In quantum chemistry, the computation of anharmonic vibrational frequencies, instead of only harmonic frequencies, is now convenient and increasingly common. For thermochemistry, one ramification is that vibrational partition functions may be constructed using anharmonic manifolds. Practical issues are discussed here, and a few examples are provided. Evaluating the accuracy of the results is hindered by the lack of experimental data for ideal-gas heat capacities at high temperature. Published by Elsevier Ltd.