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).

中文翻译：

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关于天文光谱中的非对称顶部旋转分配函数

摘要 配分函数在确定分子云中发射线的柱密度方面起着重要作用，因为在典型条件下，两者是线性相关的。在这里，我们专注于将量子和离心失真校正项连续应用于不对称顶部分子的经典旋转分配函数，以努力揭示每个项的相对重要性。例如，在与星际分子云相关的温度下，我们会这样做，例如包含一到四个重原子（水、甲胺、乙烯醇和乙醇醛）的不对称顶部分子。特别关注甲胺，最近证明，经典分配函数的值与数百开尔文的数值总和（精确）值显着不同 [Sharma 等人，Astron。新闻报。338, 125 (2017)]。我们表明，经典值实际上在精确值的 1% 以内，从 ~50 K 到远高于 400 K；添加三个简单的校正项将误差降低到 ≲0.001%（低至 10 K）。