Methyl mercaptan (also known as methanethiol), CH3SH, has been found in the warm and dense parts of high -- as well as low -- mass star-forming regions. The aim of the present study is to obtain accurate spectroscopic parameters of the S-deuterated methyl mercaptan CH$_3$SD to facilitate astronomical observations by radio telescope arrays at (sub)millimeter wavelengths. We have measured the rotational spectrum associated with the large-amplitude internal rotation of the methyl group of methyl mercaptan using an isotopically enriched sample in the 150-510 GHz frequency range using the Koln millimeter wave spectrometer. The analysis of the spectra has been performed up to the second excited torsional state. We present modeling results of these data with the RAM36 program. CH$_3$SD was searched for, but not detected, in data from the Atacama Large Millimeter/submillimeter Array (ALMA) Protostellar Interferometric Line Survey (PILS) of the deeply embedded protostar IRAS 16293-2422. The derived upper limit corresponds to a degree of deuteration of at most ~18%.
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