The saturated n-propyl cyanide was recently detected in Sagittarius B2(N). The next larger unbranched alkyl cyanide is n-butyl cyanide. We provide accurate rest frequency predictions beyond the millimeter wave range to search for this molecule in the Galactic center source Sagittarius B2(N) and facilitate its detection in space. We investigated the laboratory rotational spectrum of $n$-butyl cyanide between 75 GHz and 348 GHz. We searched for emission lines produced by the molecule in our sensitive IRAM 30 m molecular line survey of Sagittarius B2(N). We identified more than one thousand rotational transitions in the laboratory for each of the three conformers for which limited data had been obtained previously in a molecular beam microwave study. The quantum number range was greatly extended to J ~ 120 or more and Ka > 35, resulting in accurate spectroscopic parameters and accurate rest frequency calculations up to about 500 GHz for strong to moderately weak transitions of the two lower energy conformers. Upper limits to the column densities of N <= 3 x 10E15 cm-2 and 8 x 10E15 cm-2 were derived towards Sagittarius B2(N) for the two lower energy conformers, anti-anti and gauche-anti, respectively. Our present data will be helpful for identifying n-butyl cyanide at millimeter or longer wavelengths with radio telescope arrays such as ALMA, NOEMA, or EVLA. In particular, its detection in Sagittarius B2(N) with ALMA seems feasible.
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