New basis sets of the atomic natural orbital (ANO) type have been developed for the main group and rare gas atoms. The ANO's have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive and negative ions, and the dimer at its equilibrium geometry. Scalar relativistic effects are included through the use of a Douglas-Kroll Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies, electron affinities, and excitation energies for all atoms and the ground-state potentials for the dimers. These calculations include spin-orbit coupling using the RASSCF State Interaction (RASSI-SO) method. The spin-orbit splitting for the lowest atomic term is reproduced with an accuracy of better than 0.05 eV, except for row 5, where it is 0.15 eV. Ionization energies and electron affinities have an accuracy better than 0.2 eV, and atomic polarizabilities for the spherical atoms are computed with errors smaller than 2.5%. Computed bond energies for the dimers are accurate to better than 0.15 eV in most cases (the dimers for row 5 excluded).