Improved Roothaan-Hartree-Fock wave functions are reported for the ground states of all the neutral atoms from He to Xe, singly char ed cations from Li+ to Cs+, and stable singly charged anions from H- to I-. Our neutral atom wave functions are an improvement over those of Clementi and Roetti [At. Data Nucl. Data Tables 14, 177 (1974)], Bunge et al. [Phys. Rev. A 46, 3691 (1992)] and Koga et al. [Phys. Rev. A 47, 4510 (1993)]. The ion wave functions are an improvement over those of Clementi and Roetti, and Koga er al. [J. Phys. B 26, 2529 (1993)]. In all cases, the current wave functions predict energies within 1.3X10(-5) hartrees of the numerical Hartree-Fock limit.