  Electronic structure methods for accurate calculation of molecular properties
have a high cost that grows steeply with the problem size, therefore, it is
helpful to have the underlying atomic basis functions that are less in number
but of higher quality. Following our earlier work [Chem. Phys. Lett. 416, 116
(2005)] where general correlation-consistent basis sets are defined, for any
atom, as solutions of purely atomic functional minimization problems, and which
are shown to work well for chemical bonding in molecules, we take a further
step here and define a new kind of atomic polarization functionals, the
minimization of which yields additional sets of diffuse functions that help to
calculate better molecular electron affinities, polarizabilities, and
intermolecular dispersion interactions. Analytical representations by
generally-contracted Gaussian functions of up to microhartree numerical
accuracy grades are developed for atoms Hydrogen through Nobelium within the
four-component Dirac-Coulomb theory and its scalar-relativistic approximation,
and also for Hydrogen through Krypton in the two-component nonrelativistic
case. The convergence of correlation energy with the basis set size is studied,
and complete-basis-set extrapolation formulas are developed.
