Context. There is a class of binary post-asymptotic giant branch (post-AGB) stars that exhibit remarkable near-infrared excess. Such stars are surrounded by Keplerian or quasi-Keplerian disks, as well as extended outflows composed of gas escaping from the disk. This class can be subdivided into disk- and outflow-dominated sources, depending on whether it is the disk or the outflow that represents most of the nebular mass, respectively. The chemistry of this type of source has been practically unknown thus far. Aims. Our objective is to study the molecular content of nebulae around binary post-AGB stars that show disks with Keplerian dynamics, including molecular line intensities, chemistry, and abundances. Methods. We focused our observations on the 1.3, 2, 3 mm bands of the 30mIRAM telescope and on the 7 and 13 mm bands of the 40 m Yebes telescope. Our observations add up ~600 h of telescope time. We investigated the integrated intensities of pairs of molecular transitions for CO, other molecular species, and IRAS fluxes at 12, 25, and 60 μm. Additionally, we studied isotopic ratios, in particular 17O/18O, to analyze the initial stellar mass, as well as 12CO/13CO, to study the line and abundance ratios. Results. We present the first single-dish molecular survey of mm-wave lines in nebulae around binary post-AGB stars. We conclude that the molecular content is relatively low in nebulae around binary post-AGB stars, as their molecular lines and abundances are especially weaker compared with AGB stars. This fact is very significant in those sources where the Keplerian disk is the dominant component of the nebula. The study of their chemistry allows us to classify nebulae around AC Her, the Red Rectangle, AI CMi, R Sct, and IRAS 20056+1834 as O-rich, while that of 89 Her is probably C-rich. The calculated abundances of the detected species other than CO are particularly low compared with AGB stars. The initial stellar mass derived from the 17O/18O ratio for the Red Rectangle and 89 Her is compatible with the central total stellar mass derived from previous mm-wave interferometric maps. The very low 12CO/13CO ratios found in binary post-AGB stars reveal a high 13CO abundance compared to AGB and other post-AGB stars.
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