The def2 basis sets are very appealing because they aredesigned to provide consistent accuracy across the wholeperiodic table and they are available for all elements upto radon (Z = 86) [5], whereas this is not true for themore commonly used basis sets from the Pople andDunning groups. We have begun using the def2 basis setsfor these reasons and have obtained generally satisfactory(often excellent) results, but in our opinion, two aspectsof the design of these basis sets required further study,namely that (1) they were designed without provision ofdiffuse functions and (2) they do not allow for scalarrelativistic effective core potentials in the fourth periodof the periodic table (especially the 3d and 4p blocks),where relativistic effects are beginning to becomechemically important. (They do include a relativisticeffective core potential starting with Rb, at the beginningof the fifth row). The present article is concerned withissue