Trial functions in pseudopotential theory

It is shown that the use of variational trial functions with non-Hermitian pseudopotentials can lead to energies which do not represent accurate upper bounds to the true energy. Such difficulties can be resolved in principle by choosing a trial function which satisfies the same criterion used to define the pseudopotential. Accurate results can be obtained more simply by direct use of the Phillips-Kleinman pseudopotential, which minimizes the difference between the trial function and the exact pseudo wave function.