We investigate the relation between the detection of the 11.3 \mu m polycyclic aromatic hydrocarbon ( PAH ) feature in the nuclear ( \sim 24 - 230 pc ) regions of 22 nearby Seyfert galaxies and the properties of the cold molecular gas . For the former we use ground-based ( 0.3 - 0.6 \arcsec resolution ) mid-infrared ( mid-IR ) spectroscopy . The cold molecular gas is traced by ALMA and NOEMA high ( 0.2 - 1.1 \arcsec ) angular resolution observations of the CO ( 2-1 ) transition . Galaxies with a nuclear detection of the 11.3 \mu m PAH feature contain more cold molecular gas ( median 1.6 \times 10 ^ { 7 } M _ { \odot } ) and have higher column densities ( N ( { H } _ { 2 } ) = 2 \times 10 ^ { 23 } { cm } ^ { -2 } ) over the regions sampled by the mid-IR slits than those without a detection . This suggests that molecular gas plays a role in shielding the PAH molecules in the harsh environments of Seyfert nuclei . Choosing the PAH molecule naphthalene as an illustration , we compute its half-life in the nuclear regions of our sample when exposed to 2.5 keV hard X-ray photons . We estimate shorter half-lives for naphthalene in nuclei without a 11.3 \mu m PAH detection than in those with a detection . The Spitzer /IRS PAH ratios on circumnuclear scales ( \sim 4 \arcsec \sim 0.25 - 1.3 kpc ) are in between model predictions for neutral and partly ionized PAHs . However , Seyfert galaxies in our sample with the highest nuclear H _ { 2 } column densities are not generally closer to the neutral PAH tracks . This is because in the majority of our sample galaxies , the CO ( 2-1 ) emission in the inner \sim 4 \arcsec is not centrally peaked and in some galaxies traces circumnuclear sites of strong star formation activity . Spatially resolved observations with the MIRI medium-resolution spectrograph ( MRS ) on the James Webb Space Telescope will be able to distinguish the effects of an active galactic nucleus ( AGN ) and star formation on the PAH emission in nearby AGN .