We have used the 30 m IRAM millimeter radio telescope to search for tw
o low-lying rotational transitions of the CO-H-2 dimer in the emission
spectra of three Galactic sources and in the absorption spectrum of a
low-latitude extragalactic continuum source. We first summarize the s
tructure of this dimer as it can be inferred currently from laboratory
infrared spectroscopy. The transitions we have observed and their ini
tial estimated frequencies are the 111- <-> 000+ line at similar to 10
9 GHz and the 110+ <-> 101- line at similar to 91 GHz. The search targ
ets were the TMC-1 and L134 dark clouds, the L1157 bipolar outflow, an
d the compact radio continuum source 2013 + 370. The spectral search c
overed the frequency ranges from 90.58 to 91.10 GHz and from 108.95 to
109.46 GHz. Several known emission lines were found, including HC3N(1
2-11), HC3N(10-9), OCS, SO, and HNC, but no other features were seen i
n the spectra. The rms noise was typically 5 mK per 1 MHz channel(appr
oximate to 3 km s(-1)). Improved laboratory values for the frequencies
were obtained after the 30 m observations were made and are also give
n here fur future reference. The frequency of the 111- <-> 000+ line m
ay now fall outside of our present search range, but the 110+ <-> 101-
frequency is likely to be within it. We conclude that the fractional
abundance of the CO-H, dimer with respect to the CO monomer is typical
ly less than or equal to x 10(-4), if the excitation temperature is at
least a few degrees above the cosmic background. This is the most str
ingent upper limit vet placed on the presence of a dimer in the inters
tellar medium.