  We propose a systematic method of analyzing pseudopotential transferability
based on linear-response properties of the free atom, including self-consistent
chemical hardness and polarizability. Our calculation of hardness extends the
approach of Teter\cite{teter} not only by including self-consistency, but also
by generalizing to non-diagonal hardness matrices, thereby allowing us to test
for transferability to non-spherically symmetric environments. We apply the
method to study the transferability of norm-conserving pseudopotentials for a
variety of elements in the Periodic Table. We find that the self-consistent
corrections are frequently significant, and should not be neglected. We prove
that the partial-core correction improves the pseudopotential hardness of
alkali metals considerably. We propose a quantity to represent the average
hardness error and calculate this quantity for many representative elements as
a function of pseudopotential cutoff radii. We find that the atomic
polarizabilities are usually well reproduced by the norm-conserving
pseudopotentials. Our results provide useful guidelines for making optimal
choices in the pseudopotential generation procedure.
