Rotational partition functions for linear molecules

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Abstract
An accurate closed-form expression for the rotational partition function of linear polyatomic molecules in 1∑ electronic states is derived, including the effect of nuclear spin (significant at very low temperatures) and of quartic and sextic centrifugal distortion terms (significant at moderate and high temperatures). The proper first-order quantum correction to the classical rigid-rotator partition function is shown to yield Qr ≊β−1 exp(β/3), where β≡hcB/kT and B is the rotational constant in cm−1; for β≥0.2 additional power-series terms in β are necessary. Comparison between the results of this treatment and exact summations are made for HCN and C2H2 at temperatures from 2 to 5000 K, including separate evaluation of the contributions of nuclear spin and centrifugal distortion.

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