  The random-phase approximation with exchange (RPAE) is used with a $B$-spline
basis to compute dynamic dipole polarizabilities of noble-gas atoms and several
other closed-shell atoms (Be, Mg, Ca, Zn, Sr, Cd, and Ba). From these, values
of the van der Waals $C_6$ constants for positronium interactions with these
atoms are determined and compared with existing data. Our best predictions of
$C_6$ for Ps--noble-gas pairs are expected to be accurate to within 1%, and to
within a few per cent for the alkaline earths. We also used accurate dynamic
dipole polarizabilities from the literature to compute the $C_6$ coefficients
for the alkali-metal atoms. Implications of increased $C_6$ values for Ps
scattering from more polarizable atoms are discussed.
