A local pseudopotential of the form V=V0kr+C, r<rc, V=-1r, r>rc, is used to fit the experimental ground-state energy of atomic sodium. This form is chosen so as to mirror as closely as possible the actual valence charge distribution of Na. This is important in the calculation of chemical properties such as bonding and cohesion. Electrostatic calculations of the cohesive energy of the bcc metal from the virial theorem and from the electrostatic self-energy of the lattice are performed and the results compared. The results bear on the accuracy of electron-gas calculations in metals and the techniques of pseudopotential calculations. The phonon spectrum is calculated and all results are compared to those obtained with a Shaw-type flat-bottom pseudopotential.