  We describe a search for molecular absorption at millimetre wavelengths
associated with dusty molecular tori in active galactic nuclei (AGN). The
sample observed consists of 11 flat-spectrum radio sources known to have red
optical to infra-red colours plus two steep-spectrum narrow-line radio
galaxies. Spectra of the sources were obtained in the 3-, 2- and 1.3-millimetre
bands at frequencies corresponding to common molecular transitions of CO, HCO+,
HCN and CS at the AGN redshift. No absorptions were detected in any of the
sources. We calculated upper limits to the column density in molecular
absorption, using an excitation temperature of 10 K, to be N(CO) < 10^{15} -
10^{16} cm^-2, equivalent to hydrogen columns of order N(H) < 10^{19} - 10^{20}
cm^-2.
  These limits are significantly lower than the values N(H) \approx (2 - 6)
10^{21} cm^-2 that might be expected if the red colours of these sources were
due to dust absorption at the quasar redshift as suggested by Webster et al.
(1995). Should the excitation temperature of the molecular transitions be
higher than 100K, the upper limits to the H2 column densities would be greater
than those derived from the red colours. To explain the lack of molecular
absorption we conclude that either the optical extinction takes place outside
the host galaxy (along the line of sight), or the excitation temperature of the
molecular transitions is very high, or the obscuration is not associated with
significant amounts of cold molecular gas. It is quite possible that the hard
X-ray flux from the central source of these AGN is strong enough to
photo-dissociate the molecules.
