Concerning the asymmetric top rotational partition function in astronomical spectroscopy

Abstract

The partition function plays an important role in determining column densities from emission lines in molecular clouds, since under typical conditions the two are linearly related. Here, we focus on successively applying quantum and centrifugal distortion correction terms to the classical rotational partition function for asymmetric top molecules, in an effort to uncover the relative importance of each term. We do this for example asymmetric top molecules that contain from one to four heavy atoms (water, methanimine, vinyl alcohol, and glycolaldehyde), at temperatures relevant to interstellar molecular clouds. Particular attention is paid to methanimine, for which it was recently attested that the value of the classical partition function significantly differs from the numerically summed (exact) value at several hundred Kelvin [Sharma et al., Astron. Nachrichten. 338, 125 (2017)]. We show that the classical values are in fact within 1% of the exact values from ~50 K to well above 400 K; the addition of three simple correction terms reduces the error to ≲0.001% (down to 10 K).