We present pseudo-potential coefficients for the first two rows of the periodic table. The pseudo potential is of a novel analytic form, that gives optimal efficiency in numerical calculations using plane waves as basis set. At most 7 coefficients are necessary to specify its analytic form. It is separable and has optimal decay properties in both real and Fourier space. Because of this property, the application of the nonlocal part of the pseudo-potential to a wave-function can be done in an efficient way on a grid in real space. Real space integration is much faster for large systems than ordinary multiplication in Fourier space since it shows only quadratic scaling with respect to the size of the system. We systematically verify the high accuracy of these pseudo-potentials by extensive atomic and molecular test calculations.

16 pages, 4 postscript figures