  We emphasize that the completeness of the partition function, that is, the
use of a converged partition function at the typical temperature range of the
survey, is very important to decrease the uncertainty on this quantity and thus
to derive reliable interstellar molecular densities. In that context, we show
how the use of different approximations for the rovibrational partition
function together with some interpolation and/or extrapolation procedures may
affect the estimate of the interstellar molecular column density. For that
purpose, we apply the partition function calculations to astronomical
observations performed with the IRAM-30m telescope towards the NGC7538-IRS1
source of two N-bearing molecules: isocyanic acid (HNCO, a quasilinear
molecule) and methyl cyanide (CH$_3$CN, a symmetric top molecule). The case of
methyl formate (HCOOCH$_3$), which is an asymmetric top O-bearing molecule
containing an internal rotor is also discussed. Our analysis shows that the use
of different partition function approximations leads to relative differences in
the resulting column densities in the range 9 to 43\%. Thus, we expect this
work to be relevant for surveys of sources with temperatures higher than 300~K
and to observations in the infrared.
