Direct partition function of the rigid diatomic rotor

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Abstract
The direct and exchange partition functions for a rigid diatomic rotor are obtained via the density matrix. An integral representation which is suitable for finding convergent high temperature expansions is formulated by use of the transformation properties of theta functions. The convergent expansion for the direct partition function is shown to consist of the asymptotic Euler–Maclaurin series with each term corrected by a series of nonanalytic terms. The nonanalytic terms are of the form exp(−Nπ2/σ) and the entire expansion is rapidly convergent at high temperature.

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