  It is well-known that both wavefunction ab initio and DFT calculations on
second-row compounds exhibit anomalously slow basis set convergence unless the
basis sets are augmented with additional `tight' (high-exponent) $d$ functions,
as in the cc-pV($n+d$)Z and aug-cc-pV($n+d$)Z basis sets. This has been
rationalized as being necessary for a better description of the low-lying $3d$
orbital, which as the oxidation state increases sinks low enough to act as a
back-donation acceptor from chalcogen and halogen lone pairs. This prompts the
question whether a similar phenomenon exists for the isovalent compounds of the
heavy p-block. We show that for the fourth and fifth row, this is the case, but
this time for tight $f$ functions enhancing the description of the low-lying
$4f$ and $5f$ Rydberg orbitals, respectively. In the third-row heavy $p$ block,
the $4f$ orbitals are too far up, while the $4d$ orbitals are adequately
covered by the basis functions already present to describe the $3d$ subvalence
orbitals.
