= Rotational symmetry number
{title2=$\sigma$}
The <rotational symmetry number> corrects a rotational phase-space count for indistinguishable molecular orientations. A linear molecule with identical ends, such as carbon dioxide with identical oxygen isotopes, has $\sigma=2$; making its ends isotopically distinct gives $\sigma=1$. In the high-temperature linear <rigid rotor> approximation, $q_{\rm rot}=8\pi^2IkT/(\sigma h^2)$. Holding the spectrum otherwise fixed, doubling $\sigma$ lowers molar rotational <entropy> by $R\log2$.
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