We present a Spitzer InfraRed Spectrometer search for 10-36 micron molecular emission from a large sample of protoplanetary disks, including lines from H2O, OH, C2H2, HCN and CO2. This paper describes the sample and data processing and derives the detection rate of mid-infrared molecular emission as a function of stellar mass. The sample covers a range of spectral type from early M to A, and is supplemented by archival spectra of disks around A and B stars. It is drawn from a variety of nearby star forming regions, including Ophiuchus, Lupus and Chamaeleon. In total, we identify 22 T Tauri stars with strong mid-infrared H2O emission. Integrated water line luminosities, where water vapor is detected, range from 5x10^-4 to 9x10^-3 Lsun, likely making water the dominant line coolant of inner disk surfaces in classical T Tauri stars. None of the 5 transitional disks in the sample show detectable gaseous molecular emission with Spitzer upper limits at the 1% level in terms of line-to-continuum ratios (apart from H2). We find a strong dependence on detection rate with spectral type; no disks around our sample of 25 A and B stars were found to exhibit water emission, down to 1-2% line-to-continuum ratios, in the mid-infrared, while almost 2/3 of the disks around K stars show sufficiently intense water emission to be detected by Spitzer. Some Herbig Ae/Be stars show tentative H2O/OH emission features beyond 20 micron at the 1-2 level, however, and one of them shows CO2 in emission. We argue that the observed differences between T Tauri disks and Herbig Ae/Be disks is due to a difference in excitation and/or chemistry depending on spectral type and suggest that photochemistry may be playing an important role in the observable characteristics of mid-infrared molecular line emission from protoplanetary disks.
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