Highly accurate adapted Gaussian basis sets are used to study the ground and some excited states for the neutral atoms and also some corresponding 6s and 4f ionized states from Cs through Lu. Our total energies are compared with those calculated with a numerical Hartree-Fock method. The mean error of our energy results is equal to 0.74 mhartree. Our calculations reproduce the experimental trend to increase or to decrease the 6s and 4f ionization potentials with increasing atomic number, although they are respectively smaller and larger than the experimental values.