron wavefunction and is the pseudo wavefunction, guarantees the equality of the all electron and pseudo wavefunctions outside the core region. In practice this is achieved using a non-local pseudopotential which uses a different potential for each angular momentum component of the pseudopotential. This also best describes the scattering properties from the ion core.
Pseudopotentials of this type are known as non-local norm-conserving pseudopotentials and are the most transferable since they are capable of describing the scattering properties of an ion in a variety of atomic environments.