  We show that efficient norm-conserving pseudopotentials for electronic
structure calculations can be obtained from a polynomial Ansatz for the
potential. Our pseudopotential is a polynomial of degree ten in the radial
variable and fulfills the same smoothness conditions imposed by the
Troullier-Martins method [Phys. Rev. B 43, 1993 (1991)] where pseudopotentials
are represented by a polynomial of degree twenty-two. We compare our method to
the Troullier-Martins approach in electronic structure calculations for diamond
and iron in the bcc structure and find that the two methods perform equally
well in calculations of the total energy. However, first and second derivatives
of the total energy with respect to atomic coordinates converge significantly
faster with the plane wave cutoff if the standard Troullier-Martins potentials
are replaced by the pseudopotentials introduced here.
